a computer code for simulation of heat and solute
TRANSCRIPT
HST3D: A COMPUTER CODE FOR SIMULATION OF HEAT AND SOLUTE TRANSPORT
IN THREE-DIMENSIONAL GROUND-WATER FLOW SYSTEMS
By Kenneth L. Kipp, Jr.
U.S. GEOLOGICAL SURVEY
Water-Resources Investigations Report 86-4095
Denver, Colorado 1987
UNITED STATES DEPARTMENT OF THE INTERIOR
DONALD PAUL HODEL, Secretary
GEOLOGICAL SURVEY
Dallas L. Peck, Director
For additional information write to:
Project Chief, WRD, Central Region U.S. Geological Survey, MS 413, Box 25046, Denver Federal Center Denver, CO 80225
Copies of this report can be purchased from:
U.S. Geological Survey Books and Open-File Reports Federal Center, Bldg. 810 Box 25425, Denver, CO 80225 [Telephone: (303) 236-7476]
CONTENTS
Abs1.
2.
3.
itract-- -------------------------------- --- --- ______ ____Introduction----- - -------- ____________ _______ _ ___ _____1.1. Overview of the simulator-- -------- -- --- _______ __1.2. Applicability and limitations------------------------- -----1.3. Purpose and scope------ ----- ------ -- _____ ________1.4. Acknowledgments-------- - - ---- --- ---- - - ---
Theory --------------------------------------------------------------2.1. Flow and transport equations-------------------- -----------
2.1.1. Ground-water flow equation------ - --- ---- - 2.1.2. Heat-transport equation-------- - ---- -----2.1.3. Solute-transport equation--- ---- _________________
2.2. Property functions and transport coefficients-- ---- - -2.2.1. Fluid-density function--- - - -- -------2.2.2. Fluid-viscosity function-- --- -- ------ _______2.2.3. Fluid enthalpy ----------------------------------------2.2.4. Porous-medium enthalpy- - ______ ______ ________2.2.5. Porous-medium compressibility-------- _______________2.2.6. Dispersion coefficients------------ ____---- --_- -
2.2.6.1. Solute dispersion- ______ ___ -__ -__2.2.6.2. Thermal dispersion _-_-_-- -- ____ _
2.3. Expanded-system equations- - ---- - ---- - _--- 2.4. Source or sink terms--the well model------------ ---------
2.4.1. The well-bore model -----------------------------------2.4.2. The well-riser model ----------------------------------
2.5. Boundary conditions------ ---- ------------- ________ ___2.5.1. Specified pressure, temperature and solute-mass
fraction------ - - ----- -- -- - - _________2.5.2. Specified-flux boundary conditions--- --- __-_2.5.3. Leakage boundary conditions---- -- ------- _______
2.5.3.1. Leaky-aquifer boundary---- -------------------2.5.3.2. River-leakage boundary----------------- ------
2.5.4. Aquifer-influence-function boundary conditions--------2.5.4.1. Pot-aquifer-influence function-------- -----2.5.4.2. Transient-flow aquifer-influence function------
2.5.5. Heat-conduction boundary condition- ------ ---------2.5.6. Unconfined aquifer, free-surface boundary condition -
2.6. Initial conditions--------------- ------------ -- - -- Numerical implementation------------------------- -----------------3.1. Equation discretization- ------- ____-____-_-_ - - -
3.1.1. Cartesian coordinates---------- ------- -- --- - 3.1.2. Cylindrical coordinates--- -------------- ________3.1.3. Temporal discretization---- --- - -- _______3.1.4 Finite-difference flow and transport equations--------3.1.5. Numerical dispersion and oscillation criteria--- - -3.1.6. Automatic time-step algorithm-------- - -- ------3.1.7. Discretization guidelines- -- --- -- - -- -
3.2. Property functions and transport coefficients - -----3.3. Source or sink terms--the well model--- - - - --------
Page13379
1011111113151718202223242626282930324049
495052535659606468747577778597100102112115116117120
111
Page3.3. Source or sink terms the well model Continued
3.3.1. The well-bore model 1203.3.2. The well-riser model 128
3.4. Boundary conditions-- ------- -_----_-__----_---------_-___3.4.1. Specified pressure, temperature, and solute-mass
fraction---- ----- --_---__-------_----- ________3.4.2. Specified-flux boundary conditions-------- ---------- 1323.4.3. Leakage-boundary conditions----- ----- ------------- 1333.4.4. Aquifer-influence-function boundary conditions-------- 134
3.4.4.1. Pot-aquifer-influence function----------------- 1343.4.4.2. Transient-flow aquifer-influence function------ 135
3.4.5. Heat-conduction boundary condition-------------------- 1393.4.6. Unconfined-aquifer, free-surface boundary condition--- 140
3.5. Initial conditions- --------------- _________ __________ 1433.6. Equation solution - ------------ ---- ____ _____________ 144
3.6.1. Modification of the flow and transport equations------ 1453.6.2. Sequential solution---- _____-_____-__------___--__ 145
3.7. Matrix solvers 1483.7.1. The alternating diagonal, D4, direct-equation
solver----- --------------------------- ---__---__ 1493.7.2. The two-line, successive-overrelaxation technique----- 1523.7.3. Choosing the equation solver-------------------------- 158
3.8. Global-balance calculations------ -------------------------- 1584. Computer-code description------------- ------------------------- - 161
4.1. Code organization ---- _------_-_----------------------- - 16!4.2. Memory allocation, array-size requirements, and subprogram
communication---------------------------------------------- 166 ^4.3. File usage 176 4.4. Initialization of variables---------------------------------- 1774.5. Program execution-------------------------------------------- 1774.6. Restart option----------------------------------------------- 177
5. The data-input file -- 1795.1. List directed input------------------------------------------ 1795.2. Preparing the data-input file---------------- -------------- 180
5.2.1. General information - - - 1805.2.2. Input-record descriptions --------------------------- 189
6. Output description------------------ ------------- ____ _______ 2307. Computer-system considerations------------ _______-_--------------- 2338. Computer-code verification----------- ----------------------------- 235
8.1. Summary of verification test problems------------------------ 2358.1.1. One-dimensional flow----------- --------------------- 2358.1.2. Flow to a well 2368.1.3. One-dimensional flow 2398.1.4. One-dimensional solute transport--------- ----------- 2418.1.5. One-dimensional heat conduction----------- ---------- 2438.1.6. One-dimensional heat transport--- ------------------- 2448.1.7. Thermal injection in a cylindrical coordinate system-- 246
IV
Page8. Computer-code verification Continued
8.2. Two example problems----------------------------------------- 2478.2.1. Solute transport with variable density and variable
viscosity--------- -------------------------------- 2478.2.2. Heat transport with variable density and variable
viscosity------------------------------------------- 3049. Notation 343
9.1. Roman- ---- - 3439.2. Greek -- - - 3609.3. Mathematical operators and special functions----------------- 363
10. References--- -------- ___________________________________________ 35511. Supplemental data---- --- - 372
11.1. HST3D program variable list with definitions - 37211.2. Cross-reference list of variables--------------------------- 39411.3. Cross-reference list of common blocks----------------------- 50911.4. Comment form and mailing-list request----------------------- 516
FIGURES
Page Figure 2.1. Sketch of well-model geometry showing the well bore and
well-riser sections and the well-datum level------------- 322.2. Sketch of geometry for a leaky-aquifer boundary
condition------------------------------------------------ 542.3. Diagrammatic section showing geometry for a river-leakage
boundary------- --------------------------------- _____ 572.4. Plan view of inner- and outer-aquifer regions and
boundaries: A, Outer-aquifer region completely surrounding inner-aquifer region; B, outer-aquifer region half-surrounding inner-aquifer region------------- 61
2.5. A, plan view, and B, cross-sectional view of inner- and outer-aquifer regions with an impermeable exterior boundary for the outer-aquifer region-------------------- 63
3.1. Sketch of finite-difference spatial discretization ofthe simulation region-------------- -------------------- yg
3.2. Sketch of finite-difference spatial discretization for acylindrical-coordinate system--------- -- ------------ 79
3.3. Sketch of a node with its cell volume showing thesubdomain volumes and the subdomain faces--------------- 80
3.4. Sketch of a node in a cylindrical-coordinate system with its cell volume showing the cell faces, the subdomain volumes, and the subdomain faces-------------- 82
3.5. Sketch of a boundary node with its half-cell volumeshowing the cell faces and the subdomain volumes-------- 96
3.6. Sketch of velocity vectors used for the dispersion- coefficient calculation for a given cell-------- ------ 118
3.7. Sketch of the matrix structure and the rectangular prism of nodes for the flow or heat-transport, or solute-transport equation in finite-difference form----- 150
PageFigure 3.8. Sketch of the matrix structure with the D4 alternating-
diagonal-plane, node-renumbering scheme----------------- 1513.9 Sketch of the matrix structure with two-line, successive-
overrelaxation node-renumbering scheme--- --- -------- 1544.1. Connection chart for the HST3D main program and
subprogram showing routine hierarchy and calculation .^* loops--------------------------------------------------- 168
8.1. Sketch of the grid with boundary conditions forexample problem i-------------- _____________ ________ 250
TABLES
Page Table 2.1. Pipe-roughness values------ ------------------- -- _____ 42
3.1. Truncation errors and oscillation criteria forone-dimensional parabolic equations------------ -------- n4
3.2. Coefficients for the analytical approximations to theVan Everdingen and Hurst aquifer-influence functions----- 139
4.1. Space allocation within the large, variably partitionedinteger array, IVPA---------------- ------ -_____-_-___ 179
4.2. Space allocation within the large, variably partitionedreal array, VPA---------------------------- ----- ----- 171
5.1. Data-input form 1825.2 Inch-pound and International System units used in the
heat- and solute-transport simulator-- -------- _______ jgg5.3. Option lists for program-control variables----------------- 228 ^8.1. Representative values for the pressure increase from
the HST3D simulator and the results of Carnahan and others (1969) 236
8.2. Comparison of drawdown values calculated by HST3D withthose of Lohman (1972, p. 19) 238
8.3. Scaled solute-concentration values calculated by HST3Dcompared to the one-dimensional finite-difference solu tion of Grove and Stollenwerk (1984) and the analytical solution of Ogata and Banks (1961) 242
8.4. Scaled temperature values calculated by HST3D compared to the one-dimensional finite-difference solution of Grove and Stollenwerk (1984) and the analytical solution of Ogata and Banks (1961) 245
8.5. Input-data file for example problem 1--- ----------------- 2518.6. Output file for example problem i-------------------------- 2568.7. Input-data file for example problem 2---------------- ---- 306
8.8. Selections from the output file for example problem 2 ---- 31211.1. HST3D program variable list with definitions 37311.2. Cross-reference list of variables---------------------- -- 39511.3. Cross-reference list of common blocks-- ---- - _______ 510
IVI
CONVERSION FACTORS
The HST3D simulator program performs calculations in metric units. However, it will accept input and produce output in inch-pound units. The conversion factors are listed below:
Multiply
kilogram (kg) meter (m) millimeter(mm) second (s) degree Celsius (°C) Kelvin (K) Joule (J) or Watt-
second (W-s) square meter (m2 ) cubic meter (m3 ) meter-second (m-s) Pascal (Pa)
meter per second (m/s) square meter per second
(m2 /s) cubic meter per second
(m 3 /s) liter per second (£/s)
kilogram per second(kg/s)
Pascal per second(Pa/s)
cubic meter per cubicmeter-second (m3 /m3 -s)
kilogram per cubicmeter (kg/m 3 )
Watt per cubic meter(W/m 3 )
Joule per kilogram(J/kg)
Joule per kilogram(J/kg)
cubic meter per kilogram(m 3 /kg)
cubic meter per squaremeter-second (m3 /m 2 -s)
Watt per square meter(W/m2 )
kilogram per square meter-second (kg/m 2 -s)
By
2.204622 3.280840
3.937008 x io~ 2 1.157407 x 10" 5
T(°F) = 1.8T(°C) + 32 T(°F) = 1.8T(K) - 459.67
9.478170 x io"4
10.7639135.31466
3.797267 x io~ 5 1.450377 x io~ 4
2.834646 x 9.300018 x
3.051187 x io6
3.051187 x io 3
1.904794 x io 5
12.53126
8.6400 x io 4
6.242797 x io~ 2
9.662109 x io' 2
4.299226 x io~4
0.3345526
16.01846
2.834646 x io 5
0.3169983
1.769611 x io 4
To obtain
pound (Ib)foot (ft)inch (in.)day (d)degree Fahrenheit (°F)degree Fahrenheit (°F)British Thermal Unit
(BTU)square foot (ft 2 ) cubic foot (ft 3 ) foot-day (ft-d) pound per square inch
(psi)foot per day (ft/d) square foot per day
(ft 2 /d) cubic foot per day
(ft 3 /d) cubic foot per day
(ft 3 /d) pound per day (Ib/d)
pound per square inchper day (Ib/in2/d)
cubic foot per cubicfoot-day (ft 3 /ft 3 -d)
pound per cubic foot(Ib/ft 3 ) 1
British Thermal Unitper hour-cubicfoot (BTU/h-ft 3 )
British Thermal Unitper pound (BTU/lb)
foot-pound force perpound mass(ft-lbf/lbm)
cubic foot per pound(ft 3 /ib)
cubic foot per squarefoot-day (ft 3 /ft 2 -d)
British Thermal Unitper hour-square foot(BTU/h-ft 2 )
pound per Fquarefoot-day (Ib/ft 2 -d)
VI1
cubic meter per meter-second(m3 /m-s)
kilogram per meter-second(kg/m-s)
Joule per kilogram-meter(J/kg-m)
Watt per meter-degree Celsius (W/m-°C)
Watt per square meter- degree Celsius (W/m2 -°C)
Joule per kilogram- degree Celsius (J/kg-°C)
Joule per cubic meter-degree Celsius (J/m 3 -°C)
9.300018 x io 5
1,000
1.310404 x 10"
13.86941
0.1761102
2.388459 x 10
1.491066 x 10
-4
-5
cubic meter per second-meter- 6.412138 x Pascal (m 3 /s-m-Pa)
cubic foot per foot-day(ft 3 /ft-d)
centipoise (cP) 2
British Thermal Unitper pound-foot(BTU/lb-ft)
British Thermal Unitper foot-hour-degreeFahrenheit(BTU/ft-h-°F)
British Thermal Unitper hour-squarefoot-degree Fahrenheit(BTU/h-ft 2 -°F)
British Thermal Unitper pound-degreeFahrenheit(BTU/lb-°F)
British Thermal Unitper cubic foot-degreeFahrenheit(BTU/ft 3 -°F)
cubic foot per day- foot-pound-squareinch (ft 3 /d-ft-psi)
1 A weight density rather than a mass density.2 Not inch-pound but common usage.
Vlll
HST3D: A COMPUTER CODE FOR SIMULATION OF HEAT AND SOLUTE TRANSPORT
IN THREE-DIMENSIONAL GROUND-WATER FLOW SYSTEMS
By Kenneth L. Kipp Jr.
ABSTRACT
The Heat- and Solute-Transport Program (HST3D) simulates ground-water
flow and associated heat and solute transport in three dimensions. The HST3D
program may be used for analysis of problems such as those related to sub
surface-waste injection, landfill leaching, saltwater intrusion, freshwater
recharge and recovery, radioactive-waste disposal, hot-water geothermal
systems, and subsurface-energy storage. The three governing equations are
coupled through the interstitial pore velocity, the dependence of the fluid
density on pressure, temperature, and solute-mass fraction, and the dependence
of the fluid viscosity on temperature and solute-mass fraction. The solute-
transport equation is for only a single, solute species with possible linear-
equilibrium sorption and linear decay. Finite-difference techniques are used
to discretize the governing equations using a point-distributed grid. The
flow-, heat- and solute-transport equations are solved, in turn, after a
partial Gauss-reduction scheme is used to modify them. The modified equations
are more tightly coupled and have better stability for the numerical solutions,
The basic source-sink term represents wells. A complex well-flow model
may be used to simulate specified flow rate and pressure conditions at the
land surface or within the aquifer, with or without pressure and flow-rate
constraints. Boundary-condition types offered include specified value,
specified flux, leakage, heat conduction, an approximate free surface, and two
types of aquifer-influence functions. All boundary conditions can be
functions of time.
Two techniques are available for solution of the finite-difference matrix
equations. One technique is a direct-elimination solver, using equations
reordered by alternating diagonal planes. The other technique is an iterative
solver, using two-line successive overrelaxation. A restart option is
available for storing intermediate results and restarting the simulation at an
intermediate time with modified boundary conditions. This feature also can be
used as protection against computer-system failure.
Data input and output may be in metric (SI) units or inch-pound units.
Output may include tables of dependent variables and parameters, zoned-contour
maps, and plots of the dependent variables versus time. The HST3D program is
a descendant of the Survey Waste Injection Program (SWIP) written for the U.S.
Geological Survey under contract.
1. INTRODUCTION
1.1. OVERVIEW OF THE SIMULATOR
The computer program (HST3D) described in this report simulates heat and
solute transport in three-dimensional saturated ground-water flow systems.
The equations that are solved numerically are: (1) The saturated ground-water
flow equation, formed from the combination of the conservation of total-fluid
mass and Darcy's Law for flow in porous media; (2) the heat-transport equation
from the conservation of enthalpy for the fluid and porous medium; and (3) the
solute-transport equation from the conservation of mass for a single-solute
species, that may decay and may adsorb onto the porous medium. These three
equations are coupled through the dependence of advective transport on the
interstitial fluid-velocity field, the dependence of fluid viscosity on
temperature and solute concentration, and the dependence of fluid density on
pressure, temperature, and solute concentration.
Numerical solutions are obtained for each of the dependent variables:
pressure, temperature, and mass fraction (solute concentration) in turn, using
a set of modified equations that more directly link the original equations
through the velocity-, density-, and viscosity-coupling terms. Finite-
difference techniques are used for the spatial and temporal discretization of
the equations. When supplied with appropriate boundary and initial conditions
and system-parameter distributions, simulation calculations can be performed
to evaluate a wide variety of heat- and solute-transport situations.
The computer code (HST3D) described in this documentation is a descendant
of a computer code for calculating the effects of liquid-waste disposal into
deep, saline aquifers, developed by INTERCOM? Resource Development and
Engineering Inc. 1976) for the U.S. Geological Survey and revised by INTERA
Environmental Consultants Inc. (1979). The parent code, known as the Survey
Waste Injection Program (SWIP), has been completely rewritten with many major
and minor modifications, improvements, and correction of several errors.
Features included in HST3D are briefly described as follows:
1. Specified-value and specified-flux boundary conditions
are independent of each other and independent of the well
or aquifer-influence-function boundary conditions. The
boundary conditions also may vary with time.
2. Specified heat- and solute-flux boundary conditions are available.
3. The leakage boundary conditions are generalized and a river-
leakage boundary condition is available.
4. Porous-medium thermal properties, dispersivity, and
compressibility, may have spatial variation defined by zones.
5. A point-distributed, finite-difference grid is employed, rather than
a cell- or block-centered grid, for less truncation error and
easier incorporation of boundary conditions.
6. The heat-conduction boundary condition is generalized to apply
to any cell face.
7. Global-flow, and heat- and solute-balance calculations are performed
including flux calculations through specified pressure, temper
ature, and mass-fraction boundaries.
8. A robust algorithm for the computation of the optimum
overrelaxation factor for the two-line, successive-overrelaxation,
matrix-solution method is used, with a convergence
criterion that includes the matrix spectral-radius estimate.
9. The code is organized for a logical flow of calculation and a
modular structure.
10. The code length is about 12,000 lines, using FORTRAN 77
language constructs for cleaner, more efficient coding than
possible with FORTRAN 66. However, clarity has not been
sacrificed for ultimate efficiency.
11. Comments have been included liberally for ease of understanding
the program.
12. All arrays with lengths depending on the size of the problem are
in two variably-partitioned arrays, integer and real, to facilitate
double-precision arithmetic.
13. Arrays required for thermal or solute calculations exclusively are
eliminated if only one of these transported quantities is being
simulated, which results in a considerable decrease in computer
storage.
14. Arrays used for a specific type of boundary condition or source-sink
condition are dimensioned only to the length required.
15. The allocation of space for the direct-equation solver is
explicitly determined during array-space allocation, rather
than estimated.
16. Logical variables are used to control the flow of program execution
for ease of option selection.
17. The input file is in free-format to facilitate input from terminals.
18. The input file is organized into logical groups for parameter
specifications.
19. User comments can be freely incorporated into the input file
for rapid identification of the data. An input-file form
is available which the user can fill out at the terminal for a
given simulation.
20. A read-echo file may be written to aid in locating errors in the
data-input file.
21. Character plots of the porous-media zones may be created on the
output file to facilitate checking the zonation.
22. Although the internal calculations of the program are performed in
metric units, the input and output can be chosen to be in
inch-pound units.
23. The output material is made easily understandable by avoiding
variable names, by logical grouping on the page, and by
including supplementary information.
24. Error tests are included to catch likely mistakes in data input.
25. Error messages are printed explicity rather than as code numbers.
26. There is no limit on the number of plots that can be created.
The number of calculated points in time per plot is limited to
three times the total number of grid points, while the number
of observed points in time is limited to two times the number
of grid points. The user can select every nth point to be
plotted, if this number is limiting.
27. The solute concentration can be chosen to be the mass fraction
or a scaled mass fraction that ranges from 0 to 1. This choice
was available in the SWIP code, but the user was not clearly made
aware of which option was selected.
28. Two types of restart option are available: a periodic check-point
dump for protection against computer-system failure, and a
specific dump for user review and possible modification of
parameters.
29. Map-contour intervals can be automatically determined to be a
multiple of 2, 5, or 10, and the contour zones are "zebra striped"
for easier reading.
30. Initial-pressure conditions can be specified to be other than
hydrostatic. For example, an initial water-table
configuration can be used.
31. The precipitation-infiltration option is contained in the
distributed flux-boundary conditions.
32. The conductive-heat-loss to overburden and underburden is a
general, heat-transfer calculation, applicable to any
cell face in the region.
33. The well-riser, heat-transfer calculation is based on heat
transfer from a known-temperature, cylindrical boundary, and
higher order assymptotic expansions have been used.
34. The well-riser calculation has been formulated to solve the
total-energy and momentum balance equations simultaneously,
using the Bulirsch-Stoer algorithm for integration of the
ordinary differential equations.
35. The well-bore equations are implicitly coupled to the system
equations for cases of cylindrical geometry.
36. The well-datum pressure and the well-flow rate allocation
calculations may be performed iteratively in conjunction with
the solution of the flow equation, or explicitly.
37. The full nine-component, or an approximate three-component,
dispersion-coefficient tensor may be used for cross-dispersive
flux calculations.
The purpose of simulation modeling the transport of heat and solute in
ground-water flow systems is to gain a quantitative understanding of how the
sources and sinks, the boundary conditions, and the aquifer parameters
interact to cause ground-water flow patterns and consequent thermal- and
solute-concentration movement in a system under investigation. Of particular
interest are the magnitudes of concentrations and discharges at interfaces
with the environment, for example, in cases of aquifer contamination.
Naturally, the quality or degree of realism of a given simulation is strongly
dependent on the quantity and quality of the parameter distribution, boundary-
condition, and source-sink data. Acquiring this data can be a major task of
the modeling project.
1.2. APPLICABILITY AND LIMITATIONS
The HST3D code is suitable for simulating ground-water flow and the
associated heat and solute transport, in saturated, three-dimensional flow
systems with variable density and viscosity. As such, the code is applicable
to the study of waste injection into saline aquifers, landfill-contaminant
movement, seawater intrusion in coastal regions, brine disposal, fresh-water
storage in saline aquifers, heat storage in aquifers, liquid-phase geothermal
systems, and similar transport situations. If desired, only the ground-water
flow or only the heat- or the solute-transport equation may be solved in
conjunction with ground-water flow. Three-dimensional cartesian or
axisymmetric, cylindrical-coordinate systems are available.
The primary limitation of this code results from the use of finite-
difference techniques for the spatial- and temporal-derivative approximations,
Where longitudinal and transverse dispersivities may be small, cell sizes will
need to be small to minimize numerical dispersion or oscillation. Further
more, if the region of solute movement is somewhat convoluted and three-
dimensional, the projection of nodal lines from regions of high-nodal density
will cause more nodes than are needed to appear in other regions. These two
factors can combine to cause an excessive number of nodes to be involved for a
given simulation, thus making the simulation prohibitively expensive because
of computer-storage and computation-time requirements. In such cases, a
simple model of the system, useful for investigating mechanisms and testing
hypotheses, may be all that is practical.
Another limitation results from a phenomenon called grid-orientation
effect (Aziz and Settari, 1979, p. 332), whereby numerical simulations of
miscible displacement converge to two separate solutions, as the mesh size is
refined, depending on whether the major velocity vectors are parallel to one
of the coordinate directions or are diagonally oriented. The effect is more
pronounced for conditions of little dispersion or piston-like displacement of
the solute, and for conditions of the viscosity of the displacing fluid much
less than the viscosity of the displaced fluid. The effect virtually is
absent if the two viscosities are nearly equal, or if the dispersion
coefficient is large. The primary cause of the grid-orientation effect
appears to be the use of a seven-point difference formula for the three-
dimensional-flow and solute-transport equations, because this formula
restricts transport in the diagonal directions. Use of a grid where the major
velocity vectors are oriented parallel to one of the coordinate directions,
has been found to give more realistic simulation results (Aziz and Settari,
1979, p. 336). To completely eliminate this problem, a higher-order
differencing scheme, or curvilinear coordinates need to be used, but these
modifications are beyond the scope of the present version of HST3D.
There is a limitation on which boundary conditions can be used with a
tilted coordinate system. The free surface and leakage boundary conditions
require that the z-axis be oriented in the vertical direction.
A limitation that is secondary for most ground-water flow and transport
modeling is that two types of transport phenomena exist that this type of
numerical simulation has difficulty in representing quantitatively. The first
phenomenon, viscous-fingering instabilities, may occur during the displacement
of a resident fluid by an injected fluid with significantly less viscosity.
The injected fluid forms channels or fingers through the resident fluid, as
described by Aronofsky (1952), Saffman and Taylor (1958), and Sheidegger
(1960). The second phenomenon may occur in the situation where a fluid of
greater density overlies one of lesser density. Rayleigh-Taylor convective
cells are formed that mix the two fluids (Wooding, 1959). Numerical
simulation tends to predict these transport instabilities later than they
occur in laboratory-scale experiments. When perturbations are present to
initiate the instabilities, the general magnitudes often are calculated to be
less than those that actually occur (Scheidegger and Johnson, 1963; and
Dougherty, 1963). However, laboratory-scale viscous fingering and convective-
cell formation may be much more unstable than the corresponding field-scale
phenomenon, because of the smaller dispersivity at the laboratory scale.
Therefore, at the field scale, numerical simulation may not be so much in
error in representing these instabilities. Nevertheless, these limitations
need to be be kept in mind when simulating fluid flow with large viscosity or
density contrasts.
Another secondary limitation is that this is a rather general computer
code. The variety of discretization, boundary-condition, and source-sink
options make this code not as computationally efficient as a simulation code
designed specifically for a given system being investigated. This limitation
is compensated by the ability of the HST3D simulator to represent a wide
variety of physical situations.
1.3. PURPOSE AND SCOPE
The purpose of this documentation is to provide the user with information
on the theory, assumptions, and equations being numerically solved, the
numerical-solution methods employed, and the various program options avail-
able. The sets of verification test problems are presented and two example
problems are described in detail with input and output files. Sections on the
code organization, input information, and output information, as well as a
list of variable-definitions and a cross-reference map are provided. The
documentation is intended to be sufficiently complete and understandable so
the user easily can obtain successful simulations, diagnose most computational
problems, develop remedies, and incorporate minor program additions or
modifications to suit specific modeling needs.
Each release of the HST3D program code is identified by a release number.
This documentation is for release 1.0, and this number will change as modifi
cations, corrections, and additions are made to the program. Updates to the
documentation will be keyed to the release number.
1.4. ACKNOWLEDGMENTS
The contributions of J.E. Carr, J.B. Gillespie, and A.H. Welch, of the
U.S. Geological Survey who provided application problems that influenced
program development, and of R.T. Miller and M.L. Merritt, also with the U.S.
Geological Survey, who helped with program testing, are gratefully
acknowledged.
10
2. THEORY
2.1. FLOW AND TRANSPORT EQUATIONS
Derivation of the saturated ground-water flow and heat- and solute-
transport equations solved by this program can be found in references such as
Bear (1972) or Huyakorn and Finder (1983). Only the assumptions leading to
these equations will be presented here. Explanations of the notation will
appear after the first usage. A complete table of notation appears in
chapter 9. In the report, all variables will be given with metric (SI) units
of measure.
2.1.1. Ground-Water Flow Equation
The partial-differential equation of ground-water flow is based on the
following assumptions:
Ground water fully saturates the porous medium within the region of
ground-water flow.
Ground-water flow is described by Darcy's Law.
The porous medium is compressible.
The fluid is compressible.
The porosity and permeability are functions of space.
The coordinate system is chosen to be alined with the principal
directions of the permeability tensor so that this tensor is
diagonal for anisotropic media.
The coordinate system is orthogonal as are the principal directions of
the permeability tensor.
The coordinate system is right-handed with the z-axis pointing
vertically upward.
The fluid viscosity is a function of space and time through dependence
on temperature and solute concentration.
Density-gradient diffusive fluxes of the bulk fluid are neglected
relative to advective-mass fluxes.
11
Dispersive-mass fluxes of the bulk fluid from spatial-velocity
fluctuations are not included.
Contributions to the total fluid-mass balance from pure-solute-
mass sources within the region are not included.
Pressure is chosen as the dependent variable for fluid flow, because no
potentiometric-head function exists for density fields that depend on
temperature and solute concentration. All pressures denoted by p are
expressed relative to atmospheric pressure. Absolute pressures are denoted by
p. The flow equation is based on the conservation of total fluid mass in a
volume element, coupled with Darcy's Law for flow through a porous medium.
Thus:
kTT-(Vp + pg) + qp* ; (2.1.1.la)
where
p is the fluid pressure (Pa);
t is the time (s);
e is the effective porosity (-);
p is the fluid density (kg/m3 );
p* is the density of a fluid source (kg/m3 );
^ is the porous-medium permeability tensor (m2 );
p is the fluid viscosity (kg/m-s);
g is the gravitational constant (m/s 2 ); and
q is the fluid-source flow-rate intensity (m3 /m3 -s); (positive
is into the region).
Equation 2.1.1.la relates the rate of change of total mass in the fluid
phase to net fluid-inflow rate, and source fluid-and-solute flow rate. Note
that the density of the fluid source is p* for q>0, and p for q<0.
12
The interstitial or pore velocity, v is obtained from Darcy's Law as:
v = - (Vp + pg) ; (2.1.1.1b) -
where
v is the interstitial-velocity vector (m/s).
2.1.2. Heat-Transport Equation
The thermal-energy-balance equation, used for heat transport, is based on
the following assumptions:
Fluid kinetic energy is negligible.
Thermal-dispersive transport takes place with a mechanism analogous to
solute-dispersive transport.
Thermal conduction occurs through the fluid and porous medium in
parallel.
Radiant-energy transfer is neglected.
Thermal effects of chemical reactions are neglected.
Changes in gravitational energy from diffusive and dispersive fluxes
of solute species are neglected.
Heating from viscous dissipation is neglected.
Heat capacities are not a function of temperature or solute
concentration.
Thermal conductivities are not functions of temperature or solute
concentration.
Thermal equilibrium exists between the fluid and solid phases.
Energy transport by a diffusive flux of solute is neglected.
Only a single fluid phase exists.
Pressure equilibrium exists between the fluid and porous-medium
phases.
Changes in fluid enthalpy with pressure, that is, pressure volume work,
reversible work, or flow work, as a parcel of fluid moves are
neglected.
13
The velocity of the porous medium during compression or expansion is
neglected.
Enthalpy dependence on solute concentration is accounted for by a
heat-capacity adjustment.
The thermal expansion of the porous medium is neglected.
The energy equation is based upon the conservation of enthalpy in both
the fluid and solid or porous-medium phases of a volume of the region.
Enthalpy is a derived property containing both internal energy and flow
energy. Temperature is the dependent variable. Thus:
9 (epc_ + (l-e)p c )T = V-CeK. + (l-e)K )! VTQ V^K'-^ ' v x 'r'c s V°iv£ ' V x ^J**-~J±
'eO, VT - V*epc_vT n I
+ qH + qp*cfT* ; (2.1.2.1)
where
T is the fluid and porous-medium temperature (°C);
T* is the temperature of the fluid source (°C);
p is the density of the solid phase (kg/m3 ); sc is the heat capacity of the fluid phase at constant pressure
(J/kg-°C);
c is the heat capacity of the solid phase at constant pressureS
(J/kg-°C);
K_ is the thermal conductivity of the fluid phase (W/m-°C);
K is the thermal conductivity of the solid phase (W/m-°C);S
gu is the thermo-mechanical dispersion tensor (W/m-°C);
qu is the heat-source rate intensity (W/m3 ); and nI is the identity matrix of rank 3 (-).
Equation 2.1.2.1 relates the rate of change of fluid and porous-medium
enthalpy to the net conductive-enthalpy flux, to the net dispersive enthalpy
14
flux, to the net advective-enthalpy flux, to the heat source, and to the fluid
source at a given temperature. It is written for a unit volume of fluid and
solid phase together; that is, a unit volume of saturated, porous medium.
Heat is injected at temperature, T*, and density, p*, by a fluid source; but
heat is withdrawn at temperature, T, and density, p by a fluid sink. A
detailed derivation of equation 2.1.2.1 is given in Faust and Mercer (1977).
2.1.3. Solute-Transport Equation
The equation for conservation of a single solute species is based on the
following assumptions:
Thermal diffusion is neglected.
Pressure diffusion is neglected.
Solute transport by local, interstitial, velocity-field fluctuations
and mixing at pore junctions is described by a hydrodynamic-
dispersion coefficient.
Forced diffusion by gravitational, electrical, and other fields is
neglected.
The only reaction mechanism is linear decay or disappearance of solute.
The only solute, porous-medium, interaction mechanism is linear-
equilibrium sorption.
No pure solute sources occur in the fluid or solid phases.
The solute mass fraction is taken to be the dependent variable because
the density field is variable. It is an amount per unit mass of fluid, that
is, a mass-based concentration. The more widely used concentration term is an
amount per unit volume of fluid; that is, a volume-based concentration. But
volume-based concentration is not conserved in a variable-density system. The
term "solute concentration," used in this report, will refer to the mass-based
concentration or mass fraction. The conservation equation for the solute in
the fluid phase can be written:
15
= V'epELVw + V'epD IVw - V«epvw - \epwij m
-pbRfg + qp*w* ; (2.1.3.la)
where
w is the mass fraction of solute in the fluid phase (-);
w* is the mass fraction of solute in the fluid source (-);
Hq is the mechanical-dispersion-coefficient tensor (m2 /s);
D is the effective-molecular diffusivity of the solute (m2 /s);
A. is the linear-decay rate constant (s" 1 );
Rf is the transfer rate of solute from fluid to solid phase per
unit mass of solid phase (kg solute/s*kg solid phase); and
p, is the bulk density of the porous medium (kg/m3 ).
A similar conservation equation can be written for the solute in the
solid phase:
w)
where
w is the mass fraction of solute on the solid phase (-).
The solute is immobile when it is on the solid phase. Under the
assumption of linear-equilibrium sorption, the fluid-phase and solid-phase
concentrations can be related by an equilibrium-distribution coefficient:
w =
where
K, is the equilibrium-distribution coefficient (m 3 /kg).
By combining equations 2.1.3.1a-c, we obtain the final solute-
conservation equation:
16
fj: (e + PbKd )pw = V-ep[ng + DjUVw-V-epyw - \(e+pbKd )pw
+qp*w* ; (2.1.3.2)
Equation 2.1.3.2 relates the rate-of-change of solute in the fluid phase
to the net dispersive and diffusive flux, the net advective flux, the solute-
source rate, the solute-injection rate with a fluid source, and the solute-
decay rate. The equation is written for a unit volume of fluid and solid
phase together; that is, a unit volume of saturated porous medium. Note that
solute is injected into the sytem at concentration, w*, and density, p*, by a
fluid source; but that solute is withdrawn at concentration w, and density p,
by a fluid sink; that is, w* = w, if q<0.
2.2. PROPERTY FUNCTIONS AND TRANSPORT COEFFICIENTS
Before the three conservation equations can be solved, information about
the fluid properties, porous-matrix properties, and transport coefficients
need to be obtained. The fluid properties are density, viscosity, heat
capacity, thermal conductivity, and reference-state enthalpy. The porous-
matrix properties are porosity, compressibility, permeability, heat capacity,
thermal conductivity, and reference-state enthalpy. The transport
coefficients are heat- and solute-dispersion tensors, and the effective
molecular diffusivity, decay and sorption coefficients of the solute. In the
HST3D simulator, density, viscosity, and porosity are functions of the
dependent variables: pressure, temperature, and solute-mass fraction. The
heat- and solute-dispersion tensors are functions of space and the inter
stitial velocity. The other parameters are either uniform or functions of
space within the simulation region.
17
2.2.1. Fluid-Density Function
Fluid density is assumed to be a function of pressure, temperature, and
solute concentration. For fluids such as water, a linear-density function is
usually adequate over the ranges of pressures, temperatures, and solute
concentrations encountered. Thus, the fluid-density function incorporated
into this simulation code is:
or
pCp.T.w) = P(P0 ,T0 ,«0 ) +
(w-w ) ; o o '
p(p,T,w) = pQ + P0Pp (p-pQ )
(T-T ) o o
(2.2.1.la)
where
p is the fluid density at a reference pressure, p , temperature, T ,
and mass fraction, w , (kg/m3 );
P is the fluid compressibility (Pa" 1 );
PT is the fluid coefficient of thermal expansion (°C~ 1 ); and
P is the slope of the fluid density as a function of mass fraction
divided by the reference fluid density (-).
Now p P is given by:
p(w ) - p(w . KV max K mmw - w . max mm
18
where
w . is the minimum solute-mass fraction (-); andmm '
w is the maximum solute-mass fraction (-). max
The user needs to specify w . and w along with p(w . ) and p(w ). Thee mm max e ^ mm r maxminimum solute-mass fraction usually will be determined by the initial
conditions. If linear decay is present, w . must be zero. The maximum
solute-mass fraction usually will be determined by source or boundary
conditions because none of the transport processes incorporated in the HST3D
simulator will concentrate solute in the fluid phase. For simplicity, WQ is
taken to be equal to w . . ^ mm
The option is available in HST3D to use a scaled, solute, mass fraction
defined by:
w - w ., = mm (2.2.1.2)
w -w . ' max mm
where
w 1 is the scaled solute-mass fraction (-);
The scaled solute-mass fraction also is dimensionless and ranges from 0 to 1.
Commonly, for input and output of mass-fraction data, it is more convenient to
deal with a scaled solute-mass fraction rather than an absolute value. With a
scaled solute-mass fraction, equation 2.2.1.1b becomes:
where
p(p,T,w') = pQ + P0P(p-P0 ) - P0PT (T-TQ ) + P0PW 'W, (2.2.1.3a)
p £ ' = p(w ) - p(w . ) . (2.2.1.3b) rorw r max mm
The errors caused by assuming constant values for fluid compressibility,
coefficient of thermal expansion, and variation of density with solute con
centration can be assessed by looking at a density table for salt brines
(Perry and others, 1963, p. 3-77).
19
Over a temperature range of about 100 °C and a solute-mass fraction range of
20 percent, the coefficient of thermal expansion varies by 60 percent and the
density-concentration coefficient, p , varies by about 10 percent (Perry and
others, 1963, p. 3-77). The variation of the fluid compressibility could
not be checked because of lack of data. However, the density dependence on
pressure for nearly incompressible fluids like water is much less than the
density dependence on temperature or solute concentration. Therefore, some
error will be introduced into the simulations by the linear-density function
where large variations in temperature and solute concentration are involved.
The relative importance of pressure, temperature, and solute con
centration for density variation can be seen from the salt-brine density table
given in Perry and others (1963) and the compressibility of water. A change
in pressure of 106 Pa results in a density change of about 0.04 percent,
whereas a change in temperature of 100 °C results in a density change of about
4 percent, but a change in solute-mass fraction of 0.25 results a density
change of about 20 percent. Thus, the salt concentration has the greatest
effect on the density for typical ranges of the variables.
2.2.2. Fluid-Viscosity Function
Fluid viscosity is strongly dependent on temperature, and, to a lesser
extent, on solute concentration. The viscosity dependence on pressure is
neglected. The viscosity as a function of temperature and scaled-solute
concentration is written as:
-3M(T,w') = 10 p (T,w') expQV
(B0w' + Bid-w')) ( -OV J
, (2.2.2.1)
where
,w') is the fluid viscosity at the reference temperature (kg/m-s);
BQ, B! are parameters describing the temperature dependence of
viscosity at the concentration extremes (°C); and
T is the reference temperature for viscosity (°C).
20
The scaled solute-mass fraction of equation 2.2.1.2 is used in the
viscosity function as well as the density function. The parameters B0 and BI
are obtained from a least-squares fit of viscosity versus temperature data.
If data are available only at a single temperature, the generalized viscosity
versus temperature graph of Lewis and Squire as given in Perry and others
(1963, p. 3-228) is used.
The concentration extremes are chosen to be the same minimum and maximum
mass fractions described in section 2.2.1. The variation of viscosity with
solute-mass fraction is specified in tabular form by the user. If viscosity
data at only the minimum and maximum mass-fraction values are available, the
equation used for viscosity as a function of concentration at a given
temperature is:
M(w') = Mi(TQV ) W Mo(T ^ , (2.2.2.2)
where
Po is the viscosity at the minimum-mass fraction or scaled
concentration of zero (kg/m-s); and
Pi is the viscosity of the maximum-mass fraction or scaled
concentration of one (kg/m-s).
Equation 2.2.2.2 is used with equation 2.2.2.1 or alone in the case of iso
thermal simulation.
The viscosity versus temperature and concentration data that could be
available may be divided into three classes. Class 1 is the greatest amount
available, namely u(T) at w . and w and u(w) for a range of w from w . to ' mm max r 6 mm
w . Class 2 is viscosity versus temperature, M(T), at only w . and w max J r * r ' mm maxClass 3 is the least amount of data required, namely two viscosity points at
a given temperature at w . and wmm max
An evaluation of the accuracy of viscosity functions given in equations
2.2.2.1 and 2.2.2.2 was presented by INTERCOM? Resource Development and
21
Engineering, Inc. (1976). They found errors ranging from 5 to 14 percent over
the temperature range from freezing to boiling for pure water. For a solution
of sodium chloride with a mass fraction ranging from 0.0 to 0.24, the
different amounts of data available resulted in errors from 5 to 18 percent at
a temperature of 65 °C. A sucrose solution with mass fractions ranging from
0.0 to 0.5 showed a maximum viscosity error of 30 percent. Other viscosity
functions of temperature and solute concentration may be more suitable for
certain situations.
2.2.3. Fluid Enthalpy
Fluid-phase enthalpy is a function of pressure, temperature, and solute
concentration. The present version of the HST3D code uses the enthalpy of
pure water obtained from the steam tables of Keenan and others (1969, p. 2-7
and 104-107), which can be described as:
A.
H(p,T) = H(p ,0) + LJ £ [1-fpJdp + J* cfodT > (2.2.3.la)psat H
where
H is the specific enthalpy of the fluid phase (J/kg);
p is the absolute pressure (Pa);
p . is the absolute pressure at saturation (Pa); and sai..I1 is the absolute temperature (K).
cf is the heat capacity of pure water at constant pressure (J/kg-°C).
The reference state for the enthalpy tables is saturated liquid water at
0 °C where the reference enthalpy is taken to be zero (Van Wylen, 1959,
p. 80). The variation of enthalpy with solute concentration is treated in an
approximate fashion, by adjusting the pure-water enthalpy by a factor that is
the ratio of the heat capacity of the solution to the heat capacity of pure
water at 0 °C, and by using an average heat capacity for the range of solute
concentrations to be simulated. The heat capacity is assumed independent of
temperature and pressure.
22
Thus,
H(p,T,w) = H(p,T,0) (cf (w)/cfQ ) (2.2.3.1b)
where
c_(w) is an average heat capacity (J/kg-°C).
During the simulations, the enthalpy is calculated as a variation from a
reference state described by a pressure, p , and a temperature, T ,
selected by the user. The reference state is pure water so the reference
mass fraction, w , is always zero. Thus, the enthalpy equation becomes:
H(p,T,w) = H(poH , ToH ,0) (c^/c f<) ) + /P [l-tpT ] & + ;T dT . (2 . 2 .3.1c)oH oH
where
p is a reference pressure for enthalpy (Pa); onp is the corresponding absolute'pressure (Pa); and onT is a reference temperature for enthalpy (°C). on
The tpT term may be neglected for temperatures less than 100 °C (373 K)
and density may be regarded as constant for pressure changes less than 108 Pa.
The chosen reference pressure and temperature needs to be within the range to
be calculated during the simulation. The heat capacity of the fluid needs to
be an average value over the solute-concentration range to be simulated. More
sophisticated treatments of the enthalpy of fluid mixtures are available in
the literature; for example, Hougen and others (1959, p. 879).
2.2.4. Porous-Medium Enthalpy
Enthalpy of the porous medium is taken to be a function of only temper
ature in the following form:
23
Hs "V1^ + cs tT-ToH} ; (2.2.4.1)
where
H is the specific enthalpy of the solid phase (porous matrix) (J/kg);S
and
c is the heat capacity of the solid phase (porous matrix) (J/kg-°C).S
Often, the enthalpy of the porous matrix is taken to be zero at a
reference state of 0 °C.
2.2.5. Porous-Medium Compressibility
Many types of compressibility for porous media have been defined (Bear,
1972, p. 52, 203-213; Thomas, 1982, p. 34, 40). The porous-medium bulk
compressibility, OL (Pa" 1 ), is defined on a volumetric basis (Bear, 1972,
p. 56; Eagleson, 1970, p. 268), assuming confined-aquifer conditions, and
one-dimensional, vertical consolidation of the porous matrix, as:
1 9V,
where
V, is the bulk or total volume of a fixed mass of porous medium,
that is, fluid plus porous matrix (m3 ).
Petroleum-reservoir engineers use the term rock compressibility, a
(Pa -1 ), defined as (Thomas, 1982, p. 34):
a = 1|^ (2.2.5.2)
24
Rock compressibility directly expresses the variation of porosity with
pressure. It is related to bulk compressibility by:
a = %^ OL : (2.2.5.3a)
for the case of a nondeforming control volume, where more porous medium enters
the control volume, as compression takes place. It is related by:
, a = -f (2.2.5.3b)i O
for the case of a deforming control volume, or where impermeable medium enters
a nondeforming control volume, as compression takes place.
By combining equations 2.2.5.2 and 2.2.5.3b we obtain:
which relates bulk compressibility to changes in porosity with changes in
pressure.
Thus we have allowed the control volume to deform as the porous matrix
and the fluid specific volumes expand or contract with changes in pressure.
However, we neglect the velocity of deformation, so that the interstitial-pore
velocity is calculated with respect to the fixed-coordinate system.
The specific storage is related to the compressibilities of the fluid and
porous medium by (Eagleson, 1970, P. 270):
S = pg(a, + ep ) (2.2.5.5) o b p
where
S is the specific storage (m ).
25
However, it is more convenient for our purposes to employ the com
pressibility parameters, because of the variable density.
2.2.6. Dispersion Coefficients
2.2.6.1. Solute Dispersion
Hydrodynamic dispersion is the name for the group of mixing mechanisms
that occur on the micro or pore scale that cause the irreversible spreading of
a solute tracer that is observed at the macro or field scale for the system.
As described by Bear (1972, p. 580-581), flow within the porous-medium
structure has variations in local flow velocity, because of the velocity
profile across the pore and mixing at pore junctions. The macroscopic effect
is mechanical dispersion of a tracer. Molecular diffusion also is present
where solute-tracer concentration gradients exist. However, diffusion in
liquids is a relatively slow process, producing significant transport rates
only at very slow ground-water flow velocities. In a laminar flow regime
within the pores, diffusion of solute from one flow path to another
contributes to the dispersion, so the separation of dispersion into a
mechanical and diffusive mechanisms is somewhat artificial. For an extensive
discussion of dispersion theory and a review of previous work, see Bear (1972,
ch. 10).
JL
The form of the hydrodynamic-dispersion-coefficient tensor D_. . (m 2 /s)
for the heat- and solute-transport simulation model is assumed to be, in
component form:
D * = D_.. + D 6.. ; (2.2.6.1.1) Sij Sij m ij
where
D_.. is the mechanical-dispersion-tensor component (m2 /s);^
D is the effective molecular-diffusion coefficient (m 2 /s); and m
6.. is the Kronecker delta function.
26
The effective molecular-diffusion coefficient is the liquid-phase
molecular diffusivity multiplied by an attenuation factor that accounts for
the effect of the tortuosity of the porous medium. The form of the
mechanical-dispersion coefficient is taken from the work of Scheidegger (1961)
and Bear (1961) as presented by Konikow and Grove (1977) and Bear (1972,
ch. 10). For an isotropic porous medium, two parameters describe the
mechanical-dispersion tensor, the longitudinal dispersivity, OL. (m) , and theLi
transverse dispersivity, a_ (m) . Then the nine components of the mechanical-
dispersion tensor are given by:
DSij = ("L - V V + "T v6ij '' (2.2.6.1.2)
where
v. is the component of interstitial velocity in the ith direction
(m/s);
2 2 2and v = (v + v + v ) ; (2.2.6.1.3)
123
where
v is the magnitude of the velocity vector (m/s).
In general, the subscript 1 is associated with the x direction; the
subscript 2 is associated with the y direction; and the subscript 3 is
associated with the z direction. Field data have shown that longitudinal
dispersivity usually is 3 to 10 times larger than transverse dispersivity
(Freeze and Cherry, 1979, p. 396; Anderson, 1979), and that their magnitudes
are dependent on the scale of observation distance over which the tracer is
transported in the system.
27
Note that while flow in the porous medium may be governed by an
anisotropic-permeability tensor, dispersion for heat and solute transport is
assumed to be described by a dispersion tensor that applies to an isotropic-
porous medium. This assumption is made because it is not feasible to obtain
all the dispersivity parameters for an anisotropic medium. If dispersive
transport is a second-order effect, relative to advective transport, this
inconsistency should not introduce serious errors. In most cases, the errors
should be less than those introduced by uncertainties in the dispersion
parameters themselves.
When the longitudinal and transverse dispersivities are not equal,
dispersive transport will cause a solute distribution to enlongate in the
direction of flow, because the longitudinal dispersivity always is greater
than or equal to the transverse dispersivity. Thus, anisotropic spreading of
solute and heat can occur in an isotropic-porous medium, even under conditions
of uniform, unidirectional flow.
2.2.6.2. Thermal Dispersion
A description of thermal dispersion is based on a direct analogy with
solute dispersion. Energy replaces solute mass as the quantity being tran
sported by mechanical dispersion, and thermal conduction replaces molecular
diffusion. Thus, the thermo-mechanical dispersion tensor is derived from the
mechanical dispersion tensor by:
DHij = P' ' (2.2.6.2.1)
where
D... . is the thermo-mechanical-dispersion tensor component (W/m-°C) .
Combining the thermo-mechanical dispersion tensor with the net thermal
conductivity of the fluid and solid phases gives the thermo-hydrodynamic- k
dispersion coefficient tensor, D... . (W/m-°C) , in component form:
28
D * = Du .. + [eK. + (l-e)K ]6.. (2.2.6.2.2) Hij Hij f v ' s j ij
2.3. EXPANDED SYSTEM EQUATIONS
When the density function, equation 2.2.Lib, and the porous-medium
compressibility relation, equations 2.2.5.3a and 2.2.5.3b are incorporated
into the system governing equations, the following expanded system equations
are obtained:
For ground-water flow:
pflb It = V * P (Vp + Pg) + qp* ; (2-3.la)
For heat transport:
ft - ps csT «b It + (1 -£) Ps cs It
V-(eK_ + (l-e)K )! VT t s
lX, VT - V-epc-vTH I
qp*cfT* ; (2.3.1b)
29
For solute transport:
w + e+K w
w
8t) dw+ p ab w ^ + p(e+pbKd ) ^ = V-ep[gg + Dm!l Vw - V-epvw
,K ) pw + qp*w* (2.3.1c)
The change in the product of bulk density and equilibrium-distribution
coefficient, PrK,, with pressure is zero, because these equations were derived
for a fixed mass of porous medium occupying a volume that under-goes slight
deformation with variations in pressure. These three expanded equations show
the implicit coupling that occurs with variable density and porosity.
2.4. SOURCE OR SINK TERMS THE WELL MODEL
Most of the ground-water flow and heat and solute sources or sinks affect
the simulations through the boundary conditions. However, a line source or
sink term is used to represent injection or withdrawal by a well. Although a
well is treated as a line source or sink for the flow and transport equations,
a well is a finite-radius cylinder for the well-bore model.
The well model for the HST3D simulator is more sophisticated than those
well models used in most ground-water flow simulators. A well can be used for
fluid injection or fluid withdrawal, with associated heat and solute injection
or production. It also can be used simply for observation of aquifer
conditions. In the present code, the well bore can communicate with any
subset of cells along the z-coordinate direction at a given x-y location.
That is, the well may be screened or it may be an open hole over several
intervals of its depth. Several options are available for specifying pressure
30
or flow-rate conditions under which the well will operate. A special
technique is used to relate the local pressure field around a well to the
pressures in the cells with which it communicates. Finally, a mathematical
model of the well riser is included to calculate pressure and heat gains and
losses as fluid moves from the land surface to the uppermost screened
interval, or vice versa.
The well can be divided into two parts as shown in figure 2.1. The lower
part, from the bottom of the borehole to the top of the uppermost screened
interval, will be referred to as the well bore; the upper part, from the top
of the screened interval to the land surface, will be referred to as the well
riser. The well-riser interval may or may not have a riser pipe within it,
and the well-bore interval may be an open hole or have cased and screened
sections. A screened section also may be just perforated casing. The term
well-datum level refers to the location at the junction between the well riser
and the well bore, equivalently referred to as the bottom hole.
Focusing attention on the well bore, we shall describe the linking of the
well model to the simulation region as a source or sink, and then describe the
pressure and flow-rate conditions that can be specified as bottom-hole
conditions. The incorporation of the well-riser calculations will then be
discussed.
Cell or nodal pressures represent a spatially averaged condition, when
the simulation region is discretized into finite-difference cells. A well
located in a cell will have a pressure at the screen at the nodal elevation
that is not necessarily the same as the cell pressure. Various analytical
approaches have been used to avoid the computational burden of a finer
finite-difference grid around each well in the region. They are summarized by
Aziz and Settari (1979, sec. 7.7) and are based on steady-state radial flow in
a cylindrical-coordinate system with homogeneous aquifer properties. Another
review may be found in Williamson and Chappelear (1981).
31
EXPLANATION
r r WELL-RISER RADIUS
rw WELL-SCREEN RADIUS
L WELL-RISER LENGTH
Figure 2.1.--Sketch of well-model geometry showing the well-bore
and well-riser sections and the well-datum level.
2.4.1. The Well-Bore Model
For three-dimensional cartesian coordinates, the present version of the
HST3D code uses a modification of the well-bore equation derived by Van Poolen
and others (1968). Consider steady-state radial flow from a well into a
homogeneous aquifer with flux across an exterior cylindrical boundary, r .
This boundary can be regarded as a radius of influence of the well. For a
cartesian-coordinate system, the exterior radius, r , is taken to be the
32
radius of a circle that encloses the equivalent area to the x-y horizontal
area of the cell in which the well is located. The average pressure within
the annulus between the well-bore radius and the radius of influence can be
calculated and the flow rate from the well per unit length of well bore can be
expressed as a function of the pressure change from the well-bore pressure to
this average pressure. At any given elevation, z, we have:
27t k (r2 - r2 ) (p - p )q = * ? w W av ; (2.4.1.1)
(J [r2 In (re/rw) - 0.5 (r2 - r2 )]
where
p is the pressure at the well bore (Pa);W
k is the average permeability between r and r (m2 );
is the average pressure between r and r (Pa); av e r w e 'r is the well-bore radius (m);
YW
r is the radius of influence of the well (m); and
q is the volumetric flow rate per unit length of well bore
(positive is flow into the aquifer) (m3 /m-s).
The time- independent factors that affect flow from a well bore can be
combined into a single term. Departing slightly from petroleum-reservoir-
engineering usage, we define a modified well index as follows:
2n k (r 2 - r2 )w e w (2.4.1.2)
r 2 In (r /r ) - 0.5 (r 2 - r2 ) e e w e w
where
W_ is the well index per unit length of well bore (m2 )
33
The average permeability k is taken to be
k = (k k ) ; (2.4.1.3) w x y '
for cartesian-coordinate systems, where
k is the permeability in the x-direction (m2 ); andA
k is the permeability in the y-direction (m2 ).
There is presently no provision for accommodating areally heterogeneous
permeability distributions in the vicinity of the well bore.
Equations 2.4.1.1 to 2.4.1.3 will be modified for use with the finite-
difference discretization in the numerical-implementation section 3.3.
For three-dimensional and cylindrical regions, the total specified flow
rate from the well needs to be allocated over the length of well bore that
communicates with the aquifer. This allocation can be done in two ways; by
fluid mobility, or by the product of fluid mobility and the pressure
difference between the aquifer and the well bore. Although there may be zones
of cased well bore through which there is no communication with the aquifer,
we shall assume for the present discussion that the well bore is screened
throughout its depth. The total well flow rate from the well to the aquifer
is given by:
£uQ = J qd£ ; (2.4.1.4a)^"\*7 ^Ti7
= J -TTT (P - P )d£ ; (2.4.1.4b) w av
34
where
Q is the volumetric well flow rate (positive is from the well
to the aquifer) (m3/s);
H is the distance along the well bore (m);
4L is the lower end of the screened interval (m); and LiSL, is the upper end of the screened interval (m).
Fluid mobility at the well can be defined as:
where
M is the well mobility per unit length of well bore (m3 /s-m-Pa).
Allocation of the specified flow rate by fluid mobility is obtained by
assuming that the pressure difference in equation 2.4.1.4b is independent of
depth. Then
q U) = M U) / j" M U) d£ ; (2.4.1.6) ** w / n
T,
represents the allocation of the total flow rate over the well-bore length as
a function of fluid mobility.
For wells drilled at an angle, 6 , to the vertical or z-axis,Vr
dz = cos 8 d£ ; (2.4.1.7)w
35
where
0 is the angle between the vertical and the well bore (degrees).
If the screened interval is not continuous from £T to £TT , the mobility is setLi U
to zero over the appropriate subintervals.
The alternative method of flow-rate allocation over the well-bore length
is derived by not regarding the pressure difference in equation 2.4.1.4b as
constant with depth. A hydrostatic-pressure distribution in the well bore is
assumed using an average fluid density. Thus, frictional hydraulic-head
losses in the well bore are neglected. This yields, from equation 2.4.1.4b.
Pwd
where
p , is the bottom-hole or well-datum pressure (Pa);
z , is the elevation of the well datum (m): and wdp is the average fluid density in the well bore (kg/m3 )
Then the well flow rate is allocated as follows:
[pwd + PW* (zwd - Z) -
This method is referred to as allocation by mobility and pressure
;rence. The average pressure, p , will be relatd
pressures in section 3.3.1 on numerical implementation.
difference. The average pressure, p , will be related to the grid-cell
36
The flow rate can be specified with a bottom-hole pressure-constraint
condition, that may affect the source or sink flow rate applied. Allocation
is by mobility and pressure difference, and equation 2.4.1.8 is used to
calculate a predicted bottom-hole pressure based on the specified flow-rate.
For an injection well, if the predicted pressure is greater than the bottom-
hole constraint pressure, then the well is pressure-limited, and the flow rate
will be less than that specified. The flow rate will be reduced to meet the
pressure constraint. If the predicted bottom-hole pressure is less than that
specified, then the desired flow rate is used. For a production well, if the
predicted bottom-hole pressure is less than the constraint pressure, the well
is pressure limited, and the flow rate will be less than desired. Otherwise,
the pressure constraint is not limiting. In other words, a well bore can
function as either a Dirchlet or a Neumann boundary condition, or it can
switch back and forth.
When bottom-hole (well-datum) pressure is specified, equation 2.4.1.9
gives the flow-rate allocation and equation 2.4.1.4b gives the total flow
rate. No constraints are applied to the calculated flow rate.
After the flow rate has been established and allocated, heat-injection
and solute-injection rates are determined from the bottom-hole pressure,
specified-temperature, and specified solute-mass-fraction values. Heat-
withdrawal and solute-withdrawal rates are determined by the ambient pressure,
temperature, and solute-mass fraction in the aquifer for each cell that
communicates with a well bore.
In the case of cylindrical coordinates with a single well at the radial
origin, the inner radius of the simulation region becomes the well-bore
surface. Thus, a specified flow rate allocated by mobility becomes a
specified-flux boundary condition. Allocation by mobility and pressure
difference using equation 2.4.1.9 is not applicable here, because the
well-bore pressure and the pressure at the inner radius of the region are
identical. Instead, the pressure profile along the well bore is not assumed
to be hydrostatic, but, rather it satisfies a steady-state momentum equation,
that includes frictional pressure losses, but neglects changes in momentum by
flow into or out from the well bore. Then, we have, for a differential-
momentum balance along the well bore:
37
w dz~ + pwg
p v' rw(2.4.1.10)
w
where
f is the hydraulic-head-loss friction factor (-); and
v is the average velocity across the well bore at a given z-level
(m/s).
The corresponding mass balance is obtained assuming no change in well-
bore storage, thus:
dpv 2p q. r w Kw^l
dz r w(2.4.1.11)
where
p is the volumetric flux from the well bore (m3/m2 -s)
Equations 2.4.1.10 and 2.4.1.11 can be combined to give:
ddz
" 2r 2 w
v f w w
/dpw
1 dz + pw8 ) /.
(2.4.1.12)
Equation 2.4.1.12 is combined with the flow equation 2.1.1.la by assuming
that the aquifer pressure and well-bore pressure are equal at the well-bore
radius. The flow equation at the inner radius of the region becomes:
38
fffi = v - p M (VP + Pg) + fj2r 2
w /dp \ //> / i 1o^71~ (it + p-8^ ; (z- 4 - 1 -")W W
for the parts of the inner radius that are screened. A fluid-flux boundary
condition of zero applies over the cased-off intervals.
Thus, the flow equation is still in its original form, but the co
efficients of pressure gradient in the z-direction, and of the gravity term,
are augmented. The flow rate to or from the well is implicitly incorporated.
When the equation is converted to discrete form, the flow rate to or from the
well will arise naturally at the upper boundary of the screened interval. The
friction-head-loss factor is calculated as described in the well-riser model,
section 2.4.2. The magnitude of the friction head-loss factor often may be
very small but it needs to be non-zero, for flow to occur in the well bore.
The total flow rate to or from the well always is satisfied by this
calculation method, and the pressure at the top of the screened interval in
the aquifer is identical to the well-datum-level pressure. Recall that these
pressures are not necessarily equal in the line-source approach used with the
cartesian coordinate system. An examination of the relative magnitudes of the
terms for advective momentum and frictional head-loss in the full momentum-
balance equation shows that, for a producing well with uniform inflow per unit
length, the advective-momenturn term dominates near the bottom of the screen.
The frictional head-loss term dominates at distances above the bottom of the
screen that are greater than about 1,000 times the well radius. Thus, a
significant region exists in which both the momentum and frictional terms are
of similar magnitude. However, a more rigorous development, retaining the
momentum term, is beyond the scope of this work. The present development
follows that of Aziz and Settari (1979, p. 337-341).
39
2.4.2. The Well-Riser Model
When flow rate or pressure is specified at the land surface for a given
well, the well-riser calculation needs to be performed in conjunction with the
well bore flow-rate allocation described above. This calculation consists of
a simultaneous solution of the macroscopic equations of total energy, momentum
and mass (Bird and others, 1960, p. 209-212) for the change in pressure and
temperature over the well-riser length.
The total-energy or enthalpy equation is written for steady flow either
up or down the well riser as a rate of change with distance along the riser,
dH dv r + VrCOS0 + V
where
H is the specific enthalpy of fluid in the riser (J/kg);
v is the average velocity across the riser at a given ^-location
(m/s);
6 is the angle between the well riser and vertical (degrees);
u is the heat transfered per unit mass per unit length to the jHrfluid in the riser (J/kg-m); and
H is the distance along the well-riser casing (m).
Energy loss by viscous dissipation has been neglected. All quantities are
averages across the riser-pipe cross section at a given level.
The equation for momentum along the well-riser axis also is written for
steady flow as a differential balance along the well riser:
dv dp p v 22P v T^ + P 8 cose + JF1 + ^£-£~ f = 0 ; (2.4.2.2) 'r r dS, r r r dS, 2r r 'r
40
where
p is the fluid density in the riser (kg/m3 );
p is the pressure in the riser (Pa);
r is the internal radius of the well riser (m); and
f is the hydraulic-head-loss friction factor (-).
Finally, the macroscopic-mass balance, written in differential form as a
rate of change along the riser, is:
p v = Q.., /Tlr2 ; (2.4.2.3a) rr r Fr/ r '
where
Q_ is the total mass-flow rate in the riser (kg/s). r r
Differentiation with respect to length yields:
dv dp Pr dT + \ dF = ° ' (2.4.2.3b)
To solve equations 2.4.2.1, 2.4.2.2, 2.4.2.3a, and 2.4.2.3b, the enthalpy
tables (Keenan and others, 1969, p. 2-7 and 104-107) are used for H (p,T),
equation 2.7a is used for the density equation of state, and the Fanning
friction factor, using the Moody correlation (Perry and others, 1963,
p. 5-20), is used to calculate f as a function of velocity. The enthalpy for
pure water is adjusted for other fluid mixtures according to equation
2.2.3.1b. For turbulent flow, the friction factor is a function of pipe
roughness. The user needs to supply a value for pipe roughness, and some
typical values for pipe roughness from Shames (1962, p. 300) are given in
table 2.1. Changes in viscosity with temperature along the riser are
neglected.
41
Table 2.1.--Pipe-roughness values
Pipe Pipe roughness
type (millimeters)
Drawn tubing 1.3 x 10~4
Steel or wrought iron 3.8 x 10~ 3
Galvanized iron 1.3 x 10~ 2
Cast iron 2.2 x 10~ 2
The heat transferred to the fluid in the riser must pass from the
surrounding medium to the riser pipe, then from the riser pipe to the fluid.
The heat transferred per unit mass of fluid per unit length of riser is then:
27trQHr U) = ;p- ̂ U (T (£) - T (£)) ; (2.4.2.4) Hr 1 a r
where
T is the fluid temperature in the well riser (°C);
T is the ambient temperature in the medium adjacent to the a
riser (°C);
U is the overall heat-transfer coefficient for the fluid, riser
pipe and surrounding medium (W/m2 -°C).
The overall heat-transfer coefficient is given by:
Ar(2.4.2.5)
r IL, r h r K K F. T (t) » rT rr rr re CJ
42
where
Ar is the wall thickness of the riser pipe (m);
Fpj(t) is the dimension!ess part of the Carslaw and Jaeger (1959,
p. 336) solution for heat flux to an infinite medium from
a constant-temperature cylindrical source (-);
h is the local heat-transfer coefficient from the fluid to therriser pipe (W/m2 -°C);
K is the thermal conductivity of the medium surrounding the riser
pipe (W/m-°C); and
K is the thermal conductivity of the riser pipe (W/m-°C).
Equation 2.4.2.5 is a simplification of the relation for the overall heat
transfer coefficient for conduction through cylindrical walls (Bird and
others, I960, p. 288) combined with the Carslaw-Jaeger solution for heat flux
to an infinite medium from a cylindrical source (Carslaw and Jaeger, 1959,
p. 336). It is valid for wall thicknesses that are small relative to the
riser-pipe radius.
The dimensionless heat-flux function, Fr ,(t), can be approximated by theLJ
following two series:
(1) For short time, t, (Carslaw and Jaegar, 1959, p. 336):
FCJ ~ FCJ ; for T<1 ; (2.4.2.6a)
where
FCJ = (7lt) "* * * " *(n} * * I *' (2.4.2.6b)
43
and where
T is the dimensionless time defined by:
D tT = f f"1 ., ^- ; (2.4.2.6c) (r + Ar )^ ' ' r r
and where
DH is the thermal diffusivity of the medium surrounding the well
riser (m2 /s).
(2) For long times, the asymptotic expansion was derived by Ritchie and
Sakakura (1956):
FCJ ~ FCJ ; f°r T >3 ' 6 ; (2.4.2.7a)
where
F = 2(An x)" 1 [l-.5772Un x)" 1 - 1.3118(£n x)"2
+ .2520 (An x)" 3 + 3.9969 (An
+ 5.0637 (An
-1.1544(An X)" 2 ]
-2 t'^An X)"3 ; (2.4.2.7b)
X = ~ ; (2.4.2.7c) e
44
and where
V is Euler's constant: = 0.5772.
6 -1 -"} In equation 2.4.2.7b, terms of higher order than (£n x) and I (£n x)
have been dropped. Carslaw and Jaeger (1959, p. 336) present a lower-order
version of equation 2.4.2.7b that is accurate for dimensionless time much
greater than 3.6. The estimated error is on the order of 10 percent for
dimensionless time, I, greater than 3.6. For a typical rock medium, this
truncation means that the time must be greater than about 3.6 x io4 s, or
about 0.4 d. The short-time approximation, equation 2.4.2.6b, is good for
time less than about 0.1 d. For intermediate time, the heat-transfer functionS L is estimated by linear interpolation between F-, evaluated at 1=1 and F-,
evaluated at 1=3.6.
Note that the heat-flux function in equation 2.4.2.5 is a function of
time; whereas, the mechanical and thermal-energy balances are at steady-state.
This is a consistent approximation, provided it is assumed that the heat
transfer from the fluid to the riser pipe and through to its outer boundary is
rapid, relative to rates of change in temperature at the fluid-inlet end of
the riser pipe; and, that changes in the fluid-temperature profile within the
riser pipe re-equilibriate quickly, relative to induced temperature changes in
the adjacent medium. This approach parallels that of Ramey (1962), with the
difference being that the heat-flux solution from a cylinder at constant
temperature is used, instead of the temperature solution for the constant
heat-flux case. The former solution is considered to more accurately describe
the physical situation.
Values for the local heat-transfer coefficient, h in equation 2.4.2.5,
can be determined from correlations, such as those of McAdams (1954, p.
241-243) or Sieder and Tate (given in Bird and others, 1960, p. 399), between
the Nusselt number, the Prandtl number, and the Reynolds number for forced
convection in tubes.
45
The correlation from McAdams (1954, p. 219) that is valid for turbulent flow
in the well-riser pipe is:
2r h r r - 0 023 f, \j . \j±.^tKf
"prvr"
_"r _
0.8 Vr"
. Kf -
0.33
(2.4.2.8)
where
|J is the viscosity of the fluid in the riser pipe (kg/m-s).
The well-riser calculation is developed by combining equations
2.4.2.1-2.4.2.3b with equation 2.2.1.1b and the derivative of equation
2.2.3.la for the enthalpy function. The resulting equations are:
v2 P - - v2 P,,,r Kp p r KT r r
3H 1 3H|3p T p 3T|p
dpr
dT
J1*-
V2 fQ . r rg cos 6f + 2r
27tr UT v2 f r T /fp T , r rCTa Tr J + 2r Fr r
(2.4.2.9)
Using the thermodynamic relationships
-1H _ _ T
T p 3T(2.4.2.10a)
and
3HI3T|p Cf
(2.4.2.10b)
46
we can reduce equation 2.4.2.9 to two simultaneous ordinary differential equations:
dT
(Of -PT T /p HT r rr2 - 1/p r
27lr
g cos 6 + v 2 f /2r r r r r
Ar
Fr r r r r
r2 _
"re CJ
2 - 1/p )c, - T P2v2 /p r r r f r^T r ^
-1(2.4.2.11)
These equations are coupled through the density, velocity, and
temperature terms. The boundary conditions are known at one end of the riser.
For injection:
at z = zLS =p. .;T=T. . ; *' inj ' (2.4.2.12a)
For withdrawal:
at z=z ,wd ;T=T,; * wd ' (2.4.2.12b)
where
z , is the elevation of the well datum (m); and wd
z, 0 is the elevation of the land surface (m).LiO
Equations 2.4.2.6a-c and 2.4.2.7a-c are used to evaluate the heat-transfer
function F_,.
47
The mass, enthalpy, and mechanical-energy-balance equations are solved
either up or down along the well riser, depending on the direction of fluid
flow, to obtain the pressure and temperature at the riser bottom for injection
conditions, or at the riser top for production conditions. Coupling this
well-riser calculation to the well-bore model enables specified pressure,
temperature, and solute concentration, or specified flow-rate conditions at
the land surface, to be employed.
When the flow rate at the land surface is specified as an injection, the
surface temperature and solute concentration also need to be specified. The
well-riser calculation will give the necessary surface pressure to achieve the
specified flow rate. If a production or withdrawal flow rate is specified,
the surface pressure, temperature, and solute concentration are determined by
the well-bore and well-riser calculations.
When the surface pressure is specified, the well-bore and well-riser
calculations determine the flow rate, surface temperature, and solute
concentration for a production well. Surface temperature and solute
concentration also need to be specified in the case of an injection well. The
ambient-temperature profile with depth along the well riser is specified by
the user.
A flow rate and pressure constraint at the surface can be specified and
the slower of the specified flow rate or the flow rate that results from the
specified-pressure constraint will be applied to the aquifer and apportioned
as described previously.
A well also can be used as an observation well. In this case, none of
the well-bore or well-riser calculations are necessary. The purpose of an
observation well is to record dependent variable data (pressure, temperature,
solute-mass fraction) for plotting versus time at the conclusion of the
simulation. The recorded data are the aquifer values at the well-datum level,
which is at the top of the uppermost screened interval.
48
In summary, a well can be a production well, an injection well, or an
observation well. The flow rate can be specified with or without a pressure
constraint, or the pressure can be specified either at the land surface or at
the well-datum level. For three-dimensional cartesian coordinates, the
allocation of the flow to each layer can be determined by the relative
mobility of the layer, or by the product of the mobility times the pressure
difference. For cylindrical coordinates, the allocation is determined by the
product of the mobility times pressure difference, with allowance for
gravitational effects, because the well-bore equations are solved
simultaneously with the ground-water flow equations for the region adjacent to
the screened intervals. Application of the well-flow terms for each layer to
the ground-water flow equation can be explicit or semi-implicit in time for
three-dimensional cartesian coordinates; it is fully implicit for cylindrical
coordinates.
2.5. BOUNDARY CONDITIONS
2.5.1. Specified Pressure, Temperature, and Solute-Mass Fraction
The first type of boundary condition, known as a Dirchlet boundary
condition, is a specified pressure condition for the ground-water flow
equation, a specified temperature condition for the energy-transport equation,
and a specified-mass fraction for the solute-transport equation. These
conditions can be specified independently as functions of location and they
also can vary independently with time. Mathematically, we have:
49
p = PB (x,t), for x on S* ; (2. 5.1. la)
1 = 1., (x,t), for x on S* ; and (2.5.1.1b)
w = w^ (x,t), for x on S 1 ; (2.5.1.1c) is w
where
p_ is the pressure at the specified boundary (Pa);
TR is the temperature at the specified boundary (°C) ;
WR is the mass fraction at the specified boundary (-);
S 1 is the part of the boundary with specified pressure;
S,*, is the part of the boundary with specified temperature; and
S 1 is the part of the boundary with specified mass fraction.W
Care needs to be used in specifying the temperature and mass fraction at
fluid-outflow boundaries, because, on boundary surfaces across which fluid
flow occurs, the advective transport of heat and solute is assumed to dominate
over any diffusive or dispersive transport. Thus, it is physically
unrealistic to specify a temperature or solute concentration at an outflow
boundary because the ambient fluid will determine the temperature, and solute
concentration there.
2.5.2. Specificd-Flux Boundary Conditions
The default boundary condition for the numerical model is no fluid, heat,
or solute flux across the boundary surfaces. Normal fluxes of fluid, heat,
and solute, known as Neumann boundary conditions, can be specified over parts
of the boundary as functions of time and location. However, they cannot be
50
specified independently, because, on boundary surfaces where a specified fluid
flux exists, the advective transport of heat and solute is assumed to dominate
over any specified diffusive or dispersive flux of these quantities. This
assumption means that, on fluid-inflow boundaries, the temperature and mass
fraction of the inflowing fluid needs to be specified. These specifications
determine the heat and solute fluxes. At fluid-outflow boundaries, the
temperature and mass fraction are determined by the ambient fluid values in
the region, thus giving the heat and solute fluxes. Therefore, it is not
physically realistic to specify temperatures and mass fractions at outflow
boundaries. On boundary surfaces where no fluid flux is given, heat and
solute fluxes may be specified. Heat fluxes represent thermal conduction and
solute fluxes represent solute diffusion.
For the reasons discussed in section 2.5.1, it also is not physically
realistic to specify dispersive heat or solute fluxes across boundary surfaces
that have specified pressures. However, total heat or solute fluxes may be
specified for inflow boundaries. These fluxes are the advective fluxes
approaching the boundary from outside the region, and they are equal to the
advective plus the dispersive fluxes leaving the boundary and entering the
region. For outflow boundaries, the boundary condition requires that the
dispersive fluxes be zero. Thus, only advective flux of heat and solute
occurs at outflow boundaries. Again, the advective transport of heat and
solute is assumed to dominate over dispersive flux.
Specified fluxes are expressed mathematically as:
qFn = (qFx> qFy' qFz) f°r - °n Sp ; (.2.5.2.la)
= C<4> qHy> 4> for ^ °° ST ' (2.5.2.1b)
qSn =(<4' qSy' <4} f°r 5 °n Sw ' (2.5.2.1C)
51
whereD
q_. is the component of the fluid flux in the ith direction at the r iboundary (m3/m2 -s); p
q... is the component of the heat flux in the ith direction at the Hiboundary (W/m2 );
n
q_. is the component of the solute flux in the ith direction at theol
boundary (kg/m2 -s);
q,., is the normal component to the boundary surface of the fluid-flux
vector (kg/m2 -s);
q., is the normal component to the boundary surface of the heat- nnflux vector (W/m2 );
qc is the normal component to the boundary surface of the solute- t>nflux vector (kg/m2 -s); and
S2 are parts of the boundary with specified-fluid, heat, or solute
fluxes respectively; u = p,T,w.
Note that the specified-fluid flux, q_, is given as a volumetric flux. Ar
fluid density also needs to be specified for the case of inflow to the region.
The density in the region at the boundary is used for computation of mass
outflow rates. Also note that flux is a vector quantity with components
expressed relative to the coordinate system of the simulation region.
Examples of physical-boundary conditions that can be represented as specified-
flux boundaries include infiltration from precipitation, lateral boundaries
where the pressure gradients can be estimated, and simple steady-state flow
fields where recharge- and discharge-boundary flow rates are known.
2.5.3. Leakage Boundary Conditions
A leakage boundary condition has the property that a fluid flux occurs in
response to a difference in pressure and gravitational potential across a
confining layer of finite thickness. Usually the permeability of this layer
will be orders of magnitude smaller than the permeability of the simulation
region and the aquifer region on the other side of the confining layer.
52
Representation of leakage boundary conditions is based on the approach of
Prickett and Lonnquist (1971, p. 30-35), which has been generalized to include
variable-density and variable-viscosity flow. The mathematical treatment of
leakage boundaries is based on the following simplifying assumptions:
(1) Changes in fluid storage in the confining layer are neglected;
(2) confining-layer capacitance effects on heat and solute transport are
neglected; (3) flow, heat, and solute transport are affected by the leakage
fluxes that enter the region, but flow, heat, and solute conditions that exist
on the far side of the confining layer outside the simulation region are not
affected by fluxes that enter or leave the simulation region; and (4) flow and
transport properties in the confining layer are based on the average of the
fluid density and viscosity on either side. These assumptions are quite
restrictive; but, in cases where they are not valid, some of the region
outside the boundary probably needs to be included in the simulation region.
Flow and transport rates are functions of differences in pressure, temper
ature, and solute-mass fraction at a point in time and are not affected by the
previous values of these differences.
2.5.3.1. Leaky-Aquifer Boundary
A leaky-aquifer boundary can be adjacent to any part of the simulation
region. For illustration, assume that it is part of the upper boundary
surface that is overlain by a confining layer. Another aquifer lies above the
confining layer with a pressure distribution at its contact with the confining
layer which is a known function of time. The geometry is shown in figure 2.2.
We are interested in the flux normal to the boundary between the confining
layer and the simulation region, located at elevation zn in figure 2.2. Under15
these assumptions, the leakage boundary flux is given by:
53
PRESSURETEMPERATURESOLUTE-MASS FRACTIONFLUID DENSITYFLUID VISCOSITYPOTENTIAL ENERGYCONFINING LAYER THICKNESSELEVATIONPERMEABILITY
NOT TO SCALE
Figure 2.2. Sketch of geometry for a leaky-aquifer boundary condition.
-(Pe- PB)g (zfi + zfi)/2], for x on S 3 ; (2.5.3.1.la)
54
with
Me ) 5
where
qT is the fluid flux across the leakage boundary (m3 /m2 -s). LI<t> is the potential energy per unit mass of fluid in the outer
aquifer (N-m/kg);
pD is the pressure at the simulation-region boundary (Pa);D
p is the pressure at the top of the confining layer (Pa);
pn is the fluid density at the simulation-region boundary (kg/m 3 ); Dp is the fluid density in the outer aquifer (kg/m 3 );
kT is the permeability of the confining layer (m2 ); LI|JT is the fluid viscosity in the confining layer (kg/m-s); LibT is the thickness of the confining layer (m); Liz_ is the elevation of the simulation-region boundary (m); t>z is the elevation at the top of the confining layer (m); and
S3 is the region boundary surface over which a leakage-
boundary condition exists.
The terms <t> , p , kT , pT , bT , and z_ are specified functions of positionG 6 Li Li Li D
along the leakage boundary; <t> and p also can be functions of time. The mass
flux is calculated using p if the flux is into the simulation region, and
using p_ if the flux is out from the simulation region. This choice ofD
density is an approximation because it will take some time for the fluid in
the confining layer to attain the limiting value after a change in flow
direction takes place. However, this approximation is consistent with the
neglect of transient flow and storage effects within the confining layer.
The heat and solute fluxes are assumed to be purely advective. They are
obtained from enthalpies and mass fractions of the outer aquifer or at the
boundary of the simulation region depending on the flux direction. Thus:
qUT = H p qT , if qT > 0, for x on S 3 ; (2.5.3.1.2a) HLi e e Li Li
= HPq, if q < 0 ; (2.5.3.1.2b)
55
qSL = WePeqL> lf qL > °» f° r - °n S* ' (2.5.3.1.3a)
' if qL < ° ; (2.5.3.1.3b)
where
q is the heat flux across the leakage boundary (W/m2 );
H is the specific enthalpy of the fluid in the outer aquifer (J/kg);
HR is the specific enthalpy of the fluid at the region boundary
(J/kg);
qCT is the solute flux across the leakage boundary (kg/m2 -s);oJ_i
w is the solute mass fraction in the outer aquifer (-); and
w_ is the solute mass fraction at the region boundary (-).
Note that H and w are specified functions of position along the leakage
boundary and time.
2.5.3.2. River-Leakage Boundary
The river-leakage boundary condition is a second type of leakage-boundary
condition that is very similar to a leaky-aquifer condition, with the
following differences: (1) This boundary condition is appropriate only for
unconfined aquifer regions and is at an upper- or lateral-boundary surface;
(2) the less-permeable boundary layer is now the riverbed-sediment layer, that
is basically a piecewise-linear feature that traverses the upper boundary of
the aquifer region; (3) a limit on the maximum flux from the river to the
aquifer is imposed. Additional assumptions for the river-leakage option are:
(1) The riverbed thickness is assumed constant over each cross section of the
river; and (2) pressure and elevation differences and fluid properties are
taken at the river centerline, representing conditions across the riverbed.
An area factor is introduced to account for the fact that the riverbed area is
only a fraction of the region boundary traversed by the river. The flux limit
is set by not allowing the flux to increase after the aquifer pressure plus
gravitational potential decreases to less than the gravitational potential at
56
the bottom of the river. Physically, this means that if the water table
declines below the bottom of the riverbed, the increased resistance to flow,
because of the porous medium becoming partially saturated, prevents further
increases in flux from the river to the aquifer. Thus, the flux limitation is
a crude approximation to the physical situation. The simplified geometry of a
NOT TO SCALE
PRESSURE T TEMPERATURE w SOLUTE-MASS FRACTION p FLUID DENSITY M FLUID VISCOSITY * POTENTIAL ENERGY b R RIVER-BED THICKNESS 2 ELEVATION k PERMEABILITY
Figure 2.3.--Diagrammatic section showing geometry for a
river-leakage boundary.
57
river-leakage boundary is shown in figure 2.3. Note that the z-axis is
positive in the vertically upward direction. The present version of the HST3D
program cannot simulate river leakage with a tilted coordinate system.
With the above assumptions, equations 2. 5. 3.1. la and 2.5.3.1.1b become:
qR = YRqL J for x on S4 ; (2. 5. 3. 2. la)
with
; (2.5.3.2.1b)
and I = % p = 0 ; (2. 5. 3. 2. Ic)D
where
qR is the fluid flux across the river-leakage boundary from the river
to the aquifer (m3/m2 -s);
qn is the maximum fluid flux from the river to the Kmaxaquifer (m3/m2 -s); and
4> is the potential energy per unit mass of fluid in the river
(Nt-m/kg);
YD is the fraction of riverbed area per unit area of aquiferK
boundary (-);
ZRFS is the elevation of the water surface of the river (m); and
S4 is the region boundary surface over which a river-leakage boundary
condition exists.
Note that <J> , p , k_, b_, M , z_, and YD are specified as functions of e e L L e u Kposition along the river length, and at 4> and p also can be functions of
time. For calculating 4> , the value of atmospheric pressure can be taken as
zero, because pressures are relative to atmospheric pressure. The mass flux
is calculated using p if the flux is into the aquifer, and using p« if the
flux is out from the aquifer. The heat and solute fluxes are assumed to be
purely advective, and are obtained from the enthalpies and mass fractions of
58
the river fluid, or from the aquifer at the leakage boundary, depending on the
flux direction, as given by equations 2.5.3.1.2a-b and 2.5.3.2.3a-b with qTLIreplaced by q^. The enthalpy variation with pressure is neglected for the
K
river-leakage boundary condition, as this variation is assumed to be small.
2.5.4. Aquifer-Influence-Function Boundary Conditions
The aquifer-influence-function (AIF) boundary conditions have been
presented in the petroleum reservoir-simulation literature. Several methods
have been used to calculate water influx at reservoir-aquifer boundaries. For
a summary, the reader is referred to Craft and Hawkins (1959, ch. 5) and Aziz
and Settari (1979, sec. 9.6).
The utility for ground-water flow simulation of fluid-flux calculations
using aquifer-influence functions results from the fact that they enable a
simulation region to be embedded within a finite or infinite surrounding
region, for which the aquifer properties are known only in a general sense,
and where the outer-aquifer-region flow field influences the inner-aquifer
region of interest only in a general way. The primary benefit of using AIF
boundary conditions is the reduction in size of the simulation region,
resulting in a savings in computer-storage requirement and computation time.
Suppose that an aquifer region can be divided into subregions (fig. 2.4),
where the inner-aquifer region is the one of primary interest, and the
outer-aquifer region is less completely identified with respect to aquifer
properties and geometrical configuration. The outer-aquifer region may
completely or partially surround the inner-aquifer region, as shown in figures
2.4A and 2.4B. Variable density and nonisothermal flow may be simulated in
the inner-aquifer region, but not in the outer-aquifer region. The actual
simulation region may be reduced to only the inner-aquifer region, and the
boundary condition at the boundary between the two regions (the AIF boundary)
is taken to be the AIF boundary condition representing the outer-aquifer
region. Aquifer-influence functions are analytical expressions that describe
the flow rate, pressure, and cumulative flow at the boundary between the
59
inner-aquifer and outer-aquifer regions, in response to pressure variations at
the boundary. For the purposes of ground-water flow simulation described
herein, the cumulative-flow aquifer-influence functions are not of concern.
Flow from the outer-aquifer region is assumed to influence the inner-aquifer
region of simulation, but flow to the outer-aquifer region does not affect any
conditions there.
The aquifer-influence functions that describe transient flow across the
AIF boundary are based upon analytical solutions to the ground-water flow
equation in the outer-aquifer region. To obtain an analytical solution, the
aquifer and fluid properties of the outer-aquifer region are assumed to be
constant and uniform, and the geometry of the boundaries between the inner-
and outer-aquifer regions need to be approximated by simple shapes.
Two types of aquifer-influence functions currently are available for the
heat- and solute-transport simulator; one type treats the outer-aquifer region
as a "pot;" the other type uses a transient-flow solution for simple-geometry
and simple-boundary conditions. An aquifer-influence function based on the
assumption of steady-state flow also exists in the petroleum-reservoir
simulation literature, but it only is a restricted form of the leakage-
boundary condition presented in section 2.5.3.1. Only one type of aquifer-
influence function is allowed in any given simulation.
2.5.A.I. Pot-Aquifer-Influence Function
The pot-aquifer-influence function is based on the assumption of an
outer-aquifer region with exterior boundaries that are impermeable (fig. 2.5).
The outer-aquifer region needs to have volume and compressibility that are
sufficiently small so that the pressure in this outer-aquifer region always
will be virtually in equilibrium with the pressure distribution along the
boundary surface between the inner- and outer-aquifer regions. Then, flow
will occur in response to the rate of change of pressure at this boundary.
The governing equation is obtained from mass conservation in a vertically
deforming, compressible, porous medium. Using the Gauss divergence theorem
(Karamcheti, 1967, p. 73) and assuming a uniform, constant, fluid density and
60
EQUIVALENT CYLINDRICAL BOUNDARY
BOUNDARY WHERE AQUIFER-INFLUENCE FUNCTIONS ARE APPLIED
i \ - - i-jf.\:- . v~ ' " ' ! L ^'^fc':--''&--':'<-''-: ':\ ' EQUIVALENT
&r?<\i]^3£&&.:.iy CYLINDRICAL BOUNDARY '- r> \V^r ; '.^fli^'^i \Vv-/Vfc:.v.-::-.i3a^ ,
BOUNDARY WHERE AQUIFER-INFLUENCE FUNCTIONS ARE APPLIED
EXTERIOR BOUNDARY OF OUTER-AQUIFER REGION
IMPERMEABLE BOUNDARY EXTERIOR BOUNDARY OF OUTER-AQUIFER REGION
Figure 2.4.--Plan view of inner- and outer-aquifer regions and
boundaries: A, Outer-aquifer region completely surrounding
inner region; B, Outer-aquifer region half-surrounding inner-
aquifer region.
61
porosity, we obtain by integration over the outer-region volume:
«A ' <«b, * VW rl V. (2.5.4.1.1)ot
where
QA is the volumetric flow rate across the boundary between
the inner- and outer-aquifer regions; (positive is into the
inner-aquifer region); (m3 /s).
9p is the spatial average of the rate of pressure change in the
atouter region (Pa/s);
CL is the bulk compressibility of the porous medium in the outer-
aquifer region (Pa ) ;
is the fluid compressibility in the outer-aquifer region (Pa" 1 );" 1
8 is the porosity in the outer-aquifer region (-); and
V is the volume of the outer-aquifer region (m3 ).
Because pressure equilibrium is assumed:
9pe = 8pB ; (2.5.4.1.2)at at
where
PB is the spatial average rate of pressure change at the3t
boundary of the inner-aquifer region (Pa/s).
Equation 2.5.4.1.1 is in a form suitable for calculating overall fluid
flow balances but it is difficult to distribute the flow over the AIF boundary
62
'^<rX,$&l^
>LAND SURFACE
AQUIFER-INFLUENCE-FUNCTION BOUNDARY
Figure 2.5. A, plan view, and B, cross-sectional view of inner-
and outer-aquifer regions with an impermeable exterior boundary
for the outer-aquifer region.
63
of the simulation region, particularly when the rate of change of boundary
pressure is not uniform over the boundary. Allocation of the flow rate will
be explained in section 3.4.4 on numerical implementation.
2.5.4.2. Transient-Flow, Aquifer-Influence Function
The transient-flow solution method employs the Carter-Tracy AIF
calculation technique (Carter and Tracy, 1960) and analytical solutions
presented by Van Everdingen and Hurst (1949). A brief summary of the method
follows. A detailed presentation is given by Kipp (1986).
Let the AIF boundary between the inner-aquifer or simulation region and
the outer-aquifer region be approximated by a cylinder of a given radius and
height. A plan view is presented in figure 2.5A. For a simulation region
that is a rectangular prism, this boundary cylinder will be a severe
approximation of the actual boundary shape. The outer boundary of this
outer-aquifer region is a cylinder at a finite or infinite radius. The
thickness of the outer-aquifer region is assumed to be uniform, with
impermeable upper and lower boundary surfaces. Ground-water flow in this
outer-aquifer region is radial at a given elevation, and the pressure
satisfies:
3p~ 1 ' (2.5.4.2.1)
where
r is the radial coordinate (m);
p is the pressure in the outer-aquifer region (Pa);
k is the permeability in the outer-aquifer region (m2 );
|J is the viscosity in the outer-aquifer region (kg/m-s);
a, is the bulk compressibility of the porous medium in the outer-
aquifer region (Pa" 1 );
64
is the compressibility of the fluid in the outer-aquifer
region (Pa" 1 ); and
e is the effective porosity of the outer-aquifer region (-)
The initial condition is:
at t = 0, p = p ; (2.5.4.2.2)
where
op is the initial uniform pressure (Pa).
Van Everdingen and Hurst (1949) used two different boundary conditions at
the AIF cylindrical boundary: one condition was constant pressure, and the
other condition was constant flow rate.
The boundary conditions are either specified pressure:
at r = r , p = p ; (2.5.4.2.3a)
where
r is the interior radius (m); and
p,, is the constant, specified pressure at the boundary (Pa);D
or specified flow rate:
9pe QA Meat r - V> 8r^ = 2*rTb k 5 (2.5.4.2.3b)
lee
65
where
QA is the constant, specified flow rate at the boundary (positive
is from the outer-aquifer region to the inner-aquifer region)
(m3/s); and
b is the thickness of the outer-aquifer region (m).
At the exterior cylindrical boundary, the condition is, for an infinite
region:
as r -> oo, p -> p ; (2.5.4.2.4a)
and, for a finite region, either no flow,
3PC at r = = ° ; (2.5.4.2.4b)
where
r£ is the exterior radius (m); ^
or specified pressure:
oat r = r_, p = p . (2.5.4.2.4c) he e
Solutions to the dimensionless form of equations 2.5.4.2.1-2.5.4.2.4 are
given in Van Everdingen and Hurst (1949) and were derived using Laplace
transform techniques. For example, the flow-rate response to a unit change in
pressure boundary condition (eq. 2.5.4.2.3a) and the pressure response to a
unit withdrawal flow-rate boundary condition (eq. 2.5.4.2.3b) for an infinite
outer-aquifer region are:
66
-\ V, J (2.5.4.2.5a)
and
-\2t'
P^(t') = ^| A> * " 2e ^ 5 (2.5.4.2.5b)
respectively, with
k t t' = -^ - ; (2.5.4.2.5c)
r (a, +eB )u I be e^pe 'e
where
J. is the Bessel function of the first kind of order i;
Y. is the Bessel function of the second kind of order i; and
t' is the dimensionless time (-).
Equation 2.5.4.2.5a was presented by Jacob and Lohman (1952) in a
different form as a solution to the constant drawdown problem for flow to a
well. These two aquifer-influence functions will be referred to as the
flow-rate response to a unit-step pressure change Q', and the pressure
response to a unit-step withdrawal flow rate, P', respectively.
The concept of superposition or convolution (Tychonov and Samarski, 1964,
p. 209) is used to derive the aquifer-influence functions from the unit-step
response functions for a transient-pressure function at the boundary between
the inner- and outer-aquifer regions. Thus, the flow-rate response of this
ground-water flow system to a time-varying pressure at the inner boundary of
the outer-aquifer region can be written as:
67
. . 3Q'(t' - T) QA = " ^o PB (T) ~^F dT ; (2.5.4.2.6a)
where
0 PB (rT ,O - p
Pg(t') = -2-<r 0 - J (2.5.4.2.6b)
p ' P
and where
p' is the dimensionless pressure (-); and
p_ is the boundary pressure at time zero that initiates flow (Pa). 15
In principle, equation 2.5.4.2.6a could be used to calculate the flow
rate into the simulation region from the outer-aquifer region. However, this
is not practical when p~(t) is not known in advance as in the present case of15
numerical simulation of ground-water flow in the inner-aquifer region. The
integral needs to be recomputed repeatedly from the initial time to the
current time, because time is a parameter in the integrand as well as being
the upper limit of the integration variable. Carter and Tracy (1960), using
an approach given by Hurst (1958), developed an approximate algorithm to
avoid the repeated computation of equation 2.5.4.2.6a as the simulation
calculation progresses. However, it requires the discretization of time and
will be treated in section 3.4.4.2.
2.5.5. Heat-Conduction Boundary Condition
A boundary condition is available for pure-heat conduction without fluid
flow or solute transport. This boundary condition provides for the simulation
of heat gain or loss at a boundary which confines the ground-water flow. The
boundary heat flux depends on the evolving temperature profile in the con
ducting medium exterior to the simulation region. One-dimensional conduction
is assumed perpendicular to the boundary surface and conduction in the
adjacent medium parallel to the boundary because of lateral temperature
68
variation is neglected. The penetration of heat into or the withdrawal of
heat from the boundary medium is assumed to progress only a finite distance
out from the boundary. Beyond this distance, the temperature is assumed to
remain at its initial uniform value. This assumption is for convenience in
the numerical implementation. Constant, uniform thermal properties are
assumed in the exterior medium. Based on these assumptions, the one-
dimensional heat-conduction equation can be used to represent the boundary
condition. This equation is:
3T 3 2Tpc ^ = K ^-^ ; (2.5.5.la) Kse se 3t e dz £ '
n
where
pc is the heat capacity per unit volume of the adjacent medium (J/m3 -°C); se se
K is the thermal conductivity of the adjacent medium (W/m-°C);
T is the temperature in the adjacent medium (°C); and
z is the coordinate in the outward normal direction to the boundary (m).
The initial condition is:
0 t = 0; T = T (z ); (2.5.5.1b)
e en
where
T is the initial temperature profile (°C).
The boundary conditions are:
at ZQ = 0 ; Tg = Tfi (t) ; (2.5.5.1c)
69
and at
= bHC' Te = Te '"EC* ' (2.5.5.Id)
where
T-, is the boundary temperature at the aquifer boundary (°C) ,D
bfff, is the effective thickness of the conducting medium outside the
region (m) .
The thermal properties of the adjacent medium are assumed constant and
uniform. Thus:
DHe=se se
where
Dff is the thermal diffusivity for the adjacent medium (m2/s).
Since the heat flux depends on the temperature profile in the exterior
medium which in turn depends on the thermal history of the simulation, a
simplifying approximation is used. This approximation eliminates the need to
recompute or save the temperature-profile history during the course of the
simulation.
The boundary-value problem specified by equations 2.5.5.1a-d can be
resolved into simpler problems, as shown by Sneddon (1951, p. 162-165) or
Tychonov and Samarski (1964, p. 203-209), using various forms of Duhamel's
Theorem. Two simpler problems, for a general time interval, are:
70
If1 = Du ir^i; on 0< ZK < bur and t < t < t! . (2.5.5.33)ot ne oz h HC o
n
Boundary conditions:
at z = 0 ; T! = 0 ; (2.5.5.3b)
at z = b ; T! = 0 . (2.5.5.3c)
Initial condition:
at t = t0 ; T! = T (z ) ; (2.5.5.3d)e n
and
= D« a~T" on 0< z < b..- and t < t< t t (2.5.5.4a) ne oz n liL. o n
Boundary conditions:
at zn = 0 ; T2 = T_(t) ; (2.5.5.4b) n D
at z = b_._ ; T 2 = 0 . (2.5.5.4c) n iiL
Initial condition:
at t = t0 ; T2 = 0 ; (2.5.5.4d)
where
TjCzjt) is the temperature solution to the first heat-conduction
problem (°C); and
is the temperature solution to the second heat-conduction
problem (°C).
71
The total temperature solution is the sum of TI and T2 and the boundary
heat flux is derived from the gradient of this temperature. However,
because the boundary-temperature function is not known in advance the
following approximation is made
qHC " "Ke 8zn Z = 0
n
(2.5.5.5a)
- Kzn z = 0
n
T2=TB (to )
3 3(T!+T2 )91- 3zB n
6TB
z =0n
T 2=TB (t0 )
(2.5.5.5b)
where
-j- nL
is the heat flux at a heat-conduction boundary at a given
boundary temperature and time (W/m2 ); and
,, is the change in boundary temperature in the time interval t toD O
Equation 2.5.5.5b is simply a Taylor-series expansion of the flux as a
function of the variable boundary temperature.
72
By interchanging the order of differentiation and using the facts that
8T,= 0 ; (2.5.5.6a)
and
(2.5.5.6b)
whereTTT is the solution to equations 2.5.5.4a-d with T,= 1 (°C);U a
we obtain:
8Te8z
n
8T + u
n 8* z = 0 nn
6TB
z = 0n
T=TB (t0 )
, for x on S 5 ; (2.5.5.7)
where
S 5 is the part of the boundary that is a heat-conduction boundary.
The temperature, T, now satisfies equations 2.5.5.1a-d with the time
dependence of the boundary condition removed in equation 2.5.5.1c. This
approach to the treatment of heat-conduction boundary conditions was presented
by Coats and others (1974) in the appendix to their paper. A heat-conduction
boundary condition also could be treated like the transient AIF boundary
condition, but that is beyond the scope of this work.
73
2.5.6. Unconfined Aquifer, Free-Surface Boundary Condition
For an unconfined aquifer, a free-surface boundary exists with a position
in space and time that is unknown before the flow equations are solved.
Therefore, two boundary conditions need to be imposed. The first is that
pressure is atmospheric at the free surface. The second is the kinematic
condition expressing the fact that the movement of this surface of atmospheric
pressure needs to satisfy a continuity equation at the free surface.
The free-surface boundary is assumed to be a sharp interface between the
fully saturated region of simulation and the unsaturated porous medium
outside. The zone of capillary fringe that is partially saturated and the
surfaces of seepage that exist with free-surface gravity flow are neglected.
Delayed yield effects also are neglected, therefore, the specific yield is
equal to the effective porosity, e, in the vicinity of the free surface. The
effective porosity under draining conditions is less than the porosity used to
calculate interstitial velocity (Bear, 1972, p. 255) but the difference is
assumed negligible for the HST3D simulator. Finally, the z-axis is assumed to
point vertically upward when an unconfined aquifer is being simulated. ^1
The heat- and solute-transport simulator treats the free-surface boundary
in an approximate fashion. The approach follows the ideas of Prickett and
Lonnquist (1971, p. 43-45) extended to a three-dimensional flow and
variable-density system. The pressure condition:
p = 0, on S6 (x,t); (2.5.6.1)
where
S6 is the free-surface location that varies in space and time;
is employed, but the kinematic boundary condition is neglected. The absolute
pressure on the free surface is atmospheric, so the relative pressure is zero.
Hydrostatic conditions are assumed to exist in the immediate vicinity of the
free surface. The location of the free surface is determined by interpolation
in the calculated pressure field to determine the location where equation
2.5.6.1 is satisfied. Under this approximate treatment, the free surface
74
moves in response to a net gain or loss of fluid in its vicinity. Thus, fluid
mass is conserved, but the kinematics of the free-surface movement are
neglected. This approximation is acceptable when the velocity of free-surface
movement is small relative to the horizontal interstitial velocity.
In addition, the computational region is fixed for the duration of the
simulation. Boundary pressures less than atmospheric imply that the free
surface is below the boundary of the region; whereas boundary pressures
greater than atmospheric imply that the free surface is above this boundary.
As will be explained in section 3.4.6, the free surface is allowed to rise
above the region boundary a short distance which is a function of the vertical
discretization. This allowance enables the free surface to move within a
reasonable range during a simulation. The fluid- and porous-matrix compres
sibilities usually are taken to be zero for unconfined flow systems, and the
user may specify compressibility values of zero for the HST3D simulator.
2.6. INITIAL CONDITIONS
This heat- and solute-transport simulation code solves only the transient
forms of the ground-water flow and the two transport equations, thus initial
conditions are necessary to begin a simulation. Several options are
available.
For the flow equation, an initial-pressure distribution within the region
needs to be specified. This can be done as a function of position or can be
set to hydrostatic conditions, with the pressure given at one elevation. In
the case of nearly uniform and constant density, an initial potentiometric-
head distribution can be specified, which is the water-table elevation. The
water-table elevation is specified for the upper layer of cells only. No
option to specify a velocity field as an initial condition exists.
75
For the heat-transport equation, the initial-temperature field needs to
be specified. Again, this can be done as a function of position, or
interpolated along the z-coordinate direction from a specified geothermal
profile.
For the solute-transport equation, the initial mass-fraction field needs
to be specified. This can be done only by specifying values as a function of
position.
As will be described in section 4.6, pressure, temperature, and mass-
fraction fields calculated by one simulation can be used as the initial
conditions for another simulation, using the restart option. This often is
the easiest way to establish a steady-state flow field before transport is
simulated. Of course, one needs to determine whether or not an initial
steady-state flow field exists for the physical situation being simulated. It
should be noted that, with a hydrostatic or other estimate of initial pressure
conditions, it could take some time to establish the steady-state flow field.
Mathematically, the initial conditions can be stated as follows:
At t=0:
p = p°(x), in V ; (2.6.la)
T = T°(x), in V ; (2.6.1b)
w = w°(x), in V ; (2.6.1c)
where
x is the vector of position (m),
V is the simulation region; and
p°, T°, w° are the initial dependent variable distributions (Pa,°C,-).
76
3. NUMERICAL IMPLEMENTATION
In order to perform numerical calculations that solve the governing
equations, we first need to discretize the partial-differential equations and
boundary condition relations in space and time. Various algorithms are used
to determine parameters and to implement the boundary conditions. Then the
flow and two transport equations are solved sequentially after they have been
modified by a partial Gauss reduction. Finally, the sets of discretized
equations are solved repeatedly, as the simulation time advances, using a
direct or an iterative equation solver. This chapter will cover each of these
steps for the numerical-simulation calculation.
3.1 EQUATION DISCRETIZATION
The classical method of finite differences is used to discretize the
partial-differential equations and boundary conditions in space and time.
Several options are available for the differencing.
The first step in spatial discretization is to construct a mesh or grid
of node points and their associated cells, that covers the simulation region
to a close approximation (fig. 3.1). The grid of node points is formed by
specifying the distribution of nodes in each of the three coordinate direc
tions; (two directions, if a cylindrical-coordinate system). The volume
associated with each node will be called a cell; it is formed by the cell
boundaries, which are planes that bisect the distance between adjacent node
points. Thus, for the case of unequal nodal spacing, the node points do not
lie at the centers of their respective cells. Boundaries are represented by
planes containing node points. Thus, half-, quarter-, and eighth-cells appear
at various sides, edges, and corners of the mesh, forming the simulation
region (fig. 3.1). The minimum number of nodes required to define a region is
eight, one node at each corner of the rectangular prism. The mesh or grid
described is called a point-distributed grid. Other terms that have been used
are face-centered mesh and lattice-centered mesh or grid. Another term that
has been used for cell is block.
77
FULL CELL\
ONE-EIGHTH CELL
ONE-HALF CELL
NODE POINT
ONE-QUARTER CELL
Figure 3.1. Sketch of finite-difference spatial discretization
of the simulation region.
The simulation region is discretized into rectangular prisms for the
cartesian-coordinate case (fig. 3.1) and into annuli with rectangular cross
sections for the cylindrical-coordinate case (fig. 3.2). Four types of
regional volume subdivisions are defined (fig. 3.3). The primary subdivision
is the cell that is the volume over which the flow, heat, and solute balances
78
are made to give the nodal finite-difference equations. The second sub
division is the element that is the volume bounded by eight corner nodes in
cartesian coordinates and four corner nodes in cylindrical coordinates. The
element is the minimum volume with uniform porous-medium properties. The
third subdivision is the zone that is a continuous set of elements with the
ONE-HALF CELL RING
ONE-QUARTER CELL RING
Figure 3.2.--Sketch of finite-difference spatial discretization for a
cylindrical-coordinate system.
79
same porous-medium properties. The one restriction is that zones need to be
convex. In other words, they need to be rectangular prisms. One zone may not
border another zone on more than one side. Sometimes multiple, adjacent zones
will have to be specified that have the same properties in order to adhere to
this restriction of convex shape. The fourth subdivision is the subdomain
that is the intersection or common volume of an element with a cell. A cell
may have as many as eight subdomains, if it is an interior cell, or as few as
one subdomain, if it is a corner cell. The finite-difference equations are
EXPLANATION(^1 LOCAL CELL-FACE NUMBER
LOCAL SUBDOMAIN-VOLUME NUMBER
2 LOCAL SUBDOMAIN-FACE NUMBER
Figure 3.3.--Sketch of a node with its cell volume showing the cell faces,
the subdomain volumes, and the subdomain faces.
80
assembled by adding the contributions of each subdomain in turn to the
equation for a given cell. The primary reason for introducing the concepts of
elements and zones for assigning porous-medium properties is so that
porous-medium properties can be defined easily at the cell boundaries without
the need for harmonic-mean calculations.
A numbering scheme local to the cell is used during coefficient cal
culation and assembly. Figure 3.3 shows the subdomain local numbering from
one to eight. The six faces are numbered as shown in figure 3.3 and each face
is subdivided into four subdomain faces with numbers for the visible faces as
shown. For the cylindrical system, the corresponding volumes and faces are
numbered in figure 3.4.
A common alternative method for constructing the mesh is to specify the
locations of the planes that form the cell walls. Their intersections form
the cells; then the node points are located in the center of each cell. This
is called a cell-centered or block-centered grid. One advantage of this grid
is that fewer cells are required to span a given simulation region, because
fractional cells do not appear at the boundaries.
The point-distributed grid was selected for this simulator, because the
finite-difference spatial approximations to the dispersive terms in the flow
and transport equations are consistent and convergent for the point-
distributed grid under conditions of variable-grid spacing; whereas, these
approximations are not necessarily consistent and convergent for the cell-
centered grid. As shown by Settari and Aziz (1972, 1974), the local trunca
tion error for the cell-centered grid has a term that does not necessarily
vanish as the grid spacing is refined. A second reason for selecting the
point-distributed grid is that the presence of nodes on the boundary surfaces
simplifies the treatment of certain boundary conditions. It is common to
approximate spatially distributed, aquifer properties as uniform zones. A
disadvantage of the point-distributed grid is that it is difficult to locate
the cell boundaries, so that they coincide with the zoned-property boundaries.
This difficulty can be avoided by making the properties uniform over an
element rather than a cell. This will be described in the parameter-
discretization section.
81
NEIGHBOR NODE
EXPLANATION
LOCAL CELL-FACE NUMBER
LOCAL SUBDOMAIN-VOLUME NUMBER
2 LOCAL SUBDOMAIN-FACE NUMBER
Figure 3.4.--Sketch of a node in a cylindrical-coordinate system
with its cell volume, showing the cell faces, the subdomain
volumes, and the subdomain faces.
82
A cartesian-coordinate grid for a region is shown in figure 3.1. Note
that the basic cell is a rectangular prism; thus, region boundaries that are
not parallel to a coordinate axis must be approximated by a staircase-like
pattern of cell boundaries. No provision for boundary faces that are
diagonally oriented to the coordinate axes exists in the present version of
the HST3D code. It can also be seen that the entire simulation region needs
to be contained in a large rectangular prism. The nodal dimensions of this
prism are the maximum number of nodes along the three coordinate axes, N , N ,
and N . Approximation of diagonal boundaries by a staircase-like pattern will zcause a set of cells to be within the large prism that are excluded from the
simulation region. These cells will be referred to as excluded cells.
The method used for spatial discretization is a subdomain weighted-
residual method with approximating functions that are piecewise linear for
the dependent variables. The unknown parameters in the approximating
functions are the nodal values of the dependent variables. The residuals are
the errors in the governing equations that result from using approximating
functions to the exact solutions, and equations for the unknown parameters
require that the average residual over each cell is zero (Crandall, 1956, p.
149; Finlayson, 1972, p. 7-9, 137, 142). The partial-differential equations
are discretized in space by integrating them over each cell volume. Then the
divergence theorem of Gauss (Karamcheti, 1967, p. 73) is used to transform the
volume integrals of the divergence terms into surface integrals of a normal
derivative. The spatial derivatives in the surface integrals are approximated
by central or upstream differences. The volume integrals are approximated
easily, using the mean value theorem of integral calculus, because all fluid
and porous medium properties are assumed to be constant throughout the sub-
domain volumes of a cell. For the integral of the time derivative, we assume
that the time derivative evaluated at the node approximates the spatial
average of the derivative over the volume of the cell. Thus, the capacitance-
coefficient matrix of the temporal derivative terms is diagonalized. This
method for spatial discretization is conceptually similar to the integrated-
finite-difference method presented by Narasimhan and Witherspoon (1976).
83
The porous-matrix hydraulic, thermal-transport, and solute-transport
properties are discretized on an element basis, with a set of elements forming
a zone of constant properties. The dependent variables that are properties of
the fluid are discretized on a cell basis. Boundary- condition fluxes and
source flow rates also are discretized on a cell basis.
To illustrate the discretization of the flow, heat, and solute equations,
we shall use a general transport equation. The procedure follows that of
Varga (1962, sec. 6.3), Spanier (1967, p. 218-222), Cooley (1974, p. 10-13) or
Roache (1976, p. 23-28) extended to include spatial first-derivative terms, to
three dimensions for cartesian coordinates, and to handling dispersive tensors
that are not necessarily diagonal. The restriction exists that all cell-
boundary planes need to be perpendicular to a coordinate direction. The
general transport equation has the form of a parabolic, partial-differential
equation:
_ (A(x,t) u(x,t)) = V-I(x,t)-Vu(x,t)-V-C(x,t)u(x,t) (3.1. la) 3t
N s+ D(x,t)u(x,t) + I E (t)6(x-x ) ;
1 S Ss=l
where
x is the vector of position, (x,y,z), (m) ;
A is the capacitance coefficient (appropriate units);
g is the tensor of diffusion or dispersion of rank 3
(appropriate units);
C is the vector of interstitial velocity (m/s);
D is the source factor for chemical reaction (appropriate units);
E is the source-term intensity (appropriate units);S
N is the number of source terms; su is the dependent variable (appropriate units); and
6(x-x ) is the delta function for a point source at x=x (-). s s
84
Initial condition is:
at t = 0; u = u°(x) ; (3.1.1b)
Boundary conditions are:
specified value:
u = uB (x,t), for x on S 1 ; (3.1.1c)D
specified flux:
-fi(x,t) s^ + C(x,t)-nu = J(x,t)-n for x on S2 ; (3.1.Id)
where
u is the initial distribution of u;
u- is the boundary distribution of u;D
is the derivative in the direction of the outward normal at the
boundary;
J*n is the specified total flux normal to the boundary surface; and
C«n is the advective flux normal to the boundary surface.
3.1.1 Cartesian Coordinates
Integration of equation 3.1.la over the cell volume associated with a
mesh point, m, at a given location with indices i, j, k, gives:
^ Au dV = Jv V-(I-Vu)dV - Jv V-CudV (3.1.1.1) m m m
N sm+ Jv D udV + I Jv E6(x-xg ) dV ;
m s=l m
85
where
V is the volume of cell m. m
Now, using the previously stated assumption about the integral of the time
derivative:
/V AudV= JV AudV (3.1.1.2)m m
Use of the Gauss divergence theorem on the dispersive and advective
terms yields:
V-(§-Vu)dV = Jg (§Vu)-ndS ; (3.1.1.3) m m
and
Jv V-(Cu)dV = Jg (Cu)-ndS ; (3.1.1.4) m m
where
S is the boundary of cell m; and
n is the outward unit normal vector to the boundary
Then equation 3.1.1.1 becomes:
|^ Jv AudV = Js [§-Vu - Cu] -ndS + Jy 0udV mm m
/ B f , 6(x-x f , )dV . (3.1.1.5) J V s(m) - -s(m) m
86
We have consolidated all the line sources within cell m into a single
equivalent line source, thus eliminating the summation. Since considerable
arbitrariness exists in selecting the finite-difference approximation of
equation 3.1.1.5, we shall choose finite differences that preserve the con
servation of u for each cell.
Following Varga, 1962, p. 253, or Cooley, 1974, p. 16, we approximate the
rate of change of u in the cell using the mean-value theorem giving:
J AudV S ^ (u(x^,t) J AdV) ; (3.1.1.6) m m
where
x is the vector of the node point location (m). m
This approximation diagonalizes the coefficient matrix of the temporal-
derivative terms. The value of the dependent variable at the node is taken to
represent the average value over the cell. Now each cell may consist of up to
eight subdomains, as shown in figure 3.3, and each subdomain may have
different spatial properties. Thus, the integral of A in equation 3.1.1.6 is
actually:
8 8I /,. AdV = I A V ; (3.1.1.7)- V . ms ms 's=l ms s=l
where
A is the value of A in subdomain s of cell m; and ms
V is the volume of subdomain s of cell m (m 3 ). ms
87
The dispersive-flux term is approximated, recognizing that the surface of
cell m is composed of six faces, and that each face belongs to four elements,
each of which may have different spatial properties (fig. 3.3). Thus:
6 4Js (I-Vu)-ndS = I I Jg (I-Vu)-ndS ; (3.1.1.8) m p=l q=l mpq
where
S is the part of the cell surface that belongs to face p in element mpqq (m2 ).
A typical integral over a cell face is of the form, for p = 2, as an
example:
;s d-vuvads = i ; [BXX + B + BXZ ]ds ; 0.1.1.9)m2 q=l m2q J J
where
B..(t) are the tensor components of B. for a face whose outwardJ
normal points in the ith direction, i=x,y, or z.
A sample subdomain volume for subdomain s=l in figure 3.3 is:
Vl = * ^i-'i-P % (yj'yj-l } % K-'W (3.1.1.10)
88
A sample cell-face area belonging to face p=2 and zone q=l in figure 3.3
is:
Sm21
Equation 3.1.1.9 is based on the fact that each cell face has a normal vector
that is alined with one of the cartesian-coordinate directions. Note that B..
is assumed to be spatially constant over the element q. The partial
derivatives are approximated by central differences across each face. Thus,
for the face midway between x. and x. , denoted by p=2, the outward normal is
in the positive x-direction. An integral over this cell face becomes:
4
where
J (B-V)-ndS = I [B(<l) m2 q=l
8u Sm2q+ g q m2q
+B (q) S 0 ] ; (3.1.1.12) xz ^ 8z| q m2q *
9ul is the gradient of u in the x-direction across the p=29x i+Jg,j,k face at y , z fc ;
9uj is the gradient of u in the y-direction for the subface3y| q in the qth element; and
9ul is the gradient of u in the z-direction for the subface 3z| q in the qth element.
89
Now
where
u. . . is the value of u at node x., y. f z, . ik i' *' k
The approximation for = depends on q. For example, for the elementdy
bounded by the planes at x. and x. -, y. and y. +1 ; and z, and
denoted by p=2, q=4 in figure 3.3, we have:
9u| ~ i+,, ,,, , q . - -,,<N I / -~ v*?« A JL« x " J8yl q=4 y - y
u.^i . , = ^(u.,., . , + u. . .). (3.1.1.15) i+^,J,k ^ i+l,j,k y
where
Similarly,
PU | A* 1' .it J t KTJ____J-"*"^! J i K /« -i i:r I / = . 1.3.1.1.9z| q=4 - - v
The advective-transport term is treated in a similar fashion, but it is
somewhat simpler. First, we break it into a sum over the faces and zones:
6 4Js (Cu)-ndS = I I Js (Cu)-ndS . (3.1.1.17)m p=l q=l mpq
90
A typical integral over a cell face, p=2, is:
4Js (Cu)-ndS = I Js CxudS ; (3.1.1.18) m2 q=l m2q
where
C is the vector component of C for a face whose outward normal points
in the x-direction.
Now if the integral is approximated, for the same example face as above,
p=2, by:
4J C udS = I C (m,2,q)% (u + u )S ; (3.1.1.19) m2 q=l 1^ 1 >J» K ijJjK mzq
where C (m,2,q) is the value of C on the face p=2 in element q.A A
This will lead to a central difference for the advective term of equation
3.1.1.5. If, instead, the following approximation is used:
4J C udS = I C (m,2,q) u S for C > 0 ; (3.1.1.20a) m2 q=l X
or
^ Cx(m,2, q) u.S ) for G < 0 ; (3.1.1.20b)
this will lead to an upstream difference for the advective term. Central
differencing may produce oscillations in the solution, whereas upstream
91
differencing cannot (Price and others, 1966; Roache 1976, p. 161-165). But
the penalty to eliminate oscillation resulting from spatial differencing is
the addition of artificial dispersion (Roache, 1976, p. 64-66; Lantz, 1970),
which can be regarded as smearing out of steep concentration or temperature
gradients caused by the numerical method rather than the dispersive mixing
term.
An approximation has the transportive property, if a disturbance in the
field of property u, is advected only in the direction of the velocity.
Recall that C represents the velocity in these equations. The central approx
imation of equation 3.1.1.19 does not have the transportive property, whereas
the upstream approximation of equations 3.1.1.20a and 3.1.1.20b does. How
ever, not all upstream approximations have the transportive property (Roache,
1976, p. 69). While the transportive property is desirable on physical
grounds, the grid spacing must be limited to avoid excessive artificial
dispersion caused by the numerical method. The criteria for avoidance will be
presented in a later section. The numerical implementation of the heat- and
solute-transport simulator offers the choice of central or upstream differenc
ing for the advective terms. If upstream differencing is selected, the user
must determine the grid spacing that limits numerical dispersion to an
acceptable amount.
The source term in equation 3.1.1.5 that is linearly proportional to the
value of the dependent variable, u, is averaged throughout the cell volume to
obtain the finite-difference approximation. The mean-value theorem is used to
approximate the integral, with x being the node-point location. The volume
integral is split into the contributions from the eight subdomains. Thus:
8Du dV = u(xm ,t) I Jy D(s)dV ; m s=l s
8 u. , ,_ I D V ; (3.1.1.21b)i,j,k _ 1 ms ms
S"* J.
92
where
D is the value of D in subdomain s of cell m. ms
The source term at the end of equation 3.1.1.5 is assumed to be a line
source in the z-direction of constant intensity, that fully penetrates the
cell at x=x ; y=y . Discretization is achieved by carrying out theS S
integration. Thus:
Jv Esm6(x-xs )6(y-yg )dV = Em . (3.1.1.22) m
This shows that a line source becomes distributed throughout the cell volume,
and the precise location is lost in the finite-difference equation.
Combining equations 3.1.1.6 through 3.1.1.22 gives the finite-difference
approximation to equation 3. 1.1. la for an interior node or cell. It is of the
form:
u. ,.,,,+ a* u. ., t ,+ 33 u. .,.,, -l,j-l,k-l 2 i,j-l,k-l 3 i+l,3-l,k-
+ a4 u. 1 . . - + 35 u. . , 1 + ae i-lk-l " ik-l b
+ a? u. , .,, , ., + as u. .,, , , + ao u. 7 -- 8 - 9
u. , . , i . -. + aoft u. . - i . , + aoi u
93
,k+l
+ aQ . (3.1.1.23)
It is important to observe that the dependent variable for each interior
node is related to 26 other nodal values of that variable, through the finite-
difference equation in space. The six nearest neighbors to a given node
appear in the terms with coefficients 35, an, ajs, ajs, aj7, and 823- The
central node is in the term with a 14 . All of the other terms result from the
cross-dispersive flux integrals of equations 3.1.1.8 and 3.1.1.9. Thus it
will be advantageous to reduce the bandwidth of the final finite-difference
equations by treating the cross-derivative dispersive-flux terms in an
approximate manner. This will be covered in section 3.2.
Boundary cells with specified flux are handled similarly to interior
cells. With the point-distributed grid, nodes will be located on boundary
faces, edges, and corners. The cells associated with these boundary nodes
will not have all eight subdomains (fig. 3.5). For example, a lateral
boundary cell will have only four subdomains, while a corner boundary cell
will have only one. The volume integrations over the cell are carried out as
before, with the appropriate reduction in the number of subdomains. Flux-
boundary conditions enter the finite-difference approximations through the
surface integrations.
Consider a side node where part of the regional boundary is an x-plane;
that is, the outward normal to the regional-boundary surface points in the
positive x-direction. The associated half-cell for the node consists of four
subdomains shown in figure 3.5. The discretization of equation 3.1.1.5
proceeds as follows. The temporal term for the rate-of-change-of-u becomes:
a a' 45T J« AudV = sr u. . . Z A V . (3.1.1.24) 3t J V 3t i,j,k =1 ms ms
94
The dispersive- and advective-flux terms are still given by equations
3.1.1.8 and 3.1.1.17, but now one of the faces, denoted by p=2 in figure 3.5,
is a boundary face for the region. Note that its outward normal points in the
positive x-direction. Using equation 3.1.1.Id for the flux-boundary
condition, the integral over this face becomes:
[fi'Vu-Cu]-ndS = - J_ J-ndS ; (3.1.1.25a) Sm2 Sm2 ~
JxqSm2q ' (3.1.1.25b)
where
J is the component of vector J in the x-direction in the qth
element.
Normally J is constant over the entire cell face. Thus, the
specified-flux boundary conditions has been incorporated in the finite-
difference equation as a source term.
The distributed-source and line-source terms simply are adjusted to
account for the reduced cell volume. Thus equation 3.1.1.22 is unchanged, but
equation 3.1.1.21b becomes:
/ DudV S u. . . I D V . (3.1.1.26) Vm x ' J ' k s=l ms ms
95
_ NEIGHBOR NODE
REGIONAL-BOUNDARY FACE
EXPLANATION
.31 LOCAL HALF-CELL-FACE NUMBER
LOCAL SUBDOMAIN-VOLUME NUMBER
Figure 3.5.--Sketch of a boundary node with its half-cell volume
showing the cell faces and the subdomain volumes.
96
In the flow equation, there is no advective term to cancel the
corresponding term in the specified-flux boundary-condition equation. Inside
the region, this means C = 0; but some of the boundary conditions have C £ 0.
Then equation 3.1.1.9 takes the form:
L (§-Vu)-ndS = J [(Cu)-n - J-n]dS ; (3.1.1.27a)m2 m2
which discretizes to:
L (§-Vu)-ndS m2
I [C u. . ,S - J S ] . (3.1.1.27b) q=1 x i,j,k q xq q
No central or upstream approximation for u is necessary, because the
boundary face contains the node point.
3.1.2 Cylindrical Coordinates
The discretization of equation 3.1.la in cylindrical coordinates is
analogous to what has just been presented. We make the assumption of
cylindrical symmetry, so no angular dependence exists. No line source terms
can be present so E=0. A cell volume becomes a ring bounded by r. , and r..i
and z, i and z, , , where r^.., is the radius of the cell wall between r^. andK ^J K" ̂J "*
(fig. 3.4).
An option is provided for automatic placement of the radial-grid lines
between the interior and exterior radius. With this option the grid lines are
spaced according to:
r.i
(3.1.2.1)
97
where
N is the number of grid points (lines) in the radial direction;
N is the exterior radius (m); and
r is the interior radius (m).
This equation gives logarithmic-node spacing in the radial direction.
The cell boundaries for the cylindrical faces are chosen to be at the log
arithmic mean radii; for example:
" riT^-TJ (3.1.2.2) '
for both the automatic and user-specified radial-grid distribution. A loga
rithmic-grid spacing will make the pressure drop uniform between adjacent grid
points for steady radial flow in a homogenous medium (Aziz and Settari, 1979,
p. 88). The discharge flux at r. , matches the analytical solution underIT^
these conditions.
Each cell ring is composed of four subdomain rings (shown in fig. 3.5).
Thus, the temporal rate-of- change of u in the cell is approximated by:
/ AudV s |r u..Z A V ; (3.1.2.3)JV 8t ik , ms ms 'm s=l
where a sample subdomain volume is, for subdomain s=l:
V X = 71 (rj - r*_^) \ (zfc - z^) . (3.1.2.4)
The surface of cell m is composed for four faces, and each face belongs
to two elements. Each element in the z-direction may have different porous-
medium properties, but these properties must be constant in the r-direction.
98
Equation 3.1.1.8 for the dispersive-flux term becomes:
4 2(I-Vu)-ndS = Z Z Jg
m p=l q=l mpq(3.1.2.5)
and typical integral over a face of a cell surface, p=2, is
L (B-Vu)-ndS = I L [B + B dS ;J S 0 = - J S 0 rr 8r rz 3z *m2 q=l m2q(3.1.2.6a)
q=lSm2q + Brz (q) a^ 8 ] . (3.1.2.6b)
§u 3r
Equation 3.1.1.13, with r taking the place of x, is used to approximate
, and equations 3.1.1.14 and 3.1.1.15 are used to approximate 9u
Representative cell face areas are, for the face p=l:
S = 271 r. j^Cz, - z, .) ; mn i-% k k-1
(3.1.2.7)
and, for the face p=3:
S = 7t(r? - r m31 i ](3.1.2.8a)
99
= 7l(r 2 - r . 2 ) . (3.1.2.8b)
The advective term is treated as in the cartesian-coordinate case, with
appropriate reduction in the number of faces and zones. Again, central or
upstream differencing in space can be selected. The distributed source term
proportional to u is also handled as in equations 3.1.1.21a and 3.1.1.21b with
appropriate reduction in the number of subdomains from eight to four.
Finally, the finite-difference approximation to equation 3. 1.1. la for
cylindrical coordinates with angular symmetry takes the form:
If (aio 'ui,k) = "i'Vi.k-1 + 32 'ui,k-i + a3 'ui+i,k-i
+ a*'Ui,k+l + a9 'Ui+l,k+r (3.1.2.9)
Note that no a0 ' term exists because annular-ring sources normally are
not encountered. The terms a 2 ', a 4 ', a 6 ', and ag ' are contributions from the
closest neighbors to the central node point appearing in the 35' term. The
other terms arise from the cross-derivative dispersive-flux integrals, and
they may be treated in an approximate fashion to reduce the matrix-band
width. The specified-flux boundary conditions are discretized in the same
manner as for the cartesian-coordinate system, with appropriate reduction in
the number of subdomains and surface faces.
3.1.3 Temporal Discretization
To approximate the time derivative, two options are offered. The first
is centered-in-time differencing, commonly known as the Crank-Nicholson
method. The time derivative is approximated by the finite difference:
100
/ m -vn+1 , m >.n (a u ) - (a )m m / « i « i N
: (3.1.3.1)t « tn+l . n
where t is the time at level n. n
The right-hand-side, F, of the equation concerned is evaluated as
follows:
F £ ^(Fn+ + Fn) ; (3.1.3.2)
where
F is the spatial-difference function evaluated at time n.
The other option is backward-in-time differencing, which has the form:
F S Fn+1 (3.1.3.3)
As with the advective spatial differencing, central-in-time differencing
has the potential for causing oscillations in the solution (Price and others,
1966; Smith and others, 1977), whereas backwards-in-time differ-encing does
not. However, backwards-in-time differencing does introduce numerical dis
persion that must be kept under control by limiting the time-step size (Lantz,
1970; Price and others, 1966; Smith and others, 1977; Briggs and Dixon, 1968).
Equations 3.1.3.1 through 3.1.3.3 for the time discretization can be
combined into a general form as:
101
f . f x(a u ) - (a u ) .,m m ^JL_ = eFn+1 + (l-6)Fn ; (3.1.3.4)
where 6=1 gives the fully implicit or backward-in-time (BT) differencing,
and 6 = \ gives the Crank-Nicholson or centered-in-time (CT) differencing.
The next step is to express the difference equation in residual form by
writing:
un+1 = un + 6u ; (3.1.3.5)
where
6u is the temporal change in u.
Equation 3.1.3.5 is inserted in equation 3.1.3.4 and the following ex
pansions of the temporal-difference terms are used. These are consistent
differencing expansions that correspond to the differentials of products. For
terms of the form (a.u) we have:i
(a.u) n+1 - (a.u)n = a. n+16u + u1^ ; (3.1.3.6)
for terms of the form (a. a.u) , we have:
f vn+1 , >.n n+1 n+l x . n+1 n* . n n* , 0 - 0 ..N(a. a.u) - (a. a.u) = a. a. ou + a. u oa.+ a.u oa . . (3.1.3.7)v ij' i J iJ i JJi
3.1.4 Finite-Difference Flow and Transport Equations
Combining equations 3.1.3.4, 3.1.3.6, and 3.1.3.7 with 3.1.1.23 or
3.1.2.9, we obtain the form of the general finite-difference equation for an
interior node. The rather large number of terms makes presentation of the
102
general equation impractical. It is more instructive to present the dis-
cretized flow, and heat and solute- transport equations individually, showing
the x-direction terms only. The additional dispersive and convective terms
for the y and z-directions follow the same pattern as their counterparts in
the x-direction.
The finite-difference approximation to the flow equation (2. 3. la) is, for
an interior node m:
c326Tm + c3t6«m = erF . +% (6P . +1 - 6P .) -
? - Pi-1 * PiV (Xi - «i-
n P*
y and z direction difference terms; (3.1.4.la)
where8
s8 os=l r s=l
8C 3 2 = tPA * e« vmj/6t J (3.1.4.1c)
o j. 4 s nis s=l
8 C 3 i = [P0 PW ^ £ « VmJ/6t J (3.1.4.Id)
U W _ £> HIDs=l
103
9=
n , p. , 4
I k , S , ; (3. 1.4. If)' v_. , , ,F-L-\ n , ^ - mlq mlq 'p. j (x.-x. ) q=l H Hr l-ss l 1-1 ^
where
C.. are the capacitance factors (various);
_. are the conductance terms for flow (m-s); and
nin is the volumetric source flow rate for cell m (m3 /s)
The flow-conductance factors, T . , (m 3 ), are defined as:
^3.1.4.2)
These factors contain the spatial information and are constants.
In equation 3. 1.4. la, the source-sink flow rate has been made
semi-implicit in time by including a term that accounts for changes in flow
rate with changes in cell pressure. It is semi-implicit, because only the
flow rate that contributes to the equation for cell m is treated implicitly.
The effect of a change in pressure in cell m on the source-sink flow rates for
other cells coupled to the cell through a well bore are not included; this
approach avoids enlarging the bandwidth of the system equation matrix,
equation 3. 6. la.
104
The finite-difference approximation to the heat-transport equation
(2.3.1b) is, for an interior node, m:
+ c21 6wm = erH . +!s (6T. +1-6T.) - er
-Tn1 - T (Tn-T JHi-i i
- es c,6 T... - 66s .^C-TXl+% f l+3g Xl+^ f l
6S c.6 T. , + 66S . , crTXl-ij f l-3g Xl-lj f 1-
4.C ^T,. i..i +5 . i c,. r.f 1+Jg Xl-% f l
fTn + Tn - Tn - n Hxy i+Jg ^
T fTn + Tn - Tn - Tn * V1
(Tn + Tn - Tn - n Hxy i-% U
CTn + Tn - Tn - Tn Hxz i-Jg u i
105
8Qn*n
where
c.T + 6 p* 6p T + 6Q c,6T nr f m 3 ra m rar f m
6 ^ p* c,6p 6T 9p r f *m m
+ y and z direction dispersive, cross-dispersive
and advective flux terms; (3.1.4.3a)
8 8C23 = [p p Hn+1I en V + pn+1Ha+1 I a, V ^^ rorp m . s s rm m , bs ms s=l s=l
8- Tn L I (p c ) a, V ]/6t ; (3.1.4.3b) m . *s s s bs ms s=l
8 8C 2 2 = [P c, Z en V + I (l-en)(p c ) V +^^ f , s s , s Ks s s mss=l s=l
8p p_,Hn Z en V ]/6t ; (3.1.4.3c) roKT m . s ms ' s=l
8C 2 i = [p P Hn I en V ]/6t ; (3.1.4.3d) £1 Korw m . s ms ' s=l
106
q=]K
I (l-en)K S 0 ]/(x. -x.) ; <1 sq m2q i+l i
(3.1.4.3e)
t
I (l-en)K S , ]/(x.-x. . a sa mla i i-lq=l
(3.1.4.3f)
m2q '(3.1.4.3g)
(pv ) n x I eu X 1-* q=l q
(3.1.4.3h)
Sm2q '> (3.1.4.31)
6S , = p? , 6v H I sn S , 1 q mlq(3.1.4.3J)
(3.1.4.3k)
107
4u ... = [ I en Du (2,q)S 0 ]/(z, -z. ) ; (3.1.4.3£) Hxz i+*& _ 1 q Hxz '^ m2q k+1 k
H = H(ToH) + cf (T-ToH); (3.1.4.3m)
where T are the thermal conductance terms (W/°C). Hi
In equation 3.1.4.3a, the same semi-implicit treatment of the source-sink
flow rate has been incorporated as in equation 3.1.4.la.
The central-or upstream-weighted value for the variables v , 6v , T and
6T is given by the general form:
u. = (l-o) u. + a u. +J (3.1.4.4)
where
a is the spatial weighting coefficient.
Central weighting is obtained with a = ^; upstream weighting is obtained with
a = 0 for a positive v .
The finite-difference approximation to the solute-transport equation
(2.3.1c) is, for an interior node, m:
108
C 136pm + C 126Tm + Cll6wm = ers . +%(6w. +1 - 6w.)
- 06S .
,-._ ~ . n t«+8S . 6w. + 6 6S . ,w.
_n n . _n nS - J_1 W - J_1+ S.j W.-
+ n n W
( j_Irj TW W WSxy i.-\
r n + n - nSxz i-\ lwi "
AW11 wn - 6A(wn+1 6M + if 6w ) mm m m m m
e
+ 6 5-5 6p 6(p*w*) 3p ^m K m
+ y and z direction dispersive, cross-dispersive and
advective-f lux terms; (3.1.4.5a)
109
where
where
8 8= [p P wn I K11 V + pn L wn A I OL V ]/6t (3.1.4.5b)LKo*p m , s s Km m - bs ms j/ v }S I S l
; (3.1.4.5C)0 s= l8
Cn = [p P wn + pn A ] I K11 V /6t ; (3.1.4.5d) 11 tr o*w m Mn , s ms 's=l
4 4 pnrc ... = [ I en D0 (2,q)S 0 + D I en S 0 ] -^1 ; (3.1.4.5e) Si+^ L q=1 q Sxx v » Hy m2q m j q m2q j xi+1 ~Xi »
4 4 pnro . ! = [ I en D0 (l,q)S , + D I en S , ] -^ ; (3.1.4.5f)Si-% . q Sxx v >H/ mlq m - q mlq j x.-x. . '
q=l ^ ^ q=l ^ ^ i 1-1
(3.1-4.5g)
8M11 = pn I if V ; (3.1.4.51) m Mn , s s ' s=l
+1 86M = pn I a, V 6p m ^m - bs s rm s=l
8+ I (K11 V )[p p 6p + p PT6T + p p 6w ] ; (3.1.4.5J)- s s Ko rp rm ro rT m ^orw m J J s=l ^
< = Es + (PbVs ' (3.1.4.5k)
n is the mass of fluid plus the effective additional fluid m rmass from sorption in cell m at time level n (kg);
T . are the conductance terms for solute transport (kg/s); and o i1C is the augmented porosity factor for subdomain s(-).S
no
In equation 3.1.4.5a, the same semi-implicit treatment of the source-sink
flow rate has been incorporated as in equation 3.1.4.la. In equations
3.1.4.1a-f, 3.1.4.3a-£, and 3.1.4.5a-k, subscripts pertaining to the y and z
directions have been omitted for clarity, unless necessary. The source den
sity, p*, temperature, T*, and mass fraction, W*, are specified functions of
time and source location. When the source-flow rate is negative, so that it
becomes a sink, the density, temperature, and mass fraction become those of
the cell. In the abbreviated subscript notation, u and u. become identicalr 'mifor a given variable, u. Note that the cross-dispersive flux terms have been
evaluated explicitly, that is, at time n, to limit the number of elements in
the coefficient matrix of the unknowns, A» to a maximum of seven for each
equation. The coefficients 2*., S., and M. are evaluated at time n.
The preceding flow and transport equations are valid for confined flow.
The forms of the capacitance terms that contain the porous-medium bulk com
pressibility are based on a slightly compressible porous matrix and a cell
volume that deforms slightly in space. The coefficients C.., and the cell*J
facial areas S are modified for the case of unconfined flow, as will be mpqshown in section 3.4.6.
The permeability tensor in the flow equation is a diagonal matrix in the
numerical implementation, because the coordinate directions are chosen to be
along the principal directions of this tensor. These directions are assumed
not to change with position in the simulation region. The finite-element
discretization technique must be used for the more general situation of
spatially variable, anisotropic, permeability directions.
In summary, the properties and variables that are spatially discretized
on a cell-by-cell basis include pressure, temperature, solute-mass fraction,
density, viscosity, enthalpy, and specified fluxes. Porous-matrix properties
that are discretized on an element-by-element or zonal basis include porosity,
permeability, thermal conductivity, heat capacity, bulk compressibility, bulk
density, equilibrium-distribution coefficient, longitudinal dispersivity, and
transverse dispersivity. Well-completion intervals also are designated on a
zonal basis.
Ill
3.1.5 Numerical Dispersion and Oscillation Criteria
For guidance in selecting the spatial and temporal discretization method,
the following results have been obtained by Lantz (1970), Roache (1976, p. 19,
48), Smith and others (1977) and Price and others (1966), expressing the
truncation errors that give rise to numerical dispersion and criteria for
avoiding oscillations in the solution. They were derived for the one-
dimensional form of equation 3.1.la with constant coefficients and no source
terms; that is:
. 8u 8 2u 8u f . A * B ^ ' C " (3.1.5.1)
Similar analyses can be performed for the more general equation:
where B, C, D, and E are functions of x and t, and A is positive.
The truncation errors and oscillation criteria for both equation forms
are given in table 3.1. The maximum values of A, B, and C should be used in
the variable coefficient case, equation 3.1.5.2. All of the methods are
stable in the sense that errors do not grow without bound. However, oscil
lations in space and time may persist without growth or decay. The oscil
lation criterion for the centered-in-time differencing was presented by Keller
(I960, p. 140) and Briggs and Dixon (1968). They are sufficient conditions;
thus, they may be conservative. Alternate conditions appear in Price and
others (1966) but they require knowledge of the maximum or minimum eigenvalue
of the spatial-discretization matrix that cannot be expressed analytically.
An important thing to note from table 3.1 is that it is possible for oscil
lations in the solution to arise from both spatial and temporal discreti
zation. For the flow equation with no advective term, oscillations from
temporal discretization are still possible. For the flow equation in
112
cylindrical coordinates, an advective-type term appears so oscillations can
also be caused by spatial discretization. If a source term that depends on u
appears in equation 3.1.5.2, the oscillation criteria for the centered-in-time
discretization are modified as shown.
When using the backwards-in-space (upstream) or backward-in-time differ
encing, one needs to check that the truncation-error terms that cause
numerical dispersion do not become large relative to the physical-dispersion
coefficient. Mathematically, for a dispersion coefficient given by equation
2.2.6.1.2; one needs to adhere to the following criteria:
- ; (3.1.5.3)
2 L
and
C6t« aT ; (3.1.5.4)
where
2 L
Ax = X..- - x. ; and (3.1.5.5a) i+l i '
6t = tn+1 - tn . (3.1.5.5b)
Note that these results are from a one-dimensional analysis with constant
coefficients, but they give guidance for grid and time-step selection. Table
3.1 shows that, in the case of variable coefficients, additional truncation-
error terms occur with backwards-in-time differencing, that can give rise to
numerical-dispersion errors.
113
Table 3.1. Truncation errors and oscillation criteria for one-
dimensional parabolic equations
[BS, backward-in-space; BT, backward-in-time; CS, centered-in-space;
CT, centered-in-time;
uxx8u lx " 8x
Discretization Method
Truncation Error
Oscillation Criterion
Equation 3.1.5.1
BS
BT
CS
CT
CAxuXX
XXC2Atu
2
0(Ax2 )
0(At2 )
Ax < 28
At < A___(Ax) 2 - B
Equation 3.1.5.2
BS
BT
CAxu2
C2Atu
XX
_ xx + B^Atu + BDu 2 t xx xx
+ 3B Cu + 2B2 uX XX X XX
CS
CT
0(Ax2 )
0(At2 )
Ax < 2B
At<MIN (B_ D Ax2 " 2
/ D
or
At<B_ D Ax2" 2 '
114
3.1.6 Automatic Time-Step Algorithm
Manual time-step selection can be difficult, when many source terms and
boundary conditions change considerably with time. In general, the more
rapidly the conditions change, the smaller the time steps will need to be for
an accurate solution. Therefore, the heat- and solute-transport simulator has
an automatic time-step option that uses an empirical algorithm (INTERCOM?
Resource Development and Engineering, Inc., 1976). The user specifies the
maximum values of change in pressure, temperature, and mass fraction
considered acceptable as well as the maximum and minimum time step allowed.
Then, at the beginning of each time step, the following adjustments are made,
depending on the conditions:
X Souif: |6u |>6u ; 6t = ^6t (1 + , '"** , ) ; (3.1.4.1)
max max ' o |ou | '
otherwise, if:
» 0<|6u | < 6u ; 6t = 6t (0.2 + 0.8 , A , ) ; (3.1.4.2) max max ' o oumax
max
otherwise, if:
6u = 0; 6t = 1.56t ; (3.1.4.3)max ' o '
where
u is pressure, temperature, or mass fraction;
o
6u is the specified maximum change in u;max * & '
6t is the new time step;
6t is the previous time step; and
|6u I is the absolute value of the maximum-calculated change in u over the max
previous time step.
115
The new time step is selected to be the minimum of the three that were
calculated on the basis of change in the pressure, temperature, and mass
fraction. The time step is constrained to a user-specified range, and the
maximum increase in 6t is limited to a factor of 1.5. This algorithm tends to
increase the time step such that the maximum acceptable change in pressure,
temperature, or mass fraction is achieved as the simulation progresses. The
minimum required time step, set by the user, is maintained for the first two
steps after boundary-condition changes occur or after the automatic time-step
algorithm is invoked.
3.1.7 Discretization Guidelines
No complete set of discretization rules exists that will guarantee an
accurate solution discretization with a minimum number of nodes and time
steps, even for the case of constant coefficients. However, the following
empirical guidelines should be useful.
1. If using the backward-in-space or backward-in-time differencing,
make some estimates of the truncation error, using parameter
values at their limits expected for the simulation. Thus,
verify that the grid-spacing and time-step selection do
not introduce excessive numerical dispersion.
2. If using centered-in-space and centered-in-time differencing,
print results every time step for a short simulation
period, 5-10 time steps. Examine the results for spatial
and temporal oscillations that are caused by the time or
space discretization being too coarse.
3. Check on spatial-discretization error by refining the mesh.
However, this often is impractical for large regions. A
check on temporal-discretization error is relatively easy to
make by refining the time-step length for a short simulation.
116
4. At each change of boundary condition or source flow rates, reduce the
time step until the abrupt changes have had time to propagate
into the region. The automatic time-step algorithm does this.
5. To adequately represent a sharp solute-concentration or tempera
ture front, span it with at least 4-5 nodes. A large number of
nodes may be required if a sharp front moves through much of the
region over the simulation time. Compromises often will have
to be made. An advantage of the centered-in-space differencing
is that oscillations will reveal when the grid is too coarse
relative to the gradients of solute concentration or temperature.
6. Well flows that highly stress the aquifer require a small time
step after a change in flow rate, to control errors from explicit
flow-rate allocation or explicit well-datum pressure calculation.
7. Sometimes, the global-balance summary table will indicate that the
time step is too large by exhibiting large residuals, particularly
if the density and viscosity variations are large.
8. To check for unusual results that could indicate discretization
error, print out all of the results some of the time, and
some of the results all of the time.
3.2 PROPERTY FUNCTIONS AND TRANSPORT COEFFICIENTS
Numerical implementation of the fluid-density function is simply the
evaluation of equation 2.2.1.1b or 2.2.1.3a. Fluid viscosity is obtained by
evaluation of equation 2.2.2.1 and equation 2.2.2.2 if necessary. The
enthalpy of pure water at the selected reference values of pressure and
temperature, H(p vt T TT»O) is obtained by a two-step interpolation. First, the On On
enthalpy of saturated fluid at the given temperature is calculated by linear
interpolation in the table of saturated enthalpy as a function of temperature;
then, adjustment to the given pressure is made by bilinear interpolation in
117
the table of enthalpy deviation from saturation as a function of pressure and
temperature. This procedure is given by equation 2.2.3.la. A sequential
search is made for each interpolation, since the number of pressure or
temperature entries is 32 or less in both tables. Equation 2.2.3.1c is used
for all subsequent fluid-enthalpy calculations. It is possible that
simulation of wide variations in pressure and temperature could require a
table look-up for all enthalpy calculations, and the algorithm in the program
code would need to be modified.
Figure 3.6. Sketch of velocity vectors used for the dispersion-
coefficient calculation for a given cell.
118
The hydrodynamic-dispersion coefficient is calculated by equation
2.2.6.1.1 with equations 2.2.6.1.2 and 2.2.6.1.3. A separate value of
D -(p>q) is associated with each element, q, of each cell face, p. Inter- sijstitial velocities are obtained from the pressure and elevation differences
across the face for the velocities normal to the face. Velocities parallel to
the face are determined by averaging velocities from each side of the face.
An x-face, with the y and z velocities interpolated to get the effective
values on the subface appears in figure 3.6. Average values are used, since
the face lies midway between x. and x.,,.3 i i+l
The thermo-hydrodynamic-dispersion tensor is calculated by equations
2.2.6.2.1 and 2.2.6.2.2. The porosity and the thermal conductivities are
defined by zones and the interstitial velocities are obtained the same as for
the hydrodynamic dispersion.
Two methods are available in the HST3D simulator for computation of the
cross-derivative dispersive-flux terms. The most rigorous treatment of the
cross-derivative terms involves explicit calculation. They are lagged one
iteration in the solution cycle of the flow, heat, and solute equations. The
cross-derivative dispersive fluxes are recalculated for each iteration based
on the conditions existing at the end of the previous iteration and then they
are incorporated into the right-hand-side vector. Therefore at least two
iterations in the solution cycle are required at each time step. This full
treatment requires storage of the nine dispersion-coefficient terms for
thermal and solute dispersion. An approximate empirical treatment of the
cross-derivative dispersion terms is available also, that consists of lumping
the cross-derivative dispersion coefficients into the diagonal dispersion-
coefficient terms. The three augmented dispersion coefficients for thermal
and solute dispersion are the only coefficients stored, and extra iterations
are not required, because the cross-derivative dispersive fluxes are not
computed.
119
3.3 SOURCE OR SINK TERMS THE WELL MODEL
In the present version of the HST3D program, only one well can exist in a
particular cell. Multiple wells in a cell must be represented by an
equivalent single well, or the spatial grid must be refined to separate them.
This restriction includes wells that are located in the same areal cell that
are completed in different vertical intervals.
Recall that a cell may contain up to four zones of different porous-media
properties over a given areal plane. If a well is completed in a cell with
multiple zones, the effective ambient permeability is taken to be that of the
lowest zone number. This is because no algorithm presently exists to
calculate the effective ambient permeability for a well in areally
heterogeneous porous media.
3.3.1 The Well-Bore Model
The volumetric flow rate per unit length of well bore is given by
equation 2.4.1.1. Discretization for a given cell, m, is achieved by choosing
the average pressure to be the cell pressure, and multiplying by the length of
well bore in that cell. Since the well bore is usually screened over the more
permeable zones of the formation region, the screened intervals are specified
by zones or sets of elements rather than by cells. The upper and lower parts
of a screened interval will be one-half of the cell thickness in length,
unless the cell in question is an upper or a lower boundary cell for the
region. Thus:
(Pw£-Pm) [W^i + W^l (3311)
w* " IV*)
120
In the case of an unconfined aquifer with a well screened through the free
surface, the screened length, L-, is adjusted as the saturated thickness
varies in time.
where
L£2 = ««*+! 'ZP ; (3.3.1.Ic)
and where
Q 9 is the volumetric-flow rate from the well to the aquifer in cell m
at well-bore level £ (m3 /s);
p is the pressure at node m (Pa);
p - is the pressure in the well bore at elevation of node m (Pa) ;
m(£) is the cell number associated with the well-bore level H\
I-.. is the length of well bore in the lower half of cell m(£) (m) ;
and
L« is the length of well bore in the upper half of cell m(£) (m) .
Equations 3.3.1.1b and 3.3.1.1c are valid for the z-coordinate directed
vertically upward.
For wells drilled at an angle 6 to the vertical:w
s(Zn -Zo.J
hi = cos 6 * (3.3.1.2.)W
L£2 cos 6w
121
The well indices may be different in the upper and lower halves of the
cell, because the porous-medium zone boundaries pass through planes of node
points. The two-term sum in equation 3.3.1.la accounts for this. When the
cell is at the upper or lower boundary of the region, or at the ends of the
screened interval for the well, the appropriate term in equation 3.3.1.la
becomes zero.
For notational convenience, we define:
where M is the well mobility defined by equation 2.4.1.5.
Flow-rate allocation by mobility is obtained by discretizing equation
2.4.1.5 to give:
; (3.3.1.4)
where
JL is the index of the bottom level of the well screen; and
JL is the index of the top level of the well screen.
If the screened interval is not continuous from JL to JL., the length, L». is
set to zero over the appropriate subintervals. For an observation well, the
dependent variable data in the aquifer are taken from the cell at location
V
122
Flow-rate allocation by the product of mobility and pressure difference
is obtained by discretization of equations 2.4.1.9 using equation 2.4.1.8. The
pressure at the well datum is given by (Thomas, 1982, p. 156):
*~*L
£ «L«w£ a
wd (3.3.1.5)
and the flow rate from the well to the aquifer at each layer is given by:
0 0 - M 0L 0 [p , + p g(z , - zj - p ] ; (3.3.1.6) T?£ w£ H ^wd Kwe wd & ^m
where z« is the elevation of the well node at level & (m).
Similar expressions were derived by Bennett and others (1982) for
constant-density fluids.
For simulations with a well completed in more than one layer, and
explicit calculation of the well-datum pressure, a large well index or
mobility can cause computational instabilities (Chapplear and Williamson,
1981). A large flow rate will be allocated to a layer with large mobility,
and the cell pressure can become nearly equal to the well-bore pressure. This
will make the flow-rate allocation small during the next time step, and an
oscillation may develop. To avoid a severe time-step limitation, a semi-
implicit, well flow-rate allocation can be used. It is available as a
calculation option in the HST3D program. Equation 3.3.1.6 becomes:
= M 0L 0 (pn , + pn g(z ,-z 0 ) - pn) - M 0L 06p . (3.3.1.7) w£ H ^wd *w 6 wd £ ^m w£ A ^m
123
This gives an implicit coefficient that is included in the matrix element
for node m in the finite-difference equations. Note that well-datum pressure
still is treated explicitly. This can put a restriction on the time step for
stability particularly when the aquifer is being stressed heavily. Also the
total flow rate in the well will not be maintained over the time step.
Therefore, iterations are necessary.
A fully implicit approach would eliminate the iterations, but would
introduce additional coefficients in the flow equation for all the cells that
were communicating with the given well. The band-width of the finite-
difference flow equations, would be increased, thus making the two matrix-
solution techniques, much more difficult to implement. However, Bennett and
others (1982) employ the fully implicit approach with a compatible matrix-
solution technique.
A compromise algorithm was developed starting from equation 3.3.1.5
expressed as a well constraint to maintain specified well-flow rate:
M .L^p -i*7v v fnWA* X* Ul
M 0L 06p' = 0. w£ x, *wd (3.3.1.8)
Equation 3.3.1.8 is written for each well in the region.
The matrix representation of the flow- and well-constraint equations being
solved simultaneously is bordered as shown by:
where
(3.3.1.9)
4 is the coefficient matrix from the discretized flow equation;
Hi is the coefficient matrix linking the pressures in each of
the cells which communicate with a well;
H2 is the coefficient matrix linking the well-datum pressures to
the flow equation through the source term;
124
HS is the coefficient matrix (diagonal) for the well-datum pressures
in the well constraint equation (eq. 3.3.1.8); and
bi is the vector of known quantities from the discretized flow
equation.
The two equations are solved iteratively at each time step for 6p and 6p ,.
The well-datum pressures are lagged one iteration in the solution of the flow
equations. The initial value for 6p , is taken to be 0. The iterations are
terminated when the maximum fractional change in 6p , is less than 0.001.
Usually, only two or three iterations are required for convergence. This
algorithm has the advantage that the sparse structure of the matrix A is
preserved, so that the implemented matrix-equation solvers can be employed.
At the first time step, equation 3.3.1.4 is used to calculate the flow
rates at each layer for each well. Equation 3.3.1.6 is used thereafter.
A reversal of flow between the well and the aquifer at any layer
communicating with a well is allowed. However, difficulties arise if there is
a reversal of flow within the well bore. An algorithm to compute a realistic
density profile in the well bore under flow-reversal conditions has not yet
been developed; therefore, the following algorithm is currently used in HST3D
to compute heat and solute flow rates in a well bore.
For a production well, heat and solute balance calculations are done from
the bottom to the top of the well-screen interval. If injection occurs at a
given layer, the density, temperature, and solute concentration injected are
based on the current values coming up the well bore from below. Any fluid
flowing down the well bore to that layer is neglected. Density, temperature,
and solute concentration values based on well-datum conditions are used if
there is no upward flow in the well bore below the given injection layer.
This algorithm is suitable for producing wells which leak into the aquifer but
have net upward flow along the entire well bore. It may be a poor approxi
mation if there are large density, temperature, or solute concentration
variations within the well and flow reversals occur in the well bore.
125
For an injection well, no account is taken of the effect of producing
layers on the density, temperature, or solute concentration in the well bore.
The conditions at the well-datum level are used for all injection layers.
Clearly, this approximation is valid only for injection wells with slight
invasion from producing layers and no flow reversals in the well bore. A more
realistic algorithm will require a complex, iterative calculation.
In the present version of the HST3D simulator, when a production or in
jection well becomes inactive, by having its flow rate set to zero, no cir
culation of fluid from one aquifer-discretization layer to another is computed
Removing this restriction would require the algorithm, described previously,
to handle flow reversals in the well bore.
For the case of a single well in the cylindrical-coordinate system,
equation 2.4.1.12, for the well bore, is discretized in space and time in the
same manner as the system flow equation. Flow- rate allocation by mobility and
pressure gradient or specified pressure at the well datum are the options
available. The augmented- flow equation 2.4.1.13, is discretized in space and
time in the manner that led to equation 3. 1.4. la. At a node along the well
screen below the top of the screen, k<JL,, the equation is:
+ C316wm =
(pk+i - # +
(pk ' »k
n f \P i i s( z i ~ 2i i)$ wk-% k k-1
+ r-direction dispersive terms; (3.3.1.10a)
«126
where
v f (z. .- - z, w w k+1 k(3. 3.1.1Gb)
4nr 3W (3.3.1.10c)v f (z, - z, w w k k-1
and where
T _ are the conductances for flow at the well bore (m-s). Wr
For the node at the top of the well-screen interval, k=&TT> the dis
cretized, augmented flow equation (2.4.1.13) becomes:
* c326Tm + c316wm = -
+ r-direction dispersive terms; (3.3.1.11)
where
Q is the specified volumetric flow rate of the well (positive is
injection to the aquifer) (m3 /s).
In the case of specified pressure at the well datum, equation 3.3.1.11
is replaced by:
= PMJ (3.3.1.12)
127
The well-bore velocity and friction factor are calculated explicitly at
the beginning of the time step. Since the friction factor is a weak function
of velocity, this causes no instabilities. Evaluating the well-conductance
factors explicitly is consistent with the treatment of the aquifer-conductance
factors.
3.3.2 The Well-Riser Model
The well-riser calculation is done by numerically solving equation
2.4.2.11. These ordinary differential equations are integrated using the
midpoint method with rational-function extrapolation, developed by Bulirsch
and Stoer (1966) and presented by Gear (1971, p. 96).
The following algorithm is applied to the well-riser calculations:
- Prk + F("rk' Trk' V ' (3.3.2.1.)
= Trk + 6("rk' Trk' V ' (3.3.2.1b)
, T*, A, + 2% ) ; (3.3.2.1c) j r j k 2 '
AOT vj.1 = T w + MG(p*, T*, H, + ~) ; (3. 3. 2. Id) rk+1 rk ^r* r' k 2 '
whereM = JL ., - £, . (3.3.2.1e)
Boundary conditions are:
at k = 0 ; p . = p° ; T . = T° ; p = p° (3.3.2.2a,b,c)7 i v*ly * v» ' *»l^ * ' * V* ' V* / / *
128
The pressure at the well datum used in evaluating equation 3.3.2.2a for
production conditions is explicitly calculated at time plane n. Equations
3.3.2.1a-d are integrated over the length of the well riser, L , yielding the
desired quantities p (L ) and T (L ). The functions F and G are evaluated by
the right-hand-side of equation 2.4.2.11 with the following equations used for
calculating density and velocity:
p = p° + p° P (p -p°) - p^CT -T°) ; (3.3.2.3a) rr rr r r p r *r r rrT r r
P°Q' (3.3.2.3b)
The midpoint method of integration is a second-order method, which means that
the error in p (L ) and T (L ) decreases as (M) 2 . The extrapolation
procedure improves the accuracy of the numerical integration by estimating
results for p (L ) and T (L ) that would be obtained if the step length, M,
were reduced to zero. Pressure and temperature at the end of the well riser
are expressed by power-series expansions as a function of step length along
the riser:
where
Pr (Lr ,M) = Pr (Lr ) +1 d M Z1 (3.3.2.4a)i = 1 p
2i = T (Lr ) +1 dTi M (3.3.2.4b)i = 1
d . are the coefficients in the series expansion for
pressure (Pa/m); and (3.3.2.4c)
d_. are the coefficients in the series expansion for
temperature (°C/m). (3.3.2.4d)
129
Equations 3.3.2.4a and 3.3.2.4b can be written in vector form by
defining:
Vf T A 0 ^ "" r '
y. = id .Pi
.V
P (L ,M)r r r'T (L ,M) r r'
so that: my(L ,M) = y(L ) + I y
i = 1
,2i
(3.3.2.5a)
(3.3.2.5b)
(3.3.2.6)
The right-hand-side of equation 3.3.2.6 is approximated by a rational
function, R , that is, a quotient of two polynomials. The coefficients of the
rational function are determined so that:
,M..) ; j = 0,1... m (3.3.2.7)
where
M . is the spatial-step length for the jth integration from 0 to L (m) .
Then, the desired solution, V (L) , is related to the approximating
rational function by:
y(L ) = R (L ,0) - r' m r* (3.3.2.8)
The algorithm is formed by defining £J (M) as the rational approximation
which agrees with y(L ,M) at M = M., M.+., ..., A£. + , where M.>M. ,* jj j*" jj^
and defining fij (0) = R* . Then the R^ give better approximations to Y(L ) as j m m m r
and(or) m increase. The extrapolation procedure is initiated by integrating
equations (3.3.2.1 a-d) for a sequence of step lengths, L/2, L/4, L/6, L/8,
... to obtain values for R°, R 1 , R 2 , .... Values of R^ for increasing jo o o m
130
and m are calculated by the recurrence relation given in Gear, 1971, p. 95.
m k The procedure is terminated when two successive approximations, R. and
R, , are sufficiently close. The tolerance estimate for the fractional
error can be set by the user with a default value of 10~ 3 .
Depending on the rate of convergence, the step size may be increased or
decreased for successive well-riser calculations. Sixth-order polynomials are
the maximum order used for the rational approximation with a maximum of 10
different step sizes.
3.4 BOUNDARY CONDITIONS
All boundary conditions are specified on a cell-by-cell rather than on a
zone-by-zone basis. The default-boundary condition is that of no dispersive
or advective flux through the boundary faces of the cell. For a cell with
three boundary faces, up to three different types of flux-boundary conditions
can be applied, each to a different face. For example, a specified flux, an
aquifer-influence function, and a leakage-boundary condition could be applied
to the faces of a corner cell.
3.4.1 Specified Pressure, Temperature, and Solute-Mass Fraction
Specified-value boundary conditions are incorporated by replacing the
flow and transport equations for those nodes, by equations of the form of
equation 3.1.1c defining the specified values. These nodes could be removed
from the set of simultaneous equations to be solved, by incorporating the
known boundary values into the remaining equations; that has not been done in
the present version of the HST3D simulator. For boundary conditions that
change discontinuously with time, the value at time t is taken to be the
limit of the value at t - 6t, as 6t -> 0; that is, the jump in the boundary-
condition value takes place after the time of change. This means that the
effective value of a boundary condition over a time interval when a change
occurs is the average value under centered-in-time differencing and the later
value under backward-in-time differencing.
131
It should be noted that an initial hydrostatic-pressure boundary condi
tion over depth will not be maintained under conditions of variable-density
flow. Specification of hydrostatic-pressure boundary conditions over depth
using a uniform initial density can cause disconcertingly large vertical flows
to occur, when realistic fluid compressibility effects are incorporated during
the simulation. Even if the compressibility is very small, the boundary
pressure values need to be specified to four or five significant digits to
avoid vertical flows caused by roundoff error.
Since a specified-value boundary condition removes the equation for the
corresponding variable (pressure, temperature, or mass fraction) from the set
to be solved, some constraints do exist on what boundary conditions can be
specified for a cell that has more than one boundary face. For example, if
the pressure is specified, then the ability to specify a fluid flux, an
aquifer-influence function, or a leakage boundary condition on the other
boundary faces is lost.
3.4.2 Specified-Flux Boundary Conditions
Discretization of the flow equations and transport equations causes the
specified-flux boundary conditions to be incorporated as source terms in the
finite-difference equations, as described by equation 3.1.1.25a and b. The
specified fluxes are input as vector components at each of the respective
boundary faces. Thus they are described on a cell-face basis, not by zone
boundary. Fluid fluxes are input as volume fluxes; heat fluxes are input as
energy fluxes; solute fluxes are input as mass fluxes.
Recall that a boundary cell can have up to three boundary faces, each
with an outward normal vector pointing in one of the coordinate directions.
The flux-vector components can specify flux only through a face whose normal
is parallel to the vector component. Thus, the number of specified-flux
vector components must be less than or equal to the number of boundary faces
for a given cell. If the normal and the vector component point in opposite
directions, flux is added to the boundary cell; if they point in the same
direction, flux is withdrawn.
132
A persistent numerical error can arise in the case where only specified-
flux boundary conditions are employed for the entire region, because of the
occurance of a zero eigenvalue for the discretized equation (Mitchell, 1969,
p. 39-44). Errors generated by discontinuous changes in the boundary condi
tions with time or by discontinuities between the initial conditions and the
boundary conditions will persist. If a specified-value boundary condition or
flux-dependent-on-value boundary condition is applied over some part of the
boundary, this problem vanishes, because the zero eigenvalue disappears.
A one-dimensional analysis shows that the integral form of derivation
used for the specified-flux boundary conditions gives a discretization error
of order AtAx. Thus, the finite-difference equations are only first-order
accurate at the boundary cells in terms of specified flux.
3.4.3 Leakage-Boundary Conditions
Leakage-boundary conditions are transformed into source-sink terms in a
» similar fashion to specified-flux conditions. They also are incorporated on a
cell basis rather than on a zone basis. Equations 2.5.3.1.1a-c and
2.5.3.2. la-c, when applied on a discrete grid, become for boundary cell, m:
- (" + P (3.4.3.1.)Lm Lm
Zm)/21 SBLm
~UT bT BLm Lm Lm
(3.4.3.1W
133
where
Q_ is the volumetric flow rate at a leakage boundary (m3/s);
Qj, is the volumetric flow rate at a river-leakage boundary (m3/s); and
S-_ is the part of the boundary cell surface that is a leakage cLiinboundary (m2 ).
The leakage-flow rate, of equation 3.4.3.la, has an explicit term for the
right-hand-side of the discretized system-flow equation, 3.1.4.la, and an
implicit factor for the left-hand-side.
3.4.4 Aquifer-Influence-Function Boundary Conditions
3.4.4.1 Pot-Aquifer-Influence Function
The aquifer-influence-function boundary conditions for a pot aquifer are
discretized by writing equation 2.5.4.1.1 for each cell face over which the
pot-aquifer boundary condition applies. Let there be M. pot-aquifer boundaryA
condition cells. Then:
Q A = t«v + e P ) -JE?5 V , m = 1, MA ; (3.4.4.1.1) j(Vm be e^pe ot em' ' A '
where
6pTQ
£- is the rate of pressure change at the boundary of the inner
region for cell m (Pa/s);
V is the volume of the outer-aquifer region that influences em ie
boundary cell m (m3 ); and
QA is the volumetric flow rate across the boundary face for cellJnJu
m between the inner- and outer-aquifer regions; (positive
is into the inner region), (m3 /s).
134
The volume of outer aquifer that influences boundary cell m usually is
taken to be the permeability-weighted fractional area of the boundary face:
V I k S A e 1 mpq AmpqV = rr-3^ 7 '» (3.4.4.1.2) em MA n 4 A p
I I I k S A111 mpq Ampq m=l p=l q=l *H ^H
where
S. ia the area of the aquifer-influence function boundary face
for cell m, face p, sub domain q (m2 ); and
k is the permeability for cell m, face p, subdomain q (m2 ).
This aquifer-influence-function flow rate gives only an implicit
coefficient for the left-hand-side of the flow equation, 3. 1.4. la.
3.4.4.2 Transient-Flow Aquifer-Influence Function
The transient-flow, aquifer-influence function is discretized by writing
equations 2.5.4.2.6a-b for each cell at which this boundary condition applies.
Thus, a different pressure history may occur at each boundary node. The
aquifer-influence-function flow rate must be suitably apportioned among the
boundary cell faces. The method used for HST3D is to make the fraction of the
total flow rate that is apportioned to a given boundary cell the same as the
ratio of that boundary-cell facial area to the total boundary facial area
between the inner-and outer-aquifer regions. For cases where the inner-
aquifer region is strongly heterogeneous, apportionment by the product of
hydraulic conductivity and facial area, using equation 3.4.4.1.2, would be
more realistic. This would require modification to the program code.
The derivation of the flow rate given by equation 2.5.4.2.6a also was
based upon a uniform pressure plus gravitational potential over the approxi-
135
mating cylindrical interface. A finite-difference flow simulation in the
inner-aquifer region will yield a nonuniform distribution of pressures at the
boundary nodes, except in special cases. In the numerical implementation of
this aquifer- influence- function calculation, the pressure at each interfacial
boundary node is taken to be the value computed by the discretized simulation
calculation. This introduces an additional approximation, because any lateral
or vertical flow in the outer-aquifer region, induced by the nonuniform
pressure plus gravitational potential distribution over the interfacial
boundary, is neglected.
Another approximation used is that the boundary between the inner- and
outer-aquifer regions is represented by a cylindrical interface (fig. 2.5a);
whereas, the actual boundary is a set of rectangular faces for the finite-
difference discretization in cartesian coordinates of a three-dimensional,
inner-aquifer region. In contrast, a two-dimensional, cylindrical gridding
for the inner-aquifer region would have an exact cylindrical boundary. For a
cartesian-coordinate system with the x-y axes horizontal, the equivalent
radius, r_ , for the approximate interfacial boundary is calculated, so that
the rectangular area and the equivalent circular area are the same; that is:
(3.4.4.2.1)
Equation 3.4.4.2.1 will be a poor approximation for long, slender
rectangular areas in the x-y plane. For boundaries between the inner- and
outer-aquifer regions that do not completely surround the inner aquifer
laterally, the apportionment factor YA > must contain an angle-of -influence
factor, fA . Then:D
* = f*S A (3.4.4.2.2) Am 6 Ampq ;
whereSAmpq is the area of the aquifer-influence function boundary
face for cell m, face p, subdomain q (m2 ); and
fn is the angle-of-influence factor for the simulation regionD
136
This factor is the fraction of a full circle that the boundary between
the inner- and outer-aquifer regions subtends. For example, an outer-aquifer
region that surrounds half of the inner-aquifer simulation region (fig. 2.5b)
would have an angle-of-influence factor of \.
The Carter-Tracy approximation is used to avoid successive recomputation
of the convolution integral that gives the flow rate at the transient aquifer-
influence-function boundary. After discretization of time, the expression for
the flow rate across the boundary between the inner-aquifer region and the
outer-aquifer region is [Kipp (1986)]:
27lk b e e
M*
""no Um m dt
4.1 dPTT p' n+1 - U
_ U dt
n+1
27lr?(a, I be
w11m
+ 6 P )b e rpe e + 6p rm
n+1 ,nn+1
(3.4.4.2.3)
The Carter-Tracy approximation is based on representing the continuous
flow rate of equation 2.5.4.2.6a by a discontinuous sequence of constant flow
rates so that the cumulative net inflow from the start of the simulation to
the given time is the same for the convolution integral and the current
constant-flow rate. This approximation is exact for constant-flow rates.
Therefore, slowly varying flow rates are more accurately handled by the
Carter-Tracy approximation than rapidly varying ones. The major disadvantage
of the Carter-Tracy approximation is the inaccuracy of the computation of the
discretized flow rate in the case where boundary-flow rates vary with time.
Effects on the computed-flow rate appear as a significant time lag and
smoothing of transients. Errors can be serious for boundary-flow rates whose
variations are large relative to the average value.
Note that the computer storage requirements for this calculation are only
the cumulative flow, W11 , the pressure at the end of the nth time step, p , and
137
the flow-rate allocation factor, y. > f°r each node on the boundary between
the inner- and outer-aquifer regions. The values of p are from the flow
simulation, so the additional storage amounts to only two times the number of
AIF boundary nodes.
Equation 3.4.4.2.3 is of the form:
= Sl (t') + a2 (t') 6pm ; (3.4.4.2.4)
where a, is the known flow rate term added to the right-hand side of the
discretized flow equation for node m; and a« is the implicit term added to the
left-hand side factor.
The values of P '(t') and _U are obtained usually from tables by inter-dt
polation. Values of the dimensionless pressure function in response to a
unit-withdrawal flow rate at the AIF boundary have been tabulated by Van
Everdingen and Hurst (1949) for the infinite cylindrical region and for
regions with a finite outer-boundary radius.
However, it is much more convenient to use the approximate analytical
representation developed by Fanchi (1985). He employed linear regression
analysis to obtain the following equation that approximates the Van Everdingen
and Hurst (1949) aquifer influence functions with very small errors. In the
notation of this report;
P '(O = bQ + Jb. t' + />2 Jfcn(t') + Z>3 An (t') (3.4.4.2.5)
Table 3.2 adapted from Fanchi (1985) contains values of the b. coefficients
for several cases. The first line gives the coefficients for the analytical
approximation to equation 2.5.4.2.5b for the case of an infinite outer-aquifer
region. The subsequent lines are for various values of R for the case of a
finite outer-aquifer region with no flow at the exterior boundary, where R is
the ratio of exterior to interior radius for the outer-aquifer region.
138
As with the previous boundary conditions, the heat- and solute-advective
transport rates across the AIF boundary are calculated by multiplying the flow
rate by the appropriate density, enthalpy, and mass-fraction values, depending
on the direction of flow.
Table 3.2 Coefficients for the analytical approximations to the Van
Everdingen and Hurst aquifer-influence functions
R
00
1.5
2.0
3.0
4.0
5.0
6.0
8.0
10.0
-0.82092
-0.10371
-0.30210
-0.51243
-0.63656
-0.65106
-0.63367
-0.40132
-0.14386
3.68X10'4
-1.66657
-0.68178
-0.29317
-0.16101
-0.10414
-0.06940
-0.04104
-0.02649
-0.28908
0.04579
0.01599
-0.01534
-0.15812
-0.30953
-0.41750
-0.69592
-0.89646
-0.02882
0.01023
0.01356
0.06732
0.09104
0.11258
0.11137
0.14350
0.15502
3.4.5 Heat-Conduction Boundary Condition
The heat-conduction boundary condition is a flux-type boundary condition,
with the heat flux dependent on the thermal parameters and the thermal history
at the boundary, and in the conducting medium, which lies outside the simu
lation region. Equation 2.5.5.7 gives the heat flux that is applied on a cell
basis to the source term in the heat-transport equation. Finite-difference
approximations to equations 2.5.5.3a-c and 2.5.5.4a-c are solved at each time
step for each heat-conduction, boundary-condition cell. Central-differencing
in time is used giving a tridiagonal-matrix equation to be solved numerically.
The user specifies the spatial mesh extending out from the boundary into the
conducting medium. Up to 10 nodes are allowed with variable spacing. The
139
first node must be on the boundary. The Thomas algorithm (Varga, 1962,
p. 195) is used to obtain the numerical solutions for T and T,,. Then the
heat flux for cell m is given by:
em
T (z 0 ) - T (z J TT7 (z 0 ) - TT7 (z n ) e n2 e nl U v n2 U nlZn2 - Znl Zn2 - Znl
L S - ; (3.4.5.1) Bm BHCm'
where
z - and z 2 are the first two nodes moving in the outward normal
direction from boundary cell m (m).
Node z - is coincident with the boundary node of the simulation region,
so the boundary temperature is:
TBm = Tm . (3.4.5.2)
Equation 3.4.5.1 is of the form:
Q = a t (t) + a2 (t) 6T ; (3.4.5.3) nL>m m
where the a^(t) term goes into the source term for the cell heat-transport
equation, and the a£(t) term goes into the thermal-coefficient matrix for
cell m. An initial temperature profile can be specified for the
heat-conduction region. However, the same profile is used for all cells with a
heat-conduction boundary condition.
3.4.6 Unconfined-Aquifer, Free-Surface Boundary Condition
The unconfined-aquifer, free-surface boundary condition is implemented by
modifying the pressure-coefficient terms in the discretized equations for flow
and solute-transport, and adjusting the fluid volume or saturated thickness of
i
140
the uppermost layer of cells in the simulation region. A free surface is not
allowed when the heat-transport equation is being solved, because no
satisfactory method has been developed to handle the conductive-heat flux
through the free-surface boundary that moves with time through the unsaturated
porous medium.
The location of the free surface within an upper-boundary cell is estab
lished by linearly extrapolating the nodal pressure to the elevation of zero
(atmospheric) pressure, using the fluid density in that cell. The fraction of
the cell thickness that is saturated is given by:
p ~ >> *» (3.4.6.1)
where
£ -, is the fraction of the cell thickness that is saturated (-); and Jb bp is the pressure at node m (Pa);
ZN is the elevation of the upper boundary (m); and
w - is the elevation of the next layer of nodes down from the upper
boundary (m).
This equation is valid for coordinate systems with the z-axis pointing
vertically upward. Remember that the pressure value is relative to atmos
pheric pressure, so that atmospheric pressure does not appear explicitly in
equation 3.4.6.1. This fraction is allowed to range from zero to two; that
is, the free surface is allowed to rise above the upper boundary of the
simulation region to a distance that is equal to the upper-layer half-cell
thickness. This rise is effectively the same as using full cells in the
vertical direction for the upper layer when a free-surface boundary condition
is being used. The extra cell height allows for a greater variation of the
free surface than is possible with the normal cell height in the upper layer.
When designing the grid for a free-surface boundary problem, the upper
most layer of cells must be made thick enough to accommodate the maximum
141
variations in the free-surface location. With the present algorithm, the free
surface may not drop below the lower boundary of the uppermost layer of cells.
No conversion to confined flow conditions is made if it does rise above the
extended upper boundary. These restrictions can be burdensome if a large
drawdown cone is created by a well pumping an unconfined aquifer, because the
uppermost layer of cells may need to be so thick that vertical gradients are
represented poorly. The present version of the HST3D program is suitable for
simulation of only modest drawdowns relative to aquifer thickness for uncon
fined conditions.
If desired by the user, a message may be printed when the free surface
rises above the extended upper boundary of the region or falls below the
bottom of the uppermost layer of cells, or cells in a lower layer become
partially saturated.
To obtain the appropriate coefficients for the flow equation (3.1.4.la)
at the free-surface boundary cells, we evaluate the terms of equation 3.1.1.8,
this time, including the saturation fraction of equation 3.4.6.1, using
equation 3.1.3.5, and assuming that the porosity is constant, the fluid
compressibility is zero and isothermal conditions exist, to obtain:
8C 33 = t I esVs img(zNz - zNz-l )6tl ' (3.4.6.2a)
s=l
and the coefficient CQI remains unchanged from equation 3.1.4.Id.
Using the same procedure as for equations 3.4.6.2a and 3.4.6.2b, the
corresponding terms for the solute-transport equation (3.1.4.4a) are:
Cn = I (e + pjO V [pn+1 f£+1 + wn p P ]/6t ; (3.4.6.3a) 11 , s Kb d s s Km Fs m Ko^w s=l
142
and
8 wn
: Z 'VPbVs Vs * -'* - - ^ ]/6t ' (3.4.6.3b)_ i 9 LI u a a S=l
Additional terms arise from the source-sink term in the solute equation
that are functions of solute-mass fraction. They form part of the GH and Cj.3
coefficients. It has also been assumed that all of the solute in a cell is
either in the fluid phase or is sorbed on the saturated part of the porous
medium. No account is taken of solute that might sorb onto the porous medium
and be left behind, when the free surface falls. This simplification is
consistent with this approximate treatment of a free-surface boundary con
dition. The other terms in the flow and transport equations have the sat
urated fraction parameter included, as necessary, for the cell facial-area
terms involving the x and y directions. No additional contributions to the
C.. terms occur, because the dispersive and advective coefficients are1J n
evaluated at time t only.
The case of a free-surface boundary with accretion of fluid by infil
tration is also handled in an approximate fashion. The fluid flux is speci
fied at the upper boundary of the cell, and the associated temperature and
mass fraction determine the amount of heat and solute that enter through the
free surface.
3.5 INITIAL CONDITIONS
The numerical implementation of the initial conditions is straight
forward. Values of pressure, temperature and mass fraction are set to the
initial value distributions for each node in the simulation region given in
the form of equation 3.1.1b, that is:
at t=0, u... = u°,., . (3.5.1)
143
The specified distributions can vary on a node-by-node basis or be zones of
constant conditions. Available options for the initial pressure distribution
include hydrostatic equilibrium, a water-table surface, or a pressure field
specified node by node. The water-table surface is specified for the upper
layer of cells only. These initial distributions are based on the initial
temperature and solute-mass fraction distributions.
The hydrostatic-equilibrium pressure distribution takes the fluid com
pressibility into account. The calculation proceeds from the bottom of the
region upward or from the top of the region downward depending on the
elevation of the specified initial pressure.
The water-table elevation surface is specified for the upper layer of
nodes only. Hydrostatic equilibrium is assumed to compute the pressure
distribution elsewhere in the simulation region. When specifying the initial
pressure field on a node-by-node basis, it is permissible to include nodes
that are outside the simulation region. This is for ease of data input by
rectangular zones or by ascending node number.
3.6 EQUATION SOLUTION
Equations 3.1.4.la, 3.1.4.2a and 3.1.4.4a can be written in matrix form
as:
C 12 C 13
C 21 C22 C 23
6wm
6Tm
6pm
EH £ E 13
.0 E23 E2 3
0 0 E 33
6w m
6T m
(3.6.la)
(3.6.1b)
R<
144
where
E.. are the coefficient vectors in the discretized equations;-ij6p is the change in pressure for node m (Pa);
6p is the change-in-pressure vector for node m (Pa);
6T is the change in temperature for node m (°C);
6T is the change-in-temperature vector for node m (°C);
6w is the change in mass fraction for node m (-);
6w is the change-in-mass-fraction vector for node m (-); and
F. are the known terms at time n in the discretized system equations.
The vectors of the changes in the dependent variables contain the values
for each node connected to node m plus node m itself. The E vectors in
equation 3.6.la have seven components each that correspond to node m and its
six neighbors in the three coordinate directions. The known terms F. are those
that do not contain 6w for i=l, 6T for i=2, or 6p for i=3. The terms E. and~~"iF. can be functions of pressure, temperature, and mass fraction at time n
which gives explicit linking of the three equations. Implicit linking is
through the £ matrix on the left-hand side. The equations are written in
reverse order to what has been done previously, with 1 referring to the
solute-transport equation, 2 referring to the heat-transport equation, and
3 referring to the flow equation. Equation 3.6.1b is written for each node
in the simulation region, giving a set of 3M simultaneous equations to be
solved for the unknown vectors, 6p, 6T and 6w, where M is the total number
of nodes in the region.
3.6.1 Modification of the Flow and Transport Equations
To avoid storing a 3M x 3M matrix and vectors of length 3M, a sequential
solution scheme has been developed by Coats and others (1974) and was used by
INTERCOM? Resource and Development and Engineering, Inc. (1976). This
algorithm consists of solving a modified flow equation then a modified
heat-transport equation, then the solute-transport equation in turn for each
time step. The modified equations are obtained by a partial Gauss reduction
145
of equation 3.6.1b transforming the capacitance matrix, £, into upper-
triangular form. Thus we have:
where
12
0 C22 ^23
0 0 C33 '
6wm
6T m
6p rm
=
"l 0 o"
C24 1 0
C34 C35 1
"»r
R2
R3
C 12C 2 i
(3.6.1.la)
23 = ^
C 13C2123 11
(3.6.1.Id)
C = . 34 - C 12C2 i) * (3.6.1.If)
r - 35 C22Cn - C 12C21
3.6.2 Sequential Solution
The finite-difference approximations (equation 3.6.1.la) to the ground-
water flow, heat transport, and solute transport equations are solved se
quentially. First, the flow equations are solved for the pressures. Then the
146
pressures are used to update the coefficients in the heat equations and back
substitute for the 6p terms on the left-hand side. Second, the heat equations
are solved for the temperatures. The temperatures and pressures are used in
the solute equation to update the coefficients and to back substitute for the
6p and 6T terms on the left-hand side. Finally the solute equations are
solved for the mass fractions, which completes an iteration. Thus only M
equations at one time are being solved with a coefficient matrix that is M x M
in size. M is the total number of active nodes in the simulation region.
Actually the storage requirement is reduced by taking advantage of the matrix
sparsity as will be described later. The solution cycle is repeated until
convergence is achieved, that is, when the fractional change in fluid density
in each cell is less than a tolerance value. The default value is 0.001
fractional change in density. Since changes in both temperature and mass
fraction cause changes in density, a secondary tolerance criterion is set to
determine whether the heat equation or the solute equation or both equations
must be solved again. The secondary tolerance is 0.0005 fractional change in
density. If the maximum density change due to temperature changes after
solution of the heat equation or due to mass-fraction changes after solution
of the solute equation is less than the secondary tolerance, then that equation
is excluded from the iterative cycle for the remainder of the calculations for
that time step. However, a final solution of the excluded equation is per
formed after convergence of the iterative cycle for the two remaining equa
tions. In practice, convergence is usually achieved within three iterations
for a given time step. Lack of convergence may indicate that the time step is
too large.
Equation 3.6.1.la is transformed into:
A 6u = b ; (3.6.2.la)
where
6u = 6w
6T
6P-J
(3.6.2.1b)
147
by shifting all the terms on the right-hand side that contain 6p, 6T or 6w to
the left-hand side. Equation 3.6.2.la is a linear-matrix equation for the
region that can be solved using techniques to be described in section 3.7.
3.7 MATRIX SOLVERS
The linearized flow and transport finite-difference equations are solved
in turn by one of the solution algorithms for linear, sparse-matrix equations.
For the present version of the simulator, two such algorithms are available.
One is a direct equation solver that uses Gauss elimination, after reordering
the equations for a savings in computation time and computer-storage require
ments. Alternating diagonal planes are used for the reordering. This method
is referred to as the D4 solution technique; it was developed by Price and
Coats (1974).
The other sparse-matrix equation solver uses the two-line, successive-
overrelaxation method. This is one of a class of block-iterative methods
described by Varga (1962, p. 199-200). In this solver, two lines of nodes
along a selected coordinate direction are solved together by direct elimin
ation. One iteration sweep consists of solving for the nodal values for each
pair of lines, plus the odd left-over line, if necessary. Overrelaxation is
used to speed convergence, and the optimum overrelaxation factor is estimated,
using the eigenvalue estimation technique of Varga (1962, p. 284-288) at the
beginning, and then, every n time steps, as specified by the user. In the
process of estimating the optimum-overrelaxation factor, the solution is
tested in all three coordinate directions, and the direction with the best-
conditioned iterative matrix is selected. It may be different for each of the
three equations.
The form of the equations to be solved is the same as equation 3.6.2.la,
but now the matrix A is a sub-matrix of the original one, containing the
coefficients of only the flow, or heat transport, or solute transport
equations. Matrix A has the banded structure under the original nodal
numbering scheme, where the index i is incremented first; the index j is
148
incremented second; and the index k is incremented third. Figure 3.7 shows
the structure of the matrix A, with the bandwidths given by N N and N where-* e J x y zN. is the number of nodes in the ith direction. The rectangular prism of
nodes also is shown in figure 3.7, which encompases the entire simulation
region.
3.7.1 The Alternating Diagonal, D4, Direct-Equation Solver
The alternating diagonal reordering scheme was developed by Price and
Coats (1974). In three dimensions, the equations are grouped by diagonal
planes of nodes. A plane is defined by a fixed sum of the nodal subscripts,
designated by the index, m, so:
i+j +k=m; m=3,4..., M ; (3.7.1.la)
where M = N + N + N x y z
If M is even, then the order of plane-index selection for reordering of the
node numbers should be m = 3,5,7,...M-1,4,6,8...M. If M is odd, then the
order should be m = 3,5,7,...M,4,6,8,...M-l. For each plane index, m, the
points should be numbered in order of decreasing k, decreasing j, and in
creasing i, assuming N >N >N . Any excluded cells are skipped during the nodea y z
renumbering. The matrix A under D4 ordering takes the form shown in
figure 3.8. This matrix can be partitioned as shown, so
~4i
4a
^r44
6uj
6U2
ki""
b 2
(3.7.1.2)
149
1
2
3
4
Nx + 1
.
N X N Y +1
.
N X N Y N Z
XX X X
XXX X X
X X ' .
"... x
' . x
'.'.'. x
X ' . X
x . ' . x
x ' .
x '.'.'.'.XX
X X XXX
X X XX
MATRIX STRUCTURE
RECTANGULAR PRISM OF NODES
Figure 3.7. Sketch of the matrix structure and the rectangular prism of
nodes of the flow or heat-transport, or solute-transport equation
in finite-difference form.
150
XX XX
XXX ' X
X * . ' .
' . ' . x
x t' . ' . x
x xxx
_____ ' . I xx xxX X I X X
xxx
X ' .
' . . xx t xxx
XX XX
Figure 3.8. Sketch of the matrix structure with the D4 alternating-
diagonal-plane, node-renumbering scheme.
where
Ai and &4 are diagonal and Aa and As are sparse matrices
Forward elimination gives:
42 (3.7.1.3)
6U
151
where
44' is a band matrix with a maximum bandwidth which is the same as for
the original matrix A-
The solution for 6u£ is obtained by standard Gaussian elimination. Back
substitution is used to compute 6u^ by:
6m = Ai 1 b t - Ai^&i*. (3.7.1.4)
The work required with the D4 reordering is from 17 to 50 percent, and the
storage is from 33 to 50 percent of that using standard ordering. When the
D4 ordering is selected with direct Gaussian elimination, the renumbering is
entirely transparent to the user. The storage requirement for the A4 matrix
is minimized by employing variable bandwidth storage ( Jennings , 1977, p. 97).
The matrix is stored by rows, with the length of each row being sufficient to
accommodate the fill-in that occurs during elimination. Two pointer arrays
are necessary: one that contains the indices of the diagonal elements, and the
other that gives the bandwidth to the right of the diagonal. The next row
begins in the location just after that specified by the diagonal-element
location, plus the right-side bandwidth.
3.7.2 The Two-Line, Successive-Overrelaxation Technique
This iterative matrix-equation solution technique, abbreviated L2SOR, is
a block successive-overrelaxation algorithm as described by Varga (1962, sec.
6.4) or Jennings (1977, p. 202). Equation 3.6.2.la for only the flow or heat
transport or solute transport equation may be written with a partitioned A
matrix (fig. 3.9) as:
152
fil Si
L2 £2 M
\\\11T .\ \ L-l
(3.7.2.1)
where the sparse submatrices P, are penta-diagonal and the submatrices L, and
II, are diagonal (fig. 3.9). There are L pairs of mesh lines with the last setK
containing only the odd remaining line, if one exists. These matrices are of
size 2N X 2N , where the nodes have been numbered in the normal way. and thex x' J '
two lines have been selected to be in the x-direction. Some rearrangement
would be necessary, if the y or z-directions were selected, but the basic
structure would be the same. Then the iterative technique is expressed by the
following equations:
[P.* + ufc.]6u. V+1= [-u>U + (l-u>)pJ6u V+ u>b ; £ = 1, 2...L ; (3.7.2.2) X> X> X> X, X, Xr Xr
where
V is the iteration counter; and
U) is the overrelaxation factor.
Direct elimination is used to solve equation 3.7.2.2, after a renumbering
is performed transverse to the direction of the two-lines. This renumbering
compresses the bandwidth so no fill-in occurs. The iterations could be
terminated when a vector-difference norm is less than a specified tolerance
(Jennings, 1977, p. 184). That is, when:
153
x j x. " " J
E LINE OF NODES
TWO LINES OF NODES
x xX
x
fe2 j- U2
Figure 3.9 Sketch of the matrix structure with the two-line, successive-
over relaxation, node-renumbering scheme.
max mx x ou - oum m
6uv+1
m= (3.7.2.3)
m
where
specified tolerance; and
m is the node number.
An alternate termination criterion is from Remson and others (1971,
p. 185). Properties of the iteration matrix are taken into account by
terminating the iteration when:
ur- x ou - oum m <
ur 6u
i o M ; m = 1, 2...M ; (3.7.2.4a)
mwhere
R(L ) is the spectral radius of the SOR iteration matrix.
154
Now from Varga (1962, p. Ill):
R(V = "opt - * (3.7.2.4D)
where
U) . is the optimum overrelaxation factor.opt *
This alternate criterion is used in the HST3D simulator. The tolerance,
SOR 1ecnp , is set to 1 x 10 by default, but it may be changed by the user.
The optimum overrelaxation factor is determined from estimates on the
eigenvalues of the associated block Gauss-Seidel matrix. This is a combina
tion of the power method and Perron-Frobenius theory of nonnegative matrices,
presented by Varga (1962, p. 283-288). The algorithm is as follows: A
two-line, Gauss-Seidel solution of the matrix equation:
4 6u = 0 ; (3.7.2.5a)
is performed with a starting vector of unit components, that is,
^+1 = [B£ + ^J" 1 l "^]^ ; A = 1, 2... L (3.7.2.5b)
with 6u° = [1] . (3.7.2.5c)
Then the minimum and maximum estimates of the dominant eigenvalue for
A. are:
* v+1 ou.
v = mm _i (3.7.2.6a) mm i « v ' 6u.
155
A V+lou.and X V = max ^ ; (3.7.2.6b) max i £ \? '
6u.i
which satisfy
A U < X r1 < RU.,) < X V+1 < X W ; (3.7.2.6c) mm mm max max
where
is the spectral radius of the Gauss-Seidel iteration matrix,
Now, since:
- * (3.7.2.7)
let"min = \T 3* ; (3.7.2.8a)
min
and
- ! (3.7.2.8b)max 1 + 1 - X
max
Then it can be shown that for the matrices, 4> that arise from the
finite-difference equations, which are diagonally dominant and irreducible
(Varga, 1962, p. 177):
I
156
\> \>+l \>+l V).<u>. <u) J <u) < u> ; (3.7.2.9)mm mm opt max max '
where
to is the optimum overrelaxation factor.
For 4 nonsymmetric, the mesh spacing must be sufficiently small to ensure
diagonal dominance. One requirement for irreducibility is that equations for
nodes with specified value boundary conditions are eliminated from the set
that forms & This elimination is not done in the present version of HST3D,
and this sometimes causes difficulties in calculating u> ., because aoptreducible matrix can have a maximum eigenvalue that is zero. The eigenvalues
of the Gauss-Seidel iteration matrix must be real and nonnegative for the
optimum-overrelaxation-factor calculation formula, equation 3.7.2.7, to apply.
The iterations are terminated when:
max min < 0 2
max
This algorithm provides an estimate of the optimum overtaxation factor
with rigorous upper and lower bounds before the iterative solution scheme is
begun. Since the matrix 4 changes with time, recomputation of the estimate of
u> is performed every n time steps, as set by the user (default is 5). The
power method algorithm converges when the dominant eigenvalue of A is real,
and it converges more quickly the smaller the ratio of the second dominant
eigenvalue to the dominant eigenvalue. The convergence rate to u> can be
discouragingly slow when this ratio is near one.
157
3.7.3 Choosing the Equation Solver
The choice of equation solver depends on the size of the problem and the
rate of convergence of the iterative method. The minimum half bandwidth of
matrix A. is the product of the two smaller numbers of nodes. N , N , and N . x' y zFor a half bandwidth of 50, the work of the direct D4 solver is equivalent to
about 68 iterations of the L2SOR solver (Price and Coats, 1974). The other
consideration is the greater storage requirement of the D4 method, because of
the pointer arrays required and the partial fill-in of the A.4' matrix that
occurs. The L280R method causes no extra fill-in of nonzero elements in the A.
matrix; however, rapid convergence rates are highly dependent on calculation
of an accurate optimum overrelaxation factor. It is difficult to give any
general rule for selection of matrix solver. Storage requirements probably
will determine the best choice. The HST3D program writes out the storage
requirements for both methods at the beginning of the simulation.
. 3.8 GLOBAL-BALANCE CALCULATIONS
Global balances for fluid mass, enthalpy, and solute mass are calculated
at the end of each time step. Cumulative totals as well as increments over
**ch -time stejv are computed. The primary use of the global-balance cal
culations is to aid in the interpretation of- the magnitudes of transport that
are occurring in the simulated system, and their distribution among the
various types of boundary conditions and sources. Each of the system equa
tions represents a mass or energy balance over each cell. By summing over the
cells, we obtain the global-balance equations that relate the total change of
mass or energy to the net boundary flow rates and the net injection through
wells. The solute balance includes sorption and disappearance by reaction.
The global-balance equations are integrated over the current time step to
obtain the incremental changes.
The fluid-flow, heat-flow, and solute-flow rates at specified-value
boundary nodes are obtained by evaluating the appropriate system equation at
each specified-boundary-value cell and computing the flow of fluid, heat, or
158
solute across the region boundary for that cell, necessary to satisfy the
fluid-balance, heat-balance, or solute-balance equation. Heat and solute
fluxes that result from cross-derivative terms are neglected for the heat-
balance and solute-balance equations for specified temperature and specified
mass-fraction cells. The temporal differencing method is taken into account,
also. This means that, for example, if the specified boundary pressure
changes over a time step, and centered-in-time differencing is used, then the
pressure at the beginning of the time step is effective over the first half of
that time step, and the pressure at the end of the time step is effective over
the second half. Therefore, the flow rate induced by the new specified
pressure is effective for only half the time step. The appropriate equation
for the boundary-flow rate calculation is the flow equation for specified-
pressure boundary cells, the heat-transport equation for specified-temperature
boundary cells, and the solute-transport equation for specified-mass fraction
boundary cells. Thus, the cell-balance equations are satisfied exactly for
specified-value boundary cells.
The fluid, heat, or solute residual is defined as the change in the
amount of the quantity present, minus the net flow of that quantity into the
region. Thus, a positive residual means that there is an excess of that
quantity present over what would be expected based on the net flows over the
time interval. The various flows, amounts present, and residuals are printed
in tabular form. Fractional residuals are defined as a ratio of the residual
to the larger of the inflow, outflow, or accumulation. The utility of the
fractional residuals is not great. It is more informative to look at the
residuals relative to the various flows and accumulations in the region.
A mass and energy balance with a small residual is necessary but not
sufficient for an accurate numerical simulation. Because the system equations
are a balance for each cell, and the method used for calculating the flows at
specified-value boundary condition cells insures that the residual will be
zero for those cells, and because the fluxes between the cells are conserva
tive, errors in the global-balance equations will result from the following
causes: (1) The approximate solution from use of the iterative-matrix equa
tion solver; (2) the degree of convergence on density of the iteration on the
159
solution cycle of the three system equations; (3) the explicit treatment of
the cross-dispersive flux terms; (4) the explicit and iterative treatment of
well flow rates; and (5) roundoff error in special cases, such as wide
variation in parameter magnitudes. Errors caused by discretization in time or
space will not be revealed by these global-balance calculations. However, the
inaccuracies resulting from too-long a time step under conditions of signifi
cantly nonlinear parameters will be evident. Significant nonlinearity can be
caused by large variations in the density and viscosity fields, for example.
160
4. COMPUTER CODE DESCRIPTION
4.1 CODE ORGANIZATION
The HST3D computer code is written in FORTRAN 77. Only code conforming
to American National Standards Institute (ANSI) standards (American National
Standards Institute, 1978) has been used to maximize program portability. The
present version of the program code consists of a main routine and 49 sub
routines. The program length is approximately 12,000 lines of code. Many
FORTRAN statements occupy multiple lines. The following is a list of the
routines and a brief description of their function:
HST3D - Main routine that drives the program execution. The basic steps
are: (1) Read, error check, initialize, and write output for
space allocation; (2) read, error check, initialize, and write
output for static or time-invariant information; (3) read, error
check, initialize and write output for transient information;
(4) start the time-step calculations by calculating flow- and
transport-equation coefficients, applying the boundary conditions,
calculating the source-sink well terms; (5) perform the assembly
and solution of the three equations in turn, iterating to
convergence; (6) perform the summary calculations; (7) write the
output information for the time plane; and (8) dump restart data
to a disc file if desired. Then return to step 4 and continue
until the time for a change in boundary conditions or source
terms occurs. At this time return to step 3. Continue until the
simulation is finished. Then (9), plot dependent variables as a
function of time if desired; and (10) close files and terminate
program execution.
The following subroutines are described in their order of execution:
READ1 - Reads the data pertaining to allocation of computer storage space
for the problem.
161
ERROR1 - Checks for errors in the data read by READ1.
INIT1 - Initializes the spatial-allocation data, including the pointers ^
for the two variable-partitioned arrays. If necessary, sets the
inch-pound-to-metric conversion factors and their inverses, and sets
the unit labels.
WRITE1 - Writes to a disc file information about the storage allocation and
array-size requirements.
READ2 - Reads the data pertaining to all the time invariant or static
information, including fluid and porous-media properties,
grid geometry, equation-solution method, and desired output.
ERROR2 - Checks the data read by READ2 for errors.
INIT2 - Initializes the calculated static data for the simulation.
WRITE2 - Writes the static data to a disc file. gl
READ3 - Reads the transient data, including boundary condition and
source-sink information, plus time-step, calculation, and
printout information.
INIT3 - Initializes the calculated transient data.
ERROR3 - Checks the transient data read by READ3 for errors.
WRITE3 - Writes the transient data to a disc file.
COEFF - Calculates the coefficients for the flow-, heat- and
solute-transport equations, and adjusts the automatic time step
if selected. These coefficients include conductances, dispersion
coefficients, and interstitial velocities.
162
WRITE4 - Writes the coefficients to a disc file as desired.
^ APLYBC - Applies the boundary conditions to the set of equations.
WELLSS - Calculates and applies the well source-sink terms.
ITER - Assembles and solves the three equations iteratively for a given time
plane.
SUMCAL - Performs the summary calculations at the end of a time step. This
includes flow, heat, and solute-mass balances, and flow rates.
WRITES - Writes to a disc file the desired information at the end of a time
step. This may include pressure, temperature, and mass-fraction
distributions, interstitial velocities, fluid viscosities, fluid
densities, and summary tables of flow rates and balances of flow,
heat, and solute mass.
^ DUMP - Dumps restart information to a disc file, if desired.
PLOTOC - Creates character-string plots of selected dependent variables
(pressure temperature, or solute-mass fraction) as a function
of time at the end of the simulation, and plots observed data
if desired.
CLOSE - Closes files, deletes unused files, prints the total simulation time
and the number of time planes, the number of restart and map records
written, and any error messages.
The following subroutines are listed in approximate order of execution. Some
are called from several routines, and some are optional.
ORDER - Determines the node numbering for the D4 reordering scheme for the
direct-matrix equation solver.
163
REWI - Reads, error checks, echo writes, and initializes array elements
that are input as zones of constant values over a rectangular
prism of cells, or are input as node by node distributions.
REWI3 - The same as REWI, but for parameters that occur in sets of three,
such as vectors or principal components of tensors.
IREWI - The same as REWI, but for parameters that are integers.
VSINIT - Calculates parameters for the viscosity function.
ETOM1 - Converts static data from inch-pound units to metric units.
ETOM2 - Converts transient data from inch-pound units to metric units.
PRNTAR - Writes one-dimensional or two-dimensional arrays in tabular form
to a disc file.
ZONPLT - Creates two-dimensional maps on the printer of the porous-media
zones contained in the simulation region.
INTERP - Performs one-dimensional or two-dimensional linear or bilinear
tabular interpolation, as required.
VISCOS - Calculates fluid viscosity as a function of temperature and solute-
mass fraction.
TOFEP - Determines temperature as a function of enthalpy and pressure by
tabular interpolation.
WELRIS - Performs the pressure and temperature calculation up or down the
well-riser pipe, using simultaneous solution of the two ordinary
differential equations.
164
ASEMBL - Assembles the coefficients of the modified flow, modified
heat-transport, and solute-transport equations at each time step.
CALCC - Calculates the elements of the change in fluid-mass, change in heat,
or change in solute-mass matrix for a given cell at each
iteration at each time step.
CRSDSP - Calculates the components of the cross-dispersion tensor, that
are evaluated explicitly in the transport equations at each
iteration.
D4DES - Solves the matrix equation, using alternating-diagonal reordering
and a direct Gaussi.an elimination algorithm.
SOR2L - Solves the matrix equation, using a two-line, successive-
overrelaxation algorithm, with the lines oriented in a
selected coordinate direction.
L2SOR - Invokes the two-line, successive-overrelaxation solver for each
coordinate direction to estimate the optimum overrelaxation
parameter, and to solve the equations.
MAP2D - Creates two-dimensional contour maps on the printer of selected
variables with contour intervals divided into zones.
PLOT - Creates plots of pressure, temperature, or mass fraction versus time.
ERRPRT - Writes the error messages for a given simulation to a disc file.
SBCFLO - Calculates the flow rates at specified-value boundary-condition
cells for the global balances.
WBBAL - Calculates flow rates for each well of fluid, heat, and solute
for the summary calculations.
WBCFLO - Calculates the flow rates at the well-bore boundary for a single well
in the cylindrical coordinate system.
165
BSODE - Integrates the coupled ordinary differential equations for pressure
and temperature up or down the well-riser casing, using the
Bulirsch-Stoer algorithm for rational polynomial extrapolation.
WFDYDZ - Calculates derivatives of pressure and temperature along
the well-riser casing for the Bulirsch-Stoer integration
algorithm.
If errors occur, the error checking that is in progress continues to
completion, but then, information to that point in the calculations is
written out, and the simulation is aborted.
A chart showing the main sequence of subroutine execution, the time step
and transient data loops and the linkage between the subroutines appears in
figure 4.1. The primary subroutines are on the left and the secondary and
utility subroutines are to the right. The sequence of execution is from top to
bottom of the leftmost column. Some utility subroutines are listed more
than once for graphical clarity.
4.2 MEMORY ALLOCATION, ARRAY-SIZE REQUIREMENTS, AND SUBPROGRAM COMMUNICATION
A semi-dynamic method for array-storage .allocation is employed in the
simulator program (Akin and Stoddart, 1975, p. 114). Instead of dimensioning
each of the arrays at some maximum value, a different approach is taken. The
various arrays whose size depends on the number of nodes in the region, or the
number of cells with a given type of boundary condition, or the number of
wells, or the type of equation solver selected, are all contained in two large
arrays; one array for real variables and one array for integer variables.
These two large arrays are partitioned into the required subarrays, based
on the storage-allocation information provided. Pointer variables are used to
indicate the location of the first element of each subarray in its large
array. Thus, the variable-length subarrays are passed to the subroutines and
functions though the calling arguments using the pointer variables. This
166
means that some subprograms have a large number of arguments. The advantage
of this approach is that the lengths of the two large, variably partitioned
arrays, VPA and IVPA, are set during compilation of the main routine, and only
the main routine must be recompiled if the lengths are to be changed. The
compiled length of the VPA array is contained in the variable ILVPA and the
compiled length of the IVPA array is contained in the variable ILIVPA.
A rough estimate of the sizes required for the two large arrays is given
by the following equations. For the large variably partitioned integer array,
ILI = 8 NXYZ + 6 NPMZ + 5 NWEL + NEC; (4.2.1)
where
ILI is the estimated length of the large variably partitioned integer
array;
NXYZ is the number of nodes in the region;
NPMZ is the number of porous medium zones;
NWEL is the number of wells; and
NBC is the number of boundary condition nodes.
For the large real array:
ILR = 70 NXYZ + 12 NPMZ + 60 NWEL + 60 NBC; (4.2.2)
where
ILR is the estimated length of the large variably partitioned integer
array.
Equations 4.2.1 and 4.2.2 are based on solving all three equations and they
overestimate the storage requirements in the interest of simplifying the
estimate calculation. During the storage-allocation step, the actual required
lengths of the large real and integer arrays are calculated and printed.
Execution is aborted if insufficient space has been set during compilation.
If redimensioning is necessary, the VPA and IVPA array sizes are
redimensioned, and the variable ILVPA and is set to the compiled dimension of
the VPA array, and the variable ILIVPA is set to the compiled dimension of the
VPA array in the main HST3D program.
167
r- READ1
- INIT1
- ERROR1
- WRITE 1
- READ 2 Q
- ERROR2
I- INIT2 U
h WRITE2 -f ZONPLT L PRNTAR
HST3D
- READS Q
- INIT3 ETOM2
O_ OO
cch-
IREWI
REWI REWI3 ORDER
REWI REWI3
ETOM1
CVISCOS INTERP
INTERP
REWI
REWI3
- ERRORS
- WRITES
- COEFF
- WRITE 4
- APLYBC
- WELLSS Q
PRNTAR
PRNTAR
WELRIS - BSODE WFDYDZ VISCOS - INTERP TOFEP - INTERP
r- ASEMBL
- D4DESr L2SOR SOR2L
^ SBCFLO
CRSDSP
- SUMCAL TWELRIS BSODE WFDYDZ - VISCOS - INTERP TOF
VISCOS INTERP
__ i-
L TOFEP - INTERP
PRNTAR MAP2D
- WRITES £
- DUMP
- PLOTOC PLOT
CLOSE ERRPRT
Figure 4.1.--Connection chart for the HST3D main program and subprogram
showing routine hierarchy and calculation loops.
168
Some of the subarrays share storage space if they are used sequentially
and the contents do not need to be retained for the duration of the
simulation. Table 4.1 shows the partitioning of the large integer array;
table 4.2 shows the partitioning of the large real array, with the shared
storage indicated by subarrays on the same horizontal line. The size of each
subarray and conditions for its inclusion (if optional) also are given. A
significant savings in space is obtained by not including arrays that deal
exclusively with either heat or solute transport in cases when transport of
only one or the other is being simulated.
All other parameters and variables are passed through common blocks.
Named common blocks are used, with the name being an abbreviation of the
subprogram where that particular common block is first used with a suffix
letter. There are many common blocks, because the variables are sorted into
usage groups, so that each subprogram has access to only the common variables
that it needs (as nearly as practical). All common blocks appear in the main
program for easy reference and for static-storage allocation on some computer
systems.
Another programming convention used is that, passing of subarrays through
one subprogram to another is done by making the entire large array available
to the calling subprogram along with the necessary pointer variables. This
reduces the number of arguments for the calling subprogram.
169
Table 4.1. Space allocation within the large, variably partitioned,integer array, IVPA
[--, no space sharing or no conditions; b.c., boundary condition]
Subarray Dimension
Other arrays that share the space
Conditions forinclusion of
optional subarrays
IBCHZI2ZJ1ZJ2ZK1ZK2ZLPRNTIWJWLCTOPWLCBOTWWQMETHMAIFC
MFBCMHCBCMLBCMSBCCIIDIAGRBWID4NO
NXYZNPMZNPMZNPMZNPMZNPMZNPMZNXYZ LEW , INZONE , JWEL , IBCMAPNWTNWTNWTNWTNWTNAIFC
NFBCNHCBCNLBCNPTCBC6(NXYZ/2+l)NXYZ/2+1NXYZ/2+1NXYZ
--------
Wells presentWells presentWells presentWells presentWells present
Aquifer influence functionb.c.Specified flux b.c.
Heat conduction b.c.Leakage b.c.
Specified value b.c.D4 matrix solverD4 matrix solverD4 matrix solverD4 matrix solver
170
Table 4.2. Space allocation within the large, variably partitionedreal array, VPA
[--, no space sharing or no conditions; b.c., mean boundary condition]
Subarray
XYZRMARXARYARZPOROSABPMKXXKYYKZZRCPPMKTHXKTHYKTHZALPHLALPHTDBKDPVPMCVPVKPMCVKPMHVPMCHVPDPTDTCDCDENVISEHTXTYTZTFXTFYTFZTHXTHXY
Dimension
NX, NRNYNZNR-1NXYZNXYZNXYZNPMZNPMZNPMZNPMZNPMZNPMZNPMZNPMZNPMZNPMZNPMZNPMZNXYZNXYZNXYZNXYZNXYZNXYZNXYZNXYZNXYZNXYZNXYZNXYZNXYZNXYZNXYZNXYZNXYZNXYZNXYZNXYZNXYZNXYZNXYZ
Other arrays that share the space
RR-- --TO------ ---- ------------POS--__--TOS--POW
HWT,PNPTOW
UTBC,TNP,TQFLXCOW
UCBC,CNP,CQFLXTC-- -- PCW
HDPRNT,UPHILB--
UVAIFC,UDENLB,AMAPUDTHHC,QHFX,KTXPM
--
Conditions for inclusion of
optional subarrays
Cartesian coordinates
Cylindrical coordinates--
Cartesian coordinates----
Heat transportHeat transportHeat transportHeat transportHeat or solute transportHeat or solute transportSolute transport
----
Solute transportSolute transportHeat transportHeat transport
--
Heat transportHeat transportSolute transportSolute transport
--
Heat transport
Cartesian coordinates
Cartesian coordinates
Heat transportHeat transport, cartesian
coordinates, full dispersion tensor
171
Table 4.2. Space allocation within the large, variably partitionedreal array, VPA Continued
Subarray Dimension
Other arrays that share the space
Conditions forinclusion of
optional subarrays
THXZ
THY
THYX
THYZ
THZ THZX
THZY
TSX TSXY
TSYZ
TSZ TSZX
TSZY
NXYZ
NXYZ
NXYZ
NXYZ
NXYZ NXYZ
NXYZ
NXYZ NXYZ
TSXZ
TSY
TSYX
NXYZ
NXYZ
NXYZ
NXYZ
NXYZ NXYZ
NXYZ
sxxSYYSZZRFRHRH1RSRS1URR1
NXYZNXYZNXYZNXYZNXYZNXYZNXYZNXYZNXYZ
QHFY,KTYPM
QHFZ,UKHCBC,KTZPM
QSFX
QSFY
QSFZ
QFFX,ARXBC,PCSQFFY,ARYBCQFFZ,ARZBC
APRNT,UVISLB
CCW
Heat transport, full dispersion tensor
Heat transport, cartesian coordinates
Heat transport, full dispersion tensor, cartesian coordinates
Heat transport, full dispersion tensor, cartesian coordinates
Heat transportHeat transport, full
dispersion tensorHeat transport, full
dispersion tensor, cartesian coordinates
Solute transportSolute transport,
cartesian coordinates, full dispersion tensor
Solute transport, full dispersion tensor
Solute transport,cartesian coordinates
Solute transport,cartesian coordinates, full dispersion tensor
Solute transport,cartesian coordinates, full dispersion tensor
Solute transportSolute transport, full dispersion tensor
Solute transport, full dispersion tensor, cartesian coordinates
Cartesian coordinates
Heat transport Heat transport Solute transport Solute transport Solute transport
172
Table 4.2.--Space allocation within the large, variably partitionedreal array/ VPA--Continued
Subarray Dimension
Other arrays that share the space
Conditions forinclusion of
optional subarrays
RHSCC24CC34CC35VA
WIQWLYRQHLYR
QSLYR
DQWDPLWRANGLWBODWRISLWRIDWRRUFKTHWR
DTHWR
KTHAWR
HTCWR
TABWR
TATWR
TWKT
TWSUR
EHWKT
EHWSUR
PWKTSPWKTDPWKTPWSURSPWSUR
NXYZNXYZNXYZNXYZ7-NXYZ
NWEL-NZNWEL-NZNWEL-NZ
NWEL-NZ
NWEL-NZNWELNWELNWELNWELNWELNWEL
NWEL
NWEL
NWEL
NWEL
NWEL
NWEL
NWEL
NWEL
NWEL
NWELNWELNWELNWELNWEL
FRAC,UZELB,TCS Solute transportUBBLB
TCWVXX,AA1 ,MOBW,UDENBC ,UKLB
VYY,AA2VZZ,AA3AA4
Wells presentWCF Wells present
Wells present,transport
Wells present,transport
Wells presentWells presentWells presentWells presentWells presentWells presentWells present,
transportWells present,
transportWells present,
transportWells present,
transportWells present,
transportWells present,
transportWells present,
transportWells present,
transportWells present,
transportWells present,
transportWells presentWells presentWells presentWells presentWells present
heat
solute
heat
heat
heat
heat
heat
heat
heat
heat
heat
heat
173
Table 4.2.--Space allocation within the large, variably partitionedreal array/ VPA--Continued
Subarray Dimension
Other arrays that share the space
Conditions forinclusion of
optional subarrays
CWKT
QWVQWMQHW
QSW
WFICUMWFPCUMWHICUM
WHPCUM
WSICUM
WSPCUM
VASBCRHSBCQFSBCPSBCQHSBC
TSBC
QSSBC
CSBC
ARXFBCARYFBC
ARZFBCQFFBCDENFBCQHFBC
TFLX
QSFBC
CFLX
ALBC
NWEL
NWELNWELNWEL
NWEL
NWELNWELNWEL
NWEL
NWEL
NWEL
7-NPTCBCNPTCBCNPTCBCNPTCBCNPTCBC
NPTCBC
NPTCBC
NPTCBC
NFBCNFBC
NFBCNFBC QFBCVNFBCNFBC
NFBC
NFBC
NFBC
NLBC
Wells present, solutetransport
Wells presentWells presentWells present, heat
transportWells present, solute
transportWells presentWells presentWells present, heat
transportWells present, heat
transportWells present, solute
transportWells present, solute
transportSpecif ied-value b.c.Specif ied-value b.c.Specif ied-value b.c.Specif ied-value b.c.Specif ied-value b.c. and
heat transportSpecif ied-value b.c. andheat transport
Specif ied-value b.c. andsolute transport
Specif ied-value b.c. andsolute transport
Specif ied-f lux b.c.Specif ied-f lux b.c.,
cartesian coordinatesSpecif ied-f lux b.c.Specif ied-f lux b.c.Specif ied-f lux b.c.Specif ied-f lux b.c. andheat transport
Specif ied-f lux b.c. andheat transport
Specif ied-f lux b.c. andsolute transport
Specif ied-f lux b.c. andsolute transport
Leakage b.c.
174
Table 4.2. Space allocation within the large, variably partitionedreal array, VPA Continued
Subarray Dimension
Other arrays that share the space
Conditions forinclusion of
optional subarrays
BLBCKLBCZELBCBBLBCHLBCDENLBCVISLBCTLBC
CLBC
QFLBCQHLBC
QSLBC
AAIF
BAIF
VAIF
WCAIF
DENOAR
PAIF
TAIF
CAIF
QFAIF
QHAIF
QSAIF
ZHCBCA1HCA2HCA3HCKARHC
NLBCNLBCNLBCNLBCNLBC PHILBCNLBCNLBCNLBC
NLBC
NLBCNLBC
NLBC
NAIFC
NAIFC
NAIFC
NAIFC
NAIFC
NAIFC
NAIFC
NAIFC
NAIFC
NAIFC
NAIFC
NHCNNHCNNHCNNHCNNHCBC
Leakage b.c.Leakage b.c.Leakage b.c.Leakage b.c.Leakage b.c.Leakage b.c.Leakage b.c.Leakage b.c. and heat
transportLeakage b.c. and solute
transportLeakage b.c.Leakage b.c. and heat
transportLeakage b.c. and solute
transportAquifer-influence-function
b.c.Aqui f er- influence- function
b.c.Aquifer- influence- function
b.c.Aquifer-influence-function
b.c.Aquifer-influence-function
b.c.Aquifer-influence-function
b.c.Aquifer- influence- function
b.c. and heat transportAquifer-influence-function
b.c. and solutetransport
Aquifer- influence- functionb.c.
Aqui f er- influence- functionb.c. and heat transport
Aquifer- influence- functionb.c. and solutetransport
Heat- conduction b.c.Heat- conduction b.c.Heat-conduction b.c.Heat-conduction b.c.Heat-conduction b.c.
175
Table 4.2. Space allocation within the large, variably partitionedreal array, VPA Continued
Subarray
DTHHCQHCBCDQHCDTTHCBCTPHCBCA4
Dimension
NHCBCNHCBCNHCBCNHCBC -NHCNNHCBC -NHCNMAXNAL
(D4 SOLVER)OR
7-NXYZ(L2SOR SOLVER)
Other arrays that share the space
------DTM1TM2TP1TP2XXXXN
Conditions for inclusion of
optional subarrays
Heat-conduction b.c.Heat-conduction b.c.Heat-conduction b.c.Heat- conduction b.c.Heat- conduction b.c.D4 direct solution method
or two-line, successive'overrelaxationiterative-solutionmethod
4.3 FILE USAGE
The heat- and solute-transport program uses several sequential-access
files on disc. The following list gives the FORTRAN unit number and a
description of each file:
FILE 5 Input data with comments stripped out.
FILE 6 Output data in character form for the line printer or video screen,
FILE 7 Plot data for dependent variables versus time.
FILE 8 Output data for a restart run.
FILE 9 Input data for a restart run.
FILE 10 Input data with comment lines
FILE 11 Echo of the input data as it is read.
176
These files must be declared or established on the computer system before
program execution. The present version of the program also requires pre-
opening of these files before starting execution. File names are assigned
when the files are opened, using the job-control language of the computer
employed.
4.4 INITIALIZATION OF VARIABLES
In general, all real and integer variables are set to zero and logical
variables are set to false by explicitly coded instructions at the beginning
of program execution. Certain input parameters are set to default values if
no data or data values of zero, are input. These are indicated in the input-
file description. Two tables are initialized for the enthalpy of pure water
as a function of temperature and pressure. These tables are used for the
heat-transport calculation.
4.5 PROGRAM EXECUTION
The program is designed to be executed by the job-control language (JCL)
or command-procedure language (CPL) of the computer employed. The data-input
file for a given program must have been created previously. The job-control
language statements should declare and open the FORTRAN files listed above,
assign file names, then start program execution. At the end of the simu
lation, the JCL or CPL statements should close all files and delete scratch
files. Unused files are deleted by the program in the CLOSE subroutine.
Execution of the command-procedure, control-statement file is usually done
interactively at a terminal, so file names can be provided by the user.
4.6 RESTART OPTION
The program has the option for restarting from an intermediate or ending
time of the simulation. The user may specify that restart information is to
177
be written to the restart file every nth time step (record 3.8.3 of the input
file). Then, the ability to continue in a later run is created. This is
useful; for example, if boundary conditions or sources need to be changed,
based on the results of the simulation, or if a steady-state flow field needs
to be established, before a heat or solute source is introduced. The other
use of the restart option is to specify that restart information is to be
written at periodic time-step intervals. This is insurance against computer-
system failure, so that long simulation runs will not have to be repeated
entirely.
The information written to disc for restart consists of the two large,
variably partitioned arrays, and those common blocks that contain parameters
and variables that are active during the simulation time-step loop. This
information can be written only at the end of a time step. To restart the
simulation, a small amount of data is needed in the input file, including the
first three lines of the READ1 record group and the transient-boundary con
dition and fluid-source information of the READS record group. After the
restart-data file is read, execution continues at the beginning of the
subroutine (READS) that reads the transient information, shown in figure 4.1.
Only the transient data that are to be changed from the last values of the
previous simulation need to be read at the beginning of a restart. From this
point onward in the simulation, there is no difference between a restart run
and one that has just gone through a change in transient-boundary conditions.
In particular, time is measured relative to the beginning of the original
simulation period.
One consequence of the way restarts are implemented is the restriction
that the number and type of boundary condition and source nodes cannot be
changed from the values for the original simulation run. To do so will cause
a fatal error resulting from a file length conflict. At the beginning of a
restart, the program will attempt to find the restart file whose time-plane
value agrees within 0.1 percent of the specified time value for restarting.
Failure to locate the specified restart file causes a fatal error.
178
5. THE DATA-INPUT FILE
The data-input file has two general characteristics: (1) It is free
format for ease of preparation at a computer terminal; and (2) it may be
freely commented for rapid identification of the data items. The free format
is supported by FORTRAN 77, and is sometimes referred to as list-directed
input.
5.1. LIST DIRECTED INPUT
The data values may be located in any position of the record, provided
they correspond in number and type with the input list. Data are separated by
commas or blanks, with multiple blanks allowed. Character strings must be
enclosed in quotation marks (apostrophies on some computers). There is a
third delimiter in addition to a comma and a blank: the slash, /. A slash
terminates a record and any remaining items in the input list are left un
changed from their previous values. On some computer systems, there must be a
space before the slash. A data item within an input list may be left
unchanged by separating the preceding item from the subsequent item with two
commas; in other words, making no entry for that item.
The list-directed input of a record continues until the end-of-record
slash is encountered, or the input list is satisfied. If the input list is
not satisfied at the end of a data line, the program will continue to read
additional data lines, until the list is satisfied, or the end of the file is
reached. Having an insufficient number of data items in the input file is a
common error. It usually results from a misinterpretation of the amount or
type of data required by a given program option.
List-directed input also allows for a repeat count. Data in the form:
n*d; (5.1.1)
179
where
n is the repeat count integer; and
d is the data item;
causes n consecutive values of d to be input,
5.2. PREPARING THE DATA-INPUT FILE
To simplify the preparation of the data-input file, a file is available
containing only comments. This file is presented as table 5.1. These
comments identify all the input-variable names, indicate the logical ones,
show the conditions for the optional items, and give the default values, where
used. The user actually can enter the data between the lines of a copy of
this file, using section 5.2.2 as a guide. This data-input form should make
it easier to create and modify the data-input file. Only the variable names
used in the program are given. For definitions see section 5.2.2 or 11.1.
Optional input records are indicated by (0) followed by the logical variables
that must be true, or the numerical conditions that must be met for inclusion
of a given input record. The numbers in brackets after a variable give the
record where that variable is read. The following section contains a
line-by-line presentation of the data-file form with an explanation of all the
variables and options.
Many published sources exist of fluid and porous-medium properties, and
transport parameters such as compressibilities, heat capacities, and
equilibrium distribution coefficients. Typical examples are Perry and others
(1963), Clark (1966), Weast and others (1964), and Mercer and others (1982).
5.2.1. General Information
Comment lines are numbered in the format C.N1.N2.N3 where C denotes a
comment record; Nl is the read-group number; and N2.N3 is the record or line
number. The read-group number denotes which subroutine, KEAD1, KEAD2, KEAD3,
180
or PLOTOC, reads that record for the values 1 through 4 respectively. The
record number identifies a line of input data, with the two component number
enabling a logical group structure to be assigned. A suffix letter associated
with N2 or N3 indicates that one of the numbered set with that letter must be
selected exclusively. Optional data records are indicated to the right of the
record list of variables, and the conditions under which these data are
required are explained. If a particular input record is not needed, it is
manditory that it be omitted. A record number in square brackets following a
variable indicates the record where that variable is first set.
Input by i,j,k range means that an array of data is to be specified for a
rectangular prism of nodes. The extent of this prism is defined by the ranges
of the i,j, and k indices. One may specify a plane, or a line, or a point
instead of a prism by making the appropriate indices equal. The value to be
entered into the array locations pertaining to the nodes contained with the
prism is specified next. There is the capability to replace, multiply or add
to existing data within the prism. The specified value fills the specified
array locations or operates on the existing values in those locations. In
some cases, three arrays are affected for the nodes within the specified
prism. There is a fourth option for data input which allows for a sequence of
different values to be entered into consecutive node locations within the
prism. The data will be loaded in order of increasing node number, that is,
in order of increasing i, then increasing j, and then increasing k. With this
input scheme, subregions of uniform parameters within the simulation region
are easily defined. A parameter distribution that varies continuously in
space is less convenient to define. It is permissible to use rectangular
prisms that include cells that are outside the simulation region.
181
Tab
le 5.1
. D
ata
-input
form
C.....H
ST
D
ATA
-INP
UT
FORM
C...
NO
TES:
C...
INPU
T LI
NES
ARE
DENO
TED
BY C.
N1.N
2.N3
WHERE
C...
Nl IS THE
READ G
ROUP N
UMBER, N2.N3
IS T
HE RECORD NU
MBER
C...
A LETTER INDICATES
AN EXCLUSIVE
RECORD S
ELEC
TION
MUST BE MADE
C...
I.E.
A
OR B
OR
CC.
..
(0)
- OP
TION
AL DATA W
ITH
COND
ITIO
NS FOR
REQUIREMENT
C...
A
RECO
RD N
UMBE
R IN
SQUARE
BRACKETS IS TH
E RECORD WHERE
THAT
PARAMETER
IS FI
RST
SET
C.....INPUT
BY I.J.K
RANGE
FORMAT IS
;C.
O.I.
. I1,I2,J1,J2,K1,K2
C.O.
2..
VAR1
,IMO
D1,[
VAR2
,IMO
D2,V
AR3,
IMOD
3]C...
USE
AS MANY OF
LI
NE 0.1
& 0.
2 SE
TS AS
NECESSARY
C...
END
WITH LI
NE 0.3
C.O.
3..
0 /
THE
SPAC
E IS REQUIRED
C...
(N
NN)
- IN
DICA
TES
THAT
THE DEFAULT
NUMBER,
NNN,
IS
USED IF A
ZERO
IS EN
TERE
D FOR
THAT V
ARIABLE
C...
(T/F
) -
INDI
CATE
S A
LOGICAL
VARI
ABLE
C...
[I
) -
INDI
CATE
S AN
IN
TEGE
R VARIABLE
C
C.....START
OF T
HE DA
TA F
ILE
_
C...
..DI
MENS
IONI
NG DA
TA -
READ
1 oo
C.I.
I .. TI
TLE
LINE
1
10
C.I.
2 .. TI
TLE
LINE
2
C.I.3
.. RESTRT(T/F),TIMRST
C.....IF RESTRT IS
TRUE,
PROCEED
TO R
EAD3
GRO
UP [3.1]
C.I.4
.. HE
AT,S
OLUT
E,EE
UNIT
,CYL
IND,
SCAL
MF;
ALL
(T/F)
C.I.5
.. NX
.NY.
NZ.N
HCN
C.I.
6 .. NP
TCBC
,NFB
C,NA
IFC,
NLBC
,NHC
BC,N
WEL
C.I.7
.. NPMZ
C.I.
8 ..
SL
METH
[I),
LCRO
SD(T
/F)
C.I.9
.. IB
C BY I,J,K
RANGE
{0.1
-0.3
} .W
ITH
NO IM
OD PA
RAME
TER,
FOR
EXCL
UDED
CELLS
C.I.10 .. RDECHO(T/F)
C
C.....STATIC
DAT
A - RE
AD2
C.....OUTPUT
INFORMATION
C.2.
1 .. PR
TRE(
T/F)
C.....COORDINATE GE
OMET
RY INFORMATION
C..... RECTANGULAR
COORDINATES
C.2.2A.1
.. UN
IGRX
,UNI
GRY,
UNIG
RZ;
ALL
(T/F); (0)
- NOT
CYLIND [1.4]
C.2.2A.2A
.. X(1),X(NX);(0) - UNIGRX [2
.2A.
1]C.2.2A.2B
.. X(I);(0) -
NOT
UNIGRX [2.2A.1]
C.2.2A.3A
.. Y(1),Y(NY);(0) - UNIGRY [2.2A.1]
C.2.2A.3B
.. Y(
J);(
0) -
NOT
UNIGRY [2
.2A.
1]C.2.2A.4A
.. Z(1),Z(NZ);(0) -
UNIGRZ [2.2A.1]
C.2.
2A.4
B .. Z(
K);(
0) -
NOT
UNIGRZ [2.2A.1]
C.....CYLINDRICAL
COORDINATES
Tab
le 5.1
. D
ata
-in
pu
t fo
rm C
on
tin
ued
C.2
.2B
.1A
.
R(1
),R
(NR
),A
RG
RID
(T/F
);(0
) -
CYL
IND
[1
.4)
C.2
.2B
.1B
.
R(I
);(0
) -
NOT
ARG
RID
[2
.2B
.1A
];(0
) -
CYL
IND
[1
.4]
C.2
.2B
.2
. U
NIG
RZ
(T/F
);(0
) -
CYL
IND
[1
.4]
C.2
.2B
.3A
.
Z(1
),Z
(NZ
);(0
) -
UN
IGR
Z [2
.2B
.3A
],CY
LIN
D
[1.4
]C
.2.2
B.3
B
. Z
(K);
(0)
- NO
T U
NIG
RZ
[2.2
B.3
A].C
YLI
ND
[1
.4]
C.2
.3.1
..
T
ILT
(T/F
);(0
) -
NOT
CYL
IND
[1
.4]
C.2
.3.2
..
TH
ETX
Z,TH
ETY
Z,TH
ETZ
Z;(0
) -
TIL
T
[2.3
.1]
AND
NOT
CY
LIN
D
[1.4
]C
.....F
LU
ID
PRO
PERT
Y IN
FOR
MAT
ION
C.2
.4.1
..
BPc!2
!4!2
'..
PO
,TO
,WO
,DEN
FOC
.2.4
.3 ..
W
1,D
EN
F1;
(0)
- SO
LUTE
[1
.4]
C.2
.5.1
..
N
OT
VO
,TV
FO
(I),
VIS
TF
O(I
),I=
1 TO
N
OTV
O;(0
) -
HEAT
[1
.4]
OR
HEAT
[1
.4]
AND
SOLU
TE
[1.4
] OR
.N
OT.
HE
AT
AND
.NO
T.SO
LUTE
[1
.4]
C.2
.5.2
..
N
OT
V1
,TV
F1
(I),
VIS
TF
1(I
),I=
1
TO
NO
TV
1;(0
) -
SOLU
TE
[1.4
] AN
D HE
AT
[1.4
]C
.2.5
.3 ..
N
OC
V,T
RV
IS,C
VIS
(I),
VIS
CT
R(I
),I=
1
TO
NO
CV
;(0)
- SO
LUTE
[1
.4]
C...
..RE
FE
RE
NC
E
CO
ND
ITIO
N
INFO
RM
ATIO
NC
.2.6
.1 ..
PAAT
MC
.2.6
.2 ..
PO
H.T
OH
C.....F
LU
ID
THER
MAL
PR
OPE
RTY
INFO
RM
ATIO
NC
.2.7
..
C
PF
,KT
HF
,BT
;(0)
-
HEAT
[1
.4]
_
C...
..SO
LUT
E
INFO
RM
ATIO
N
oo
C.2
.8 ..
D
M,D
EC
LAM
;(0)
- SO
LUTE
[1
.4]
^
C...
..PO
RO
US
M
EDIA
ZO
NE
INFO
RM
ATIO
NC
.2.9
.1
..
IPM
Z,I1
Z(IP
MZ)
,I2Z(
IPM
Z),J
1Z(I
PMZ)
,J2Z
(IPM
Z),K
1Z(I
PMZ)
,K2Z
(IPM
Z)C.....USE
AS M
ANY
2.9.1
LINE
S AS
NECESSARY
C.2.
9.2
.. EN
D WITH 0
/C.....POROUS
MEDIA P
ROPE
RTY
INFO
RMAT
ION
C.2
.10
.1
..
KX
X(I
PM
Z),
KY
Y(I
PM
Z),
KZ
Z(I
PM
Z),
IPM
Z=1
TO
NP
MZ
[1.7
]C
.2.1
0.2
..
P
OR
OS
(IPM
Z)JP
MZ=
1 TO
NP
MZ
[1.7
]C
.2.1
0.3
..
AB
PM
(IPM
Z),IP
MZ=
1 TO
NP
MZ
[1.7
]C.....POROUS
ME
DIA
THER
MAL
PROP
ERTY
IN
FORM
ATIO
NC.
2.11
.1
.. RCPPM(IPMZ),IPMZ=1 TO
NPMZ [1
.7];
(0)
- HE
AT [1.4]
C.2.11.2 .. KTXPM(IPMZ),KTYPM(IPMZ),KTZPM(IPMZ),IPMZ=1 T
O NPMZ [1
.7];
(0)
- HEAT [1.4]
C.....POROUS ME
DIA
SOLUTE A
ND T
HERM
AL D
ISPERSION
INFORMATION
C.2.12 .. ALPHL(IPMZ),ALPHT(IPMZ),IPMZ=1 TO
NPM
Z [1
.7];
(0)
- SO
LUTE
[1
.4]
OR H
EAT
[1.4
]C.....POROUS
ME
DIA
SOLUTE PR
OPER
TY INFORMATION
C.2.13 .. DBKD(IPMZ),IPMZ=1
TO NP
MZ [1
.7];
(0)
- SOLUTE [1.4]
C...
..SO
URCE
-SIN
K WELL INFORMATION
C.2.14.1 .. RDWDEF(T/F);(0)
- NWEL [1.6]
> 0
C.2.14.2 .. IM
PQW(
T/F)
;(0)
-
NWEL [1
.6]
> 0
AND
NOT
CYLIND [1.4]
C.2.
14.3
. .. IWEL,IW,JW,LCBOTW,LCTOPW,WBOD,WQMETH[I];(0)
- RD
WDEF
[2.14.1],
C.2.14.4 .. WC
F(L)
;L =
1
TO NZ
(EXCLUSI
VE)
BY ELEMENT
C.2.14.5 .. WR
ISL,
WRID
,WRR
UF,W
RANG
L;(0
) -
RDWDEF [2
.14.
1] AND
WRCA
LC(W
QMET
H [2
.14.
3] >3
0)C.2.14.6 .. HT
CWR,
DTHA
WR,K
THAW
R,KT
HWR,
TABW
R,TA
TWR;
(0)
- RDWDEF [2
.14.
1]
WRCA
LC(W
QMET
H [2
.14.
3] >30) AND
HEAT [1.4]
C...
..US
E AS
MANY 2.14.3-6 LI
NES
AS NECESSARY
C.2.
14.7
.. EN
D WITH 0
/
Tab
le 5
.1.
Data
-input
form
Conti
nued
C.2
.14
.8 ..
MX
ITQ
W{1
4},T
OLD
PW
{6.E
-3},
TO
LFP
W{.
001}
tTO
LQW
{.00
1},D
AM
WR
C{2
.},D
ZM
IN{.
01},
EP
SW
R{.
001}
;(0)
-
RDW
DEF
[2.1
4.1
]C
.....
AND
WR
CA
LC(W
QM
ETH
[2.1
4.3]
>3
0)C
.....B
OU
ND
AR
Y
CO
ND
ITIO
N
INFO
RM
ATIO
NC
.....
SP
EC
IFIE
D
VALU
E B
.C.
C.2
.15
..
IB
C
BY I.
J.K
RA
NGE
{0.1
-0.3
} W
ITH
NO
IM
OD
PA
RA
ME
TER
,;(0)
-
NPTC
BC
[1.6
] >
0C
.....
SP
EC
IFIE
D
FLUX
B
.C.
C.2
.16
..
IB
C
BY I.
J.K
RA
NGE
{0.1
-0.3
} W
ITH
NO
IM
OD
PA
RA
ME
TER
,;(0)
-
NFBC
[1
.6]
> 0
C.....
AQU
IFER
AND
R
IVER
LE
AKAG
E B
.C.
C.2
.17
.1 ..
IB
C
BY I.
J.K
RA
NGE
{0.1
-0.3
} W
ITH
NO
IM
OD
PA
RA
ME
TER
;(0)
- NL
BC
[1.6
] >
0C
.2.1
7.2
..
K
LBC
.BB
LBC
.ZE
LBC
BY
I.
J.K
RA
NGE
{0.1
-0.3
};(0
) -
NLBC
[1
.6]
> 0
C.....
RIV
ER
LEAK
AGE
B.C
.C
.2.1
7.3
..
11,1
2,J
ltJ2
,KR
BC
,BB
RB
C,Z
ER
BC
;(0)
- NL
BC
[1.6
] >
0C
.2.1
7.4
..
EN
D W
ITH
0
/C
.....
AQU
IFER
IN
FLU
ENC
E FU
NCTI
ONS
C.2
.18
.1
..
IBC
BY
I.
J.K
RA
NGE
{0.1
-0.3
} W
ITH
NO
IM
OD
PA
RA
ME
TER
;(0)
- N
AIFC
[1
.6]
>0C
.2.1
8.2
..
U
VAIF
C B
Y I.
J.K
RA
NGE
{0.1
-0.3
};(0
) -
NAI
FC [1
.6]
> 0
C.2
.18
.3 ..
IA
IF;(
0)
- N
AIFC
[1
.6]
> 0
C.....TRANSIENT, CARTER-TRACY A
.I.F
.C.2.18.4 .. KOAR,ABOAR,VISOAR,POROAR,BOAR,RIOAR,ANGOAR;(0) -
IAIF
[2
.18.
3] =
2 ^
C.....
HEAT C
ONDU
CTIO
N B.
C.oo
C.2.
19.1
.. IBC
BY I.J.K
RANGE
{0.1-0.3
} .W
ITH
NO IM
OD P
ARAMETER ,F
OR H
CBC
NODES;(0)
- HE
AT [1.4]
AND
NHCBC
[1.6]
> 0
*"
C.2.
19.2
.. ZHCBC(K);(0) - HEAT [1
.4]
AND
NHCB
C [1.6]
> 0
C.2.19.3 .. UDTHHC B
Y I,
J,K
RANGE
{0.1
-0.3
} FO
R HCBC N
ODES;(0) -
HEAT
-[1.
4]
AND
NHCBC
[1.6
] >
0C.2.19.4 .. UKHCBC B
Y I.J.K
RANG
E {0
.1-0
.3}
FOR
HCBC N
ODES;(0) - HE
AT [1
.4]
AND
NHCB
C [1
.6]
>0C.
....
FREE
SURFACE
B.C.
C.2.20 .. FR
ESUR
(T/F
),PR
TCCM
(T/F
)C.
....
INIT
IAL
CONDITION
INFORMATION
C.2.21.1
.. ICHYDP.ICT.ICC;
ALL
(T/F
);IF
NO
T.HE
AT,
ICT
= F,
IF
NOT.SOLUTE,
ICC
= F
C.2.
21.2
.. IC
HWT(
T/F)
;(0)
- FRESUR [2.20]
C.2.21.3A
.. ZPINIT,PINIT;(0) -
ICHY
DP [2
.21.
1] AND
NOT
ICHWT
[2.2
1.2]
C.2.
21.3
B .. P
BY I.J.K
RANGE
{0.1-0.3};(0)
- NO
T IC
HYDP
[2
.21.
1] AN
D NO
T IC
HWT
[2.2
1.2]
C.2.21.3C
.. HW
T BY I.J.K
RANGE
{0.1-0.3};(0)
- FRESUR [2.20] AN
D ICHWT
[2.21.2]
C.2.21.4A
.. NZ
TPRO
,ZT(
I)tTVD
(I)
tI=l
,NZT
PRO;
(0)
- HEAT [1.4]
AND
NOT
ICT
[2.21.1],
LIMIT
OF 10
C.2.
21.4
B .. T
BY I,J,K
RANGE
{0.1-0.3};(0)
- HEAT [1
.4]
AND
ICT
[2.2
1.1]
C.2.21.5 ..
NZTPHC,
ZTHC
(I),
TVZH
C(I)
;(0)
- HE
AT [1
.4]
AND
NHCBC
[1.6]
> O.LIMIT
OF 5
C.2.21.6 .. C
BY I.J.K
RANGE
{0.1
-0.3
};(0
) - SOLUTE [1
.4]
AND
ICC
[2.2
1.1]
C.....CALCULATION
INFORMATION
C.2.
22.1
.. FD
SMTH
.FDT
MTH
C.2.22.2 .. TO
LDEN
{.00
1},M
AXIT
N{5}
C.2.22.3 .. NT
SOPT
{5},
EPSS
OR{.
0000
1},E
PSOM
G{.2
},MA
XIT1
{50}
,MAX
IT2{
100}
;(0)
- SLMETH [1.8]
= 2
C.....OUTPUT INFORMATION
C.2.
23.1
..
PR
TPMP
.PRT
FP.P
RTIC
.PRT
BC.P
RTSL
M.PR
TWEL
; ALL
(T/F)
C.2.
23.2
..
IPRPTC,PRTDV(T/F);(0)
- PR
TIC
[2.2
3.1]
C.2.23.3 ..
OR
ENPR
[I];
(0)
- NO
T CYLIND [1.4]
C.2.23.4 .. PLTZON(T/F);(0)
- PRTPMP [2.23.1]
Table 5.1. Da
ta-i
nput
form Continued
00
Ln
.. TR
ANSI
ENT
DATA -
READ3
1 ..
THRU(T/F)
..IF T
HRU
IS TRUE PR
OCEE
D TO
RE
CORD
3.99
..TH
E FO
LLOW
ING
IS FO
R NOT
THRU
..SOURCE
-SINK
WELL
IN
FORM
ATIO
N2.1
.. RD
WFLO
(T/F
),RD
WHD(
T/F)
;(0)
-
NWEL [1
.6]
> 0
2.2
.. IW
EL,Q
WV,P
WSUR
,PWK
T,TW
SRKT
,CWK
T;(0
) -
RDWFLO [3.2.1]
OR R
DWHD
[3.2.1]
..US
E AS
MAN
Y 3.
2.2
LINE
S AS
NE
CESS
ARY
2.3
.. EN
D WI
TH 0
/..BOUNDARY CO
NDIT
ION
INFO
RMAT
ION
SPEC
IFIE
D VALUE
B.C.
RDSP
BC,R
DSTB
C,RD
SCBC
,ALL
(T/F
);(0
) -
NOT
CYLIND [1
.4]
AND
NPTCBC [1
.6]
> 0
PNP
B.C. BY
I.J.K
RANG
E (0.1-0.3};(0)
- RDSPBC [3.3.1]
C.2
C
C..
C.3
C..
C..
C..
C.3
C.3
C..
C.3
C..
C..
C.3
C.3
C.3
C.3
C.3
C.3
C..
C.3
C.3
C.3
C.3
C.3
C.3
C.3
C..
C.3
C.3
C.3
C.3
C..
C.3
C..
C.3
C..
C.3
C.3
C.3
C.3
C..
C.3
C.3
C.3
,23.5
.. OCPLOT(T/F)
3.1
3.2
3.3
3.4
3.5
3.6
RANGE
{0.1
-0.3
}; (0)
- RDSPBC [3
.3.1
] AN
D HEAT [1
.4]
RANGE
{0.1
-0.3
}; (0)
- RDSPBC [3.3.1]
AND
SOLUTE [1
.4]
4.1
4.2
4.3
4.4
4.5
4.6
4.7
5.2
5.3
5.4
5^5
TSBC BY I.
J.K
CSBC BY
I.J.K
TNP
B.C.
BY I.J.K
RANGE
{0.1-0.3};(0)
- RDSTBC [3.3.1]
AND
HEAT
[1
.4]
CNP
B.C.
BY I.J.K
RANGE
{0.1-0.3};(0)
- RDSCBC [3.3.1]
AND
SOLUTE [1
.4]
SPECIFIED
FLUX
RDFLXQ,RDFLXH,RDFLXS,ALL(T/F);(0)
- NF
BC [1
.6]
> 0
QFFX
.QFF
Y.QF
FZ B.C. BY
I.J.K
RANG
E {0
.1-0
.3};
(0)
- RDFLXQ [3.4.1]
UDENBC
BY I.
J.K
RANGE
{0.1-0.3};(0)
- RDFLXQ [3
.4.1
]BY I.J.K
RANGE
{0.1-0.3};(0)
- RDFLXQ [3
.4.1
] AN
D HEAT [1
.4]
BY I.J.K
RANGE
{0.1-0.3};(0)
- RDFLXQ [3
.4.1
] AN
D SOLUTE [1
.4]
TFLX B.C.
CFLX B.C.
QHFX
.QHF
Y.QH
FZ B
QSFX
.QSF
Y.QS
FZ B.
C LEAKAGE
BOUN
DARY
RDLBC(T/F);(0) -
NLBC
[1
.6]
1(0) -
R {0
.1-0
.BY
I.J.K
RANG
E {0
.1-0
.3};
(0)
- RDFLXH [3,
BY I.J.K
RANG
E {0
.1-0
.3};
(0)
- RDFLXS [3,
> 0
.5]
.1]
PHILBC.DENLBC.VISLBC BY I,J,K
RANG
E {0
.1-0
.3};
(0)
- RDLBC
[3.5.1]
TLBC
BY
I.J.K
RANGE
{0.1-0.3};(0)
- RDLBC
[3.5
.1]
AND
HEAT [1
.4]
CLBC BY
I.J.K
RANGE
{0.1-0.3};(0)
- RDLBC
[3.5
.1]
AND
SOLUTE [1.4]
RIVE
R LE
AKAG
E I1
,I2,
J1,J
2,HR
BC,D
ENRB
C,VI
SRBC
,TRB
C,CR
BC;(
0) -
RDLBC
[3.5
.1]
.USE AS
MANY 3.5.5
LINE
S AS
NE
CESS
ARY
5.6
.. EN
D WI
TH 0
/ A.
I.F.
B.C.
RDAIF(T/F);
(0)
- NA
IFC
[1.6
] >
0 DE
NOAR
BY
I,J,
K RANGE
{0.1-0.3};(0)
- RDAIF
[3.6
.1]
TAIF BY I.J.K
RANGE
{0.1-0.3};(0)
- RDAIF
[3.6.1]
AND
HEAT
[1.4]
CAIF BY
I.J.K
RANGE
{0.1-0.3};(0)
- RDAIF
[3.6
.1]
AND
SOLUTE [1.4]
6.1
6.2
6.3
6.4
..CALCULATION
INFORMATION
7.1
.. RDCALC(T/F)
7.2
.. AU
TOTS
(T/F
);(0
) - RDCALC [3
.7.1
]7.
3.A
.. DELTIM;(0) - RDCALC [3
.7.1
] AN
D NO
T AUTOTS [3
.7.2
]
Tab
le 5
.1.
Data
-in
pu
t fo
rm
Conti
nued
C.3
.7.3
.B ..
DP
TA
S{5
E4}
,DT
TA
S{5
.},D
CT
AS
{.25
},D
TIM
MN
{1.E
4},D
TIM
MX
{1.E
7};(
0)
- RD
CALC
[3
.7.1
] AN
D AU
TOTS
[3
.7.2
] C
.3.7
.4 ..
TI
MC
HG
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.3.8
.1 ..
PR
IVE
L,P
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RIG
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ALL
[I]
C.3
.8.2
..
IP
RP
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;(0)
-
IF
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[3.8
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NOT
= 0
C.3
.8.3
..
CH
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C...
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INFO
RM
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.3.9
.1 ..
RD
MPD
T,PR
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.3.9
.2 ..
MA
PP
TC
,PR
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P[I]
;(0)
-
RDM
PDT
[3.9
.1]
C.3.
9.3
.. YPOSUP(T/F).ZPOSUP(T/F)..LENAX.LENAY.LENAZ;(0) - RD
MPDT
[3.9.1]
C.3.
9.4
.. IM
AP1{
1},I
MAP2
{NX}
.JMA
P1{1
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AP2{
NY}.
KMAP
1{1}
.KMA
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MIN.
AMAX
,NMP
ZON{
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0) -
RDMP
DT [3.9.1]
C.....ONE
OF T
HE 3.
9.4
LINES
REQU
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FOR E
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T VA
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LEC.....
TO B
E MA
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C.....END
OF F
IRST
SET O
F TR
ANSI
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INFO
RMAT
ION
C- ------------------------------------------
C.....READ S
ETS
OF R
EAD3
DATA AT EA
CH T
IMCH
G UNTIL
THRU
(LIN
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C...
..EN
D OF
CALCULATION LINES
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THRU=.TRUE.
C.3.
99.1
.. TH
RUT C.
....TEMPORAL P
LOT
INFORMATION
C.3.99.2 ..
PLOTWP.PLOTWT.PLOTWC;
ALL
(T/F)
C...
..PL
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FORM
ATIO
N; (0
) -
PLOTWP [3.9
9J OR P
LOTWT
[3.99] OR P
LOTW
C [3.99]
C.4.1
..
IWEL.RDPLTP(T/F)
C.4.
2 ..
IDLAB
C.4.3
..
NTHP
TO.N
THPT
C.PW
MIN.
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X.PS
MIN.
PSMA
X.TW
MIN.
TWMA
X.TS
MIN.
TSMA
X.CM
IN.C
MAX;
(0
) -
RDPLTP [4
.1]
C.4.4
..
TO.POW.POS.TOW.TOS.COW
C.....USE
AS M
ANY
4.4
LINES
AS N
ECES
SARY
C.4.
5 ..
EN
D WI
TH -
1. /
C.....READ D
ATA
FOR AD
DITI
ONAL
WELLS.
4.1-
4.5
LINE
SC.4.6
..
END
WITH
0 /
C.
....
END
OF D
ATA
FILE
A set of record pairs is needed where the first is:
1.1 II, 12, Jl, J2, Kl, K2;
where li, Jj, Kk are inclusive node-index ranges in the i,j, and k directions,
and the second is:
1.2 VAR1, IMOD1, [VAR2, IMOD2, VAR3, IMOD3];
where VARi is the value of the ith variable;
IMODi is the modification code for the ith variable;
1 means insert the data into the variable location;
2 means multiply the existing value of the variable by VARi;
3 means add VARi to the existing value of the variable;
4 means read in values of VARi on a node-by-node basis in the
order of increasing i, then j, then k. In this case, the value
of VARi in record 1.2 is not used and needs to be given a value
of zero. Note that this type of input is only suitable for
zones of cells with a continuous sequence of nodes in the
i-direction. Zones of cells whose i-direction index is a
discontinuous sequence are more easily treated by using one
of the first three types of modification code.
The brackets indicate that some input lists need three values of VAR and
IMOD, while others need only one. As many lines of type I.I and 1.2 are used
as necessary, then the following line is entered to terminate the input:
1.3 0 /.
The generic dimensions for the various parameters are indicated, and the
units must be selected from table 5.2. unless the conversion factors in the
HST3D program are modified. The units for output will match the units for
input. The few exceptions, where the units are not combinations of the
fundamental units, are indicated. The conversion factors from inch-pound
units to metric units are contained in the following subprograms: READ1,
187
ETOM1, ETOM2. They are specified in PARAMETER statements and the variable
names are in the form, CNVxxx. The conversion factors from metric units to
inch-pound units are defined in the INIT1 subprogram, and the variable names
are in the form CNVxxI. The unit labels are contained in variables named
UNITxx and are defined in the INIT1 subprogram also. By changing the
appropriate conversion factors, and unit labels the user can employ the most
convenient units for a particular simulation series.
The notation (T/F) indicates a logical variable. All index ranges are
inclusive unless stated otherwise. All pressure values are relative to
atmospheric unless stated otherwise.
Table 5.2. International System and inch-pound units used in the heat- and solute-transport simulator
Quantity(genericunits)
International System units
Inch-pound units
Mass (M) Length (L) Time (t) Temperature (T) Energy (E)
Fluid Volumetric Flow Rate(L3 /t)
Density (M/L3 )
Velocity (L/t) Pressure (F/L2 )
Viscosity (M/Lt)
Diffusivity (L2 /t)
Permeability (L2 ) Thermal Conductivity (E/L-t-T) or (F/t-T)
Specific Heat Capacity (FL/M-T or E/M-T)
kilogram (kg) meter (m) second (s) degree Celsius (°C) Joule (J) orwatt-second (W-s)
liter per second (£/s)
kilogram per cubicmeter (kg/m3 )
meter per second (m/s) Pascal (Pa)
kilogram permeter-second(kg/m-s)
square meter persecond (m2 /s)
square meter (m2 ) Watt per meter-degree
Celsius (W/m-°C)
Joule per kilogram- degree Celsius (J/kg-°C)
pound (Ib)foot (ft)day (d)degree Fahrenheit (°F)British Thermal Unit
(BTU) cubic foot per day
(ft3 /d) pound per cubic foot
(Ib/ft3 ) 1foot per day (ft/d) pound per square inch
(psi) centipoise (cP) 2
square foot per day(ft2 /d)
square foot (ft2 ) British Thermal Unitper foot-hour-degreeFahrenheit(BTU/ft-h-°F)
British Thermal Unitper pound-degreeFahrenheit (BTU/lb-°F)
188
Table 5.2.--InternationaI System and inch-pound units used in the heat- and solute-transport simulator Continued
Quantity(genericunits)
International system units
Inch-pound units
Heat-Transfer Coefficient (E/t-L2 -T)
Volumetric flux (L3/L2 -t)
Heat flux (E/L2 -t)
Mass flux (M/L2 -t)
Watt per square meter- degree Celsius (W/m2 -°C)
cubic meter per squaremeter-second(m3 /m2 -s)
Watt per squaremeter (W/m2 )
kilogram per square meter-second (kg/m2 -s)
British Thermal Unit per hour-square foot- degree Fahrenheit (BTU/h-ft2 -°F)
cubic foot per square foot-day (ft 3 /ft 2 -d)
British Thermal Unit per square foot-hour (BTU/ft2 -h)
pound per square foot- day (Ib/ft 2 -d)
1A weight density rather than a mass density. 2Not Inch-Pound but common usage.
5.2.2. Input Record Descriptions
The following order generally has been observed for data input: (1)
Fundamental and dimensioning information, (2) spatial geometry and mesh
information, (3) fluid properties, (4) porous medium properties, (5) source
information, (6) boundary condition information, (7) initial condition
information, (8) calculation parameters, (9) output specifications. Items 5,
6, 8 and 9 have transient data associated with them, and data are input in the
item-order given. The static data are read only once while the transient data
are read at each time a change in the data is to occur. Only the data that
are being changed need to be entered, because any unmodified data will remain
the same over the next time interval of simulation. Each input record number
identifies a particular record in the input-data form listed in table 5.1.
189
Dimensioning data for space allocation - READ1
1.1 Title line 1.
A character string of up to 80 characters. It is wise to start in column
two in case the string begins with the letter 'c 1 .
1.2 Title line 2.
A character string of up to 80 characters. It is wise to start in column
two in case the string begins with the letter 'c 1 .
1.3 RESTRT (T/F), TIMRST.
RESTRT - True if this run is to be a restart of a previous simulation.
TIMRST - Time within the range of a previous simulation from which
this restart is to continue (t). A search is made of the restart-
record file for data pertaining to the time value specified or
within 0.1 percent of that time. Enter zero if this is not a
restart of a previous simulation.
If this is a restart run, proceed to the READ3 group for input of transient
data.
1.4 HEAT, SOLUTE, EEUNIT, CYLIND, SCALMF; all (T/F).
HEAT - True if heat transport is to be simulated.
SOLUTE - True if solute transport is to be simulated.
EEUNIT - True if the input data are in inch-pound units; otherwise,
metric units are assumed. The conversion factors are set for the
inch-pound and metric units given in table 5.1 and appear after
the table of contents also. The program uses metric units
internally.
CYLIND - True if cylindrical coordinates with no angular dependence
are to be used; otherwise, cartesian, x,y,z, coordinates are used.
190
SCALMF - True if a scaled-mass fraction determined by equation 2.2.1.2
is to be used for data input and output; otherwise, the unsealed
mass fraction will be used.
1.5 NX, NY, NZ, NHCN.
NX - The number of nodes in the x-direction for cartesian coordinates,
or r-direction for cylindrical coordinates.
NY - The number of nodes in the y-direction. Unused for cylindrical
coordinates, but a space in the input record must be included.
NZ - Number of nodes in the z-direction.
NHCN - Number of nodes for the heat-conduction boundary condition. This
may be included only in a heat-transport simulation. These nodes
are used for the finite-difference solution of equations 2.5.5.3a-d
and 2.5.5.4a-d.
1.6 NPTCBC, NFBC, NAIFC, NLBC, NHCBC, NWEL.
NPTCBC - Number of cells (nodes) with a specified pressure, temperature,
and(or) mass-fraction boundary condition.
NFBC - Number of cells with a specified-flux boundary condition; flow,
heat, and(or) solute.
NAIFC - Number of cell faces with an aquifer-influence-boundary condition,
NLBC - Number of cell faces with a leakage-boundary condition.
NHCBC - Number of cell faces with a heat-conduction boundary condition.
NWEL - Number of wells in the simulation region.
These values must be the exact counts for the simulation. A cell with more
than one face on the region boundary may be counted more than once for the
above counts. A specified-value boundary-condition cell may not have any
other type of boundary condition.
191
1.7 NPMZ.
NPMZ - Number of porous medium zones in the region. Porous medium
hydraulic, thermal-, and solute-transport properties vary by zone.
1.8 SLMETH, LCROSD (T/F).
SLMETH - Solution method (integer):
Enter 1 to select the direct, D4, matrix-equation solver; or
Enter 2 to select the iterative, two-line, successive-overrelax-
ation, matrix-equation solver.
LCROSD - True if the off-diagonal cross-dispersive terms in the heat and
solute equations are to be lumped into the diagonal terms
to give amplified coefficients. Otherwise, the coefficients in
the dispersion tensor are computed explicitly in time. Lumping
the coefficients reduces storage requirements and the number
of iterative cycles of the flow, heat, and solute equations,
but it is an empirical simplification.
1.9 IBC by i,j,k range for excluded cells.
IBC - Index of cells excluded from the simulation region. For space
allocation, the location of the excluded cells must be known.
Excluded cells are denoted by IBC = -1.
1.10 RDECHO (T/F).
RDECHO - True if a file is to be written that echos the input data as
they are read that is used for locating data-input errors.
Static data - READ2.
The following data are invariant throughout the simulation.
192
2.1 PRTRE (T/F).
ftPRTRE - True if a read-echo printout of data input by i,j,k range is
desired.
The following 12 records describe the gridding of the simulation region.
2.2A.1 UNIGRX, UNIGRY, UNIGRZ; All (T/F); optional, used for cartesian-
coordinate systems.
UNIGRi - True if the grid in the ith direction is uniform.
2.2A.2A X(1),X(NX); Optional, used if uniform grid in the x-direction.
X(l) - Location of the first node point in the x-direction (L).
X(NX) - Location of the last node point in the x-direction (L).
2.2A.2B X(I), 1=1 to NX; Optional, used for nonuniform grid in the
x-direction.
2.2A.3A Y(l), Y(NY); Optional, used if uniform grid in the y-direction.
Y(l) - Location of the first node point in the y-direction (L).
Y(NY) - Location of the last node point in the y-direction (L).
2.2A.3B Y(J) J=l to NY; Optional, used for nonuniform grid in the y-direction.
2.2A.4A Z(l), Z(NZ); Optional, used for uniform grid in the z-direction.
Z(l) - Location of the first node point in the z-direction (L).
Z(NZ) - Location of the last node point in the z-direction (L).
2.2A.4B Z(K), K=l to NZ; Optional, used for nonuniform grid in the z-direction,
193
2.2B.1A R(l), R(NR), ARGRID (T/F); Optional, used for cylindrical-coordinate
systems.
R(l) - Interior radius of cylindrical-coordinate system (L). Required by
cylindrical-coordinate system.
R(NR) - Exterior radius of cylindrical-coordinate system (L). Required
if a cylindrical-coordinate system.
ARGRID - True if automatic gridding or node location in the r-direction
is desired. A logarithmic spacing in R will be used according
to equation 3.1.2.1.
2.2B.1B R(I), I = 1 to NX; Optional, used for user-specified radial gridding
for a cylindrical-coordinate system.
R(I) - Array of node locations along the r-axis (L). Required by
cylindrical-coordinate system if automatic gridding is not
selected.
2.2B.2 UNIGRZ (T/F).
2.2B.3A Z(l), Z(NZ); Optional, used if uniform grid in the z-direction for
cylindrical coordinates.
2.2B.3B Z(K), K = 1 to NZ; Optional, used for nonuniform grid in the
z-direction for cylindrical coordinates.
Z(K) - Array of node locations along the z-axis (L).
The following two records describe a tilted-coordinate system.
2.3.1 TILT (T/F); Optional, required only if a cartesian-coordinate
system is used.
TILT - True if a tilted-coordinate system is desired with the z-axis
not in the vertical upward direction.
194
No tilt may be specified if a free-surface boundary condition is to be
employed (Record 2.20).
2.3.2 THETXZ, THETYZ, THETZZ; Optional, required only if a tilted-
coordinate system is being used.
THETXZ - Angle that the x-axis makes with the vertical upward
direction (DEC).
THETYZ - Angle that the y-axis makes with the vertical upward
direction (DEC).
THETZZ - Angle that the z-axis makes with the vertical upward
direction (DEG).
Fluid properties
2.4.1 BP.
BP - Compressibility of the fluid (F/L2 )" .
Fluid density data
2.4.2 PRDEN, TRDEN, WO, DENFO.
PRDEN - Reference pressure for density (relative to atmospheric)
(eq. 2.2.1.1b) (F/L2 ).
TRDEN - Reference temperature for density (eq. 2.2.1.1b) (T).
WO - Reference mass fraction for density (eq. 2.2.1.1b) and
minimum-mass fraction for scaling (eq. 2.2.1.2) and p p term
(eq. 2.2.1.1c) (-). Needs to be zero if solute decay takes
place. Should be zero if solute transport is not being
simulated.
DENFO - Fluid density at the minimum solute mass fraction (eq. 2.2.1.1c
or eq. 2.2.1.3b) (M/L3 ). (kg/m3 ) or (lb/ft 3 ).
195
2.4.3 Wl, DENF1; Optional, required only if a solute transport is being
simulated.
Wl - Maximum-mass fraction for scaling (eq. 2.2.1.2) and p p term
(eq. 2.2.1.1c) (-). Should be equal to or greater than the
maximum mass-fraction value specified by any boundary
condition or initial condition.
DENF1 - Fluid density at the maximum solute mass fraction (eq. 2.2.1.1c
or eq. 2.2.1.3b) (M/L 3 ) (kg/m3 ) or (lb/ft3 ).
If solute transport is being simulated and a scaled-mass fraction has been
selected for input and output (SCALMF in record 1.4), WO and Wl are used to
perform the scaling according to equation 2.2.1.2 and slope calculation of
equation 2.2.1.3b.
Fluid-viscosity data
2.5.1 NOTVO, (TVFO(I), VISTFO(I), I = 1 to NOTVO); Optional, required
if only flow; or flow and heat transport; or flow, heat and solute
transport are being simulated. Not used if only flow and solute
transport are being simulated.
NOTVO - Number of viscosity versus temperature points for fluid at
minimum or reference solute-mass fraction (minimum of one point).
TVFO - Array of temperature points (T).
VISTFO - Array of viscosity points at minimum solute-mass fraction, WO,
(M/Lt) (kg/m-s) or (cP).
2.5.2 NOTV1 (TVF1(I), VISTFl(I) I = 1 to NOTV1); Optional, required only
if heat and solute transport are being simulated.
NOTV1 - Number of viscosity versus temperature points for fluid at
maximum solute mass fraction (minimum of one point).
TVF1 - Array of temperature points (T).
VISTF1 - Array of viscosity points at maximum solute-mass fraction, Wl,
(M/Lt), (kg/m-s) or (cP).
196
2.5.3 NOCV, TRVIS, (CVIS(I), VISCTR(I), I = 1 to NOCV); Optional, required
only if solute transport is being simulated.
NOCV - Number of viscosity versus mass-fraction points (minimum of two
points).
TRVIS - Reference temperature for viscosity versus mass-fraction data (T)
CVIS - Array of mass-fraction (or scaled-mass-fraction) points (-).
VISCTR - Array of viscosity points for fluid at reference temperature
(M/Lt), (kg/m-s) or (cP).
If only solute transport is being simulated, only record number 2.5.3 is
needed from this group.
Reference condition information
2.6.1 PAATM.
PAATM - Atmospheric absolute-pressure value used to relate gage
pressure to absolute pressure (F/L2 ).
If zero is entered, standard atmospheric pressure of 1.01325X10 5 Pa is used.
2.6.2 POH, TOH.
POH - Reference pressure (relative to atmospheric) for enthalpy
variations, P , (F/L 2 ). This value should be within the range Onof pressure to be simulated.
TOH - Reference temperature for enthalpy variations or the
constant temperature for isothermal simulations, T (T).on
This value should be within the range of temperature to be
simulated.
These values are used in equation 2.2.3.1c.
197
Fluid thermal properties
2.7 CPF, KTHF, BT; Optional, required only if heat transport is being
simulated.
CPF - Fluid heat capacity at constant pressure (FL/M-T). An average
value for the range of solute concentration and temperature to
be simulated should be used (eq. 2.2.3.1b and eq. 2.2.3.1c).
KHTF - Fluid thermal conductivity (F/t-T). An average value for the
range of solute concentration and temperature to be simulated
should be used.
BT - Fluid coefficient of thermal expansion (T ). An average value for
the range of solute concentration and temperature to be simulated
should be used.
Solute information
2.8.1 DM, DECLAM; Optional, required only if solute transport is being
simulated.
DM - Effective molecular diffusivity for the solute in the porous
media (L2 /t).
DECLAM - Solute-decay-rate constant (t~ ).
The following two records describe the zonation of the simulation region.
2.9.1 IPMZ, IIZ(IPMZ) I2Z(IPMZ),J1Z(IPMZ),J2Z(IPMZ),K1Z(IPMZ),K2Z(IPMZ).
IMPZ - Porous-medium zone number.
Records of this form define the zones within the simulation region and
assign zone numbers. These zones are used to assign values to the porous-
medium properties. The ranges of the indices in the I, J, and K directions
define the rectangular prism for a given zone. The zones must be convex
and non-overlapping as explained in section 3.1 and the entire simulation
198
region must be covered by the set of zones. No zones may be defined that
» include elements outside the simulation region. For cylindrical coordinates,
J1Z and J2Z must equal 1. The subscript IPMZ identifies data that are input
by zone number in subsequent records. The number of 2.9.1 records must
equal NPMZ.
2.9.2 End the input with 0 / .
Porous-media properties
2.10.1 KXX(IPMZ), KYY(IPMZ), KZZ(IPMZ); IPMZ = 1 to NPMZ.
KXX - Permeability in the x-direction or r-direction for zone IPMZ (L2 ).
KYY - Permeability in the y-direction for zone IPMZ (L2 ). Not used for
cylindrical coordinates, but a zero or blank space must be
indicated in the input record.
KZZ - Permeability in the z-direction for zone IPMZ (L2 ).
^ 2.10.2 POROS(IPMZ), IPMZ = 1 to NPMZ.
POROS - Porosity of the medium in zone IPMZ (-).
2.10.3 ABPM(IPMZ), IPMZ = 1 to NPMZ.
ABPM - Porous-medium bulk vertical compressibility in zone IPMZ
(F/L2 ) . This compressibility is determined on a fixed mass
of porous medium undergoing vertical compression.
Porous-media thermal properties
2.11.1 RCPPM(IPMZ), IPMZ = 1 to NPMZ; Optional, required only if heat
transport is being simulated.
RCPPM - Heat capacity of the porous-medium solid phase per unit volume
for zone IPMZ (F/L 2 -T).
199
2.11.2 KTXPM(IPMZ), KTYPM(IPMZ), KTZPM(IPMZ), IPMZ = 1 to NPMZ; Optional,
required only if heat transport is being simulated.
KTXPM - Thermal conductivity of the porous medium in the x-direction for
zone IPMZ (F/t-T).
KTYPM - Thermal conductivity of the porous medium in the y-direction
for zone IPMZ (F/t-T). Not used if cylindrical coordinates, but
a zero or a blank space in the input file must be denoted.
KTZPM - Thermal conductivity of the porous medium in the z-direction
for zone IPMZ (F/t-T).
Solute and thermal dispersion information
2.12 ALPHL(IPMZ), ALPHT(IPMZ), IPMZ = 1 to NPMZ; Optional, required only
if heat or solute transport is being simulated.
ALPHL - Longitudinal dispersivity for zone IPMZ (L).
ALPHT - Transverse dispersivity for zone IPMZ (L).
Solute sorption information
2.13 DBKD(IPMZ) IPMZ = 1 to NPMZ; Optional, required only if solute
transport is being simulated.
DBKD - Dimensionless linear-equilibrium-distribution coefficient. This
is the porous-medium bulk density times the distribution
coefficient (-).
Well-model information
2.14.1 RDWDEF (T/F); Optional, required only if there are wells
in the simulation region.
RDWDEF - True if well definition data are to be read.
200
2.14.2 IMPQW (T/F); Optional, required only if there are wells in the region
and cartesian coordinates are being used.
IMPQW - True if semi-implicit well-flow calculations are to be made.
Otherwise, well-flow rates are calculated explicitly at the
beginning of the time step.
Record lines 2.14.3-6 are repeated as often as necessary for each well in the
simulation. Each well must be defined at this point, whether or not it is
active at the start of the simulation.
2.14.3 IWEL, IW, JW, LCBOTW, LCTOPW, WBOD, WQMETH; Optional, required only
if there are wells in the_ simulation region and well-definition
data are to be read.
IWEL - Well number.
IW - Cell number in x-direction of well location.
JW - Cell number in y-direction of well location. Not used in
cylindrical coordinates, but a zero or a blank entry must be
included.
LCBOTW - Cell number in z-direction of lowermost completion layer for
the well.
LCTOPW - Cell number in z-direction of uppermost completion layer for
the well. This is the location at which the dependent-
variable data are taken if this is an observation well.
WBOD - Well bore outside diameter. This is the drilled diameter or
diameter of the screen or perforated casing (L).
WQMETH - Index for well-flow calculation method (integer).
10 - Specified well-flow rate with allocation by mobility
and pressure difference.
11 - Specified well-flow rate with allocation by mobility.
20 - Specified pressure at well datum with allocation by mobility
and pressure difference.
201
30 - Specified well-flow rate with a limiting pressure at well
datum. Flow-rate allocation by mobility and pressure
difference.
40 - Specified surface pressure with allocation by mobility and
pressure difference. Well-riser calculations will
be performed.
50 - Specified surface-flow rate with limiting surface pressure.
Allocation by mobility and pressure difference. Well-riser
calculations will be performed.
0 - Observation well or abandoned well.
2.14.4 WCF(L), L = 1 to NZ-1; Optional, required only if there are wells
in the simulation region and well-definition data are to be read.
WCF - Well-completion-factor.array on an element-by-element basis (-).
Element L goes from the node at z-level L to the node at z-level
L+l. An element completion factor of one means the geometric-mean
of the horizontal permeability for that element will be used in
the well index. An element completion factor of zero means the
well is cased off from the aquifer in that element. A reduced
permeability around the well bore can be approximately represented
by specifying a completion factor less than one. Note that this
is not the same as a well skin factor, which is not included in
the present version of the program. If WCF is zero for the
element between LCBOTW and LCBOTW+1 or for the element between
LCTOPW-1 and LCTOPW, then LCBOTW or LCTOPW should be adjusted
as necessary to range from the bottom to the top completion
layer that communicate with the aquifer. The well-completion
factor also can be used to compute an approximate effective
permeability for a well that is completed in a cell that
contains multiple zones of different permeability.
2.14.5 WRISL, WRID, WRRUF, WRANGL; Optional, required only if well-
definition data are to be read and well-riser calculations are to be
made (WQMETH is 40 or 50).
202
WRISL - Well riser-pipe length (L).
WRID - Well riser-pipe inside diameter (L).
WRRUF - Well riser-pipe roughness factor (L) (see table 2.1).
WRANGL - Well riser-pipe angle with vertical direction (DEG).
2.14.6 HTCWR, DTHAWR, KTHAWR, KTHWR, TABWR, TATWR; Optional, required
only for heat-transport simulations, and if well-riser calculations
are to be done.
HTCWR - Heat-transfer coefficient from the fluid to the well-riser
pipe (E/tL2T).
DTHAWR - Thermal diffusivity of the medium adjacent to the well-riser
pipe (L2 /t).
KTHAWR - Thermal conductivity of the medium adjacent to the well-riser
pipe (F/t-T).
KTHWR - Thermal conductivity of the well-riser pipe (F/t-T).
TABWR - Ambient temperature at the bottom of the well-riser pipe (T).
TATWR - Ambient temperature at the top of the well-riser pipe (T).
2.14.7 End this data set with 0 /.
2.14.8 MXITQW, TOLDPW, TOLFPW, TOLQW, DAMWRC, DZMIN, EPSWR; Optional,
required only if wells are in the region, and if well-riser calculations
are to be done.
MXITQW - Maximum number of iterations allowed for the well-flow rate
allocation calculation. Default of 20.
TOLDPW - Tolerance on the change in well-riser pressure for the well-
riser iterative calculation (F/L2 ). Default of 6xlO~3 Pa.
This is the primary convergence test.
TOLFPW - Tolerance on the fractional change in well-riser pressure for
the well-riser iterative calculation. Default of 0.001. This
is the secondary convergence test.
203
TOLQW - Tolerance on the fractional change in well flow rate because of
temperature and mass-fraction changes for the source term in the
flow equation. Default of 0.001. This is the tertiary
convergence test.
DAMWRC - Damping factor for well-pressure adjustment during the
iterations for allocating flow rates. Default of 2.
DZMIN - Minimum value of step length along the well riser (L).
Default of I percent of riser length.
EPSWR - Fractional tolerance for the integration of the pressure and
temperature equations along the well riser. Default of 0.001.
Boundary-condition information
Specified value
2.15 IBC by i,j,k range; Optional, required only if specified value
boundary-condition cells are present.
IBC - Index of boundary-condition type. This is in the form nj^na
where ni refers to pressure; n£ refers to temperature; and
na refers to mass fraction. The value for n. is set to I to
indicate that a specified value boundary condition for variable
i exists at that cell.
Remember that a specified value for cell removes that cell from the calculation.
Therefore, no other boundary conditions at that cell can be specified for the
equation concerned.
Specified flux
2.16 IBC by i,j,k range; Optional, required only if specified flux boundary-
condition cells are present.
IBC - Index of boundary-condition type. This is in the form niOOn4n5n6
where ^=1,2,3, meaning that the flux is through the x,y, or z
boundary face respectively. Values for n^ ns, and ne are set to
204
2 to indicate that a specified flux boundary condition, for a
chosen equation, is required at that cell, where 0.4 refers to the
flow equation, ns refers to the heat-transport equation, and HQ
refers to the solute-transport equation.
Aquifer leakage
2.17.1 IBC by i,j,k range for aquifer-leakage boundary cells; Optional,
required only if leakage boundary conditions are being used.
IBC - Index of boundary-condition type. It is of the form njOOSOO for
aquifer leakage, where nj indicates the direction of the normal
to the leakage boundary face. Values for nj are 1 for the
x-direction; 2 for the y-direction; and 3 for the z-direction.
The number 3 in the hundreds place denotes an aquifer-leakage
boundary condition.
2.17.2 KLBC, BBLBC, ZELBC by i,j,k range; Optional, required only if leakage
boundary conditions are being used.
KLBC - Permeability of confining layer for aquifer-leakage boundary
condition (L2 ). Appears in equations 2.5.3.la and 3.4.3.la.
BBLBC - Confining-layer thickness for leakage boundary condition (L).
ZELBC - Elevation of the far side of the confining layer away from
the simulation region (L).
For leakage across lateral boundaries of the simulation region, ZELBC is
automatically set equal to the elevation of the corresponding boundary node.
River leakage
2.17.3 I1,I2,J1,J2, KRBC, BBRBC, ZERBC; Optional, required only if the
river-leakage boundary condition is being used.
205
I1,I2,J1,J2 - Node or cell number ranges in the x and y directions
for a river-leakage boundary-condition segment. River
segments are lines in the x-, y-, or diagonal direction.
KRBC - Permeability multiplied by effective-riverbed-area factor
for river-leakage boundary-condition (L 2 ). The effective-
riverbed-area factor is the ratio of the riverbed area to
the boundary-face area for a given cell.
BBRBC - Thickness of the confining layer that forms the riverbed (L).
ZERBC - Elevation of the top of the confining layer that forms the
riverbed defined in figure 2.4 (L).
Use as many 2.17.3 records as necessary to describe the river.
2.17.4 End this data set (records 2.17.3) with 0 /.
Aquifer-influence functions
2.18.1 IBC by i,j,k range for aquifer-influence-function boundary cells;
Optional required only if aquifer-influence-function boundary conditions
are being used.
IBC - Index of boundary-condition type. It is in the form n 100400
for aquifer-influence functions, where nx indicates the direction
of the normal to the influence-function-boundary face. Values for
n^ are 1 for the x-direction; 2 for the y-direction; and 3 for
the z-direction. The number 4 in the hundreds place denotes an
aquifer-influence-function boundary condition.
2.18.2 UVAIFC by i,j,k range; Optional, required only if aquifer-influence
functions are used.
UVAIFC - Temporary storage for input of user-specified factors for
aquifer-influence-function spatial allocation.
206
These factors are defined on a zonal basis, so the factor for all
boundary zones which include a common cell for which an aquifer-influence-
function boundary condition applies must be the same. If default weighting of
the aquifer-influence functions in proportion to their boundary-cell facial
area is desired, no values for UVAIBC need to be entered (except the closing
0 /).
2.18.3 IAIF; Optional, required only if aquifer-influence functions are
being used.
IAIF - Index of aquifer-influence function.
1 - Pot aquifer for outer-aquifer region.
2 - Transient-aquifer influence function with calculation
using the Carter-Tracy approximation.
2.18.4 KOAR, ABOAR, VISOAR, POROAR, BOAR, RIOAR, ANGOAR; Optional, required
only if transient-aquifer-influence functions are being used.
KOAR - Permeability for the outer-aquifer region (L2 ).
ABOAR - Porous-medium bulk vertical compressibility for the outer-
aquifer region (F/L2 )" 1 .
VISOAR - Viscosity of the fluid in the outer-aquifer region (M/Lt),
(kg/m-s) or (cP).
POROAR - Porosity for the outer-aquifer region (-).
BOAR - Total thickness of the outer-aquifer region (L).
RIOAR - Radius of the equivalent cylinder that contains the inner-
aquifer region (L). Usually determined by equation 3.4.4.2.1.
ANGOAR - Angle of influence of the outer-aquifer region (DEG.).
This is the angle subtended by the part of the equivalent
cylindrical boundary that is subject to flux determined by the
aquifer-influence function.
The following three records describe the gridding and parameters for heat-
conduction boundary conditions.
207
2.19.1 IBC by i,j,k range for heat-conduction boundary-condition nodes;
Optional, required only if a heat simulation, and if heat-conduction
boundary condition cells are to be used.
IBC - Index of boundary-condition type, denoted by a number in the
form niOOOAO where ni indicates the direction of the outward
normal to the heat-conduction boundary-condition cell face. The
values for ni are: 1 for the x-direction; 2 for the y-direction;
and 3 for the z-direction. The signs of the normal is disregarded
The 4 indicates that this cell has a heat-conduction boundary
condition on one of its faces. Only one face of a given cell can
be assigned a heat-conduction boundary condition.
2.19.2 ZHCBC(K) K = 1 to NHCN; Optional, required if heat simulation is
being done, and there are heat-conduction boundaries (NHCBC > 0).
ZHCBC - Array of node distances along the outward pointing normal from
a heat-conduction boundary surface (L). The first value must
be zero. All heat-conduction boundary-condition cells use
the same nodal distribution.
2.19.3 UDTHHC by i,j,k range for heat-conduction boundary-condition cells;
Optional, required only if a heat simulation, and if there are heat-
conduction boundary-condition cells.
UDTHHC - Temporary storage for input of thermal diffusivity of the
heat-conducting medium outside the simulation region as a
function of boundary-cell location (L 2 /t).
2.19.4 UKHCBC by i,j,k range for heat-conduction boundary-condition cells;
Optional, required only if a heat simulation, and if there are heat-
conduction boundary-condition cells.
UKHCBC - Temporary storage for input of thermal conductivity of the
heat-conducting medium outside the simulation region as a
function of boundary-cell location (E/L-t-T).
208
Free-surface boundary condition
2.20 FRESUR (T/F), PRTCCM (T/F).
FRESUR - True if the region is unconfined, so that a free-surface
boundary exists.
PRTCCM - True if a message is to be printed when a free surface rises
above the top of a cell or falls below the bottom of a cell,
or if a cell below the uppermost layer becomes unsaturated.
Initial conditions
2.21.1 ICHYDP (T/F), ICT (T/F), ICC (T/F).
ICHYDP - True if initial condition of hydrostatic pressure
distribution is to be specified.
ICT - True if an initial-condition temperature distribution is to be
specified.
ICC - True if an initial-condition mass-fraction distribution is
to be specified.
2.21.2 ICHWT (T/F); Optional, required only if a free-surface boundary exists
ICHWT - True if an initial-condition water-table-elevation distribution
is to be input.
2.21.3A ZPINIT, PINIT; Optional, required only if an initial-condition
hydrostatic-pressure distribution is being specified.
ZPINIT - Elevation of the initial-condition pressure (L).
PINIT - Pressure for hydrostatic, initial-condition distribution (F/L2 ).
2.21.38 P by i,j,k range; Optional, required only if a non-hydrostatic
pressure distribution is being specified as an initial condition.
P - Pressure distribution for the initial condition (F/L 2 ).
209
2.21.3C HWT by i,j,k range; Optional, required only if desired in
conjunction with a free-surface boundary condition.
HWT - Water-table-elevation distribution for the initial condition (L).
Specified for the upper layer of cells only.
2.21.4A NZTPRO (ZT(I), TVD(I); I = 1 to NZTPRO); Optional, required only if
a heat simulation is being done.
NZTPRO - Number of points in the temperature-versus-depth profile for
initial-condition temperature distribution. Limit of 10.
ZT - Array of locations along the z-axis for initial-temperature
distribution (L). These locations must span the entire
z-axis range of the region.
TVD - Array of initial temperatures along the z-axis (T).
2.21.4B T by i,j,k range; Optional, required only if ICT is true.
T - Temperature distribution for the initial condition (T).
2.21.5 NZTPHC, ZTHC(I), TVZHC(I), I = 1 to NZTPHC; Optional, required only
if a heat-transport simulation is being done, and if there are heat-
conduction boundary conditions.
NZTPHC - Number of points in the outward normal direction to the heat-
conduction boundary-condition surfaces for initial-condition-
temperature profile. Limit of 5.
ZTHC - Array of node locations in the outward normal direction for
initial-condition-temperature profile for heat-conduction
boundary-condition cell faces (L). The first value must be
zero, and these nodes must span the mesh defined by ZHCBC in
record 2.19.2.
TVZHC - Array for the initial-condition temperature-profile values
for heat-conduction boundary-condition cell faces (T).
210
The same initial-condition profile is used for each heat-conduction boundary
condition cell.
2.21.6 C by i,j,k range; Optional, required only if ICC is true.
C - Mass-fraction (or scaled mass fraction) distribution for the
initial condition (-).
Calculation information
2.22.1 FDSMTH, FDTMTH.
FDSMTH - Factor for spatial-discretization method.
0.5 - centered-in-space differencing used for advective terms.
0 - upstream differencing in space used for advective terms.
FDTMTH - Factor for temporal-discretization method.
0.5 - centered-in-time or Crank-Nicholson differencing used.
1. - backward-in-time or fully-implicit differencing used.
2.22.2 TOLDEN, MAXITN.
TOLDEN - Tolerance in fractional change in density for convergence
over a solution cycle of flow, heat, and solute equations at
a given time plane. Default set at 0.001.
MAXITN - Maximum number of iterations allowed for a cycle of pressure,
temperature, and mass-fraction solutions allowed at a given
time plane. Default set at 5.
2.22.3 NTSOPT, EPSSOR, EPSOMG, MAXIT1, MAXIT2; Optional, required only
if the two-line, successive-overrelaxation method for solving
the system matrix equations is selected.
211
NTSOPT - Number of time steps between recalculations of the optimum-
overrelaxation parameter. Default set at 5.
EPSSOR - Tolerance for the two-line, successive-overrelaxation iterative
solution of the matrix equations at each time plane. Default
set at 1 x 10~ 5 . The maximum fractional change in any of the
values of the dependent variable must be less than or equal to
this tolerance times (2-U) ,_).opt
EPSOMG - Tolerance on the fractional change in the overrelaxation
parameter during the iterative calculation to determine the
optimum value. Default set to 0.2.
MAXIT1 - Maximum number of iterations allowed for the calculation of
the optimum overrelaxation parameter. Default set at 50.
MAXIT2 - Maximum number of iterations allowed for the solution of the
matrix equations. Default set at 100.
Output of static data
2.23.1 PRTPMP (T/F), PRTFP (T/F), PRTIC (T/F), PRTBC (T/F), PRTSLM (T/F),
PRTWEL (T/F).
PRTPMP - True if a printout of porous-media properties is desired.
PRTFP - True if a printout of fluid properties is desired.
PRTIC - True if a printout of initial conditions is desired.
PRTBC - True if a printout of static boundary-condition information
is desired.
PRTSLM - True if a printout of solution-method information is desired.
PRTWEL - True if a printout of static-well bore information is desired.
2.23.2 IPRPTC, PRTDV (T/F); Optional, required only if initial-condition
printouts of the dependent variables are desired.
212
IPRPTC - Index of printout for initial-condition information. It is
of the form ni^na, where n. is set to 1 for printout of the
ith variable, otherwise n. is set to 0. The variables are ni' i
for pressure; 0.2 for temperature; and 0.3 for mass fraction.
In addition, n^ is set to 2 for both pressure and
potentiometric head to be printed for isothermal cases; 0.2 is
set to 2 for both temperature and fluid enthalpy to be printed,
PRTDV - True if a printout of the density and viscosity arrays
is desired.
2.23.3 ORENPR; Optional, required only for a cartesian-coordinate system.
ORENPR - Index for orientation of the array printouts (integer);
12 - Means x-y printouts for each plane along the z-axis,
areal layers.
13 - Means x-z (or r-z) printouts for each plane along the
y-axis, vertical slices.
A negative value means the y or z-axis is positive down the page.
2.23.4 PLTZON (T/F); Optional, required only if printout of porous-media
properties has been requested.
PLTZON - True if a line-printer plot of the porous-media property
zones is desired.
2.23.5 OCPLOT (T/F).
OCPLOT - True if plots of observed and calculated values of the
dependent variables are to be plotted versus time at the end
of the simulation.
213
Transient data - READS
Groups of transient data are read by subroutine READS; one at the beginning
and others during the simulation, as necessary, whenever sources, boundary
conditions, calculation parameters, or output options are to be changed.
Only the parameters that are to be changed need to be input. The remaining
parameters will keep their previous values.
3.1 THRU (T/F).
THRU - True if the simulation is through, and the closing procedures
can begin. Proceed to record 3.99 if the simulation is finished,
Well information
3.2.1 RDWFLO (T/F), RDWHD (T/F); Optional, required only if there are wells
in the simulation region.
RDWFLO - True if well-flow-rate data is to be read at this time.
RDWHD - True if well-head data is to be read at this time.
3.2.2 IWEL, QWV, PWSUR, PWKT, TWSRKT, CWKT; Optional, required only if
well-flow or well-head data are to be read at this time.
IWEL - Well number.
QWV - Volumetric flow rate for this well (L3 /t), (£/s) or (ft3/d).
PWSUR - Pressure at the land surface for this well (F/L2 ).
Used when surface conditions are specified and the well-riser
calculation is to be done.
PWKT - Pressure at the well datum for this well (F/L 2 ).
Used when well-datum conditions are specified, and no well-riser
calculation is to be done.
TWSRKT - Fluid temperature at the land surface or well datum for this
well (T). Used when surface conditions are specified for an
injection well, and used for the well-datum value, when
well-datum conditions are specified.
214
CWKT - Mass fraction (or scaled-mass fraction) at the well datum for
this well (-). Surface and well-datum concentrations are equal,
so this variable also is used to specify surface conditions for
an injection well.
As many records of type 3.2.2 are used as necessary to define conditions at
all the wells. Data do not have to be input for any well that does not have
its conditions changed at this time.
3.2.3 End this data set with 0 /.
Boundary-condition information
Specified value
3.3.1 RDSPBC (T/F), RDSTBC (T/F), RDSCBC (T/F); Optional, required only if
there are specified-pressure, temperature or mass-fraction boundary-
condition cells.
RDSPBC - True if specified-pressure boundary-condition data are to
be read at this time.
RDSTBC - True if specified-temperature boundary-condition data are
to be read at this time.
RDSCBC - True if specified mass-fraction boundary-condition data
are to be read at this time.
3.3.2 PNP by i,j,k range; Optional, required only if specified-pressure
boundary-condition values are to be input.
PNP - Pressure at specified-pressure boundary-condition nodes (F/L 2 ).
3.3.3 TSBC by i,j,k range; Optional, required only if specified-pressure
boundary-condition values are to be read, and if a heat-transport
simulation is being done.
215
TSBC - Temperature associated with a specified-pressure boundary
condition node (T). If inflow occurs, this temperature will
determine the heat-inflow rate.
3.3.4 CSBC by i,j,k range; Optional, required only if specified-pressure
boundary-condition values are to be read, and if solute transport
is being simulated.
CSBC - Mass fraction (or scaled-mass fraction) associated with a
specified-pressure boundary-condition node (-). If inflow
occurs, this mass fraction will determine the solute-inflow
rate.
3.3.5 TNP by i,j,k range; Optional, required only if specified-temperature
boundary-condition data are to be read.
TNP - Temperature at specified-temperature boundary-condition nodes
(T).
3.3.6 CNP by i,j,k range; Optional, required only if specified mass-
fraction values are to be input.
CNP - Mass fraction (or scaled-mass fraction) for specified mass-
fraction boundary-condition nodes.
Specified flux
3.4.1 RDFLXQ (T/F), RDFLXH (T/F), RDFLXS (T/F); Optional, required only if
specified-flux boundary conditions exist.
RDFLXQ - True if specified fluid-flux values are to be read at this
time.
RDFLXH - True if specified heat-flux values are to be read at this
time.
216
RDFLXS - True if specified solute-flux values are to be read at this
time.
3.4.2 QFFX, QFFY, QFFZ by i,j,k range; Optional, required only if
specified fluid-flux values are to be read at this time.
QFFX, QFFY, QFFZ - Components of the fluid-flux vector for a boundary
cell in the x,y, and z-coordinate directions, respectively
(L3 /L2 t).
3.4.3 UDENBC by i,j,k range; Optional, required only if specified fluid-
fluxes values are to be read at this time.
UDENBC - Density associated with specified-fluid flux (M/L3 ); (kg/m3 ) or
(lb/ft 3 ). If inflow, this density determines the mass flux.
3.4.4 TFLX by i,j,k range; Optional, required only if specified fluid
fluxes are to be read at this time, and if heat transport is being
simulated.
TFLX - Temperature associated with specified fluid flux (T). If inflow,
this temperature determines the heat flux.
3.4.5 CFLX by i,j,k range; Optional, required only if specified fluid
fluxes are to be read at this time, and if solute transport is
being simulated.
CFLX - Mass fraction (or scaled mass fraction) associated with specified
fluid flux (-). If inflow, this mass fraction determines the
solute flux.
3.4.6 QHFX, QHFY, QHFZ by i,j,k range; Optional, required only if
specified heat-flux values are to be read at this time.
217
QHFX, QHFY, QHFZ - Components of the specified heat-flux vector for
a boundary cell in the x,y and z-coordinate directions
respectively. Heat flux should be specified only through faces
where there is no fluid flux (E/L2 -t).
3.4.7 QSFX, QSFY, QSFZ by i,j,k range; Optional, required only if
specified solute-flux values are to be read at this time.
QSFX, QSFY, QSFZ - Components of the specified solute flux for a
boundary cell in the x,y and z coordinate directions respectively.
Solute flux should be specified only through faces where there is
no fluid flux (M/L 2 -t).
Leakage boundary conditions
3.5.1 RDLBC(T/F); Optional, required only if leakage boundary-condition
cells are employed.
RDLBC - True if leakage boundary-condition data are to be read this
time.
3.5.2 PHILBC, DENLBC, VISLBC by i,j,k range; Optional, required only if
leakage boundary-condition data are to be read at this time.
PHILBC - Potential energy per unit mass of fluid (eq. 2.5.3.1.1b) on the
other side of the aquitard from the simulation region (E/M).
DENLBC - Density of the fluid on the other side of the aquitard (M/L 3 ),
(kg/m3 ) or (lb/ft 3 ).
VISLBC - Viscosity of the fluid on the other side of the aquitard
(M/L-t); (kg/m-s) or (cP).
3.5.3 TLBC by i,j,k range; Optional, required only if leakage boundary-
condition data are to be read at this time, and if heat transport
is being simulated.
218
TLBC - Temperature of the fluid on the other side of the aquitard (T).
3.5.4 CLBC by i,j,k range; Optional, required only if leakage boundary-
condition data are to be read at this time, and if solute transport
is being simulated.
CLBC - Solute-mass fraction (or scaled-mass fraction) on the other side
of the aquitard (-).
River leakage
3.5.5 I1,I2,J1,J2, HRBC, DENRBC, VISRBC, TRBC, CRBC; Optional, required
only if river-leakage boundary-condition data are to be read at this
time.
I1,I2,J1,J2 - Node or cell number ranges in the x and y directions
for a river-leakage boundary-condition segment. They should
correspond to the segments used to define the river in data record
2.22.4.
HRBC - Potentiometric head in the river (L).
DENRBC - Density of the river fluid (M/L3 ); (kg/m3 ) or (lb/ft 3 ).
VISRBC - Viscosity of the river fluid (M/L-t); (kg/m-s) or (cP).
TRBC - Temperature of the river fluid (T).
CRBC - Solute-mass fraction (or scaled-mass fraction) of the river
fluid (-).
As many records of type 3.5.5 are used as necessary to include all the cells
at which a river-leakage boundary condition exists.
3.5.6 End this data set (record 3.5.5) with 0 /.
Aquifer influence functions
3.6.1 RDAIF (T/F); Optional, required only if aquifer-influence-function
boundary-condition cells are employed.
219
KDAIF - True if aquifer-influence-function boundary-condition data
are to be read at this time.
3.6.2 DENOAR by i,j,k range; Optional, required only if aquifer-influence-
function cells are employed.
DENOAR - Density of the fluid in the outer-aquifer region (M/L 3 );
(kg/m3 ) or (lb/ft3 ).
3.6.3 TAIF by i,j,k range; Optional, required only if aquifer-influence-
function boundary condition cells are employed, and if heat transport
is being simulated.
TAIF - Temperature of the fluid in the outer-aquifer region associated
with a given aquifer-influence-function cell (T).
3.6.4 CAIF by i,j,k range; Optional, required only if aquifer-influence-
function cells are employed, and if solute transport is being
simulated.
CAIF - Mass fraction of solute in the outer-aquifer region associated
with a given aquifer-influence-function cell (-).
Calculation information
The following data pertains to time-step control and the time when new
transient data will be read.
3.7.1 RDCALC (T/F).
RDCALC - True if calculation information is to be read at this time.
3.7.2 AUTOTS (T/F); Optional, required only if calculation information
is to be read at this time.
220
AUTOTS - True if automatic time-step adjustment is desired for the
next interval of simulation time.
3.7.3A DELTIM; Optional, required only if automatic time-step calculation
is not being used and calculation information is being read at this time
DELTIM - Time-step length (t).
3.7.3B DPTAS, DTTAS, DCTAS, DTIMMN, DTIMMX; Optional, required only if
automatic time-step calculation is being used and calculation
data are being read at this time.
DPTAS - Maximum change in pressure allowed for setting the time step
automatically (F/L2 ). Default set at 5 x 104 Pa.
DTTAS - Maximum change in temperature allowed for setting the time step
automatically (T). Default set at 5 °C.
DCTAS - Maximum change in mass fraction (or scaled-mass fraction)
allowed for setting the time step automatically (-). Default
set at 0.25 (scaled).
DTIMMN - Minimum time step required (t). This time step will be used
for the first two steps after a change in boundary conditions,
that is, at TIMCHG. Default set at 104 s.
DTIMMX - Maximum time step allowed (t). Default set at 10 7 s.
3.7.4 TIMCHG.
TIMCHG - Time at which new transient data will be read or at which
the simulation will be terminated (t).
Output information
3.8.1 PRIVEL, PRIDV, PRISLM, PRIKD, PRIPTC, PRIGFB, PRIWEL, PRIBCF.
PRIVEL - Printout interval (integer) for velocity arrays. These are
interstitial velocities at the cell boundaries.
221
PRIDV - Printout interval (integer) for fluid density and fluid-
viscosity arrays.
PRISLM - Printout interval (integer) for solution-method information,
number of iterations, maximum changes in dependent variables,
and so forth.
PRIKD - Printout interval (integer) for conductance and dispersion-
coefficient arrays.
PRIPTC - Printout interval (integer) for pressure, temperature, and
mass-fraction arrays.
PRIGFB - Printout interval (integer) for flow-balance information for
the region.
PRIWEL - Printout interval (integer) for well information.
PRIBCF - Printout interval (integer) for specified-value boundary-
condition flow rates.
For all of the above printout intervals:
0 - Means no printout of this information.
n - Means that printout will occur every nth time step and at the
end of the simulation.
-1 - Means that printout will occur only at the time at which
new transient data will be read and at the end of the
simulation.
3.8.2 IPRPTC; Optional, required only if dependent-variable printouts
are desired.
IPRPTC - Index for printout of pressure, temperature and mass-fraction
arrays. It is of the form n^^ns where ni is for the pressure;
0.2 is f°r ^e temperature; and TLQ is for the mass-fraction
array. The n. are set to 1 if printout is desired for the ith
variable, nj is set to 2 if both pressures and potentiometric
heads are to be printed for isothermal cases. n2 is set to 2
if both temperatures and fluid enthalpies are to be printed.
222
3.8.3 CHKPTD (T/F), NTSCHK, SAVLDO (T/F).
CHKPTD - True if check-point dumps are to be made for possible restarts
of the simulation.
NTSCHK - Number of time steps between successive check-point dumps.
If set to -1, a dump will occur only at the times when new
transient data are read and at the end of the simulation.
SAVLDO - True if only the last check-point dump is to be saved.
The following four records are for the generation of contour maps on the
line printer.
3.9.1 RDMPDT (T/F), PRTMPD (T/F).
RDMPDT - True if control data for map generation are to be read at
this time.
PRTMPD - True if control data for map generation are to be written
to the output file.
3.9.2 MAPPTC, PRIMAP; Optional, required only if contour-map-control data are
to be read at this time.
MAPPTC - Index for a zoned contour map. It is in the form ni^ns, where
nj is for pressure; H£ is for temperature; n^ is for mass
fraction. The n. are set to 1 if a contour map is desired for
the ith dependent variable.
PRIMAP - Printout interval (integer) for contour maps. Number of time
steps between map generations.
0 - means no contour maps.
n - means contour maps at every nth time step.
-1 - means contour maps at the time when new transient data
will be read and at the end of the simulation.
3.9.3 YPOSUP (T/F), ZPOSUP (T/F), LENAX, LENAY, LENAZ; Optional, required
only if contour-map-control data are to be read at this time.
223
YPOSUP - True if the y-axis is positive upward on the page for this
contour-map set.
ZPOSUP - True if the z-axis is positive upward on the page for this
contour-map set.
LENAX - Length of the x-axis on the page for this contour-map set (in).
LENAY - Length of the y-axis on the page for this contour-map set (in).
LENAZ - Length of the z-axis on the page for this contour-map set (in).
3.9.4 IMAP1, IMAP2, JMAP1, JMAP2, KMAP1, KMAP2, AMIN, AMAX, NMPZON;
Optional, required only if contour-map-control data are to be read at
this time.
IMAP1, IMAP2 - Range of node numbers along the x-axis for a contour map.
Default set from 1 to NX.
JMAP1, JMAP2 - Range of node numbers along the y-axis for a contour
map. Set to 1,1 for cylindrical coordinates. Default
set from 1 to NY.
KMAP1, KMAP2 - Range of node numbers along the z-axis for a contour map.
Default set from 1 to NZ.
AMIN, AMAX - Range of the dependent variable for a contour map
(appropriate units). If a pair of null entries, automatic
scaling of the range will be performed of that dependent
variable.
One pair of the indices iMAPl and iMAP2 may be set equal to produce a contour
map for just one plane.
NMPZON - Number of zones into which the contour map will be divided.
Default set at 5. Limit of 32.
Up to three records of type 3.9.4 may be needed, depending on which
combinations of pressure, temperature, and mass fraction are selected for
mapping. The record order is: (1) Pressure-map data, (2) temperature-map
data, and (3) solute-mass-fraction map data.
224
This ends the transient data set that is read at a given time. At simulation
time equal to TIMCHG, another transient-data set will be read, until the
simulation is finished. At that time, THRU is read as true in the following
record.
3.99.1 THRU (T/F).
THRU - Set to true at this point to signify the end of the simulation.
3.99.2 PLOTWP(T/F), PLOTWT(T/F) PLOTWC(T/F).
PLOTWP - True if observed and(or) calculated well pressures are to be
plotted versus time.
PLOTWT - True if observed and(or) calculated well temperatures are to
be plotted versus time.
PLOTWC - True if observed and(or) calculated well mass fractions are
to be plotted versus time.
Temporal-plot information
The following data records of type 4.N are required only if character-string
plots of variables versus time are desired at selected wells.
4.1 IWEL, RDPLTP (T/F); Optional, required only if temporal plots are to
be made, and new plot-control parameters are to be set for
subsequent plots (RDPLTP is true).
IWEL - Well number. This number must agree with the number associated
with the calculated data.
RDPLTP - True if new plotting-control parameters are to be read at this
time for subsequent plots.
4.2 IDLAB; Optional, required only if temporal plots are to
be made, and new plot-control parameters are to be read for
subsequent plots (RDPLTP is true).
225
IDLAB - Identification label for this well's plots. A character
string of up to 80 characters. Space over at least one
character position from the left.
4.3 NTHPTO, NTHPTC, PWMIN, PWMAX, PSMIN, PSMAX, TWMIN, TWMAX, TSMIN, TSMAX,
CMIN, CMAX; Optional, required only if temporal plots are to
be made, and new plot-control parameters are to be read for subsequent
plots (RDPLTP is true).
NTHPTO - Index for plotting the first, then every nth observed data
point versus time. Default set to one. A blank may be
entered if no observed data are to be plotted.
NTHPTC - Index for plotting the first then every nth calculated value
versus time. Default set to one.
PWMIN, PWMAX - Minimum and maximum values of pressure at the well datum
that set the axis range for the temporal plots (F/L2 ).
PSMIN, PSMAX - Minimum and maximum values of pressure at the land
surface that set the axis range for the temporal plots
(F/L2 ).
TWMIN, TWMAX - Minimum and maximum values of temperature at the well
datum that set the axis range for the temporal plots (T).
TSMIN, TSMAX - Minimum and maximum values of temperature at the land
surface that set the axis range for the temporal plots
(T).
CMIN, CMAX - Minimum and maximum values of solute-mass fraction (scaled-
mass fraction) at the well datum and the land surface that
set the range for the temporal plots (-).
The pressure, temperature and solute-mass fraction ranges for the plots
can be specified by the user or established automatically. The latter option
is invoked by entering zeros for the maximum and minimum values.
226
4.4 TO, POW, POS, TOW, TOS, COW; Optional, required only if there are
observed data.
TO - Time of observation (t).
POW - Pressure observed at the well-datum level (F/L2 ).
POS - Pressure observed at the land surface in the well (F/L 2 ).
TOW - Temperature observed at the well-datum level (T).
TOS - Temperature observed at the land surface in the well (T).
COW - Mass fraction (or scaled-mass fraction) observed in the well at
the well datum or the land surface (-).
It is assumed that the observed data are in the same units that will be used
for output of the calculated data. As many records of type 4.4 are used as
necessary to enter all the observed well data. There may be wells for which
only calculated data are available; for these wells, no records of type 4.4
will be read.
4.5 End this data set with -1. / .
Indicates the end of the observed data set for this well.
As many records of type 4.1-4.4 are used as necessary for all of the wells for
which observed or calculated data are being plotted.
4.6 End this data set with 0 / .
Indicates the end of the temporal-plot information and the observed data for
all the wells.
This ends the input-data-file description. For quick reference, a list of
the definitions for the various program-control options is provided in
table 5.3.
227
Table 5.3. Option lists for program-control variables
Variable Option definitions
SLMETH 1 - Selects the direct, D4, equation solver.2 - Selects the iterative, two-line, successive-
overrelaxation equation solver.
In the following, ni denotes outward normal direction to the boundary face: 1 is the x-direction; 2 is the y-direction; and 3 is the z-direction.
IBC -1 - Cell is excluded from the simulation region. 100 - Specified-pressure boundary-condition node. 010 - Specified-temperature boundary-condition node. 001 - Specified-solute-concentration boundary-condition
node.ni00200 - Specified-fluid-flux boundary-condition cell. ni00020 - Specified-diffusive-heat-flux boundary-condition
cell. ni00002 - Specified-diffusive-solute-flux boundary-condition
cell.ni00300 - Leakage boundary-condition cell.^00400 - Aquifer-influence-function boundary-condition cell. ni00040 - Heat-conduction boundary-condition cell.
IAIF 1 - Pot aquifer for outer region.2 - Transient-aquifer-influence function with
calculation using the Carter-Tracy approximation.
WQMETH 10 - Specified well-flow rate with allocation bymobility and pressure difference.
11 - Specified well-flow rate with allocation bymobility.
20 - Specified pressure at well datum with allocationby mobility and pressure difference.
30 - Specified well-flow rate with a limiting pressureat well datum. Flow-rate allocation by mobilityand pressure difference.
40 - Specified surface pressure with allocation bymobility and pressure difference. Well-risercalculations will be performed.
50 - Specified surface-flow rate with limiting surfacepressure. Allocation by mobility and pressuredifference. Well-riser calculations will beperformed.
0 - Observation well or abandoned well.
FDSMTH 0.5 - Centered-in-space differencing for advective terms 0.0 - Upstream differencing for advective terms.
FDTMTH 0.5 - Centered-in-time differencing.1.0 - Backward-in-time or fully implicity differencing.
228
Table 5.3. Option lists for program-control variables Continued
Variable Option definitions
IPRPTC
ORENPR
Ixx - Printout of pressure field.2xx - Printout of pressure and potentiometric-head fieldsxlx - Printout of temperature field.x2x - Printout of temperature- and fluid-enthalpy fields.xxl - Printout of solute-concentration field.
12 - Printouts of arrays by areal (x-y) layers.13 - Printouts of arrays by vertical x-z or (r-z) slices
A negative value means the y or z-axis is to be positive down the page.
PRIxxx 0 - No printout.n - Printout every nth time step and at the end of the
simulation.-1 - Printout only at the time of new transient data
being read and at the end of the simulation.
MAPPTC Ixx - Pressure-contour maps desired to be produced, xlx - Temperature-contour maps to be produced, xxl - Solute-concentration contour maps to be produced.
229
6. OUTPUT DESCRIPTION
Various types of output result from running the HST3D program. Most of
the output is to disc files to be displayed on a video screen or routed to a
line printer. These files are written in ASCII format. The two exceptions
are the optional check-point/restart dumps written in binary format to a disc
file, and the calculated dependent-variable data for the wells that
periodically are written, also in binary format, to a disc file for the
temporal plots that can be made at the end of the simulation.
Output is generated at several stages during the simulation. Some
information, such as the heading, title, array-partitioning data, and
problem-geometrical information, is printed always. The heading contains the
program version number which will change when major modifications or correc
tions are made. The units employed for the ouput are the same as those used
for the input data, either metric or inch-pound as specified in record 1.4.
Table 5.2 and the input-record descriptions (section 5.2.2) give the inch-pound
and the metric units employed. For easier reading, variables are identified
in the output by descriptors rather than program-variable names. Much of the
output is optional, and the numbers of the records containing the control
variables in the data-input-form list of table 5.1 are indicated. The writing
of a file that echos each record of input data, as it is read, is optional
(record 1.10). The static data that may be printed include porous-media
properties, fluid properties, initial-condition distributions, boundary-
condition information, solution-method information, well information (record
2.23.1), and density and viscosity distributions (record 2.23.2). The selec
tion of which of the dependent variables (pressure, temperature or mass
fraction) will have initial conditions printed is made in record 2.23.2.
Print intervals can be selected individually for information that is
printed at the end of a time step. The information printed may include the
velocity distribution, the density and viscosity distributions, the solution
method information, the conductance and dispersion-coefficient distributions,
the dependent-variable distributions, the regional fluid-flow, heat-flow and
solute-flow rates, the regional cumulative-flow results, and the specified-
230
value boundary-condition flow rates (record 3.8.1). The selection of of the
dependent variables which will be printed is determined in record 3.8.2.
Contour maps of pressure, temperature, and mass fraction can be produced
on the line printer; they are zoned into intervals and may cover subregions of
the simulation as specified by the user (record 3.9.A). The contour-mapping
routine produces character-string plots. Alternating zones of symbols and
blanks are used to make perception easier. The user can make a programming
change (set variable, ZEBRA, to false) to cause the symbol-filled zones to be
adjacent to each other. Contour intervals are automatically calculated to be
a multiple of 2, 5, or 10. The lower and upper limits can be chosen by the
user or determined from the range of the data to be contoured. In the former
case, values below the specified-lower limit are contoured with a zone of
minus signs and values above the specified-upper limit are contoured with a
zone of plus signs. The contour zones contain their lower-boundary values;
the upper-boundary values belong to the next zone above with the exception of
the highest zone of the map which does contain its upper-boundary value. The
maps are either areal or vertical slices along nodal planes of the three-
dimensional region (record 2.23.3), with the orientation sepcified in record
3.9.3. The size of the maps on the paper is chosen by the user (record
3.9.3). An echo printout of the mapping specifications can be requested
(record 3.9.1). Bilinear interpolation is used to locate the contour-interval
boundaries; cells excluded from the simulation region are indicated by X's.
If multiple pages are used for the contour maps, no printing is done across
the paper folds. Thus, separation and alinement of the various pages is
necessary to eliminate gaps.
Temporal plots of selected variables are also in character-string format.
The plots that may be produced at the end of the simulation include well-datum
pressure, well-surface pressure, well-datum temperature, well-surface
temperature, and well solute-mass fraction (or scaled-mass fraction) (record
3.99.2). For observation wells, the well-datum value is taken to be the value
in the aquifer cell at the well-datum level. Observed (record 4.4) and
calculated data of the same type are plotted together for comparison purposes.
The time axis runs down, and the dependent-variable axis runs across the page.
231
A limit of 500 lines is set. If the time series to be plotted of any
calculated variable contains more than three times the total number of node
points in the region, or the series of any observed variable contains more
than two times the number of node points in the region, array-storage problems
will occur and program execution will be terminated. These problems may be
avoided by plotting the first point followed by only every nth point
thereafter (record 4.3). The user may specify the ranges of the variables to
be plotted. However automatic scaling of the plot is available using the
minimum and maximum values of the variables. Axis subdivisions that are a
multiple of 2, 5 or 10 are produced. The present version of the HST3D code
contains no provision for producing line plots on pen-plotting devices or
video screens.
232
7. COMPUTER-SYSTEM CONSIDERATIONS
The heat- and solute-transport simulation program was developed initially
on a Control Data Cyber 170/720 computer 1 , and finally on a Prime 9950
computer. The Cyber computer has a very fast arithmetic central-processing
unit relative to the Prime, while the Prime has virtual storage that the Cyber
does not have. Therefore, the programming philosophies needed to create the
optimum code for execution of large, long-running simulations are in direct
opposition for these two machines. Specifically, the Cyber, with its fast
arithmetic, but limitations on storage, is most efficiently used with a code
that minimizes storage requirements. This is accomplished to a certain extent
by recalculating some quantities each time they are needed, rather than
storing them. On the other hand, the virtual storage of the Prime means that
storage space is not a limiting factor; but, the slower arithmetic means that
the running time for large, long simulations may become inconveniently long.
This implies that the most efficient code for the Prime will use more storage
than the Cyber and never compute a quantity more than once.
The present version of the heat- and solute-transport code is not optimal
for either type of machine, but it tends to be oriented toward the Prime.
Further optimization of the program will require timing tests. The storage
requirement on the Prime computer for the executable-code module is about 1.1
megabytes, exclusive of the variably partitioned arrays, when compiled with the
interactive-debug option and no optimization.
The language used for this program is FORTRAN-77, although some
FORTRAN-IV coding still exists. An attempt has been made to use only the ANSI
standard FORTRAN-77 for maximum portability (American National Standards
Institute, 1978).
Double-precision arithmetic has been used for all real variables.
Separate variably partitioned arrays were defined for real and integer vari-
1Use of brand names in this report is for identification purposes only and
does not constitute endorsement by the U.S. Geological Survey.
233
ables, so that the real variables could be made double precision. FORTRAN-77
intrinsic function names were used in their generic form, so that no changes
had to be made for use with double-precision variables.
Although the standards for FORTRAN-77 have been followed as closely as
possible, there are always problems of portability to different computer
systems. Development experiences revealed some differences between the Prime
and Cyber computers that affect program portability.
There are no alternate entry points into any of the subroutines, to avoid
computer incompatibilities. The Prime uses dynamic storage of variables and
of compiled code during program execution. However, all variables in common
blocks are automatically made static. Static data items retain their values
between subprogram references, while dynamic data items in a subprogram lose
their values upon return from that subprogram. By including all common blocks
in the main program, potential problems with computer systems that do not make
common block variables automatically static should be avoided. Variables are
explicitly initialized where necessary, so no reliance is made on system-
default initialization.
The Cyber computer FORTRAN compiler allows only 63 arguments in a
subprogram-argument list. The Prime compiler allows 256. There are a few
subroutines in the heat- and solute-transport program that have more than 63
arguments. To reduce the number to within the limit for the Cyber computer,
some subarrays would need to be eliminated from the argument list,
necessitating some receding. The eliminated subarrays would be passed by
passing the entire variably partitioned arrays along with appropriate pointer
indices.
The Cyber requires the BLOCKDATA subprogram to be contained in the same
file as an executable subprogram; whereas, the Prime allows it to be compiled
from its own separate file. The version of the code discussed in this docu
mentation has the main program, and each subprogram, including BLOCKDATA,
contained in a separate file.
234
8. COMPUTER-CODE VERIFICATION
Verification of a computer program is the process of ensuring that the
code performs the intended calculations correctly. This is in contrast to
computer-model validation, which is the demonstration that a particular model
with a particular set of parameters adequately describes a given physical
situation. Program verification is accomplished by running various test
problems for which an analytical solution is known, or for which numerical
results from another verified program are available.
8.1. SUMMARY OF VERIFICATION TEST PROBLEMS
Several sets of test problems have been used for verification and are
summarized hereinafter. Verification is a continuing process, as many
combinations of program options could be tested.
8.1.1. One-Dimensional Flow
Test problem set 1 tested the ability of HST3D to simulate compressible
flow and was based on the analog between confined ground-water flow and heat
conduction. A thermal-conduction problem was taken from Carnahan and others
(1969, p. 443). The physical situation was that of one-dimensional confined
flow of a compressible fluid when a unit-step increase of pressure was applied
at both ends of the region. The dimensions of the simulation region were 1.0
meter in each direction. Eleven equally spaced nodes were used to discretize
the region in the x-direction, with two nodes each in the y- and z-directions.
The initial condition was hydrostatic equilibrium. The porosity was set to
1.0 so no porous medium was present. The parameters were set to the following
values:
235
Porosity, 1.0
Permeabilities
x-direction, l.xio~8 m2 ; y- and z-directions l.xio"20 m2
Fluid compressibility, lxio~ 5 Pa" 1
Fluid density (at reference conditions), 1,000 kg/m3
Fluid viscosity (at reference conditions), 0.001 kg/m-s.
A fixed time step of 1.25xlO~2 was used and the results compared at 2.5xlO~2 s.
Backwards-in-time differencing was used with the direct method for matrix
solution.
Variations on the basic problem included using centered-in-time differ
encing, reduction of the time step length by a factor of 10, using the itera
tive solver for the matrix equation, and entering data in inch-pound units.
The results agreed to five significant digits with the numerical solution
of Carnahan and others (1969, p. 446-447). Representative values for pressure
increase at 2.5xiO~2 s are shown in table 8.1. The results were symmetric
about the mid-point of the region in the x-direction as expected.
Table 8.1. Representative values for the pressure increase from theHST3D simulator and the results of Carnahan and others (1969)
[Values at time of 2.5X10" 2 seconds]
Distancealongcolumn(meters)
00.20.40.5
Change inpressurecalculated
by HST3D (Pa)
1.000000.324710.101040.07965
Change inpressurecalculated
by Carnahan (Pa)
1.000000.324710.101040.07965
8.1.2. Flow to a Well
Flow to a single well in a cylindrical-coordinate system was the basis
for test problem set 2, providing another test of the flow-simulation part of
HST3D. Both confined and unconfined conditions were simulated. The
confined-flow problem was taken from Lohman (1972, p. 19) and the unconfined-
236
flow problem was example 1 from Boulton (1954). A specified flow rate from
the well was used for both problems.
A cylindrical region of 2,000 ft external radius and 100 ft thickness was
used for the confined-flow problem. The theoretical results of Lohman were
based on the this solution for an infinite region, so comparisons were
restricted to time values sufficiently small so that the outer boundary did not
affect the flow field. Twenty-one nodes were used in the radial direction
logarithmically spaced by the automatic discretization algorithm, except for
those at 200 and 400 ft. Two nodes defined the vertical discretization. The
well flow rate was allocated by mobility and the upper, lower and outer
boundaries were impermeable. The initial condition was that of hydrostatic
equilibrium. A time step of 3jO s was used for a duration of 600 s. The
parameters used for the confined problem were the following:
Porosity, 0.20
Fluid compressibility, 3.33X10~6 psi' 1
Porous-medium compressibility, 3.94X10" 6 psi" 1
Permeability, 5.31X10" 10 ft 2 (hydraulic conductivity 137 ft/d)
Well radius, 0.1 ft
Well flow rate, 96,000 ft 3 /d
Fluid density at reference conditions, 62.4 lb/ft3
Fluid viscosity at reference conditions, 1 cP
The calculated fluid drawdown was compared with the results of Lohman
(1972, p. 19) for several locations at six values of time. The drawdown
values agreed to within 0.01 to 0.1 ft (table 8.2). The differences were
due mostly to spatial-discretization error, since they were reduced by 30 to
50 percent by doubling the number of nodes in the radial direction.
A cylindrical region of 2,000 ft radius and 800 ft thickness was used for
the unconfined-flow problem. The theoretical solution of Boulton (1954) was
used for comparison. This solution was based on a linearized free-surface
boundary condition valid for small values of drawdown and included a correc
tion for the fact that a line sink of constant intensity represented the well
flow.
237
Sixteen nodes were distributed in the radial direction, logarithmically
spaced, except at 160 ft, and nine nodes were distributed in the vertical
direction. Advantage was taken of the fact that the free surface can rise
above the upper plane of nodes. The well flow rate was allocated by mobility.
The lower and outer boundaries were impermeable while the upper boundary was a
free surface. The initial condition was that of hydrostatic equilibrium. The
automatic-time-step algorithm was used to simulate from 10 s to 3X105 s.
Table 8.2. Comparison of drawdown values calculated by HST3D withthose of Lohman (1972, p. 19)
Drawdown (feet)
Time (second)
60 120240300480600
HST3D
0.56 0.911.291.421.671.79
radius200
Lohman
0.66 0.991.361.491.751.86
(feet)
HST3D
0.15 0.330.610.720.941.05
400Lohman
0.16 0.380.670.770.991.12
The parameters for the unconfined-flow problem were the following:
Porosity, 0.15
Fluid compressibility, 1X10~ 15 psi" 1
Porous-medium compressibility, lxiO~ 15 psi" 1
Permeability, 6.7X10" 12 ft 2 (hydraulic conductivity 2X10~ 5 ft/s)
Well radius, 0.1 ft
Well flow rate, 1 ft 3/s
Fluid density at reference conditions, 62.4 lb/ft 3
Fluid viscosity at reference conditions, 1 cP
The calculated drawdown of fluid was compared with the result of
Boulton's (1954) example 1. His only reported value was at a time of 3.47
days and a radius of 160 ft. The drawdown was 2.13 ft compared to the HST3D
result of 2.20 ft. Use of five nodes in the vertical direction reduced the
drawdown calculated by HST3D to 1.96 ft. This indicated the effect of
spatial-discretization error, particularly when vertical flow is important.
238
The agreement is very good considering that the HST3D simulator does not
take the kinematic boundary condition at the free surface into account.
Therefore greater discrepancies should appear as the well bore is approached.
8.1.3. One-Dimensional Flow
Three cases of ground-water flow for which analytic solutions are
available (Bear, 1972, p. 301, 367, 380) formed test problem set 3. They were
one-dimensional, confined flow; one-dimensional, unconfined flow; and
one-dimensional, unconfined flow with influx from precipitation. The
simulation region was 400 x 400 x 100 meters in the x-, y- and z-directions
respectively. The flow field was horizontal in the y-direction for all cases.
Specified-pressure boundary conditions were used on the inlet and outlet
boundaries with impermeable lateral and bottom boundaries.
The parameters employed were the following:
Porosity, 0.15
Fluid compressibility, 5X10~ 15 Pa" 1
Porous-medium compressibility, 8.8xiO~ 14 Pa" 1
Permeability, 1.18X10" X1 m2
Fluid density at reference conditions, 1,000 kg/m3
Fluid viscosity at reference conditions, 0.001 kg/m-s
Spatial discretization was accomplished using five equally spaced nodes
in the x- and y-directions and two nodes in the z-direction. All cases were
run to steady-state with a time step of 86,400 s.
Case 1: Confined flow
The upper boundary surface was made impermeable and the other boundary
conditions for this case were specified potentiometric heads of 200 m along
the y = 0 boundary and 100 m along the y = 400 m boundary. The analytical
solution was a linear potentiometric-head variation between the two boundaries
239
(Bear, 1972, p. 301). The results at steady-state agreed with the analytical
solution to five significant digits. Global-balance results were verified by
hand calculation.
Case 2: Unconfined flow
The upper boundary was defined as a free surface and the region dimension
in the z-direction was extended to 200 m. The permeabilities in the x-, y-,
and z-directions were modified to 1.18xiO~9 m2 , 1.18X10" 10 m2 and 1.18xiO~ 5 m2
respectively. The high permeability in the z-direction was to make the Dupuit
approximation of hydrostatic equilibrium in the vertical direction valid. The
specified potentiometric heads were 200 m along the y = 0 m boundary and 150 m
along the y = 400 m boundary.
The simulation was run to 172,800 s, which was essentially steady-state.
The results for potentiometric head were compared with the analytical
solution (Bear, 1972, p. 367) based on the Dupuit approximation. Agreement to
five significant digits was obtained at the three interior-node locations
along the y-axis. The global-balance results were verified by hand
calculation.
Better agreement with the analytical solution was obtained for this test
problem than for the unconfined flow to a well in test problem set 2. This
improved agreement was attributed to the fact that the analytical solution for
this problem was based on the Dupuit assumption of negligible vertical flow
and a high vertical-permeability value was used in the HST3D simulation to
achieve hydrostatic equilibrium. The unconfined case of test problem set 2
had significant vertical flow. Because the HST3D simulation does not attempt
to satisfy the non-linear, kinematic, free-surface boundary condition, de
scribed in sections 2.5.6 and 3.4.6, the poor results obtained in cases of
significant vertical flow at the free surface were not surprising.
240
Case 3: Unconfined flow with precipitation recharge
Case 2 was modified by the addition of areal recharge at a uniform rate
and distribution. The region dimension in the z-direction was extended to
275 m. The areal-recharge flux was set to -1,157X10~ 3 m3 /m2 s with the
negative sign denoting flux in the negative z-direction.
The simulation was run to 172,800 s, which was essentially steady-state.
The results for potentiometric head were compared with the analytical solution
from Bear (1972, p. 380). This solution also was based on the Dupuit
approximation. Agreement to five significant digits was obtained at the three
interior-node locations along the y-axis. The global-balance results were
verified by hand calculation.
8.1.4. One-Dimensional Solute Transport
Flow with solute transport in a one-dimensional column was the basis of
test problem set 4. A steady-state flow field was established by specifying
an initial-pressure gradient along the column. The boundary condition at
the column inlet was a specified scaled-solute concentration of a unit-step
at time zero. The column length was 160 m discretized by 21 equally
distributed nodes in the x-direction. The y- and z-directions were 1 m with
two nodes in each direction. The following parameter values were chosen:
Porosity, 0.5
Fluid compressibility, lxio~ 10 Pa" 1
Porous-medium compressibility, IxiO" 10 Pa" 1
Permeability, IxiO" 10 m2
Fluid density at reference conditions, 1,000 kg/m3 (independent of
solute concentration)
Fluid viscosity at reference conditions, 0.001 kg/m-s
Interstitial velocity along the column, 2.7778xlO~ 4 m/s
Longitudinal dispersivity, 10 m
Molecular diffusivity, IxiO" 10 m2 /s
241
The initial solute concentration in the column was zero. A time-step
length of 720 s was used for a total simulation time of 7,200 s. The HST3D
options tested included the spatial and temporal differencing methods and the
two different equation solvers. A second case with a column that was 4-meters
wide was also tested.
The results were compared to a one-dimensional finite-difference trans
port program (Grove and Stollenwerk, 1984), and to an analytical solution
(Ogata and Banks, 1961). The calculated solute-mass fraction values agreed
with the finite-difference program results to four significant digits.
Differences between the HST3D results and the analytical solution were as much
as 0.035 units of scaled-mass fraction. The results at the end of the simu
lation period appear in table 8.3.
Table 8.3. Scaled solute-concentration values calculated by HST3Dcompared to the one-dimensional finite-difference solution of Grove and Stollenwerk (1984) and the analytical solution of Ogata and Banks (1961)
[Values at time of 7,200 seconds; CSCT, centered-in-space and centered-in- time differencing; BSBT, backward-in-space and backward-in-time differ encing]
HST3D
0
CSCT 1.0000 BSBT 1 . 0000
Scaled solute concentration (-)Distance along the column
(meters)8 16 24
0.31665 0.05939 0.007843 0.37500 0.09414 0.01824
32
0.000801 0.00295
One-dimensional finite-differ ence solution CSCT 1.0000
Analytical solution 1.0000
0.31666 0.05939 0.007843 0.000801
0.29808 0.02439 0.000469 0.000002
The discrepancies are attributed to spatial- and temporal-discretization
errors, because reducing the spatial and temporal steps by factors of eight
and five respectively, reduced the maximum difference to 0.003 units of
scaled-mass fraction. The differences between the two differencing schemes
were the result of numerical-dispersion errors. The simulation was not run
242
long enough for the difference between the analytic and numerical boundary
condition at the far end of the column to affect the solution. Flow and
solute global-balance residuals were at least eleven orders of magnitude
smaller than the net amounts entering the region.
8.1.5. One-Dimensional Heat Conduction
Test problem set 5 involved heat transport without fluid flow. A heat-
conduction problem was taken from Carnahan and others (1969, p. 443). The
physical situation was that of one-dimensional heat conduction when a unit-
step increase of temperature was applied at both ends of a column. The
dimensions of the region were J. m in each direction. Eleven equally spaced
nodes were used to discretize the region in the x-direction, with two nodes
each in the y- and z-directions. The initial condition was a uniform temper
ature of 1 °C. The parameters were set to the following values:
Porosity, 1.0 (no porous medium present)
Fluid compressibility, 5X10~6 Pa" 1
Permeability, 1X10~8 m2
Fluid density, 1,000 kg/m3
Fluid viscosity, 0.001 kg/m-s (independent of temperature)
Fluid thermal expansion factor, 0. °C~ 1
Fluid heat capacity, 1.0 J/kg °C
Fluid thermal conductivity, 1.0 W/m-°C
A time step of 0.0125 s was used for a total simulation time of 0.0250 s.
The options tested included backwards-in-time differencing, direct and itera
tive solvers of the matrix equations, and inch-pound and metric units for data
entry and output. The results agreed to five significant digits with those of
Carnahan and others (1969, p. 446, 447) and matched the numerical values for
scaled-pressure rise given in table 8.1. Heat-balance residuals were 12
orders of magnitude less than the amount of heat that entered the region.
243
8.1.6. One-Dimensional Heat Transport
Test problem set 6 was heat transport with fluid flow and was the analog
to problem set 4. A steady-state flow field was established by specifying an
initial-pressure gradient along the column. The boundary condition at the
column inlet was a specified scaled-temperature of a unit-step at time zero.
The dimensional-temperature step was 10 °C. The column length was 160 m
discretized by 21 equally distributed nodes in the x-direction. The y- and
z-directions were 1 m with two nodes in each direction. The following
parameter values were used:
Porosity, 0.5
Fluid compressibility, IxlO" 10 Pa" 1
Porous-medium compressibility, IxlO" 10 Pa" 1
Permeability, IxlO" 10 m2
Fluid density at reference conditions, 1,000 kg/m3 (independent of
temperature)
Fluid viscosity at reference conditions, 0.001 kg/m-s (independent of
temperature)
Interstitial velocity along the column, 2.7778xlO~2 m/s
Longitudinal dispersivity, 10 m
Porous-medium product of density and heat capacity, 800 J/m3-°C
Porous-medium thermal conductivity, 1.8 W/m-°C
Fluid heat capacity, 4,200 J/kg-°C
Fluid thermal conductivity, 0.6 W/m-°C
Fluid thermal expansion factor, 0. °C~ 1
The initial temperature in the column was 10 °C. A time step length of
1076.5 s was used for a total simulation time of 10,765 s. Centered-in-space
and centered-in-time differencing were used for discretization.
The results were compared to a one-dimensional finite-difference trans
port program (Grove and Stollenwerk, 1984), and to an analytical solution
(Ogata and Banks, 1961). The scaled temperature values matched the analogous
solute-transport problem of set 4 as expected. Numerical differences in the
244
fourth significant digit were attributed to the fact that the thermal-
dispersion coefficient was slightly larger than the solute-dispersion
coefficient. The results at the end of the simulation period appear in
table 8.4.
Table 8.4. Scaled temperature values calculated by HST3D compared to the one-dimensional finite-difference solution of Grove and Stollenwerk (1984) and the analytical solution of Ogata and Banks (1961)
[Values at time of 10,765 seconds]
Scaled temperature (-)Distance along the column
(meters)0 8 16 24 32 56
HST3D 1.0000 0.31670 0.05941 0.007846 0.000802 0.000005
One -dimensionalfinite-differencesolution
Analyticalsolution
1.0000 0.31671 0.05941 0.007847 0.000802 0.000000
1.0000 0.29815 0.02441 0.000470 0.000002 0.000000
The time at which the temperature profile essentially matched the solute-
concentration profile is a factor of about 1.5 later. This is because the
thermal-storage coefficient, which includes the porous-matrix solid phase as
well as the fluid phase, is greater than the solute-storage coefficient
involving only the fluid phase. The effect of spatial- and temporal-
discretization errors can be seen by comparing the results to the analytical
solution. The simulation was not run long enough for the difference between
the analytic and the numerical boundary condition at the far end of the column
to affect the solution. Flow and heat global-balance residuals were at least
eight orders of magnitude smaller than the net amounts entering the region.
245
8.1.7 Thermal Injection in a Cylindrical Coordinate System
Simulation of the injection of hot water at 60 °C into an aquifer
initially at 20 °C for 90 days, followed by production for an equivalent time
period, formed test problem set 7. A cylindrical-coordinate system was used
with a fully penetrating well. Both density and viscosity were taken to be
functions of temperature. Results from this test problem were compared to the
results obtained by Voss (1984) p. 207-212 using his SUTRA finite-element
transport-simulation program. Options tested included the approximate,
augmented-diagonal treatment of the cross-derivative dispersion fluxes, the
explicit evaluation of the cross-derivative dispersion fluxes, central and
upstream differencing for the advective terms, and equal and unequal longi
tudinal and transverse dispersivities.
A list of the parameters employed will not be presented here, because
this test problem also is given as an example for the user. The complete set
of parameters and other data that define the problem is presented in section
8.2.2.
The region had an interior radius of 1 m, exterior radius of 226 m, and a
thickness of 30 m. At the upper and lower surfaces, the boundary conditions
were no fluid flow and no heat flow. At the exterior radius, a hydrostatic
pressure was specified with any fluid entering the region having a temperature
of 20 °C. The initial condition was hydrostatic equilibrium of the fluid at
20 °C.
The results for the temperature field at 30, 90, 120, 150, 180 days were
compared to those of Voss (1984, p. 207-212) for his particular case of
options. The profiles were in general agreement with some deviation for the
withdrawal phase. The warmer water was extracted more rapidly in the HST3D
simulation. This can be attributed to the fact that Voss used a line sink of
constant intensity per unit length to represent the well whereas the HST3D
simulator allocated the flow from each layer in proportion to the local-fluid
mobility. The increased mobility of the warmer fluid caused increased flow
from the upper parts of the well bore and decreased flow from the lower. The
246
total-flow rate was held constant. The finite-difference methods used by the
HST3D simulator showed some spatial oscillation of about 3 °C. Use of
upstream differencing removed this problem at the cost of increased dispersion
which reduced the sharpness of the temperature front considerably.
8.2. TWO EXAMPLE PROBLEMS
Two example problems are presented for the purpose of giving the new
HST3D program user some experience in learning to run a successful simulation,
One involves solute transport and the other involves heat transport. These
examples also will aid in adapting the HST3D program to run on computer
systems other than the PRIME. The problem descriptions, data files and
selected parts of output are included for comparison. Several ways are
available to input some of the data so an exact match with the data files
presented is not necessary to execute these examples correctly.
8.2.1. Solute Transport with Variable Density and Variable Viscosity
The first example problem is based upon displacement of a fluid of one
density and viscosity by another fluid of different density and viscosity.
The density and viscosity differences are caused by different amounts of
dissolved solute. The system is isothermal. The region is a square slice of
porous medium, that is oriented vertically, so that gravitational effects will
occur in the flow field. The dimensions are 2 m in the x-direction by 0.2 m
in the y-direction by 2 m in the z-direction. The z-direction is oriented
vertically upward. Except at the inlet and outlet corners, the boundaries are
confining. The porous medium is homogeneous and isotropic.
The parameters to be used are as follows:
Permeability, lxlO~8 m2
Porosity, 0.10
Density of fluid initially present, 800 kg/m3
247
Viscosity of fluid initially present, 1.3X10 3 kg/ra-s
Scaled-solute-mass fraction of fluid initially present, 0.
Temperature of region (isothermal), 20 °C
Density of injected fluid, 1,000 kg/m3
Viscosity of injected fluid, 7><10~ 4 kg/m-s
Scaled-solute-mass fraction of injected fluid, 1.0
Longitudinal dispersivity, 0.1 m
Transverse dispersivity, 0.1 m
Fluid compressibility, 0. Pa" 1
Porous-medium compressibility, 0. Pa" 1
The molecular diffusivity of the solute is neglected. Absolute mass
fractions of solute are needed for solute-mass balance calculations. They
may be chosen as 0.0 for the fluid initially in the region and 0.005 for the
injected fluid. The initial condition is one of hydrostatic equilibrium with
a pressure of 0.0 Pa at an elevation of 2 m. The injection location is at the
lower left-hand corner of the region. The injection boundary is maintained at
a scale-solute concentration of 1.0 with an injection pressure of 25,000 Pa.
The outlet is at the upper right-hand corner of the region and is open to the
atmosphere. The region is illustrated in figure 8.1.
Construct a numerical model of this system with nodal dimensions
11 x 2 x ll and observe the migration of the fluid containing solute from the
lower left-hand corner to the upper right-hand corner for a total simulation
time of 10 s. Use a time-step length of 0.2 s. Use the approximate method
for calculating the cross-derivative dispersive terms. Print out results at
10 s with a contour plot of solute concentration. Use a contour interval of
0.2.
A listing of the data file that will run example problem 1 is given in
table 8.5. The input-data form (table 5.1) was used to construct this file,
but comments pertaining to unnecessary data items have been eliminated for
brevity.
248
The output file for this problem is contained in table 8.6. The header
shows the release number for the version of the program. The problem title
and information relating to dimensioning requirements is next. Then follows
the static data. Read-echo printouts were selected for data input by i,j,k
range. The conductance factors are constant for this simulation. The
numbering sequence for boundary-condition cells is primarily for debugging
purposes. In this problem, the approximate method for handling the
cross-derivative dispersion terms using amplified-diagonal values was chosen.
The next section of the printout contains the transient data including
both input parameters and output variables at selected time steps. For this
example, the input data for boundary conditions, calculation information, and
mapping data are printed. The, printout interval was set to print at the end
of the simulation only at time step 50. No cross-derivative dispersive
conductances appear, because the approximate method was selected for handling
cross-dispersive fluxes. The output at the end of the time step, and end of
the simulation in this case, includes some calculation information, pressure
and solute-mass fraction, density and viscosity, the global-balance summary,
boundary-condition flow rates, a contour map of solute-mass fraction, and the
velocity field. The contour map was made for only one plane of cells because
the .other is identical by symmetry. The velocity field is that which would be
used for the next time step, if one were to be calculated. In the global-
balance summary, we can see that the flow-balance residual is about 5 orders of
magnitude less than the other amounts. The solute-balance residual is about 5
orders of magnitude less than the amount of inflow and amount of change.
Similar results exist for the cumulative amounts. The map of the solute-
mass fraction field shows the asymmetry that is caused by the denser injected
fluid tending to stay in the bottom part of the region. The same case was run
under conditions of constant density and viscosity and the results were
symmetric about the diagonal as expected.
249
SPECIFIED PRESSURE BOUNDARY NODES AND ASSOCIATED ONE-EIGHTH CELLS
p = OPa
= AY=AZ = 0.2m
SPECIFIED PRESSURE BOUNDARY NODES AND ASSOCIATED ONE-EIGHTH CELLS
p = 25,000 Pa
Figure 8.1. Sketch of the grid with boundary conditions
for example problem 1.
250
Tab
le 8.5
. In
put-
data
fi
le fo
r
exam
ple
p
rob
lem
1
C..
..H
ST
D
ATA
-INP
UT
FORM
C..
N
OTE
S:C.
. INPUT
LINE
S ARE
DENOTED
BY C.
N1.N
2.N3
WHE
REC.
. Nl IS THE
READ G
ROUP
NUMBER
, N2
.N3
IS TH
E RE
CORD
NUM
BER
C..
A LETTER INDICATES
AN EX
CLUS
IVE
RECORD S
ELECTION MUST BE M
ADE
C..
I.E. A
OR B
OR C
C..
(0)
- OPTIONAL D
ATA
WITH C
ONDITIONS
FOR
REQUIREMENT
C..
A RECORD N
UMBER
IN SQUARE BRACKETS IS
THE
RECORD W
HERE TH
AT PA
RAME
TER
IS FIRST
SET
C.....INPUT
BY I,J,K
RANGE
FORMAT IS
;C.O.I..
I1,I
2,J1
,J2,
K1,K
2C.
O.2.
. VAR1,IMOD1,[VAR2,IMOD2,VAR3,IMOD3]
C...
USE
AS MA
NY OF
LI
NE 0.1
& 0.2
SETS A
S NECESSARY
C...
END
WITH LI
NE 0.
3C.O.3..
0 /
THE
SPAC
E IS
RE
QUIR
EDC.
..
{NNN
} -
INDICATES
THAT T
HE DE
FAUL
T NU
MBER
, NNN, IS
USED
C...
IF A
ZERO
IS ENTERED
FOR
THAT
VAR
IABL
EC...
(T/F)
- IN
DICA
TES
A LOGICAL
VARI
ABLE
C...
(I]
- IN
DICA
TES
AN IN
TEGE
R VA
RIAB
LEC
C.....START
OF T
HE DATA F
ILE
C...
..DI
MENS
IONI
NG DA
TA -
READ1
C.I.I
.. TITLE
LINE
1
EXAM
PLE n SOLUTE T
RANS
PORT
WITH V
ARIA
BLE
DENS
ITY
AND
VISC
OSIT
Y C.I.2
.. TI
TLE
LINE
2
DIAG
ONAL
FLOW IN
X-
Z PLANE
C.I.3
.. RESTRT(T/F),TIMRST
F /
C.I.
4 .. HE
AT,SOLUTE,EEUNIT,CYLIND,SCAL
MF
; ALL
(T/F)
F T
F F
TC.
I.5
.. NX
,NY,
NZ,N
HCN
11 2
11 0
C.I.6
.. NP
TCBC
,NFB
C,NA
IFC,
NLBC
,NHC
BC,N
WEL
4 5*
0C.I.7
.. NP
MZ
1 C.I.8
.. SLMETH{I],LCROSD(T/F)
1 T
C.I.
9 ..
IBC
BY I,J,K
RANG
E {0
.1-0
.3}
,WIT
H NO
IMOD P
ARAM
ETER
,F
OR E
XCLUDED
CELLS
0 /
C.I.10 .. RD
ECHO
(T/F
) F C
C.....STATIC DATA -
READ2
C.....OUTPUT INFORMATION
C.2.
1 ..
PR
TRE(
T/F)
Tabl
e 8.5. Input-data file for
exam
ple problem 1 Continued
F C.....COOR
DINA
TE GE
OMET
RY IN
FORM
ATION
C..... RECTANGULAR
COORDINATES
C.2.
2A.1
..
UN
IGRX
,UNI
GRY,
UNIG
RZ;
ALL
(T/F
) ;
(0)
- NO
T CYLIND [1.4]
3*T
C.2.2A.2A
.. X(
1),X
(NX)
;(0) - UNIGRX [2
.2A.
1]0.
2.
C.2.2A.2B
.. X(
I) ;(
0) -
NOT
UNIGRX [2
.2A.
1]C.2.2A.3A
.. Y(
1),Y
(NY)
;(
0) -
UNIGRY [2
.2A.
1]0.
.2
C.2.2A.3B
.. Y(J) ;(
0) -
NOT
UNIGRY [2
.2A.
1]C.
2.2A
.4A
.. Z(1),Z(NZ) ;(
0) - UNIGRZ [2
.2A.
1]0.
2.
C.2.2A.4B
.. Z(
K) ;(
0) -
NOT
UNIGRZ [2.2A.1]
C.2.2B.3B
.. Z(
K) ;(0) - NO
T UNIGRZ [2
.2B.
3A],
CYLI
ND [1
.4]
C.2.
3.1
.. TI
LT(T
/F)
;(0)
-
NOT
CYLIND [1.4]
F C.2.
3.2
.. TH
ETXZ
,THE
TYZ,
THET
ZZ;(
0) - TI
LT [2.3.1]
AND
NOT
CYLI
ND [1.4]
C.....FLUI
D PROPERTY INFORMATION
C.2.4.1
.. BP
0. C.2.4.2
.. PR
DEN.
TRDE
N.WO
.DEN
FO0.
20
. 0.
80
0.C.
2.4.
3 ..
W1
.DEN
F1 ;(
0) - SOLUTE [1.4]
.005
1000.
C.2.
5.1
.. NO
TVO,
TVFO
(I),
VIST
FO(I
) ,1=1 TO NO
TVO;
(0)
- HEAT [1.4]
OR H
EAT
[1.4]
AND
SOLUTE [1.4]
OR .NOT.HEAT
AND
.NOT
.SOL
UTE
[1.4]
C.2.
5.2
.. NOTV1,TVF1(I),VISTF1(I)
,1=1 TO NO
TV1;
(0)
- SOLUTE [1
.4]
AND
HEAT [1
.4]
C.2.5.3
.. NOCV,TRVIS,CVIS(I),VISCTR(I) ,1=1 TO
NOCV;(0) - SOLUTE [1.4]
2 20.
0. .0
013
1. .0
007
C...
..RE
FERE
NCE
COND
ITIO
N INFORMATION
C.2.6.1
.. PA
ATM
0. C.2.6.2
.. PO
.TO
0. 20
.C.....SOLUTE INFORMATION
C.2.8
.. DM
.DEC
LAM
;(0)
- SOLUTE [1
.4]
0. 0.
C...
..PO
ROUS
MEDIA
ZONE IN
FORM
ATIO
NC.
2.9.
1 ..
IPMZ,I1Z(IPMZ),I2Z(IPMZ),J1Z(IPMZ),J2Z(IPMZ),K1Z(IPMZ),K2Z(IPMZ)
1 1
11 1
2 1
11C.....USE
AS MANY 2.9.1
LINE
S AS
NE
CESS
ARY
C.2.
9.2
.. EN
D WI
TH 0
/0
/C.....POROUS ME
DIA
PROPERTY INFORMATION
C.2.10.1 .. KX
X(IP
MZ),
KYY(
IPMZ
),KZ
Z(IP
MZ),
IPMZ
=1 T
O NPMZ [1.7]
Tab
le 8.5
. In
pu
t-d
ata
fi
le fo
r ex
ampl
e pro
ble
m 1 C
onti
nu
ed
3*1
.E-8
C.2
.10
.2 ..
P
OR
OS
(IPM
Z).IP
MZ=
1 TO
NPM
Z [1
.71
.1 C.2
.10
.3 ..
A
BP
M(IP
MZ)
,IPM
Z=1
TO N
PMZ
(1.7
] 0
. C...
..PO
RO
US
M
EDIA
SOL
UTE
AND
THER
MAL
D
ISPE
RSI
ON
IN
FORM
ATIO
NC
.2.1
2 ..
A
LPH
L(IP
MZ)
.ALP
HT(
IPM
Z)
,IPM
Z=1
TO N
PMZ
(1.7
) ;(
0)
- SO
LUTE
11
.41
OR H
EAT
11.4
1 .1
.1
C...
..PO
RO
US
M
EDIA
SOL
UTE
PROP
ERTY
IN
FORM
ATIO
N C
.2.1
3 ..
D
BK
D(IP
MZ)
,IP
MZ=
1 TO
NP
MZ
[1.7
1 ;(
0)
- SO
LUTE
[1
.41
0. C...
..BO
UN
DA
RY
C
ON
DIT
ION
IN
FORM
ATIO
N C
.....
SP
EC
IFIE
D V
ALUE
B
.C.
C.2
.15
..
IBC
BY
I.J.K
RAN
GE
(0.1
-0.3
) W
ITH
NO
IMO
D PA
RAM
ETER
, ;(
0)
- NP
TCBC
[1
.6]
> 0
111211
101
11
11
1 2
11
11
100
0 /
^
C..
...F
RE
E
SURF
ACE
B.C
.ui
C.2.
20 ..
FR
ESUR
(T/F
),PR
TCCM
(T/F
) w
p /
C.....INIT
IAL
CONDITION
INFORMATION
C.2.21.1
.. IC
HYDP
.ICT
.ICC
; ALL
(T/F);IF NOT.HEAT,
ICT
* F, IF NOT.SOLUTE,
ICC
* F
TFT
C.2.21.2
.. IC
HWT(
T/F)
;(
0) - FR
ESUR [2
.20]
C.2.21.3A
.. ZPINIT.PINIT ;(0) -
ICHYDP [2
.21.
1] AND
NOT
ICHW
T [2
.21.
212.
0.
C.2.21.6 .. C
BY I.
J.K
RANGE
{0.1
-0.3}
;(0)
- SOLUTE [1
.4]
AND
ICC
[2.21.1]
1 11
1
2 1
110.
1
0 /
C.....CA
LCUL
ATIO
N INFORMATION
C.2.22.1
.. FDSMTH.FDTMTH
.5 .5
C.2.
22.2
.. TO
LDEN
{.00
1}.M
AXIT
N{5)
0. 0
C.....OUTP
UT INFORMATION
C.2*.23.1
.. PRTPMP.PRTFP. PRT 1C. PRTBC, PRTS LM
. PRTWE L; ALL
(T/F
)T
T T
T T
TC.
2.23
.2 .. IP
RPTC
.PRT
DV(T
/F)
;(0)
-
PRTI
C [2
.23.
1]101
TC.
2.23
.3 .. ORENPR[I];(0)
- NOT
CYLIND [1.4]
13 C.2.23.4
.. PL
TZON
(T/F
)
Table 8.5. Input-data file for example problem 1 Continued
F C.2.
23.5
.. OCPLOT(T/F)
F C
C..... TRANSIENT
DATA -
READ3
C.3.
1 ..
THRU(T/F)
F C...
..IF
THR
U IS
TRU
E PR
OCEE
D TO
RECORD
3.99
C.....THE
FOLLOWING
IS F
OR N
OT T
HRU
C.....BOUNDARY C
ONDITION IN
FORM
ATIO
N C.....
SPEC
IFIE
D VALUE
B.C.
C.3.
3.1
.. RD
SPBC
,RDS
TBC,
RDSC
BC,A
LL(T
/F);
(0)
- NOT
CYLIND [1.4]
AND
NPTCBC [1.6]
> 0 OR C
YLIND
AND
NPTCBC >
1
TFT
C.3.3.2
.. PN
P B.
C. BY I.
J.K
RANGE
{0.1
-0.3}
;(0)
- RDSPBC [3.3.1]
111211
2500
0.
1 11
11
1
2 11 11
0. 1
0 /
C.3.
3.4
.. CS
BC B
Y I.
J.K
RANG
E {0.1-0.3}; (0)
- RDSPBC [3
.3.1
] AND
SOLUTE [1.4]
0 /
C.3.3.6
.. CN
P B.
C. BY I.
d.K
RANGE
{0.1
-0.3
} ;(0) -
RDSC
BC [3
.3.1
] AND
SOLU
TE [1.4]
111211
1.
1 0
/C.
....
CALC
ULAT
ION
INFORMATION
C.3.7.1
.. RDCALC(T/F)
T C.3.
7.2
.. AU
TOTS
(T/F
) ;(0) - RDCALC [3
.7.1
] F C.
3.7.
3.A
.. DELTIM ;(0) - RDCALC [3
.7.1
) AND
NOT
AUTO
TS [3
.7.2
] .2 C.3.7.4
.. TIMCHG
10.
C...
..OU
TPUT
IN
FORM
ATIO
NC.
3.8.
1 ..
PRIVEL,PRIDV,PRISLM,PRIKD,PRIPTC,PRIGFB,PRIWEL,PRIBCF
; ALL
[I]
8*-l
C.3.
8.2
.. IP
RPTC
;(0) -
IF P
RIPTC
[3.8
.1]
NOT
= 0
101
C.3.
8.3
.. CH
KPTD
(T/F
),NT
SCHK
,SAV
LDO(
T/F)
F
/C.....CONTOUR
MAP
INFORMATION
C.3.
9.1
.. RD
MPDT
.PRT
MPD;
ALL
(T/F)
T T
C.3.
9.2
.. MAPPTC,PRIMAP[I) ;(
0) -
RDMP
DT [3.9.1]
Table 8.5. Input-data file for example problem 1 Continued
001
-1C.3.9.3
.. YP
OSUP
(T/F
)fZPOSUP(T/F)
fLEN
AX,L
ENAY
fLENAZ ;(
0) - RDMPDT [3.9.1]
F T
10.
0. 10
.C.3.9.4
.. IM
APl{
l}tIMAP2{NX}
fJMA
Pl{l
}fJMAP2{NY},KMAPl{l}
tKMAP2{NZ},AMIN,AMAX
tNMP
ZON{
5}:(
0) - RDMPDT [3
.9.1
]1
11 1
1 1
11 0.
1. 10
C...
..ON
E OF
THE 3.9.4
LINES
REQU
IRED
FOR E
ACH
DEPENDENT
VARIABLE
C...
..
TO B
E MAPPED
C...
..EN
D OF
FIRST S
ET O
F TRANSIENT
INFORMATION
C- ------------------------------------------
C...
..RE
AD S
ETS
OF R
EADS D
ATA AT E
ACH
TIMCHG U
NTIL T
HRU
(LIN
ES 3
.N1.
N2)
C...
..EN
D OF
CAL
CULA
TION
LINES F
OLLOW, T
HRU=.TRUE.
C.3.99.1
.. THRU
T C...
..TE
MPOR
AL P
LOT
INFO
RMAT
ION
C.3.
99.2
.. PLOTWP.PLOTWT.PLOTWC;
ALL
(T/F)
3*F
C...
..EN
D OF
DAT
A FI
LE
Tab
le 8.6
. O
utp
ut
file
fo
r ex
ampl
e pro
ble
m 1
**************************************************
* * * *
* *
**************************************************
* THREE
DIMENSIONAL
FLOW
, HEAT A
ND S
OLUTE
* TR
ANSP
ORT
SIMU
LATO
R -
(HST
3D):
RELE
ASE
- 1.
0
N5
EXAM
PLE
fl SOLUTE T
RANSPORT W
ITH
VARI
ABLE
DENSITY
AND
VISCOSITY
DIAG
ONAL
FLOW
IN X-
Z PLANE
***
FUNDAMENTAL
INFORMATION
***
CARTESIAN
COORDINATES
ISOTHERMAL S
IMUL
ATIO
N SOLUTE T
RANSPORT S
IMUL
ATIO
N INPUT
DATA
IS
EXPECTED IN
ME
TRIC
UNI
TS
SOLUTE CO
NCEN
TRAT
ION
IS EXPRESSED
AS S
CALE
D MASS FRACTION W
ITH
RANG
E(0-1)
***
PROB
LEM
DIME
NSIO
NING
INFORMATION
***
NUMBER O
F NO
DES
IN X-DIRECTION
............................................ NX ..
. 11
NUMBER O
F NODES
IN Y-DIRECTION
............................................ NY ..
. 2
NUMBER O
F NO
DES
IN Z-DIRECTION
............................................ NZ ..
. 11
NUMBER O
F POROUS M
EDIA
ZON
ES .............................................. NP
MZ
. 1
NUMB
ER O
F SP
ECIF
IED
PRESSURE,
TEMPERATURE
OR M
ASS
FRACTION B.C. ..
....
....
. NPTCBC
4NUMBER O
F SP
ECIF
IED
FLUX
B.C. CE
LLS
(FLOW, HEAT O
R SO
LUTE
)...
.............. NFBC
. 0
NUMBER O
F HEAT C
ONDUCTION
B.C. CE
LLS
...................................... NHCBC
0NUMBER O
F NO
DES
OUTSIDE
REGION FOR
EACH HEAT C
ONDUCTION
B.C. CELL ..
....
...
NHCN
0NUMBER O
F AQUIFER
INFL
UENC
E FUNCTION CELLS
................................ NAIFC
0NUMBER O
F LEAKAGE
CELL
S ...................................................
NLBC
. 0
NUMBER O
F WELLS
....
....
....
....
....
....
....
....
....
....
....
....
....
....
...
NWEL
. 0
DIRECT D
4 SO
LVER
IS
SELECTED
ABBREVIATED
DIAG
ONAL
CRO
SS-D
ISPE
RSIV
ITY
COEF
FICI
ENT
STORAGE
ALLO
CATE
DTH
E A4
ARR
AY IN D4
DES
IS DIMENSIONED
....
....
....
....
....
....
....
....
....
..
3799
ELEMENTS
THE
TOTAL
STORAGE
REQU
IRED
BY T
HE DIRECT M
ETHOD
IS ........................
5009
ELEMENTS
THE
TOTAL
STOR
AGE
REQUIRED B
Y TH
E IT
ERAT
IVE
METHOD IS .....................
1694
ELEMENTS
TOTA
L LENGTH O
F LABELED
COMM
ON BLOCKS ..
....
....
....
....
....
....
....
....
...
6681
BYTES
REQUIRED
COMP
ILED
LE
NGTH
OF
VARIABLE LE
NGTH
REAL A
RRAY
(VPA A
RRAY
) ..
....
....
13
076
ELEMENTS
250000
ELEMENTS
LENG
TH O
F VA
RIAB
LE LE
NGTH
IN
TEGE
R AR
RAY
(IVP
A AR
RAY)
..
....
. 1779
ELEMENTS
20000
ELEM
ENTS
Tab
le 8
.6.
Ou
tpu
t fi
le fo
r ex
am
ple
pro
ble
m
1 C
onti
nued
***
TIM
E
INV
AR
IAN
T OR
STA
TIC
DA
TA *
**
X-D
IRE
CTI
ON
NO
DE
COO
RDIN
ATES
(
M)
1234
56
78
9
100.
00
0.20
0.
40
0.60
0.
80
1.00
1.
20
1.40
1.
60
1.80
112.
00
1 2
0.00
0.
20
Y-D
IRE
CTI
ON
NO
DE
COO
RDIN
ATES
(
M)
Z-D
IRE
CTI
ON
NO
DE
COO
RDIN
ATES
(
M)
123456789
100.
00
0.20
0.
40
0.60
0.
80
1.00
1.
20
1.40
1.
60
1.80
112.
00
Z-AXIS IS
POSITIVE V
ERTICALLY
UPWARD
** A
QUIF
ER P
ROPE
RTIE
S **
(R
EAD
ECHO
)REGION
PORO
US ME
DIUM
M.
C.=M
ODIF
ICAT
ION
CODE
II
12
Jl
J2
Kl
K2
ZONE
IN
DEX
....
....
....
.. .......................................................
Tab
le 8
.6. O
utp
ut
file
fo
r
exam
ple
pro
ble
m
1 C
onti
nued
PORO
US M
EDIA
PR
OPE
RTI
ES
ro Ui oo
l.OOOOE-08
l.OO
OOE-
08
1 l.OOOOE-08
10.1000
X-DIRECTION
PERM
EABI
LITI
ES
( M*
*2)
Y-DIRECTION
PERM
EABI
LITI
ES
( M*
*2)
Z-DIRECTION
PERMEABILITIES
( M*
*2)
POROSITY (-)
***
INTE
RM
EDIA
TE
COM
PUTE
D DA
TA *
**
X-D
IRE
CTI
ON
CO
NDUC
TANC
E FA
CTO
R BE
TWEE
N X
(I)
AND
X(I
+1
) (
M**
3)
VER
TIC
AL
SLI
CE
S
J =
1
23
45
67
10
6SZ
to to to to to to to to o
rororororor\jroro>-» ooooooooo
m m m m m ni m m m ni rn i i i i i i i i i i iotototototototototoo
o om m m m m m m rn m m m i i i i i i i i i i iO tO *O *O tO *O *O *O tO tO O
<J1 h-* h^ h-* * * h-* h-* h-> h-* * -* CT1
m ni m m m i i i i i i i i i ooooooooo to to to to to to to to to
500r~ i i o
to to to to to to to to to
m m m m m m m m m i i i i i i i i ito to to to to to to to to
ooooooooo
o II
yom o
ooo o
o3D
m
o o o om m m m m m m m m m mi i i i i i i i i iotototototototototoo
m m m m m m m m m m i i i i i i i i i i i >-*OOOOOOOOOK-» o to to to to to to to to to o
m m m m m ni m m m ni ni i i i i i i i i io to to to to to to to to to o
o o m m m m m m ni rn m m m i i i i i i i i i i i i-«OOOOOOOOO>-» OtOtOtOlOtOtOtOtOtOO
m m m m m m m m m m m i i i i i i i i i
OtOtOtOtOtOtOiOtOtOO
o o m m m m m ni m rn m m m i i i i i i i i i i iotototototototototoo
. __ _ _ooooo>-» otototototototototooOtOtOtO«OtOtO«OtOtOO
to to to to to to to to toI I I I I I I I I I I otototototototototooOtOtOtOlOtOtOtOtOtOO
OOOOOOOOO^Iooooooooo ni nn ni m m ni m m m i i i i i i i i i^
o ooo o o o o
tototototototototo
rsirvjrorororororo*-*
oooooooooOOOOOOOOO1
m m m m m m m m m
to to to to to to to to to
rsirsjrorororororoi-*
m ni m m m m m m rn i i i i i i i i ito to to to to to to to to
otototototototototoo
m m m m m m nn ni m m m i i i i i i i i i iotototototototototoo
o to to to to to to to to to o
o om m m m m m m m m m mi i i i i i i i i i io to to to to to to to to to o
OtOtOtOlOtOtOtOtOioo
otototototototototoo
t* tr
00*
en I o
Ift
(D X to
K.n> o o
ioo
to a
OtOtOlDiOtOtOtOtOtOO
o»O) ooui ui0000oo00
O) O> O> O> O> O> O> O) O> O>oooooooooo I I I I I I I I I II i I 11 I 11 I liI 11 I Ii I li I Ii I Ii I Ii Ioooooooooo
O3c
H-U
§
Of Ofoo
I IUJ UJoo oo oo00
CVJl-H
O)O)oo
I IUJ UJ 00oo oo00
O* O* O* O) O) O* O) O) O) O) -,0000
oooooooooo
O) O) O) O) O) O) O) O) O) O)ooooooooooI i I I i I I i I I i I 11 i I i I Ij I I i I I i I I i Ioooooooooo
OOOO OOO i
§ H Q O
0)0)oo
I IUJ UJoo oo00oo
Ioooooooooo
I I I I I I I I I II i I 11 I I i I I i I I i I I i I I f I li I Ii I Ii I
:ooo OOO
0) H &
I-p3
3 O
I I
vo00
,0(0 EH
O)O)ooI I
UJ UJoo oo oo ooCNJl-H
IS4
O
UJ UJ 00oo oo oo
O> O)ooUJ UJ 00oo0000
O) O) O) O) O) O) O) O) O) O)oooooooooo I I I I I I I I I II i I I i I I i I I i I I i I I i I Ij I I i I I i I I i Ioooooooooo
O) O) O) O) O> O) O) O) O) O)
0)0)oo
I IUJ UJ 00oo oo00
O) O)oo
00oo00oo
UJ CO
O
< u.UJ O
Ia oO
OUJ
aINI
UJ O
UJ
O) O) O) O) O) O) O) O) O) O)oooooooooo
O) O) O) O) O) O) O) O) O) O)oooooooooo
I I I I I I I I I II i I I i I I i I I i I I i I I i I I i I I i I I i I I i I
UJ UJ 00 00oo oo
oo>o>o>o>a>O)O)o>o>o«-"OOOOOOOOOi-H
I I I I I I I I I I IUJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ
I I I I I I I I I II i I I i I I i I I i I I i I I i I I i I I i I I i I I i Ioooooooooo
I I I IUJ UJ UJ UJ OOOO
OOOO in in in in
O O) 00 I--
260
Cn Cn Cn Cn Cn Cn Cn Cn Cn Cn
O O O O O
Cn Cn CD Cn Cn Cn Cn Cn Cn O)-- ooo
73
,L 3a H
' I
oooooooooo O oooooooooo
I IM en en en en en en en en en en
|O
£ """"" J0)
(^4 111 111 111 111 111 111 ijj ijj 111 ijj CD
L£ < > <__> * > <__> < / <__> <__> <__> <__> <__> 3E
<Uuj i
en en cncncncncncncncn '
(It LUU-ILULULULULUUJLULU O * ' 'w i * t \ t \ / \ / \ / \ / \ / \ /~\ / i t \ rv (/ )
OOOOOOOOOO ^
> Q-f__| ^_^ 1_^ ^_^ ^_^ ^_^ ^_^ ,_4 ^_^ ^_^ QQ jg
3 to SQ. Cncncncncncncncncncn-P
° ^-0000000000 Q-
oa.......... Q_
. *
cn en en en en en en en en en -K
111111111111111111111111111111 2»^
3 o
cn en en en en en en en en eni i i i i i i i i ii.11»11111»11»11.11»1111111111
i i i i i i i i i i i i i i i i111 111 111 QJ LL! LiJ UJ ''' ' *' ' *' ' *' 111 111 111 11 i 111
in to in in in in 10101010101010101010 LOLOLOLOLOLOLOLOLOLO O
ocnoor^voto<d-roe\j I i oenoor^voto^-rocsjt t
261
10.10
00 10.1000 1
0.00
00
Tab
le 8
.6.
Ou
tpu
t fi
le fo
r ex
am
ple
pro
ble
m
1 C
onti
nued
LONG
ITUD
INAL
DIS
PERS
IVIT
Y (
M)
TRANSVERSE
DIS
PERS
IVIT
Y (
M)
DENS
ITY
- DI
STRI
BUTI
ON C
OEFFICIENT P
RODUCT
(-)
MOLECULAR
DIFF
USIV
ITY-
TORT
UOSI
TY PR
ODUC
T ..
....
....
....
....
. DM
..
. 0.000
( M*
*2/S
)SOLUTE LI
NEAR
DEC
AY R
ATE
CONSTANT ..
....
....
....
....
....
....
DECLAM 0
.000
(1/S)
SCALE
FACT
ORS
FOR
SCALED M
ASS
FRACTION.. ....................
WO ..
. 0.00000
Wl ..
. 0.00500
ATMOSPHERIC
PRESSURE (ABSOLUTE) ..
....
....
....
....
....
....
.. PAATM
1013
25.0
(
PA)
REFERENCE
PRES
SURE
FOR
ENT
HALP
Y ............................ PO
H ..
0.0
(PA)
ISOTHERMAL AQU
IFER
TEMPERATURE .............................
TOH
..
20.0
(D
E6.C
)
***
FLUID
PROPERTIES *
**PHYSICAL
FLUID
COMP
RESS
IBIL
ITY
....
....
....
....
....
....
....
....
....
.. BP
..
. O.
OOE-
01
(I/
PA)
REFERENCE
PRES
SURE
FOR
DENSITY .............................
PO ..
0.0
( PA
)RE
FERE
NCE
TEMPERATURE
FOR
DENS
ITY
....
....
....
....
....
....
.. TO
..
20.0
(DE6.C)
FLUID
DENSITY
AT S
OLUTE
SCALED M
ASS
FRAC
TION
OF
ZERO
.......
DENFO
800.0
(KG/ M
**3)
FLUID
DENSITY
AT S
OLUTE
SCALED M
ASS
FRAC
TION
OF
ONE
........ DENF1
1000.
(KG/
M**3)
VISC
OSIT
Y-CO
NCEN
TRAT
ION
DATA T
ABLE A
T 20
.0 D
EG.C
SCALED M
ASS
FRAC
TION
VI
SCOS
ITY
(KG/ M
-S)
I-H O OO OI + + + +111 111 111 111 UJ
VO T CO CM flO T On CO r*. VO VO in CO m CM Onf i on in *""* vo
CX.3Ef-n OOOO111 111 111 111 111 VO « « « T CO CM floo an<9*anoor^.vovoinooincMon on
. f-i co T vo P*. on ....co T in «-««-««-< «-<
'O CD CO<u i i JJ UJ UJ O T T T T5 oo «-H oooo G o o i + + + + HCOO UJ UJUJUJUJjj « » VO ..... « T CO CM «-H _ Ji f-i P*. I i-i oo ̂ r on oo r*. vo vo in co m CM on cog i i z r*.vocoor>.^-t-<cninf-ivoO Z i-i in in »-i r*. CM CO T o CM T inO i-i ex. « r-i co T vo r*. enI ex. M inI
Q OJH O04 I I 0)
§§f-i OOOO
i + + + +UJ 1 1 i 1 1 i UJ UJvovo ^- en oo r*. vo vo m oo m e\j en vo- -- - '
oI I
\n oo jj ">
Q * = * * **
a) 2 SOOOO+ + + + II
1-3 VO.««'«'TCOCMi <in^-q>opp^.vovpinqpincMg?
>a£ ohx OO =3 i-i
J, Q OOOO h->f Z LUCO =33 O OS UJ COcv o ex. oc i « o T T ^ Tjj a. a: i-> oooot: -JQH- i + - + -JJ <£ i l _| OO UJ UJUJUJUJO i-4 3 < i-i VO.«««'.«TCOCMf-l
I h- I i-i Q T T CTl CO r*. VO VO in CO ID CM O>I i « u. H- r*.vocoor*.T« lOimt <vo1 z I-H uj ininf-ip*.CMOOTOC\jTin
~ aix at vo uj i i s in -K U. OO
orac I-H oooo <cz ex. i + + + -
O LU UJ UJ LU LU_J - _J vo ..... T co cvj I-H< t < co T cn oo r*. vo vo to oo ir> c\j en«- < i-i co r*. vo co o r>. T «-< en ir> I-H voH- > H- uj in in I-H r*. e\j oo T o c\j T ir>i i uj i i oz J z ini-l UJ i-l _J
v»-J f-i OOOO
5 1 + + + + UJ UJ UJ UJ UJi-i vo « T co e\j f-i
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Table 8.6. Output file for example problem 1 Continued
11 10 9 8 7 6 5 4 3 2 1
11
to11
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Tab
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NJ
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CALCULATION
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Tab
le 8.6
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utp
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file
fo
r ex
am
ple
pro
ble
m
1 C
onti
nued
CHAN
GE
IN
FLU
ID
IN
REG
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..................................
6.98
5026
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0 (K
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FLU
ID
IN
REG
ION
............................................
7.09
8503
E+0
1 (K
G)
RES
IDU
AL
IMBA
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E .........................................
-2.6
03
85
0E
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(K
G)
FRAC
TIO
NAL
IM
BALA
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.......................................
0.00
00
SOLU
TE
INFL
OW
..............................................
1.66
5237
E-0
1 (K
G)
SOLU
TE
OUTF
LOW
.............................................
2.25
3053
E-0
4 (K
G)
CHAN
GE
IN
SOLU
TE
IN
REG
ION
.................................
1.66
3889
E-0
1 (K
G)
SOLU
TE
IN
REG
ION
...........................................
1.66
3889
E-0
1 (K
G)
RES
IDU
AL
IMBA
LANC
E .........................................
9.05
7561
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5 (K
G)
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MU
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1011 10 9 8 7 6 5 4 3 2
Table
8.6. Output fi
le fo
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ntin
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1 1.
623
11 10 9 8 7 6 5 4 3 2 1
11
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90
J =
2
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11
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J =
1
10
1111 -9.5797E-05
10 9 8 7 6 5 4 3 2 1 11
J =
2
10
10 9 8 7 6 5 4 3 2 1
Table 8.6. Output jf
ile for example problem 1 Continued
NJ
11 10 9 8 7 6 5 4 3 2 1
11-9
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7E-0
5
11 10 9 8 7 6 5 4 3 2 1
SOLUTE
(KG/S)
VERTICAL S
LICES
J =
1
10
8.11
32E-03
Table 8.6. Output f'
ile for example problem 1 Continued
11
N>
11 10 9 8 7 6 5 4 3 2 1 11 10 9 8 7 6 5 4 3 2 1
J =
2
10
8.11
32E
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302
U) o to
Tab
le 8.6
. O
utp
ut
file
fo
r
exa
mp
le p
rob
lem
1
C
onti
nued
0.13
130.
1168
0.10
097.
8480
E-0
23.
9222
E-0
2
LAST
TIM
E PL
ANE
CALC
ULAT
ED
LAST
TIM
E PL
ANE
IND
EX
JOB
COM
PLET
ED10
. 50(S
)
8.2.2. Heat Transport with Variable Density and Variable Viscosity
The second example problem is based upon thermal injection of a hot fluid
through a well followed by production for an equivalent time period. The
cylindrical coordinate system is used. Injection is for 90 days, followed by
90 days of withdrawal. Temperature of the injected fluid is 60 °C; flow rate
is 203 £/s for both injection and withdrawal. Initial temperature in the
aquifer is 20 °C. The other parameters are:
Well radius, 1 m
Region outer radius, 246 m
Aquifer thickness, 30 m
Permeability, 1.02X10" 10 m2
Porosity, 0.35
Fluid compressibility, 0. Pa" 1
Porous matrix compressibility, 0. Pa" 1
Fluid heat capacity, 4,182 J/kg-°C
Porous-medium heat capacity, 840 J/kg-°C
Fluid density at 20 °C, 1,000 kg/m3
Porous-medium density of the solid, 2,650 kg/m3
Thermal conductivity of the fluid, 0.6 W/m-°C
Thermal conductivity of the porous medium, 3.5 W/m-°C
Coefficient of thermal expansion of the fluid, 0.375 °C~ 1
Fluid viscosity at 20 °C, 0.001 kg/m-s
Longitudinal dispersivity, 4 m
Transverse dispersivity, 1 m
The well flow rate is to be allocated by mobility explicitly in time.
The upper and lower boundaries are impermeable and thermally insulated. The
boundary condition at the outer radius is specified as hydrostatic pressure
with a specified temperature of 20 °C. The boundary condition pressures and
temperatures do not vary with time.
Construct a numerical model of this system, and observe the movement of
the injected hot water and subsequent withdrawal, for a total simulation time
304
of 180 days. Automatic spacing of 26 nodes in the radial direction and
uniform spacing of 11 nodes in the vertical direction are to be used. Use
backwards-in-time differencing with a fixed time step of 3 days. The
cross-derivative dispersion terms should be calculated explicitly. Print
results at 30 day intervals including contour maps of temperature. Use a
contour range of 20 to 60 °C, with a contour interval of 5 °C.
The data file that will run example 2 is given in table 8.7. Again, the
comments that do not pertain to this problem have been eliminated for brevity.
Table 8.8 contains selections from the output file for this problem.
Only key results are presented with highlights of the output described.
The initial heat in the region includes both the enthalpy of the fluid
and of the porous matrix. The effective ambient permeability at the well bore
is defined element by element, thus, 10 values occur. The well-flow rate is
calculated explicitly at the beginning of each time step. The temperature
field at the end of the injection period shows the less-dense fluid rising up
over the cooler, resident fluid. Some numerical overshoot or spatial oscil
lation is apparent, with temperatures up to 62.5 °C appearing. This gives a
zone of plus signs on the contour map of temperature. At the value of time
step selected, only two cycles for solution of the pressure and temperature
equations were needed, which is the minimum necessary for the explicit calcu
lation of the cross-derivative dispersive-flux terms. During the production
part of the cycle, we can see the preferential withdrawal of the warmer water
from the upper part of the region, caused by the enhanced mobility of the
water at higher temperature. An additional zone, shown as minus signs on the
contour maps, shows that the temperature is below the lower limit of 20 °C
selected for these plots. Again, this is a spatial-oscillation effect, caused
by the coarseness of the grid in conjunction with central differencing for the
advective terms. The global-balance summary shows that, at the end of 90 days
of withdrawal, about 86 percent of the heat has been recovered. Only about
0.1 percent of the heat left the region through the boundary at the exterior
radius. The fluid-withdrawal and heat-withdrawal rates are shown on a per-
layer basis at the end of the simulation. The well is producing water at
about 38 °C at this time.
305
Table 8.7. Input-data file fo
r example problem 2
OJ o
C C C C C C C C C.. c.o
c.o
C..
C..
c.o
C..
C..
C..
,HST D
ATA-INPUT
FORM
NO
TES:
INPUT
LINES
ARE
DENOTED
BY C
.N1.N2.N3
WHERE
Nl IS
THE R
EAD
GROUP
NUMBER,
N2.N
3 IS T
HE R
ECORD
NUMB
ERA
LETTER I
NDICATES A
N EXCL
USIVE
RECORD S
ELECTION M
UST
BE M
ADE
I.E.
A
OR B
OR
C (0)
- OPTIONAL D
ATA
WITH
CON
DITI
ONS
FOR
REQUIREMENT
A RECORD N
UMBER
IN S
QUARE
BRACKETS IS
THE R
ECORD
WHERE
THAT
PARAMETER I
S FIRST
SET
.INPUT B
Y I.J.K
RANGE
FORMAT IS
; ,.
I1,I2,J1,J2,K1,K2
.. VA
R1,IMOD1,[VAR2,IMOD2,VAR3,
IMOD
3]
USE
AS M
ANY
OF L
INE
0.1
& 0.2
SETS A
S NECESSARY
END
WITH L
INE
0.3
,. 0
/ THE
SPACE
IS R
EQUI
RED
{NNN
} -
INDICATES
THAT
THE D
EFAU
LT N
UMBE
R, NNN, IS U
SED
IF A
ZERO
IS E
NTERED F
OR THAT
VARI
ABLE
(T/F)
- INDICATES
A LO
GICA
L VARIABLE
[I]
- IN
DICA
TES
AN INTEGER VARIABLE
C.....START
OF T
HE DA
TA F
ILE
C.....DIMENSIONING D
ATA
- READ1
C.I.
I .. TITLE
LINE 1
EXAM
PLE
12 T
HERMAL INJECTION
AND
WITHDRAWAL,
CYLINDRICAL
SYST
EM,
C.I.2
.. TITLE
LINE
2
VARI
ABLE
DENSITY A
ND VIS
COSI
TY
C.I.3
.. RE
STRT
(T/F
),TI
MRST
F
/C.I.4
.. HE
AT.S
OLUT
E.EE
UNIT
.CYL
IND.
SCAL
MF;
ALL
(T/F)
T F
F T
FC.I.5
.. NX
.NY.NZ.NHCN
26 1
11 0
C.I.6
.. NPTC
BC,N
FBC,
NAIF
C,NL
BC,N
HCBC,N
WEL
11 0
0 0
0 1
C.I.7
.. NP
MZ1 C.I.8
, 1
FC.I.9
. 0
/C.I.10
F
SLME
TH[I
],LC
ROSD
(T/F
)
IBC
BY I,J,K
RANGE
{0.1
-0.3
} .W
ITH
NO IMOD P
ARAM
ETER
, FOR
EXCL
UDED
CELLS
. RD
ECHO
(T/F
)
C.....STATIC D
ATA
- READ2
C.....OUTPUT INFORMATION
C.2.1
.. PRTRE(T/F)
F
Tab
le 8.7
. In
put-
data
fi
le fo
r ex
am
ple
pro
ble
m 2 C
onti
nued
C...
..CO
OR
DIN
AT
E
GEOM
ETRY
IN
FOR
MAT
ION
C...
..CY
LIN
DR
ICA
L CO
ORD
INAT
ESC
.2.2
B.1
A ..
R
(1),
R(N
R),
AR
GR
ID(T
/F);
(0)
- C
YLIN
D
[1.4
]1.
24
6.
TC.2.2B.1B
.. R(
I);(
0)
- NOT
ARGRID [2.2B.1A];(0)
- CYLIND [1
.4]
C.2.
2B.2
..
UNIGRZ(T/F);(0)
- CYLIND [1
.4]
T C.2.2B.3A
.. Z(1),Z(NZ);(0) -
UNIGRZ [2
.2B.
3A].
CYLI
ND [1
.4]
0. 30.
C.2.2B.3B
.. Z(
K);(
0) -
NOT
UNIGRZ [2.2B.3A].CYLIND [1
.4]
C.....FLUID
PROPERTY INFORMATION
C.2.
4.1
.. BP
0. C.2.
4.2
.. PO.TO.WO.DENFO
0. 20
. 0.
1000.
C.2.5.1
.. NO
TVO.
TVFO
(I).
VIST
FO(I
).I=
1 TO
NOTVO;(0)
- HE
AT [1.4]
OR H
EAT
[1.4
] AN
D SOLUTE [1
.4]
OR .N
OT.H
EAT
AND
.NOT
.SOL
UTE
[1.4
]2
20.
.001 60
. 4.62E-4
C...
..RE
FERE
NCE
CONDITION
INFORMATION
C.2.
6.1
.. PAATM
0. C.2.
6.2
.. POH.TOH
0. 20
.C.....FLUID
THER
MAL
PROP
ERTY
IN
FORM
ATION
C.2.7
.. CPF,KTHF.BT;(0)
- HE
AT [1
.4]
4182.
.6 3
.75E
-4C.....POROUS MEDIA
ZONE
INFORMATION
C.2.9.1
.. IP
MZ.I
1Z(I
PMZ)
.I2Z
(IPM
Z),J
1Z(I
PMZ)
.J2Z
(IPM
Z),K
1Z(I
PMZ)
,K2Z
(IPM
Z)1
1 26
1
1 1
11C.....USE
AS MANY 2.9.1
LINE
S AS N
ECES
SARY
C.2.
9.2
.. END
WITH 0
/
0 /
C.....POROUS ME
DIA
PROP
ERTY
INFORMATION
C.2.10.1
.. KXX(IPMZ),KYY(IPMZ),KZZ(IPMZ),IPMZ=1 TO
NP
MZ [1
.7]
1.02
E-10
..1.
02E-
10C.2.10.2 ..
POROS(IPMZ),IPMZ=1 TO
NP
MZ [1
.7]
.35
C.2.
10.3
..
ABPM(IPMZ),IPMZ=1
TO NP
MZ [1
.7]
0.
C.....POROUS MEDIA
THER
MAL
PROPERTY INFORMATION
C.2.
11.1
.. RC
PPM(
IPMZ
),IP
MZ=1
TO
NPMZ [1
.7];
(0)
- HE
AT [1
.4]
2.226E6
C.2.
11.2
.. KT
XPM(
IPMZ
),KT
YPM(
IPMZ
),KT
ZPM(
IPMZ
),IP
MZ=1
TO
NP
MZ [1
.7];
(0)
- HEAT [1.4]
3*3.5
C..!..POROUS ME
DIA
SOLUTE A
ND T
HERM
AL DISPERSION INFORMATION
C.2.12 ..
ALPHL(IPMZ),ALPHT(IPMZ),IPMZ=1 TO
NP
MZ [1
.7];
(0)
- SO
LUTE
[1
.4]
OR H
EAT
[1.4]
Table 8.7. Input-data file for example problem 2 Continued
4. 1.
C.....SOURCE-SINK
WELL IN
FORM
ATIO
NC.2.14.1 ..
RDWDEF(T/F);(0)
- NWEL [1.6]
> 0
T C.2.14.3.
.. IWEL,IW,JW,LCBOTW,LCTOPW,WBOD,WQMETH[I];(0)
- RDWDEF 12.14.1],
1 1
1 1
11 2.
11
C.2.14.4 .. WC
F(L)
;L =
1 T
O NZ (E
XCLU
SIVE
) BY EL
EMEN
T10*1.
C...!.USE
AS M
ANY
2.14
.3-6
LINES A
S NE
CESS
ARY
C.2.
14.7
.. END
WITH 0
/0
/C.....BOUNDARY C
ONDITION IN
FORM
ATIO
NC.....
SPEC
IFIE
D VALUE
B.C.
C.2.15 .. IB
C BY
I.J.K
RANGE
{0.1-0.3}
WITH N
O IMOD P
ARAMETER,;(0)
- NPTCBC [1.6]
> 0
26 2
6 1
1 1
11100
O/
C...
..FR
EE S
URFACE B
.C.
C.2.
20 .. FRESUR(T/F),PRTCCM(T/F)
F /
g
C...
..IN
ITIAL
CONDITION
INFO
RMAT
ION
oo
C.2.
21.1
.. ICHYDP.ICT.ICC;
ALL
(T/F
);IF
NOT.HEAT, ICT
= F,
IF
NOT.SOLUTE, ICC
= F
T T
FC.2.21.3A
.. ZPINIT,PINIT;(0) -
ICHY
DP [2.21.1] AND
NOT
ICHWT
[2.21.2]
30.
0.C.
2.21
.4B
.. T
BY I.J.K
RANG
E (0.1-0.3};(0)
- HEAT [1.4]
AND
ICT
[2.21.1]
1 26
1 1
1 11
20.
10
/C.
....
CALC
ULAT
ION
INFORMATION
C.2.22.1 .. FD
SMTH
.FDT
MTH
.5 1
.C.2.22.2 ..
TO
LDEN
{.00
1},M
AXIT
N{5)
0. 10
C...
..OU
TPUT
INFORMATION
C.2.23.1
.. PRTPMP,PRTFP,PRTIC,PRTBC,PRTSLM,PRTWEL;
ALL
(T/F)
6*T
C.2.
23.2
.. IPRPTC,PRTDV(T/F);(0)
- PRTIC
[2.2
3.1]
110
FC.
2.23
.4 ..
PLTZON(T/F);(0)
- PRTPMP [2.23.1]
F C.2.
23.5
..
OC
PLOT
(T/F
)F C
C..... TRANSIENT
DATA -
READ3
Table 8.7. Input-data file for
example problem 2 Continued
C.3.1
.. TH
RU(T
/F)
F C.....IF THRU IS
TR
UE PR
OCEE
D TO
RECORD 3.99
C.....THE
FOLL
OWIN
G IS
FO
R NO
T THRU
C.....SOURCE-SINK
WELL IN
FORM
ATIO
NC.
3.2.
1 ..
RD
WFLO
(T/F
),RD
WHD(
T/F)
;(0)
-
NWEL [1
.6]
> 0
T F
C.3.2.2
.. IW
EL,Q
WV,P
WSUR
,PWK
T,TW
SRKT
,CWK
T;(0
) -
RDWFLO [3
.2.1
] OR R
DWHD [3
.2.1
]1
203. 0.
0.
60.
0.C.
....
USE
AS M
ANY
3.2.2
LINE
S AS
NECESSARY
C.3.2.3
.. EN
D WITH 0
/0
/C
.....B
OU
ND
AR
Y
CO
ND
ITIO
N
INFO
RM
ATIO
NC
.....
SP
EC
IFIE
D
VALU
E B
.C.
C.3
.3.1
..
R
DS
PB
C,R
DS
TBC
,RD
SC
BC
,ALL
(T/F
);(0)
-
NOT
CYL
IND
[1
.4]
AND
NPTC
BC
[1.6
] >
0T
F F
C.3.3.2
.. PN
P B.C. BY I.J.K
RANGE
(0.1
-0.3
};(0
) -
RDSPBC [3
.3.1
]26
26
1 1
11 11
0.
126
26
1 1
10 10
£
2.94
21E4
1
§
26 2
6 1
1 9
95.8842E4 1
26 2
6 1
1 8
88.8263E4 1
26 2
6 1
1 7
71.
1768
4E5
126
26
1 1
6 6
1.47
105E
5 1
26 2
6 1
1 5
51.
7652
6E5
126
26
1 1
4 4
2.05947E5
126
26
1 1
3 3
2.35368E5
126
26
1 1
2 2
2.64
789E
5 1
26 2
6 1
1 1
12.9421E5 1
0 /
C.3.3.3
.. TS
BC BY I.
J.K
RANGE
{0.1-0.3}; (0
) -
RDSPBC [3
.3.1
] AN
D HE
AT [1.4]
26 2
6 1
1 1
1120
. 1
0 /
C.....CALCULATION
INFO
RMAT
ION
Tab
le 8.7
. In
put-
data
fi
le fo
r
exa
mp
le p
roble
m 2
C
onti
nued
C.3
.7.1
..
RD
CA
LC(T
/F)
T C.3
.7.2
..
AU
TO
TS
(T/F
);(0
) -
RDCA
LC
[3.7
.1]
F C.3
.7.3
.A ..
DE
LT
IM;(
0)
- RD
CALC
[3
.7.1
] AN
D NO
T AU
TOTS
[3
.7.2
]2.
592E
5C
.3.7
.4 ..
TIM
CH
G7.
7760
E6
C..
...O
UT
PU
T
INFO
RM
ATIO
NC
.3.8
.1
..
PR
IVE
L,P
RID
V,P
RIS
LM,P
RIK
D,P
RIP
TC
,PR
IGF
B,P
RIW
EL,
PR
IBC
F;
ALL
[I]
0 0
10 0
10
-1
0 30
C.3
.8.2
..
IPR
PT
C;(
0)
- IF
P
RIP
TC
[3.8
.1]
NOT
= 0
010
C.3
.8.3
..
CH
KP
TD
(T/F
),N
TS
CH
K,S
AV
LDO
(T/F
)F
/C.
....
CONT
OUR
MAP
INFORMATION
C.3.9.1
.. RDMPDT,PRTMPD; ALL
(T/F)
T T
C.3.9.2
.. MA
PPTC
,PRI
MAP[
I];(
0) - RDMPDT [3
.9.1
]01
0 10
C.3.
9.3
.. YP
OSUP
(T/F
),ZP
OSUP
(T/F
),LE
NAX,
LENA
Y,LE
NAZ;
(0)
- RDMPDT [3
.9.1
]F
T 12.
0. 6.
C.3.
9.4
.. IM
AP1{
1},I
MAP2
{NX}
,JMA
P1{1
},JM
AP2{
NY},
KMAP
1{1}
,KMA
P2{N
Z},A
MIN,
AMAX
,NMP
ZON{
5}:(
0) - RDMPDT [3.9.1]
0 0
0 0
0 0
20.
60.
8C.
....
ONE
OF T
HE 3.9.4
LINE
S REQUIRED FO
R EA
CH D
EPENDENT V
ARIABLE
C.....
TO BE M
APPE
DC.....END
OF FI
RST
SET
OF T
RANS
IENT
INFORMATION
C_ __________________________________________
C...
..RE
AD S
ETS
OF READS
DATA A
T EACH T
IMCH
G UN
TIL
THRU
(LIN
ES 3.N1.N2)
C..... TRANSIENT
DATA -
RE
AD3
C.3.
1 .. THRU(T/F)
F C.....IF T
HRU
IS T
RUE
PROC
EED
TO RECORD 3
.99
C.....THE
FOLLOWING
IS FO
R NO
T THRU
C...
..SO
URCE
-SIN
K WE
LL INFORMATION
C.3.
2.1
.. RD
WFLO
(T/F
),RD
WHD(
T/F)
;(0)
-
NWEL
[1.6]
> 0
T F
C.3.2.2
.. IW
EL,Q
WV,P
WSUR
,PWK
T,TW
SRKT
,CWK
T;(0
) - RDWFLO [3
.2.1
] OR
RD
WHD
[3.2
.1]
1 -203.
0. 0.
60
. 0.
C...
..US
E AS
MANY
3.2.2
LINE
S AS
NECESSARY
C.3.
2.3
.. EN
D WITH 0
/0
/C.
....
BOUN
DARY
CO
NDIT
ION
INFORMATION
C.....
SPECIFIED
VALUE
B.C.
C.3.3.1
.. RDSPBC,RDSTBC,RDSCBC,ALL(T/F);(0)
- NO
T CYLIND [1
.4]
AND
NPTCBC [1
.6]
> 0
Tabl
e 8.7. Input-data fi
le fo
r ex
ampl
e problem
2 Continued
F F
FC.....CALCULATION
INFORMATION
C.3.7.1
.. RD
CALC
(T/F
)T C.
3.7.2
.. AU
TOTS
(T/F
);(0
) - RD
CALC
[3
.7.1
]F C.3.
7.3.
A ..
DE
LTIM
;(0)
-
RDCALC [3.7.1]
AND
NOT AU
TOTS
[3.7.2]
2.59
2E5
C.3.
7.4
.. TI
MCH6
1.55
52E7
C...
..OU
TPUT INFORMATION
C.3.
8.1
.. PR
IVEL
,PRI
DV,P
RISL
M,PR
IKD,
PRIP
TC,P
RI6F
B,PR
IWEL
,PRI
BCF;
AL
L (I
)0
0 10 0
10 -1
-1 30
C.3.8.2
.. IPRPTC;(0) -
IF PRIPTC [3
.8.1]
NOT
= 0
010
C.3.8.3
.. CHKPTD(T/F),NTSCHK,SAVLDO(T/F)
F /
C.....CONTOUR
MAP
INFORMATION
C.3.
9.1
.. RDMPDT,PRTMPD; AL
L (T
/F)
T T
u,
C.3.
9.2
.. MA
PPTC
,PRI
MAP[
I];(
0) -
RDMP
DT [3.9.1]
C
010
10
M
C.3.
9.3
.. YPOSUP(T/F),ZPOSUP(T/F),LENAX,LENAY,LENAZ;(0)
- RD
MPDT
[3
.9.1
)F
T 12.
0. 6.
C.3.
9.4
.. IMAP1{1},IMAP2{NX},JMAP1{1
},JMAP2{NY},KMAP1{1},KMAP2{NZ},AMIN,AMAX,NMPZON{5}:(0) - RDMPDT [3
.9.1
)0
0 0
0 0
0 20
. 60.
8C.....ONE
OF T
HE 3.9.4
LINES
REQU
IRED
FOR
EACH
DEPENDENT V
ARIA
BLE
C...
..
TO BE MA
PPED
C...
..EN
D OF
SEC
OND
SET
OF T
RANSIENT INFORMATION
C- ------------------------------------------
C.....READ S
ETS
OF RE
AD3
DATA AT
EACH
TIM
CH6
UNTIL
THRU
(LIN
ES 3.
N1.N
2)C.....END
OF CALCULATION
LINES
FOLLOW
, THRU=.TRUE.
C.3.
99.1
..
TH
RUT C.
....
TEMP
ORAL
PLOT INFORMATION
C.3.99.2 .. PL
OTWP
.PLO
TWT.
PLOT
WC;
ALL
(T/F
)3*
FC.
....
END
OF D
ATA
FILE
S1N3W
3T3 OOOOZ
S1N3W
313 660Z
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wa
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"8
Table 8.8. Selections from th
e output file for example problem 2 Continued
***
TIM
E IN
VA
RIA
NT
OR
STA
TIC
DA
TA *
****
* C
YLI
ND
RIC
AL
(R-Z
) CO
ORD
INAT
E DA
TA **
* AQ
UIF
ER
INTE
RIO
R
RAD
IUS
....
....
....
..
RIN
T .
1.00
0 (
M)
AQU
IFER
EX
TER
IOR
R
ADIU
S ..
....
....
....
RE
XT
. 2
46
.0
( M
)
R-D
IRE
CTI
ON
NO
DE
COO
RDIN
ATES
(
M)
1234
56
78
9
101.
00
1.25
1.
55
1.94
2.
41
3.01
3.
75
4.67
5.
82
7.26
11
12
13
14
15
16
17
18
19
209.04
11.2
7 14.05
17.5
1 21.82
27.20
33.90
42.25
52.66
65.63
21
22
23
24
25
2681.80
101.95
127.06
158.
37
197.38
246.00
R-C
OO
RD
INAT
E C
ELL
BOUN
DARY
LO
CAT
ION
S (B
ETW
EEN
NO
DE
(I)
AND
NODE
(I-*
-!))
(
M)
12
34
56
78
9
101.
12
1.39
1.
74
2.17
2.
70
3.36
4.
19
5.23
6.
51
8.12
11
12
13
14
15
16
17
18
19
2010.12
12.61
15.72
19.59
24.41
30.43
37.92
47.26
58.9
1 73.42
21
22
23
24
2591.50
114.05
142.
14
177.16
220.80
Z-DI
RECT
ION
NODE
COORDINATES
( M)
Tabl
e 8.8. Se
lect
ions
from the
output file for
exam
ple problem 2 Continued
123456789
100.
00
3.00
6.
00
9.00
12
.00
15.0
0 18
.00
21.0
0 24
.00
27.0
0
1130
.00
Z-AXIS IS
POS
ITIV
E VE
RTIC
ALLY
UPWARD
** A
QUIF
ER P
ROPE
RTIE
S **
(R
EAD
ECHO
)REGION
POROUS M
EDIUM
M.C.
=MOD
IFIC
ATIO
N CO
DE
II
12
Jl
J2
Kl
K2
ZONE
IN
DEX
OJ
PORO
US M
EDIA P
ROPERTIES
1 1.
0200
E-10
1.02
00E-
10
X-DIRECTION
PERM
EABI
LITI
ES
( M*
*2)
Z-DI
RECT
ION
PERM
EABI
LITI
ES
( M*
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10.3500
PORO
SITY
(-)
sie
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CO *"*Jo>cococo cnOOO^ VO VO VOm m m m i i i i
vo vo vo vo
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from
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fo
r ex
am
ple
p
roble
m 2 C
onti
nued
LON
GIT
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ITY
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M)
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SVER
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RIC
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SURE
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l.
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60.0
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321
Tabl
e 8.8. Selections fr
om th
e output fi
le for
example problem 2 Continued
Co ro
4 3 2 1 11 10 9 8 7 6 5 4 3 2 1
120.3
120.3
120.3
60.14
2149
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RAT
E
ELEM
ENT
LEVE
L EF
FEC
TIVE
AM
BIEN
T LA
YER
NO
. P
ER
ME
AB
ILIT
Y
NO.
( M
**2)
WEL
L NO
. 1
11
10
1.02
0E-1
0 10
9
1.02
0E-1
0 9
1690
. 26
25.
4078
. 63
34.
1690
. 26
25.
4078
. 63
34.
1690
. 26
25.
4078
. 63
34.
84
5.0
13
13.
2039
. 31
67.
,.
1.99
6192
E+0
9 (K
G)
; 1.
9961
92E
+06
( M
**3)
..
3.31
3955
E-H
4 (
J)
WEL
L D
IAM
ETER
(
M)
2.00
0E+0
0 AL
LOC
ATIO
N
BY M
OB
ILIT
Y
WEL
L FL
OW
FACT
OR
( M
**3) 1.53
0E-1
0 3.
060E
-10
3.06
0E-1
0
Tabl
e 8.8. Selections from the
output file fo
r example
problem
2 Continued
U>
11 10 9 8 7 6 5 4 3 2 1
1.020E-10
1.020E-10
020E-10
020E-10
020E-10
020E-10
1.02
0E-1
0 1.020E-10
EXPLICIT W
ELL
FLOW R
ATE
AT EACH LAYER
INDE
X NU
MBER
S FOR
SPEC
IFIE
D P,
T OR C
NODES
VERT
ICAL
SLICES
J =
1
.060
E-10
.0
60E-
10
.060E-10
.060E-10
.060E-10
060
E-10
.0
60E-
101.
530E
-10
10
11 10 9 8 7 6 5 4 3 2 1
1112
1314
1516
1718
1920
Tab
le 8.8
. Sele
cti
ons
from
th
e outp
ut
file
fo
r ex
am
ple
pro
ble
m
2 C
onti
nued
11 10 9 8 7 6 5 4 3 2 1
2122
2324
2526
11.
10. 9.
8.
7.
6,
5,
4,
3.
2,
1.
to
N5
4s
***
CALC
ULAT
ION
INFO
RMAT
ION
***
TOLE
RANC
E FO
R P
.T.C
IT
ERAT
ION
(F
RAC
TIO
NAL
DE
NSIT
Y CH
ANGE
) ...
TOLD
EN
0.00
10
MAX
IMUM
NU
MBER
OF
ITER
ATIO
NS
ALLO
WED
ON
P.T
.C
EQUA
TIO
NS ..
...
MAX
ITN
10
BAC
KWAR
DS-
IN-T
IME
(IM
PLI
CIT
) D
IFFE
REN
CIN
G
FOR
TEM
PORA
L D
ERIV
ATIV
E C
ENTE
RED
-IN-S
PAC
E DI
FFER
ENCI
NG
FOR
CONV
ECTI
VE
TERM
S TH
E C
RO
SS-D
ERIV
ATIV
E HE
AT A
ND S
OLU
TE
FLUX
TER
MS
WIL
L BE
CA
LCUL
ATED
EX
PLIC
ITLY
***
TRAN
SIEN
T DA
TA *
**
11 10 9 8 7 6
SPEC
IFIE
D BO
UNDA
RY P
RESSURES
( PA)
VERT
ICAL
SLICES
J =
1
2345
10
Tab
le 8
.8.
Sele
cti
ons
from
th
e o
utp
ut
file
fo
r
exa
mp
le p
rob
lem
2
C
on
tin
ued
Ui
11 10 9 8 7 6 5 4 3 2 1 11 10 9 8 7 6 5 4 3 2 1
11 21
1213
1415
2223
2425
16 26,0
000
.942
1E+0
4 .8
842E
+04
8.82
63E
+04
1768
E+0
5 47
10E
+05
7653
E+0
5 05
95E
+05
2.35
37E
+05
2.64
79E
+05
2.94
21E
+05
1718
1920
ASSO
CIA
TED
BO
UNDA
RY
TEM
PERA
TURE
S FO
R IN
FLO
W
(DE
G.C
)
VER
TIC
AL S
LIC
ES
J =
1
1234567
10
Tab
le 8.8
. S
ele
cti
ons
from
th
e outp
ut
file
fo
r ex
am
ple
pro
ble
m 2 C
on
tin
ued
11 10 9 8 7 6 5 4 3 2 1
ro
11 10 9 8 7 6 5 4 3 2 1
1112
1314
1516
1718
1920
2122
11 10 9 8 7 6 5 4 3 2 1
2324
2526
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
20.0
Tabl
e 8.8. Se
lect
ions
fr
om the
output fi
le for
example problem 2 Co
ntin
ued
UJ to
WELL
NO. 1
FIXEI
TIME
FLOW R
ATE
SURFACE
WELL
DAT
UM
PRES
SURE
INJECTION
INJECTION
( M**3/S
) PR
ESSU
RE
PRES
SURE
LI
MITE
D?
TEMP
ERAT
URE
MASS
FRACTION
( PA
) (
PA)
(DEG.C
) (-
)
0.2030
NO
60.0
0
***
CALC
ULAT
ION
INFORMATION
***
3 TI
ME S
TEP
LENGTH ..
....
....
....
....
....
....
....
....
...
DELT
IM
2.59
2E+0
5 (S
);
3.00
(D)
AT W
HICH N
EXT
SET
OF T
IME
VARY
ING
PARAMETERS W
ILL
BE READ ..
....
....
....
....
....
....
....
. TI
MCHG
7.776E+06
(S);
90.0
(D)
***
MAPP
ING
DATA
***
LENGTH O
F X-AXIS ..
....
....
....
.12.
0 (IN.)
LENGTH O
F Y-AXIS ...............
0.0
(IN.)
LENGTH O
F Z-AXIS ...............
6.0
(IN.)
Z-AXIS IS
POSITIVE U
PWAR
D
MAP
NO.
11
12
Jl
J2
Kl
K2
MINIMUM
VALU
E MA
XIMUM
VALU
E NU
MBER
OF
OF V
ARIA
BLE
OF V
ARIABLE
ZONE
S
2 1
26
1 1
1 11
20.
60.
8
***
OUTPUT A
T EN
D OF
TIM
E ST
EP N
O.
30 *
**
TIME ..................................................
7.77
6E+0
6 (S
);
90.0
(D)
CURRENT
TIME STEP LE
NGTH
..
....
....
....
....
....
....
....
....
. 2.592E+05
(S);
3.00
(D)
NO.
OF P.
T.C
LOOP
IT
ERAT
IONS
USED ..........................
2MA
XIMU
M CHANGE IN P
RESSURE
.................................
-1.4460E+02
( PA)
AT LOCATION (22, 1
MAXI
MUM
CHANGE IN T
EMPERATURE ..
....
....
....
....
....
....
....
1 .8
286E
+00
(DEG
.C)
AT LOCATION (24. 1
TEMPERATURE
(DEG.C)
VERT
ICAL
SLICES
J =
1
a0)
4J
ooooooooooo to to to to to to to to to to to
oCsj
O> O> O> Ot O> O> Ot O> Ot O> O> ininuDinuDinininininin
-Pa o ui
§"S -Q O
ooooooooooo to to to to to to to to to to to
ooooooooooo
00
ooooooooooo to to to to to to to to to to to
0>
ooooooooooo to to to to to to to to to to to
00to to to to to to to to to to to
to to to to to to to to to to to
ooooooooooo oooooooooooooooooooooo to to to to to to to to to to to
Itoooooooooooo to to to to to to to to to to to to to to to to to to to to to toevj
CsJCSJCsJCsjCsJCsjCsJCVJCsJCsJCSJ
O
<U*q-U
I
S oooooooooo to to to to to to to to to to
ooooooooooo to to to to to to to to to to to
ooooooooooo
to to to to to to to to to to to
ooooooooooo to to to to to to to to to to to
tr>CM
OsJOsJOsJCSJOsJOsJCSJCSJCVJCSJOsJ
o H 4J O<u
ooooooooooo to to to to to to to to to to to
ooooooooooo
ooooooooooo to to to to to to to to to to toCO CSJ
CO
CO
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(0 EH
OOOOOOi_ _ _ _ _oooooooooooooooooooooo to to to to to to to to to to to ooooooooooo to to to to to to to to to to to
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ooooooooooo to to to to to to to to to to to ooooooooooo to to to to to to to to to to toOOOOOr-lt-Ht-HfHt-Ht-HUDUDUDtOtOtOtOtOtOtOtO
328
Tab
le 8.8
. S
ele
cti
ons
from
th
e outp
ut
file
fo
r ex
am
ple
pro
ble
m
2 C
onti
nued
***
GLO
BAL
FLOW
BA
LANC
E SU
MM
ARY
CURR
ENT
TIM
E
STEP
RATES
AMOUNTS
U3
NJ
vo
FLUI
D INFLOW ..
....
....
....
....
....
....
....
....
....
....
....
. 1.999550E+02
(K
G/S)
5.
1828
33E+
07
(KG)
FLUID
OUTF
LOW
..............................................
2.014491E+02
(KG/S)
5.221562E+07
(KG)
CHANGE IN
FLUID
IN REGION ..
....
....
....
....
....
....
....
....
-1
.493
657E
+00
(KG/S)
-3.8
7155
8E+0
5 (KG)
RESIDUAL IMBALANCE
....
....
....
....
....
....
....
....
....
....
. 4.
9054
15E-
04
(KG/S)
1.27
1484
E+02
(K
G)FR
ACTI
ONAL
IM
BALA
NCE
.......................................
0.0000
HEAT INFLOW ..
....
....
....
....
....
....
....
....
....
....
....
..
5.01
1149
E+07
(
J/S)
1.
2988
90E+
13
( J)
HEAT O
UTFL
OW ...............................................
1.732711E+07
( J/
S)
4.49
1186
E-H2
(
J)CH
ANGE
IN HEAT IN
REGION ..
....
....
....
....
....
....
....
....
. 3.
2784
93E+07
(
J/S)
8.
497854E-H2
( J)
RESIDUAL IM
BALA
NCE
....
....
....
....
....
....
....
....
....
....
. 5.
4653
75E+02
(
J/S)
1.
4166
25E+
08
( J)
FRAC
TION
AL IM
BALA
NCE
.......................................
0.0000
CUMULATIVE S
UMMA
RYAMO
UNTS
FLUID
INFL
OW ...............................................
1.55
4850
E+09
(KG)
FLUI
D OU
TFLO
W ..............................................
1.566620E+09
(KG)
CHANGE IN FL
UID
IN REGION ..
....
....
....
....
....
....
....
....
-1
.176
905E
+07
(KG)
FLUID
IN REGION ............................................
1.98
4422
E+09
(KG)
RESIDUAL IM
BALA
NCE
....
....
....
....
....
....
....
....
....
....
. 8.
2283
76E+
02
(KG)
FRAC
TION
AL IM
BALA
NCE
.......................................
0.00
00
HEAT
INFL
OW ...............................................
3.89
6669
E+14
(
J)HEAT
OUTFLOW
..............................................
1.31
2503
E-H4
( J)
CHANGE IN
HEAT
IN R
EGION
....
....
....
....
....
....
....
....
...
2.584199E+14
(
J)HEAT IN
REGION .............................................
5.89
8154
E+14
( J)
RESI
DUAL
IMBALANCE
....
....
....
....
....
....
....
....
....
....
. 3.
2711
83E+
09
( J)
FRAC
TION
AL IM
BALA
NCE
.......................................
0.00
00
CUMULATIVE S
PECIFIED P
CELL F
LUID N
ET INFLOW ...............
-1.566620E+09
(KG)
CUMULATIVE FL
UX B
.C.
FLUI
D NE
T IN
FLOW
..
....
....
....
....
....
O.
OOOO
OOE-
01
(KG)
CUMULATIVE LEAKAGE
B.C. FLUID
NET
INFLOW ...................
O.OO
OOOO
E-01
(KG)
CUMULATIVE A
QUIF
ER IN
FLUE
NCE
FLUID
NET
INFLOW ..
....
....
....
O.
OOOO
OOE-01
(KG)
CUMULATIVE SPECIFIED
T CELL O
R AS
SOCI
ATED
WIT
HSPECIFIED
P CE
LL H
EAT
NET
INFL
OW..
....
....
....
....
....
. -1.312503E+14
( J)
CUMULATIVE FL
UX B.C. HEAT N
ET IN
FLOW
..
....
....
....
....
....
. O.
OOOO
OOE-
01
( J)
CUMULATIVE LE
AKAG
E B.
C. HE
AT N
ET INFLOW ....................
O.OO
OOOO
E-01
( J)
CUMULATIVE A
QUIF
ER IN
FLUE
NCE
HEAT N
ET INFLOW ...............
O.OO
OOOO
E-01
(
J)CUMULATIVE HEAT CONDUCTION B.C. HEAT NE
T INFLOW ............
O.OO
OOOO
E-01
( J)
Table 8.8. Selections from the
output file for example problem 2 Continued
u>
o
11 10 9 8 7 6 5 4 3 2 1
FLUID
(KG/S)
VERTICAL S
LICESSP
ECIFIED
PRES
SURE
, TE
MPER
ATUR
E, OR
MAS
S FRACTION B
.C.
FLOW R
ATES
POSI
TIVE
IS
INTO T
HE R
EGIO
N
J =
1
5 6
10
11 10 9 8 7 6 5 4 3 2 1
1112
1314
1516
1718
1920
11 10 9 8
2122
2324
2526
-23.
71-21.04
-20.08
-19.
41
Tabl
e 8.8. Se
lect
ions
from the
output fi
le fo
r example problem 2 Continued
-18.
92-18.58
-18.36
-18.
26-1
8.26
-18.
36-6.482
11 10 9 8 7 6 5 4 3 2 1
ASSO
CIAT
ED H
EAT
( J/S)
VERT
ICAL
SLICES
J =
1
10
11 10 9 8 7 6 5 4 3 2 1
1112
1314
1516
1718
1920
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Tab
le 8
.8.
Sele
cti
ons
from
th
e o
utp
ut
file
fo
r
exa
mp
le p
rob
lem
2 C
onti
nued
GR
ID
NODE
LO
CAT
ION
S AL
ONG
TH
E PA
GE
AX
IS
IS
PO
SIT
IVE
UP
TH
E PA
GE
0.00
0 3
.00
6
.00
9
.00
12
.0
15.0
18
.0
21
.0
24
.0
27
.0
30
.0
***
TRAN
SIEN
T DA
TA *
**
***
TRAN
SIEN
T W
ELL
DATA
**
*W
ELL
FLOW
RA
TE
SURF
ACE
WEL
L DA
TUM
PR
ESSU
RE
INJE
CTI
ON
IN
JEC
TIO
N
NO.
( M
**3/
S)
PRES
SURE
PR
ESSU
RE
LIM
ITE
D?
TEM
PERA
TURE
M
ASS
FRAC
TIO
N(
PA)
( PA
) (D
EG
.C)
(-)
....
....
... .^
^..
....
....
....
....
....
....
....
....
....
....
^..
.^......................................
***
CALCULATION
INFORMATION
***
FIXED
TIME ST
EP LE
NGTH
.....................................
DELTIM
2.592E+05
(S);
3.00
(D)
TIME A
T WHICH
NEXT
SET O
F TI
ME V
ARYI
NGPA
RAME
TERS
WILL B
E READ ..
....
....
....
....
....
....
....
. TI
MCHG
1.555E+07
(S);
180.
(D
)
***
MAPPING
DATA *
**
LENGTH O
F X-AXIS ...............12.0
(IN.)
LENG
TH O
F Y-AXIS ...............
0.0
(IN.)
LENG
TH O
F Z-AXIS ...............
6.0
(IN.)
Z-AXIS IS POSITIVE U
PWARD
MAP
NO.
II
12
Jl
J2
Kl
K2
MINI
MUM
VALU
E MA
XIMU
M VA
LUE
NUMB
ER O
FOF
VAR
IABL
E OF
VARIABLE
ZONES
2 1
26
1 1
1 11
20.
60.
8
***
OUTPUT A
T EN
D OF
TIME
STEP
NO.
40
***
TIME
..
....
....
....
....
....
....
....
....
....
....
....
....
1.037E+07
(S);
12
0.
(D)
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O
§rrH'
3Cn> a
jakjatenenenenenenenenenenenenenenenenenenenenro co »-*
Tab
le 8.8
. Sele
cti
ons
from
th
e o
utp
ut
file
fo
r
exa
mp
le pro
ble
m 2
C
onti
nued
56.5
455
.27
53.6
551
.79
49.7
947
.82
46.0
644
.71
43.9
7
53.2
051
.14
48.7
046
.05
43.3
740
.88
38.7
837
.29
36.5
8
45.1
642
.46
39.6
236
.82
34.2
231
.96
30.1
829
.03
28.5
7
31.4
129
.83
28.2
726
.82
25.5
524
.50
23.7
123
.23
23.0
5
21.7
021
.45
21.2
020
.99
20.8
120
.67
20.5
820
.51
20.4
9
19.9
819
.97
19.9
819
.98
19.9
819
.98
19.9
819
.98
19.9
8
VER
TIC
AL
PLAN
E AT
RO
W
NO.
1
VER
TIC
AL
CR
OSS
-SEC
TIO
N
OF
SIM
ULA
TIO
N
REG
ION
-TE
MPE
RATU
RES
PAGE
1
u>
****
4**4
*4*4
*444
*444
*444
4*44
444*
4444
444*
4444
4444
4*
33*3333
4444
4444
4444
4444
4444
4444
4444
4444
4444
4444
4444
4444
44
333333
4444
4444
4444
4444
4444
4444
4444
4444
4444
4444
4444
4444
44
3333
333
4444
4444
4444
4444
4444
4444
4444
4444
4444
4444
4444
4444
4 3333333
*444
44444444444444444444444444444444444444444444
3333
333
4444
4444
4444
4444
4444
4444
4444
4444
4444
4444
4444
444
3333
3333
44
4444
4444444444444444444444444444444444444444
3333
333
4444
4444
4444
4444
4444
4444
4444
4444
4444
4444
4444
4 33
3333
3*4
4444
44444444444444444444444444444444444444
3333
3333
44
4444
4444444444444444444444444444444444444
3333
333
4444
444444444444444444444444444444
4444444
3333
333
222222
*444
444444444444444444444444444444444444
3333
333
222222
4444
444444444444444444444444444444
44444
3333
333
222222
4444
4444
4444
4444
4444
4444
4444
4444
4444
4 3333333
2222222
444444444444444444444444444444444444
3333333
2222
222
*444
4444
4444
4444
4444
4444
4444
4444
444
3333333
2222
222
444444444444444444444444444444444
33333333
2222222
2222
222222
222222
22222
22222
222222
22222
222222
22222
222222
44444444444444444444444444444444
*444444444444444444444444444444
44444444444444444444444444444
4444
4444
4444
4444
4444
4444
4444
44
4444
4444
4444
4444
4444
4444
4*4444444444444444444444444
4444
4444
4444
4444
4444
4444
4 44
4444
4444
4444
4444
4444
44
44444444444444444444444
33333333
3333
3333
33333333
3333
3333
33333333
33333333
33333333
33333333
3333
3333
2222222
2222
222
222222
2222
22222222
222222
2222
222
2222222
222222
1111
1111
111111111
1111
1111
1111
1111
111111111
111111111
1111
1111
11111111111
1111111111
1111
1111111
1111111111
11111111111
111111111111
11111111111
11111111111
11111111111
11111111111
111111111111
11111111111
11111111111
11111111111
11111111111
1111
1111
111
1111
1111
111
1111
1111
111111111111
Table 8.8. Selections from the
output file for example problem 2 Continued
M444
4444
4444
4444
4444
4 44
4444
4444
4444
4444
444
4444
4444
4444
4444
4444
4*444444444444444444
4444
4444
4444
4444
444
4444
4444
4444
4444
44444444444444444444
*444
4444
4444
4444
4 444444
44444444444
44444444444444444
3333
3333
3 333333333
3333
3333
3 33
3333
33
3333
3333
33
3333
33
333333333
3333
3333
333333333
3333
3333
3*
3333
33 *
222222
2222222
2222222
2222222
2222222
2222222
2222222
2222222
2222222
2222
222
2222*22
1111
1111
11
1111
1111
111
111111111111
1111
1111
1111
11
1111
1111
111
1111
1111
1111
1 11
1111
1111
11
1111
1111
1111
1 11
1111
1111
11
1111
1111
1111
11
*111
1111
111
*
MAP
LEGE
NDHORIZONTAL G
RID
NODE
RAN
GE,
FROM
1 TO 2
6 VE
RTIC
AL G
RID
NODE
RAN
GE,
FROM
1 TO
11
DEPENDENT
VARI
ABLE
RAN
GE
MAP
CHARACTER
000E+01
500E+01
000E
+01
500E
+01
000E
+01
500E+01
000E+01
500E
+01
OOOE+01
500E
+01
OOOE+01
500E
+01
OOOE+01
500E+01
1.00
14.0
197.
0.000
5.500E+01
- 6.000E+01
GRID
NOD
E LO
CATI
ONS
ACROSS T
HE P
AGE
1.25
1.55
1.
94
2.41
17.5
21.8
27.2
33.9
246.
GRID
NODE LOCATIONS
ALONG
THE
PAGE
AXIS IS
POS
ITIV
E UP T
HE P
AGE
3.00
6.00
9.00
12
.0
3.01
42.3
3.75
52.7
4.67
65.6
5.82
81.8
7.26
102.
9.04
127.
11.3
158.
15.0
18.0
21.0
24.0
27.0
30.0
***
OUTP
UT A
T END
OF T
IME
STEP
NO.
60
***
TIME
..................................................
1.55
5E+0
7 (S
);
180.
(D)
CURRENT
TIME
STEP
LENG
TH ...................................
2.592E+05
(S);
3.00
(D)
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339
Tab
le 8.8
. Sele
cti
ons
from
th
e outp
ut
file
fo
r ex
am
ple
pro
ble
m
2 C
onti
nued
CU
MU
LATI
VE
LEAK
AGE
B.C
. FL
UID
NET
IN
FLO
W ..
....
....
....
....
. O
.OO
OO
OO
E-01
(K
G)
CU
MU
LATI
VE
AQU
IFER
IN
FLU
ENC
E FL
UID
NE
T IN
FLO
W ..
....
....
....
O
.OO
OO
OO
E-01
(K
G)
CU
MU
LATI
VE
SP
EC
IFIE
D T
C
ELL
OR A
SSO
CIA
TED
WIT
HS
PE
CIF
IED
P
CEL
L HE
AT
NET
INF
LO
W.......................
-5.3
0154
6E+
11
( J)
CU
MU
LATI
VE
FLUX
B
.C.
HEAT
NE
T IN
FLO
W ..
....
....
....
....
....
. O
.OO
OO
OO
E-01
(
J)C
UM
ULA
TIVE
LE
AKAG
E B
.C.
HEAT
NE
T IN
FLO
W ..
....
....
....
....
..
O.O
OO
OO
OE-
01
( 'J
)C
UM
ULA
TIVE
AQ
UIF
ER
INFL
UEN
CE
HEAT
NE
T IN
FLO
W ..
....
....
....
. O
.OO
OO
OO
E-01
(
J)C
UM
ULA
TIVE
HE
AT
COND
UCTI
ON
B.C
. HE
AT
NET
INFL
OW
..
....
....
..
O.O
OO
OO
OE-
01
( J)
***
WEL
L SU
MM
ARY
***
UJ *>
o
WELL
NO.
I
1 1
TOTA
L
LOCATION
J K
1 1-
11
- PRODUCTION
- IN
JECT
ION
FLOW
RATES
FLUI
D (KG/S)
-202.
202.
0.00
0
(POSITIVE
HEAT
( J/
s)-3.155E+07
3.155E+07
0.00
0
IS IN
JECT
ION)
SO
LUTE
(K
G/S)
CUMU
LATI
VE PRODUCTION
FLUID
HEAT
SOLUTE
(KG)
(
J)
(KG)
1.56E+09
1.56E+09
3.36E+14
3.36
E+14
CUMULATIVE IN
JECT
ION
FLUI
D HEAT
SOLUTE
(KG)
(
J)
(KG)
1.55E+09
1.55E+09
3 3
.90E
+14
.90E
+14
THE
FOLL
OWIN
G PA
RAME
TERS
WERE IN
EFFECT D
URING
THE
TIME
STEP
JUST
COMPLETED
WELL
TOP
COMPLETION LAYER
WELL D
ATUM
WE
LL H
EAD
WELL
DAT
UM
WELL
HEAD
MASS
NO.
CELL
PRESSURE
PRESSURE
PRES
SURE
TEMPERATURE
TEMPERATURE
FRACTION
( PA)
( PA
) (
PA)
(DEG
.C)
(DEG.C)
(-)
1 -4.1870E+04
-4.1870E+04
38.4
0.0
PER
LAYER
FLUI
D PR
ODUC
TION
/INJ
ECTI
ON R
ATES
- (K
G/S)
(INJECTION IS
POSITIVE)
LAYER
NO.
11 10 9 8 7 6 5 4 3 2
1-10.5
-21.0
-20.9
-20.7
-20.4
-20.2
-19.
9-1
9.6
-19.
4-1
9.3
WELL
NUM
BER
T3 0>
Co o
I CN
§2a,
tO
0) «! U
to§ H 4J O 0)
CD
CD
0> rH XI10
o0.
O I I
b
ot !
b
UJ Ot O.
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341
Tab
le 8.8
. Sele
cti
ons
from
th
e outp
ut
file
fo
r ex
am
ple
pro
ble
m 2 C
onti
nued
2222
2222
2222
2222
2222
2222
2222
2222
222
2222
2222
2222
2222
*222
2222
2222
2222
2222
2222
222
2222
2222
2222
*222
2222
222
2222
2222
22
2222
2222
2 22
2222
22*2
2222
2 22
2222
2 22
2222
2****£** * * *
*
111111111111111111
111111111111111111
1111111111111111111
1111111111111111111
111111111111111111
1111111111111111111
1111111111111111111
11111111111111111111
1111111111111111111
1111111111111111111
11111111111111111111
1111111111111111111
1111111111111111111
p-
to
MAP
LEGE
NDHO
RIZO
NTAL
GRID
NODE
RAN
GE,
FROM
1
TO 2
6 VE
RTIC
AL G
RID
NODE
RA
NGE,
FR
OM
1 TO
11
DEPENDENT
VARIABLE R
ANGE
MAP
CHAR
ACTE
R
OOOE
+01
500E
+01
OOOE
+01
500E
+01
OOOE+01
500E+01
QOOE
+01
500E+01
OOOE
+01
500E
+01
OOOE+01
500E
+01
OOOE
+01
500E+01
5.500E+01
- 6.OOOE+01
GRID N
ODE
LOCATIONS
ACROSS T
HE P
AGE
1.00
1.25
1.55
1.94
2.41
14.0
17.5
21.8
27
.2
33.9
197.
246.
GRID N
ODE
LOCA
TION
S ALONG
THE
PAGE
AX
IS IS
PO
SITI
VE UP T
HE PAGE
0.000
3.00
6.
00
9.00
12
.0
3.01
42.3
15.0
3.75
52.7
18.0
4.67
65.6
21.0
5.82
7.26
9.04
11.3
81.8
102.
127.
158.
24.0
27.0
30.0
JOB
COMPLETED
LAST
TIM
E PLANE
CALC
ULAT
ED
LAST
TIM
E PLANE
INDE
X ..
...
1.56E+07
(S)
60
9. NOTATION
9.1 ROMAN
a. coefficients of the various u.., in the spatially discretized i ijk v
equations.
a'. coefficients of the various u., in the spatially discretized
equations for the cylindrical-coordinate system.
a 1 implicit term for aquifer-influence-function or heat-conduction
boundary conditions (appropriate units).
82 implicit term coefficient for aquifer-influence-function or
heat-conduction boundary conditions (appropriate units).
A matrix of coefficients for the 6u vector for the finite-difference
equations (eq. 3.6.2.la).
£ Banded, sparse submatrices of the matrix A f° r tne finite-
difference equations.
A capacitance coefficient (appropriate units).
A value of capacitance coefficient within subdomain s of cell m. ms
b vector of known terms on the right-hand side for the finite-
difference equations.
b thickness of an outer-aquifer region (m).
bu _ effective thickness of a heat-conducting medium exterior to thenL
region (m).
b thickness of an aquitard layer (m).
343
b-, thickness of a riverbed sediment (m). K
Jb. coefficient in the approximation to the transient aquifer-influence
function given by equation 3.4.4.2.5.
B coefficient of dispersion or diffusion (appropriate units).
B O ,BI parameters for the temperature-dependence of viscosity (°C).
£ tensor of diffusion or dispersion of rank 3 (appropriate units).
B. . tensor components of B_.«J
c f average heat capacity of the fluid phase at constant pressure
(J/kg-°C).
c, heat capacity of pure water at constant pressure (J/kg-°C)
c heat capacity of the solid phase (porous matrix) at constant pressure
(J/kg-°C).
c heat capacity of the exterior heat-conducting medium at co...
pressure (J/kg-°C).
C.. coefficient in the capacitance matrix for the discretized equations
(appropriate units).
C vector of interstitial velocity (m/s).
C. (m,p,q) vector components of C in the ith direction, for the cell m,
face p, in element q (m/s).
d input data item.
d . coefficient in the series expansion for pressure (eq. 3.3.2.4c)
(Pa/m).
344
d_. coefficient in the series expansion for temperature (eq. 3.3.2.4d)
d coefficient vector for series expansion (eq. 3.3.2.5b).
H- submatrices on the diagonal of matrix A-
D effective-molecular-diffusivity coefficient of the solute (m2 /s). m
D,, thermal diffusivity of the medium surrounding a well riser (m2 /s) rlrm
Du thermo-mechanical dispersion tensor from flow mechanisms (W/m-°C) H
DH thermal diffusivity for an exterior medium at a heat-conduction
boundary (m2 /s).
Dw .. thermo-mechanical-dispersion-tensor component (W/m-°C).
»DC mechanical-dispersion-coefficient tensor (m2 /s).
D0 .. mechanical-dispersion-tensor component (m2 /s).
D0 . . hydrodynamic-dispersion coefficient (m2 /s).
D.,. . thermo-hydrodynamic-dispersion coefficient (W/m-°C) .
D coefficient for a source proportional to the dependent variable
(appropriate units).
D value of D in cell m for subdomain s. ms
345
E. coefficient vector for a node; i = 1 for flow equation, i = 2 for
heat- transport equation, i = 3 for solute- transport equation.
E source-term intensity (appropriate units).
E f ^ source-term intensity for source s in cell m (appropriate units) s ̂ m^
E value of source term in cell m. m
f-,0 fraction of cell thickness that is saturated for a free-surface r bboundary condition (-).
f head-loss friction factor for a well riser (-).
f head-loss friction factor.for a well bore (-). w
f« angle-of-influence factor for aquifer-influence-function boundary
condition (-).
CJ heat-flux function (Carslaw and Jaeger) to an infinite medium from
a constant-temperature cylindrical source (-).
F. vector component of the known terms at time level n in the three
discretized system equations for a given node, i = 1,2,3.
F spatial finite-difference function.
F spatial finite-difference function evaluated at time level n.
e FCJ approximation to FCJ function for small dimensionless time.
F_ T approximation to F_ T function for large dimensionless timeLJ LJ
F function for the well-riser calculation (eq. 2.4.2.11).
346
g gravitational constant (m/s 2 ).
I g component of gravitational acceleration in the direction normal
to the face p.
G function for the well-riser calculation (eq. 2.4.2.11).
h heat-transfer coefficient from the fluid to a riser pipe (W/m2 -°C)
H specific enthalpy of the fluid phase (J/kg) .
H~ specific enthalpy of fluid at a region boundary (J/kg) .
H specific enthalpy of fluid in an outer aquifer (J/kg) .
H specific enthalpy of fluid in a well riser (J/kg) .
H specific enthalpy of the solid phase (J/kg) .at
J_ vector of specified total flux at a boundary (appropriate units)
J. component of specified flux at a boundary in the ith direction.
J. component of specified flux at a boundary in the ith direction in
element q.
]| porous-medium permeability tensor (m2 ).
k permeability of an outer-aquifer region (m2 ).
k- permeability of an aquitard layer (m2 ).
k_ permeability of a riverbed sediment (m2 ).
k mean permeability around a well between r and r (m2 )w * we
347
k permeability in the x-direction (m2 ).A
k permeability in the y-direction (m2 ).
k permeability in the direction normal to face p for subdomain q (m2 ).
k r(n average radial permeability around the well in cell m at level £ (m2 ) win \x* J
k permeability for cell m, face p, subdomain q (m2 ).
K, equilibrium-distribution coefficient (m3/kg) .
K thermal conductivity of a medium exterior to the simulation region
(W/m-°C) .
Kf thermal conductivity of the fluid (W/m-°C) .
K thermal conductivity of a riser pipe (W/m-°C) .
K thermal conductivity of the medium surrounding a riser pipe (W/m-°C)
K thermal conductivity of the solid phase (porous matrix) (W/m-°C) . s
K Augmented porosity factor for subdomain s (eq. 3.1.4.4k) (-) .S
H distance along the well bore or well riser (m) .
S,, lower end of a well-screen interval (m) .
JL index of the bottom level of a well screen Li
&.. upper end of a well-screen interval (m) .
$,,, index of the top level of a well screen.
348
L length of a well riser (m) .
I,,.. length of a well bore in the lower half of cell m at level £ (m)
L length of a well bore in the upper half of cell m at level £ (m)
L. submatrices below the diagonal of matrix &.
m cell number with coordinate indices i,j,k.
m(i-l) cell number with coordinate indices i-l,j,k.
m(£) cell number associated with well bore level £.
M total number of nodes in the simulation region.
MA number of pot-aquifer boundary-condition cells.
^ M well mobility per unit length of well bore (m3/s-m-Pa) .
IM £ well mobility per unit length of well bore at level £ (m3/s-m-Pa)
m mass of fluid plus effective additional fluid mass from sorption
in cell m (kg) .
n data repeat factor.
n vector in the outward normal direction to the boundary.
N number of grid points in the r-direction,
N number of grid points in the x-direction,
N number of grid points in the y-direction,
349
N number of grid points in the z-direction.z
N number of line sources in the region, s
p fluid pressure relative to atmospheric pressure (Pa),
p absolute pressure (Pa).
p average pressure around a well between r and r (Pa).
P-. pressure at a boundary (Pa) .D
p' dimensionless pressure at an aquifer-influence-function boundary (-)
(eq. 2.5.4.2.6b).
p pressure in the outer-aquifer region (Pa).
p initial specified pressure in an outer-aquifer region (Pa) .
p. . pressure of injected fluid (Pa)
p pressure at node m (Pa).
p pressure at a reference state for density (Pa).
p pressure at a reference state for enthalpy (Pa) .OH
p absolute pressure at a reference state for enthalpy (Pa) .OH
p pressure averaged across a riser cross section (Pa) .
p , pressure averaged across a riser cross section at location
(Pa).
350
* p intermediate value of pressure averaged over a riser cross section
(Pa).
p absolute pressure of saturated water at zero degrees Celsius (Pa), sat
p pressure at the well bore (Pa),
p , pressure at a well datum (Pa).
p £ pressure in the well bore at level $, (Pa).
p initial pressure distribution (Pa).
P'. dimensionless pressure response to a unit-step withdrawal flow rate
q fluid-source, flow-rate intensity (m3/m3 -s).
» fi q_. specified fluid-flux-vector components (m3 /m2 -s) r 1
qF normal component of fluid flux (m3/m2 -s).
qf fluid flux from a well (m3 /m2 -s).
qu heat-source-rate intensity (W/m 3 ). M
qw« heat flux at the heat-conduction boundary (W/m2 )
qu . specified heat-flux-vector components (W/m2 ). HI
q.jT heat flux across a leakage boundary (W/m2 ).ML
q,, normal component of heat flux (W/m2 ). Mn
351
qT fluid flux across a leakage boundary (m3/m2 -s).
q_ fluid flux across a river-leakage boundary (m3 /m2 -s).
R limit on the fluid flux from a river to the aquifer (m3/m2 -s).
n
qc . specified solute-flux-vector components (kg/m2 -s). t)i
qCT solute flux across a leakage boundary (kg/m2 -s).oLi
q_ normal component of solute flux (kg/m2 -s).
q volumetric flow rate per unit length of well bore; (positive
is from the well to the aquifer) (m3/m-s).
Q fluid-mass-source flow rate (kg/s).
Q'A dimensionless flow rate per unit thickness at an aquifer-influence-
function boundary (-).
QA constant specified flow rate at an aquifer-influence-function
boundary (m3/s).
QA volumetric flow rate across the boundary for cell m between the inner-
and outer-aquifer regions; (positive is into the inner region)
(m3/s).
Q,, specified flow rate per unit thickness at the aquifer-influence- r$
function boundary of the region (m3/m-s).
Q,., mass flow rate in a well riser (kg/s).
u_ heat-flow rate across a heat-conduction boundary at cell m (W). nLm
352
Qff heat transfered per unit mass per unit length to the fluid in a
^ riser (J/kg-m).
QT volumetric-flow rate across a leakage boundary at cell m (m3/s).
Q_ volumetric-flow rate of a source term for cell m at time level n mincluding specified-flux boundary condition and line sources (m3/s)
Q',, dimensionless flow-rate response to a unit step change of pressure.
Q-. volumetric-flow rate across a river-leakage boundary at cell m Km(m3/s).
0 volumetric-flow rate from a well to the aquifer (m3/s).
00 volumetric-flow rate from a well to the aquifer at well bore
level H (m3 /s).
V r distance along the r-coordinate direction (m).
r radius of influence of a well (m).
r,, exterior radius of an outer-aquifer region (m).£l
TI interior radius of the region, cylindrical coordinates (m).
r. i radius of the cell boundary between the node at r. and the node at
r_ interior radius of outer-aquifer region (m).
r,. exterior radius of the region, cylindrical coordinates (m)r
r inner radius of a well-riser pipe (m).
353
r well-bore radius (m).w
R ratio of exterior to interior radius for an outer-aquifer region
for the aquifer-influence-function boundary condition (-).
R,. transfer of solute from fluid to solid phase per unit mass of
solid phase (kg/s-kg).
R. right-hand side terms for the ith equation, i = 1,2,3 for pressure,
temperature, and mass fraction respectively.
R rational-function vector that approximates the right-hand-side of
equation 3.3.2.6.
spectral radius of the Gauss-Seidel iteration matrix.
S specific storage for a confined aquifer (eq. 2.2.5.5) (m" 1 ).
.p area of the aquifer-influence-function boundary face for cell £,
face p, element q (m2 ).
S boundary surface of cell m (m2 ).
S part of the boundary surface of cell m that belongs to face p (m2 )
S part of the boundary surface of cell m that belongs to face p in
element q (m2 ).
S. part of the boundary surface of cell m that is an aquifer-influence-
function boundary (m2 ).
S_.T part of the boundary surface of cell m that is a leakage boundary BLm
(m2 ).
354
part of the boundary surface of cell m that is a heat-conduction
boundary (m2 ).
5 1 parts of the region boundary where specified-value boundary
conditions are applied (Dirchlet boundary conditions);
u = p, T, or w.
5 2 parts of the region boundary where specified-flux boundary
conditions are applied (Neumann boundary conditions);
u = p, T, or w.
5 3 part of the boundary that is an aquifer-leakage boundary.
54 part of the boundary that is a river-leakage boundary.
5 5 part of the region boundary that is a heat-conduction boundary,
5 6 part of the region boundary that is a free-surface boundary,
t time (s).
t time at level n (s)
t' dimensionless time defined by equation 2.5.4.2.5c (-).
T temperature of the fluid and porous medium (°C).
T ambient temperature of the medium adjacent to a well riser (°C).3-
T_ temperature at a boundary (°C).D
T temperature in the medium exterior to a heat-conduction boundary
T temperature at a reference state for density (°C). o
355
T temperature at a reference state for enthalpy (°C).
T temperature at a reference state for fluid viscosity (°C).
T temperature of the fluid averaged across a riser cross section (°C).
TI temperature solution to the first heat-conduction problem
(eq. 2.5.5.3a-d) (°C).
T£ temperature solution to the second heat-conduction problem
(eq. 2.5.5.4a-d) (°C).
T* temperature of a fluid source (°C).
T initial-temperature distribution (°C).
T initial-temperature profile in the exterior medium (°C).
T. . temperature of injected fluid (°C).
T.. unit-step temperature-response solution to heat-conduction problem
(eq. 2.5.5.6b) (°C).
T , temperature of the fluid at a well datum (°C)
absolute temperature (K).
T . conductance for flow (kg/s-Pa) or (m-s). Fl.
r__. conductance for heat transport (W/°C). Hi
r_. conductance for solute transport (kg/s).Ol
r conductance for flow at a well bore in the cylindrical coordinate
system (m-s).
356
u generic dependent variable (appropriate units)
u-j boundary-condition distribution of u.15
u initial-condition distribution of u.
u. .. value of u at x., y., z. at time t . ijk i' y j 9 k
u., value of u at x., z, in cylindrical-coordinate system at time t .
UT overall heat-transfer ̂ coefficient for the fluid, riser-pipe, and
surrounding medium (W/m2 -°C).
H. submatrices of matrix & above the diagonal, i
v interstitial-velocity vector (m/s).
v magnitude of the interstitial velocity (m/s).
v. interstitial-velocity component in the ith direction (m/s).
v velocity averaged across a riser cross section at a given z-level
(m/s).
v velocity averaged across a well-bore cross section at a given z-level
(m/s).
V region of the aquifer for simulation.
V, bulk or total volume of a fixed mass of porous medium (m3 ).
V volume of an outer-aquifer region (m3 ).
357
V. volume of an outer-aquifer region that influences boundary cell $,
(m3 ).
V volume of cell m (m3 ). m
V volume of subdomain s in cell m (m3 ). ms
w mass fraction of solute in the fluid phase (-).
w_ mass fraction of solute at a boundary (-).
w mass fraction of solute in an outer aquifer outside a leakage
boundary (-).
w . minimum solute-mass fraction for scaling (-).
w maximum solute-mass fraction for scaling (-). max 6
w mass fraction of solute at a reference state for density (-).
w' scaled-mass fraction of solute defined by equation 2.2.1.2 (-).
w mass fraction of solute initial distribution (-).
w* mass fraction of solute in the fluid source (-).
w mass fraction of solute on the solid phase (-).
W cumulative net flow from an outer- to an inner-aquifer region (m3 )
W_ well index per unit length of well bore defined by equation 2.4.1.2
(m2 ).
x position vector of node point m (m).
358
x distance along the x-coordinate direction (m).
x vector of position in the simulation region including the boundary
(m).
location vector of line source s in cell m (m).
y distance along the y-coordinate direction (m).
Y Pressure and temperature vector in a well riser.
z distance along the z-coordinate or vertical direction (m).
z.. elevation of the region boundary (m).D
z elevation of the top of an aquitard layer (m).
ZQ elevation of the node in a well at level Si (m).
W ZTC elevation of the land surface (m).J-jO
z elevation of the node of cell m (m). m
z coordinate in the outward-normal direction to the boundary (m).
z_ elevation of a river bottom (m) .
z c elevation of the water surface of a river (m) Krb
z , elevation of a well datum (m) . wd
359
9.2 GREEK
OL bulk compressibility of the porous medium (Pa ).
OL bulk compressibility of the porous medium in an outer region (Pa ).
OL. dispersivity longitudinal to the flow direction (m).
OL, dispersivity transverse to the flow direction (m).
1 Of rock compressibility (Pa ).
YA apportionment factor for aquifer-influence-function flow rate (-).
YT, fraction of riverbed area per unit area of aquifer boundary (-). K
p fluid compressibility (Pa ).
PT fluid coefficient of thermal expansion (°C ).
P slope of fluid density as a function of mass fraction divided by
the reference fluid density (-).
P fluid compressibility in an outer region (Pa ).
p' slope of fluid density as a function of scaled-mass fraction dividedW
by the reference fluid density (-).
e effective porosity (-).
8 effective porosity of an outer-aquifer region (-)
X linear decay constant (s ).
360
A. . minimum estimate of spectral radius or maximum eigenvalue mm r e(eq. 3.7.2.6a).
A. maximum estimate of spectral radius or maximum eigenvalue
(eq. 3.7.2.6b).
[j viscosity of the fluid (kg/m-s).
H viscosity of the fluid in an outer-aquifer region (kg/m-s).
HT viscosity of fluid in an aquitard layer (kg/m-s).JL
H(T ,w') viscosity at the reference temperature (kg/m-s).
jj,, viscosity of the fluid in a riverbed (kg/m-s).K
p average viscosity at cell face p at time t (kg/m-s).
Ho viscosity at the minimum mass fraction (kg/m-s).
Hi viscosity at the maximum mass fraction (kg/m-s).
H viscosity of the fluid in a riser pipe (kg/m-s).
V counter index for successive-overrelaxation iteration.
$ potential energy per unit mass of fluid in the aquifer outside
a leakage boundary (Nt-m/kg).
p fluid density (kg/m3 ).
p, bulk density of the porous medium (mass/unit volume of dry porous
medium) (kg/m3 ).
361
p_ fluid density at the region boundary (kg/m3 ).15
p fluid density outside a leakage boundary (kg/m3 )
p fluid density at a reference pressure, temperature, and mass
fraction (kg/m3 ).
p fluid density averaged across a well-riser cross section (kg/m3 ).
p_. fluid density of the river (kg/m3 ).K
p density of the solid phase of the porous matrix (mass/unit volume of ssolid phase) (kg/m3 ).
p density of the solid phase of the porous matrix exterior to the
simulation region (mass/unit volume of solid phase) (kg/m3 ).
p average fluid density in a well bore (kg/m3 ).
p average density at cell face p at time t (kg/m3 ).
p* density of a fluid source (kg/m3 ).
a spatial weighting coefficient (eq. 3.1.4.4).
T dimensionless time for heat transfer from a defined well riser by
equation 2.4.2.6c (-).
Q factor for time differencing (eq. 3.1.3.4).
8 angle between the well riser and the z-coordinate (deg)
Q angle between the well bore and the z-coordinate (deg).
362
U) overrelaxation factor (eq. 3.7.2.2).
^ U) optimum overrelaxation factor (eq. 3.7.2.7).
9.3 MATHEMATICAL OPERATORS AND SPECIAL FUNCTIONS
6u vector of dependent variables for the finite-difference equations
6u temporal change in u.
Au spatial change in u.
6u maximum temporal change in u.max * &
6u specified maximum temporal change in u.
u average value of u.
Ar wall thickness of a well-riser pipe (m)
6t current time-step length.
6t previous time-step length.o
V del operator; e r + e ^ + e x in cartesian coordinates; ^ ' x 9x y 8y z 8z '
3 13 3^ + eQ r^ + e^ in cylindrical coordinates
r 8r 6 r 80 z 8z J
| | absolute value.
363
8 derivative in the outward-normal direction at a boundary 8n
6.. Kronecker delta function; =1 for i=j, = 0 for i^j.J
6(x-x ) delta function for the point source in a cell at x s r s
1 identity matrix of rank 3.
J Bessel function of the first kind, order n.
Y Bessel function of the second kind, order n,
Euler's constant ~ 0.577.
x - spatial average of the rate of pressure change at the aquifer- influence-function boundary (Pa/s).
ex spatial average of the rate of pressure change in an outer- aquifer region (Pa/s)
rr average rate of pressure change at the boundary of an inner region (Pa/s)
aQmimplicit term for fluid line sources at the nth time level
n (kg/s-Pa).
364
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techniques for groundwater resource evaluation: Urbana, State of
Illinois, Department of Registration and Education, Illinois State
Water Survey ISWS-71-BUL-55, 62 p.
Ramey, H.H., Jr., 1962, Wellbore heat transmission: Journal of Petroleum
Technology, v. 14, no. 4,^ p. 427-435.
Remson, Irwin, Hornberger, G.M., and Moltz, F.J., 1971, Numerical methods in
subsurface hydrology: New York, Wiley-Interscience, 389 p.
Ritchie, R.H., and Sakakura, A.Y., 1956, Asymptotic expansions of solutions of
the heat conduction equation in internally bounded cylindrical geometry:
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Roache, P.J., 1976, Computational fluid dynamics: Albuquerque, New Mexico,
Hermosa Publishers, 446 p.
Saffman, P.G., and Taylor, G.I., 1958, The penetration of a fluid into a
porous medium or Hele-Shaw cell containing a more viscous liquid:
London, England, Proceedings of the Royal Society of London, Series A-
Mathematical and Physical Sciences, v. 245, no. 1242, p. 312-329.
Scheidegger, A.E., 1960, Growth of instabilities of displacement fronts in
porous media--A discussion of the Muskat-Aronofsky model: Physics of
Fluids, v. 3, no. 2, p. 153-162.
____1961, General theory of dispersion in porous media: Journal of
Geophysical Research, v. 66, no. 10, p. 3273-3278.
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Journal of Physics, v. 39, no. 9, p. 1,253-1,263.
369
Settari, Antonin, and Aziz, Khalid, 1972, Use of irregular grid in reservoir
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v. II, 287 p.
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Society of Petroleum Engineers of the American Institute of Mining,
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individual wells and grids in reservoir modelling: Society of Petroleum
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Investigations Report 84-4369, 429 p.
370
Weast, R.C., Selpy, S.M., and Hodgman, C.D., eds., 1964, Handbook of chemistry
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reservoir simulation, Part 1 Theory: Society of Petroleum Engineers
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371
11. SUPPLEMENTAL DATA
Because of the excessive length (about 12,000 lines), no program listing
is provided for the HST3D code. However, listings of the major program
variables and a cross-reference table are provided to aid the user in error
tracing and program modification.
11.1 HST3D PROGRAM VARIABLE LIST WITH DEFINITIONS
The following program-variable list (table 11.1) contains all of the
major variable names with brief definitions. Minor variables including loop
indices, array subscripts, and temporary results, have not been included.
Most temporary variables begin with the letter U with the remainder of the
name based on the corresponding major variable. Variably partitioned array
pointers begin with the letter I.
372
Tabl
e 11.1. Definition li
st fo
r se
lect
ed HST3D program variables
A1HC
A2HC
A3HC
A4 AAIF
ABOA
RABPM
ALBC
ALPHL
ALPHT
AMAX
AMIN
ANGO
ARAPLOT
APRN
TARGRID
ARRAY
ARWB
ARX
ARXB
CAR
XFBC
ARY
ARYB
CAR
YFBC
ARZ
ARZB
CAR
ZFBC
AST
AUTOTS
BAIF
BBLBC
BLAN
KBLANKL
BLBC
BOAR
BP BT B\l
C COO
Cll
C12
C13
C21
C22
- HEAT CO
NDUC
TION
B.
C. GE
OMET
RIC
FACTOR
- HEAT CONDUCTION B.
C. GE
OMET
RIC
FACTOR
- HEAT C
ONDUCTION
B.C. GE
OMET
RIC
FACTOR
- SUB-MATRIX O
F SYSTEM EQ
UATI
ONS
FOR
D4 S
OLVE
R- AQUIFER
INFLUENCE
FUNCTION B.C. CONSTANT T
ERM
- POROUS M
EDIUM
COMP
RESS
IBIL
ITY
FOR
OUTE
R AQUIFER
REGION
- POROUS MEDIUM C
OMPR
ESSI
BILI
TY-
LEAKAGE
B.C.
CONSTANT T
ERM
- LO
NGITUDINAL D
ISPERSIVITY
- TRANSVERSE DISPERSIVITY
- UP
PER
LIMIT
OF VARIABLE FOR
CONT
OUR
MAP
- LO
WER
LIMIT
OF VARIABLE FOR
CONTOUR
MAP
- ANGLE
OF INFLUENCE
FOR
CARTER
-TRA
CY AQ
UIFE
R IN
FLUE
NCE
FUNC
TION
B.
C.- OU
TPUT
ARRAY FOR
CONTOUR
MAP
- OUTPUT LI
NE FOR
ARRAY
PRIN
TING
- TRUE IF
AU
TOMA
TIC
RADIAL NO
DE LOCATIONS
TO BE SET
- OUTPUT A
RRAY FOR
PRIN
TED
TABLES
- CR
OSS-
SECT
IONA
L AR
EA O
F WELL BO
RE-
CELL-FACE
AREA IN Y-Z
PLANE
- CELL-FACE
AREA IN
Y-
Z PLANE
FOR
BOUN
DARY
CONDITIONS
- CELL-FACE
AREA
IN
Y-
Z PLANE
FOR
FLUX
B.C
- CE
LL-F
ACE
AREA
IN
X-Z
PLANE
- CELL-FACE
AREA
IN
X-Z
PLANE
FOR
BOUN
DARY
CO
NDIT
IONS
- CELL-FACE
AREA
IN
X-
Z PLANE
FOR
FLUX
B.
C- CELL-FACE
AREA
IN X-
Y PLANE
- CELL-FACE
AREA IN X-
Y PLANE
FOR
BOUN
DARY
CONDITIONS
- CE
LL-F
ACE
AREA
IN
X-
Y PL
ANE
FOR
FLUX
B.
C _
*'
- TRUE IF A
UTOM
ATIC
TIME
STEP
PING
IS
DE
SIRE
D- AQUIFER
INFL
UENC
E FU
NCTI
ON B.C. TEMPORAL COEFFICIENT
- TH
ICKN
ESS
OF CONFINING
LAYER
OR R
IVER B
ED
LEAKAGE
B.C.
TE
MPOR
AL COEFFICIENT
THIC
KNES
S OF
OU
TER
AQUI
FER
REGION FOR
A.I.F.B.C.
FLUI
D CO
MPRE
SSIB
ILIT
YFL
UID
COEFFICIENT
OF T
HERM
AL EXPANSION
VISCOSITY
FUNCTION T
HERM
AL PA
RAME
TER
SOLUTE MASS FR
ACTI
ONSOLUTE CONCENTRATION
AT T
HE EN
D OF A
WELL
RISE
R, IN
ITIA
L VALUE
Cll
THRO
UGH
C33
ARE
COEF
FICIEN
TS IN
THE
CAPACITANCE
MATRIX
Tabl
e 11.1. De
fini
tion
li
st fo
r selected HST3D program variables Continued
C23
C24
C31
C32
C33
C34
C35
CAIF
CC24
CC34
CC35
CCLBL
CCW
CFLX
CHAPRT
CHARC
CHARS
CHKPTD
CI CIBC
CICALL
CLBC
CLINE
CMX
CMY
CMZ
CNP
CM
CNVD
CNVD
FICN
VD I
CNVE
CNVE
PICNVFF
CNVGZ
CNVHC
CNVH
CICNVHF
CNVH
FICN
VHI
CNVHTC
CNVH
TICNVL
CNVL2
CNVL
2I
- C2
4.C3
4, AND
C35
ARE
COEF
FICI
ENTS
OF
THE
TRANSPORT
TERMS
SOLUTE M
ASS
FRAC
TION
IN
OUTER
AQU
IFER
REG
ION
CC24.CC34.CC35 A
RE C
ONDU
CTAN
CE C
OFACTOR
ARRAYS
LABEL
FOR
SOLUTE M
ASS
FRAC
TION
IN
A W
ELL
FOR TEMPORAL P
LOTS
CALCULATED S
OLUTE
MASS
FRA
CTIO
N IN
A W
ELL
SOLUTE M
ASS
FRAC
TION
FOR
INFLOW A
T A
SPECIFIED
FLUX
B.C.
CHARACTER
ARRAY
FOR
PRINTOUT
'C1
NUMERIC
CHARACTERS T
HAT
ILLU
STRA
TE T
HE C
ONTO
UR-M
AP Z
ONES
TRUE IF C
HECK P
OINT D
UMPS A
RE DESIRED
NODAL
CONN
ECTI
ON IN
DEX
FOR
D4 N
UMBERING S
CHEME
CHAR
ACTE
R REPRESENTATION O
F IBC
CHAR
ACTE
R RE
PRES
ENTA
TION
OF
ICAL
LSOLUTE M
ASS
FRAC
TION
FOR
IN
FLOW
AT
LEAKAGE
B.C.
CHARACTER
LINE F
OR C
ONTO
UR M
APSOLUTE C
ONCENTRATION A
T CE
LL F
ACE
BETW
EEN
X(I-
l) AND
X(I)
SOLUTE C
ONCENTRATION A
T CELL F
ACE
BETW
EEN
Y(J-
l) AN
D Y(J)
SOLUTE C
ONCENTRATION A
T CE
LL F
ACE
BETW
EEN
Z(K-
l) AND
Z(K)
SOLUTE M
ASS
FRACTION F
OR S
PECI
FIED
VALUE B
.C.
CONVERSION F
ACTOR
CONVERSION F
ACTOR
FOR
DENSITY
(ENGLISH T
O METRIC)
CONV
ERSI
ON F
ACTOR
FOR
DIFFUSIVITY
(METRIC
TO E
NGLI
SH)
CONVECTOR
FOR
DENSITY
(MET
RIC
TO E
NGLISH)
CONV
ERSI
ON F
ACTOR
FOR
ENER
GY (ENGLISH T
O ME
TRIC
)CONVERSION F
ACTOR
FOR
PRESSURE ENERGY (METRIC
TO E
NGLI
SH)
CONVERSION F
ACTOR
FOR
FLUID
FLUX (ENGLISH T
O ME
TRIC
)CO
NVER
SION
FACTOR
FOR
GRAVITY
TIMES
ELEV
ATIO
N (ENGLISH T
O ME
TRIC
)CO
NVER
SION
FACTOR F
OR H
EAT
CAPA
CITY
(E
NGLI
SH T
O ME
TRIC
)CO
NVER
SION
FACTOR F
OR H
EAT
CAPACITY (METRIC
TO E
NGLI
SH)
CONV
ERSI
ON FACTOR F
OR H
EAT
FLUX
(E
NGLI
SH T
O METRIC)
CONVERSION FACTOR F
OR H
EAT
FLUX (METRIC
TO E
NGLISH)
CONV
ERIS
ON FACTOR F
OR T
HERM
AL E
NERG
Y (METRIC
TO ENGLISH)
CONV
ERSI
ON FA
CTOR
FOR
HEA
T TRANSFER C
OEFF
ICIE
NT (E
NGLI
SH T
O ME
TRIC
)CO
NVER
SION
FACTOR F
OR H
EAT
TRANSFER C
OEFF
ICIE
NT (M
ETRI
C TO E
NGLI
SH)
CONV
ERSI
ON FACTOR F
OR LE
NGTH (ENGLISH T
O METRIC)
CONVERSION F
ACTOR
FOR
LENGTH
SQU
ARED
(ENGLISH T
O ME
TRIC
)CO
NVER
SION
FA
CTOR
FOR
LENGTH
SQUA
RED
(METRIC
TO ENGLISH)
Tabl
e 11.1. De
fini
tion
list for
sele
cted
HST3D program variables Continued
u>
^j Ul
CNVL
3CNVL3I
CNVLI
CNVM
FICNVMI
CNVP
CNVPI
CNVSF
CNVT
1CN
VT1I
CNVT
2CNVT2I
CNVT
CCN
VTCI
CNVT
HCN
VTMI
CNVUUI
CNVVF
CNVVLI
CNVVSI
COLS
COHORT
CONLBL
CONVC
CONVP
CONV
RGCO
NVT
COW
CPAR
CPARI
CPF
CPX
CPY
CPZ
CSBC
CVIS
CWKT
CYLIND
D DAMWRC
DASH
ESDB
KDDC DC
MAX
DCTA
S
CONVERISON FACTOR FOR
LENGTH C
UBED
(E
NGLI
SH T
O ME
TRIC
)CO
NVERSION F
ACTO
R FO
R LENGTH C
UBED
(M
ETRI
C TO ENGLISH)
CONVERSION F
ACTO
R FOR
LENGTH (METRIC
TO EN
GLIS
H)CO
NVERSION FA
CTOR
FOR M
ASS
FLOW R
ATE
(MET
RIC
TO EN
GLIS
H)CO
NVERSION F
ACTOR
FOR
MASS (MET
RIC TO EN
GLIS
H)CO
NVERSION F
ACTOR
FOR
PRESSURE
(E
NGLI
SH TO
METRIC)
CONVERSION FA
CTOR
FOR
PRESSUR
E (M
ETRI
C TO ENGLISH)
CONVERSION FACTOR F
OR S
OLUT
E FLUX (ENGLISH T
O METRIC)
FIRS
T CONVERSION FA
CTOR
FOR T
EMPERATURE (ENGLISH T
O ME
TRIC
)FI
RST
CONVERSION FA
CTOR
FOR T
EMPERATURE (M
ETRI
C TO ENGLISH)
SECO
ND C
ONVERSION
FACT
OR F
OR TEMPERATURE (ENGLISH TO
METR
IC)
SECO
ND C
ONVERSION
FACT
OR FOR TEMPERATURE
(MET
RIC
TO EN
GLIS
H)CO
NVERSION FA
CTOR
FOR
THERMAL CONDUCTIVITY (ENGLISH T
O ME
TRIC
)CO
NVERSION FACTOR FOR THERMAL
CONDUCTIVITY (METRIC
TO EN
GLIS
H)CO
NVERSION F
ACTO
R FOR
TIME (D
AYS
TO S
ECON
DS)
CONV
ERSI
ON FA
CTOR
FOR
TIM
E (SEC
ONDS
TO
DAYS)
CONVERSION F
ACTO
R FOR
FLUID
CONDUCTANCE
(MET
RIC TO EN
GLIS
H)CO
NVERSION FA
CTOR
FOR V
OLUMETRIC
FLOW
RATE
(ENGLISH T
O ME
TRIC
)CO
NVERSION FACTOR F
OR V
ELOC
ITY
(METRIC TO EN
GLIS
H)CO
NVERSION FA
CTOR
FOR V
ISCOSI
TY (K
G/M-
S TO CP
)NU
MBER
OF
COLU
MNS
REQU
IRED
FOR
CONT
OUR
MAPS
TRUE IF
COMPUTATION O
F AN
OPTIMUM O
VER-
RELA
XATI
ON F
ACTOR
IS T
O BE DO
NELA
BEL
FOR
SOLUTE CO
NCEN
TRAT
ION
PRINTOUT
TRUE IF S
OLUTE
CALC
ULAT
ION
HAS
CONVERGED
FOR A
GIVEN
TIME S
TEP
TRUE IF
PR
ESSU
RE CALC
ULAT
ION
HAS
CONVERGED
FOR A
GIVE
N TIME STEP
TRUE IF H
ELL-RISER
CALC
ULAT
ION
HAS
CONVERGED
TRUE
IF
TEM
PERA
TURE
CA
LCUL
ATION
HAS
CONVERGED
FOR A
GIVEN
TIME S
TEP
SOLU
TE M
ASS
FRACTION O
BSERVED
VALUES IN
A W
ELL
CHARACTER
REPRESENTATION O
F INPUT
PARAMETER
INITIAL
CHAR
ACTE
R RE
PRES
ENTA
TION O
F IN
PUT
PARAMETER
HEAT
CAP
ACIT
Y OF FLUID
AT M
INIM
UM S
OLUTE
CONC
ENTR
ATIO
NSO
LUTE
CO
NCEN
TRAT
ION
AT CELL FA
CE BE
TWEE
N X(I) AND
X(I+1)
SOLU
TE CO
NCEN
TRAT
ION
AT C
ELL
FACE BE
TWEE
N Y(
J) AND
Y(J+1)
SOLU
TE CONCENTRATION
AT C
ELL
FACE
BE
TWEE
N Z(
K) AND
Z(K+1)
SOLUTE MA
SS FRACTION F
OR INFLOW A
T A
SPECIFIED
PRES
SURE
B.
C.SO
LUTE
CONCENTRATION
DATA FOR
CONCENTRATION-VISCOSITY
TABLE
SOLUTE MA
SS FRACTION A
T WE
LL D
ATUM LEVEL
TRUE IF A C
YLIN
DRIC
AL C
OORDINAT
E SYSTEM IS
BE
ING
USED
DIAG
ONAL
ELEMENTS OF T
HE SY
STEM EQ
UATI
ON M
ATRIX
DAMPING
FACT
OR F
OR W
ELL
RISER
CALCULATION
POROUS MEDIUM BULK D
ENSITY TI
MES
LINEAR E
QUIL
IBRI
UM S
ORPT
ION
COEFFICIENT
CHANGE IN S
OLUTE
MASS FRACTION
MAXIMUM
CHANGE IN S
OLUTE
MASS
FRACTION
SPEC
IFIE
D MA
XIMU
M CHANGE IN
SOLUTE
MASS
FRACTION FOR
AUTOMATIC
TIME S
TEP
ADJUSTMENT
Table 11.1. Definition list for selected HST3D program variables Continued
UJ
DDNMAX
DDV
DECLAM
DEHIR
DELTIM
DELX
DELY
DELZ
DEN
DENO
DENC
DENCHC
DENCHT
DENF
ODE
NF1
DENFBC
DENG
LDENLBC
DENN
DENNP
DENOAR
DENP
DENT
DENW
DENWKT
DENWRK
DET
DFIR
DM DOTS
DP DPMAX
DPTAS
DPUD
TDPWKT
DQFDP
DQHBC
DQHCDT
DQHD
PDQHDT
DQHWDP
DQHWDT
DQSB
CDQSDC
DQSDP
MAXI
MUM
CHANGE IN DE
NSIT
YCHANGE IN
DE
PEND
ENT
VARIABLE FO
R FL
OW A
T SP
ECIF
IED
VALU
E B.C.
SOLUTE DE
CAY
FACTOR
CHANGE IN ENTHALPY IN
TH
E REGION
CURR
ENT
TIME STEP
NODE S
PACI
NG IN
X-DIRECTION
NODE SPACING
IN Y-DIRECTION
NODE SP
ACIN
G IN Z
-DIRECTION
FLUI
D DE
NSIT
YFLUID
DENS
ITY
AT R
EFERENCE CONDITIONS
COEFFICIENT
FOR
FLUI
D DE
NSIT
Y VA
RIAT
ION
WITH S
OLUTE
MASS FRACTION
DENS
ITY
CHAN
GE DUE
TO S
OLUTE
CONC
ENTR
ATON
CH
ANGE
SDE
NSIT
Y CHANGE DUE
TO T
EMPERATURE CH
ANGE
SFLUID
DENSITY
AT M
INIM
UM S
OLUTE
MASS FR
ACTI
ONFL
UID
DENSITY
AT M
AXIM
UM S
OLUTE
MASS FR
ACTI
ONFL
UID
DENSITY
FOR
INFL
OW A
T SP
ECIF
IED
FLUX
B.C.
CHANGE IN
PRESSURE ES
TIMA
TE OVER
WEL
L RISER
LENGTH
FLUID
DENSITY
FOR
INFL
OW A
T LEAKAGE
B.C.
FLUID
DENSITY
AT T
IME
LEVEL
NFLUID
DENSITY
AT T
IME
LEVEL
N+l
FLUI
D DENSITY
IN OUTER
AQUI
FER
REGION FO
R A.
I.F.
B.C.
COEFFICIENT
FOR
FLUID
DENS
ITY
VARI
ATIO
N WI
TH PR
ESSU
RECOEFFICIENT
FOR
FLUI
D DE
NSIT
Y VA
RIAT
ION
WITH
TEMPERATURE
FLUID
DENS
ITY
IN A
WEL
L BO
REFL
UID
DENS
ITY
IN A
WEL
L BO
RE A
T TH
E WELL D
ATUM
FLUI
D DENSITY
IN A
WELL
RISER
AT LEVEL
KDETERMINANT
OF T
HE WELL R
ISER EQUATIONS
CHANGE IN FL
UID
IN T
HE REGION
MOLE
CULA
R DIFFUSIVITY
OF T
HE SOLUTE
CHANGE IN
PR
ESSU
REMA
XIMU
M CHANGE IN PRESSURE
SPECIFIED
MAXIMUM
CHANGE IN P
RESS
URE
FOR AUTOMATIC
TIME
STE
P AD
JUST
MENT
DERIVATIVE OF
THE
TR
ANSI
ENT
AQUI
FER
INFL
UENC
E FUNCTION W
ITH
TIME
CHANGE IN
PRESSURE A
T A
WELL D
ATUM
DERIVATIVE OF
FL
OW R
ATE
WITH P
RESS
URE
CHANGE IN
HEAT
FLOW FO
R AN
Y B.C.
DERIVATIVE OF
HEAT
FLOW
RA
TE WITH T
EMPERATURE FO
R HE
AT C
ONDU
CTIO
N B.C.
DERIVATIVE OF
HEAT
FLOW W
ITH
PRESSURE
DERIVATIVE OF
HEA
T FLOW W
ITH
TEMPERATURE
DERIVATIVE OF
WELL
HEAT FL
OW W
ITH
PRES
SURE
DERIVATIVE OF
WELL
HEAT FLOW W
ITH
TEMPERATURE
CHANGE IN
SOLUTE FL
OW RA
TE FO
R AN
Y B.
C.DERIVATIVE OF
SOLUTE
FLOW RATE WI
TH C
ONCE
NTRA
TION
DERIVATIVE OF
SOL
UTE
FLOW RATE WI
TH PR
ESSU
RE
Tab
le 11.1
. D
efi
nit
ion li
st
for
sele
cte
d H
ST3D
pro
gra
m varia
ble
s C
onti
nued
-vj
-vj
DQSWDC -
DERIVATIVE OF WE
LL S
OLUTE
FLOW
WIT
H CO
NCEN
TRAT
ION
DQSWDP - DE
RIVA
TIVE
OF
WELL
SOLUTE
FLOW W
ITH
PRESSURE
DQWD
P -
DERIVATIVE OF
WELL
FLOW
RA
TE WITH PRESSURE
DQWDPL -
DERIVATIVE OF
WELL
FLOW RATE AT A
LAYER
WITH
PRESSURE
DQWLYR -
CHANGE IN W
ELL
FLOW
RATE
AT A
LA
YER
DSIR
-
CHANGE IN
SOLUTE IN T
HE REGION
DT
- CHANGE IN T
EMPERATURE
DTADZW -
DERIVATIVE OF
AMB
IENT
TEM
PERA
TURE
AT
A WE
LL R
ISER W
ITH
DISTANCE IN T
HE Z-DIRECTION
DTHA
WR - TH
ERMA
L DIFFUSIVITY
OF T
HE ME
DIUM
SUR
ROUN
DING
A W
ELL
RISER
DTHH
C - TH
ERMA
L DI
FFUS
IVIT
Y OF
THE EXTERNAL M
EDIUM
AT A
HEA
T CONDUCTION BOUNDARY
DTIM
MN - SP
ECIF
IED
MINIMUM
TIME S
TEP
FOR
AUTOMATIC
TIME S
TEP
ADJUSTMENT
DTIMMX - SPECIFIED
MAXIMUM
TIME
STEP FO
R AU
TOMA
TIC
TIME
STEP A
DJUSTMENT
DTMAX
- MAXI
MUM
CHAN
GE IN T
EMPERATURE
DTTAS
- SP
ECIF
IED
MAXI
MUM
CHANGE IN TEMPERATURE
FOR AU
TOMA
TIC
TIME S
TEP
ADJUSTMENT
DX
- X-COORDINATE SPACING
FOR
PLOT
OF
PO
ROUS
MEDIA
ZONE
SDY
- Y-CO
ORDI
NATE
SPA
CING
FO
R PLOT O
F PO
ROUS
ME
DIA
ZONE
SDY
Y -
CHANGE IN DEPENDENT
VARIABLE VECTOR FO
R WE
LL RISER
INTEGRATION
DZ
- CHANGE IN Z-COORDINATE VALUE
DZMIN
- SPECIFIED
MINI
MUM
CHANGE IN Z-
COOR
DINA
TE FOR
WELL
RIS
ER INTEGRATION
EEUNIT - TRUE IF
ENGLISH
ENGINEERING
UNIT
S ARE
BEING
USED
FOR
DATA IN
PUT AN
D OU
TPUT
EH
- FLUID
ENTH
ALPY
EHO
- FLUID
ENTH
ALPY
AT
REFERENCE
CONDITIONS
EHOO
-
ENTH
ALPY
AT
THE
END
OF A
WEL
L RI
SER,
INITIAL
VALU
EEH
DT
- FLUID
ENTH
ALPY
TABLE
FOR
DEVIATIONS FROM S
ATURATED CONDITIONS WITH PRESSURE A
ND T
EMPERATURE
EHIR
-
ENTH
ALPY
IN
THE REGION
EHIRO
- IN
ITIA
L EN
THAL
PY IN T
HE REGION
EHIRN
- EN
THAL
PY IN T
HE REGION A
T TIME LEVEL
NEH
MX
- ENTHALPY AT
CEL
L FA
CE BE
TWEE
N X(
I-l)
AN
D X(I)
EHMY
-
ENTHALPY A
T CELL F
ACE
BETW
EEN
Y(J-
l) AN
D Y(J)
EHMZ
-
ENTH
ALPY
AT
CELL FA
CE BETWEEN
Z(K-
l) AND
Z(K)
EHPX
-
ENTH
ALPY
AT
CEL
L FA
CE BETWEEN
X(I) AND
X(I+
1)EH
PY
- EN
THAL
PY A
T CELL F
ACE
BETW
EEN
Y(J)
AN
D Y(
J+1)
EHPZ
-
ENTHALPY A
T CE
LL FA
CE BE
TWEE
N Z(K) AND
Z(K+
1)EH
ST
- FLUID
ENTH
ALPY
TA
BLE
AT S
ATUR
ATIO
N AS
A F
UNCTION
OF T
EMPERATURE
EHWEND -
ENTHALPY AT
THE
END
OF T
HE WE
LL R
ISER
EHWKT
- EN
THAL
PY IN A
WELL
AT T
HE W
ELL
DATUM
EHWSUR -
ENTHALPY IN
A W
ELL
AT T
HE LAND S
URFA
CEEO
D - WELL-RISER P
IPE
ROUGHNESS
DIVI
DED
BY PI
PE IN
SIDE
DI
AMET
EREPS
- TO
LERA
NCE
FACTOR FOR
TEMPERATURE
CALC
ULAT
ED F
ROM
ENTH
ALPY
AND PR
ESSU
REEPSFAC - TO
LERA
NCE
FACTOR FOR
TWO-
LINE
SUCCESSIVE OV
ERRE
LAXA
TION
CALCULATION
EPSOMG - TO
LERA
NCE
FACTOR F
OR C
ONVERGENCE OF
OPT
IMUM
OVER-RELAXATION PARAMETER
CALCULATION
EPSSOR - TO
LERA
NCE
FOR
CONVERGENCE
OF T
WO-LINE
SUCCESSIVE-OVER-RELAXATION EQ
UATI
ON SO
LVER
EPSWR
- TOLERANCE
FOR
CONVERGENCE
OF W
ELL
RISER
CALCULATION
ERREX
- TR
UE IF
PROGRAM
ABOR
T DU
E TO
ERROR
CONDITIONS
ERRE
XE - TRUE IF
PROGRAM AB
ORT
DUE
TO EXECUTION
ERRO
RS
Tabl
e 11.1. Definition li
st fo
r se
lect
ed HST3D program variables Continued
U) ~~j 00
ERRE
XI - TRUE IF
PROGRAM AB
ORT
DUE
TO IN
PUT
ERRO
RSEV
MAX
- MAXI
MUM
EIGENVALUE ES
TIMA
TEEV
MIN
- MINI
MUM
EIGE
NVAL
UE ESTIMATE
EX
- 'X
1EX
TRAP
-
EXTR
APOL
ATED
RES
ULTS
OF THE
WELL-RISER INTEGRATION
F1AIF
- FACTOR F
OR A
QUIF
ER INFLUENCE
FUNCTION B.C.
F2AIF
- FACTOR FO
R AQ
UIFE
R IN
FLUE
NCE
FUNCTION B.
C.FCJ
- FUNCTION FOR
WELL R
ISER
HEAT
TRANSFER U
SING CARSLAW-JAEGER S
OLUTION
FDDP
-
FRACTIONAL CH
ANGE
IN
WE
LL-D
ATUM
PR
ESSU
REFDSMTH -
FACTOR F
OR S
PATIAL D
IFFE
RENCIN
G ME
THOD
FDTMTH -
FACTOR FOR
TEMP
ORAL
DIF
FERE
NCIN
G ME
THOD
FFPH
L -
FRIC
TION
AL H
EAD
LOSS
IN W
ELL
RISE
RFI
R -
FLUI
D IN TH
E RE
GION
FIRO
-
INITIAL
FLUI
D IN T
HE REGION
FIRN
-
FLUID
IN TH
E RE
GION
AT
TIME
LEVEL
NFI
RVO
- IN
ITIA
L VO
LUME
TRIC
AMO
UNT
OF FL
UID
IN T
HE REGION
FLOREV - TR
UE IF
FL
OW REVERSAL O
CCURS
AT A
GIVEN
LEVEL
IN A
WEL
LFLOW
- TRUE IF
A W
ELL
IS PRODUCING
OR INJECTING
AT A
T LE
AST
ONE
LEVEL
FMT
- CH
ARAC
TER
STRING FO
R PR
INT
FORMAT
FPR3
- 4*
PI*R
**3
FRAC
- FRACTION OF
CELL T
HAT
IS FILLED FOR
UNCO
NFIN
ED F
LOW
FRAC
N -
FRAC
TION
OF
CE
LL FILLED A
T TIME LE
VEL
NFRACNP -
FRACTION OF
CELL F
ILLED AT
TIME
LEVE
L N+l
FRESUR - TR
UE IF A
FR
EE S
URFA
CE BOUNDARY IS
ALLOWED
FRFAC
- FRICTION FACTOR F
OR F
LOW
IN A
WEL
L RISER
PIPE
FRFLM
- FR
ICTI
ON FACTOR IN
WELL
BORE
AT
BOUNDARY BE
TWEE
N LEVEL
L-l
AND
LFRFLP
- FRICTION FACTOR IN W
ELL
BORE A
T BOUNDARY BE
TWEE
N LE
VEL
L AN
D L+
lFS
- FU
NCTI
ON TA
BLE
FOR
INTERPOLATION
FSCON
- TRUE IF A
FRE
E SU
RFAC
E RISES
ABOVE
THE
TOP
OF A
CELL AND
CONVERTS T
O CO
NFIN
ED C
ONDI
TION
SFSLOW
- TRUE IF
FR
EE SURFACE
FALLS
BELOW
BOTTOM O
F CELL
FTDAIF -
FACTOR F
OR D
IMEN
SION
LESS
TIME
FOR
A.I.
F.B.
C.GCOSTH - CO
MPON
ENT
OF GRAVITY
ALON
G A
WELL
RISER
GRAV
- GRAVITATIONAL
CONS
TANT
GX
- CO
MPON
ENT
OF GR
AVIT
Y IN TH
E X-DIRECTION
GY
- CO
MPON
ENT
OF GR
AVIT
Y IN T
HE Y-DIRECTION
GZ
- CO
MPON
ENT
OF GRAVITY
IN T
HE Z-DIRECTION
HDPRNT -
POTENTIOMETRIC H
EAD
FOR
PRINTOUT
HEAT
- TRUE IF
HEAT T
RANS
PORT
IS BEING
SIMU
LATE
DHT
CU
- OV
ERAL
L HEAT TR
ANSF
ER C
OEFFICIENT FO
R WELL R
ISER
CA
LCUL
ATON
HTCW
R - HEAT T
RANS
FER
COEFFICIENT
FROM T
HE FLUID
TO A
WEL
L RI
SER
PIPE
HWT
- ELEVATION
OF T
HE WATER
TABLE
THE
UNDEFINED
'I1 VARIABLES
ARE
POIN
TERS
FOR
THE
LARG
E VA
RIAB
LY PARTITIONED
ARRA
YS
I12X
- '12X
1 FORMAT
I1Z
- ZO
NE INDEX
I2Z
- ZO
NE IN
DEX
Table 11.1. Definition li
st for selected HST3D program variables Continued
IBC
- IN
DEX
OF BO
UNDA
RY CONDITION
TYPE
FO
R A
CELL
IBCMAP -
INDE
X OF
BO
UNDA
RY CONDITION
TYPE FO
R CO
NTOU
R MAP
ICAL
L -
INDE
X OF
CA
LL T
O ARRAY-INPUT
ROUTINE
ICC
- TRUE IF INITIAL
CONDITION
SOLU
TE MA
SS FRACTION V
ALUES
TO BE READ
ICHW
T - TR
UE IF
INITIAL
CONDITION
WATER-TABLE
ELEVATION
TO BE READ
ICHY
DP - TR
UE IF
INITIAL
CONDITION
OF HYDROSTATIC
PRES
SURE
DI
STRI
BUTI
ONIC
MAX
- IN
DEX
IN X-DIRECTION
OF CELL W
ITH
MAXI
MUM
CHANGE IN SOLUTE CO
NCEN
TRAT
ION
ICON
-
INDEX
OF CO
NNEC
TED
NODES
ICT
- TR
UE IF INITIAL
CONDITION
TEMPERATURE
DISTRIBUTION TO
BE RE
ADIC
XM
- IN
DEX
FOR
VA ARR
AY OF CO
NNEC
TING
NO
DE IN N
EGATIVE
X-DIRECTION
ICXP
-
INDEX
FOR
VA ARR
AY O
F CO
NNEC
TING
NODE
IN POSITIVE X-DIRECTION
ICYM
-
INDE
X FO
R VA A
RRAY OF
CO
NNEC
TING
NODE
IN NEGATIVE Y-DIRECTION
ICYP
-
INDE
X FOR
VA A
RRAY OF
CO
NNEC
TING
NOD
E IN
POSITIVE Y-DIRECTION
ICZM
-
INDE
X FOR
VA A
RRAY OF
CO
NNEC
TING
NO
DE IN NEGATIVE Z-DIRECTION
ICZP
-
INDE
X FOR
VA A
RRAY
OF
CONN
ECTI
NG NO
DE IN
PO
SITI
VE Z-DIRECTION
ID4
- IN
DEX
FOR
D4 NODE RENUMBERING
ID4C
ON -
INDE
X OF CONNECTED
NODES
FOR
D4 NO
DE RENUMBERING
ID4NO
- IN
DEX
OF NEW
NODE
NUMBERS FOR
D4 RENUMBERING
SCHEME
IDIA
G -
INDE
X OF DIAGONAL ELEMENTS IN TH
E A4
MATRIX
IDIR
-
INDE
X OF
DIRECTION
FOR
TWO-
LINE
-SOR
SOL
VER
IDNUM
- IDENTIFICATION NUMBER F
OR T
EMPO
RAL
PLOT
IDRC
ON -
INDE
X OF
DIRECTION
TO N
EIGHBORING CO
NNEC
TED
NODE
IE
- IN
DEX
OF ERROR
NUMBER
IE1
- IN
DEX
LIMIT
OF ER
ROR
NUMBER
IE2
- IN
DEX
LIMIT
OF ERROR
NUMB
ERIE
NDIV
-
INDE
X OF
LA
ST LOCATION IN T
HE IVPA A
RRAY
IEND
VV -
INDE
X OF
LA
ST LOCATION IN
THE VP
A ARRAY
IEQ
- IN
DEX
OF EQUATION BEING
SOLV
EDIER
- IN
DEX
OF ERROR
NUMBER
I ERR
-
LOGICAL
FLAGS
FOR
ERROR
MESS
AGES
IF12
-
'F12
1 FORMAT
IFAC
E -
INDE
X OF
FACE OF
APP
LIED
B.
C.IFMT
-
INDE
X OF FORMAT T
YPE
IFOR
M - CH
ARAC
TER
STRING C
ONTAINING
FORMAT S
TATE
MENT
IG12
-
'G12
1 FORMAT
1112
- '112'
FORMAT
115
- '1
5' FORMAT
ILAVFL - TO
TAL
LENG
TH OF
ALL LA
BELE
D CO
MMON
BLOCKS
ILBL
-
INDE
X OF
LABEL
CHARACTERS FO
R TE
MPOR
AL P
LOT
ILH
- IN
DEX
OF ELEMENT
IN EQUATION MATRIX FOR
D4 SO
LVER
ILIVPA -
LENGTH OF
IV
PA A
RRAY
AS
DIMENSIONED
ILNX
I -
(LOG(XI))**-!
ILVPA
- LENGTH OF VPA
ARRA
Y AS
DIMENSIONED
IMAP
1 -
IMAP
1, IMAP2, JM
AP1,
JM
AP2,
KM
AP1,
KMAP2
ARE
NODE RANGES FO
R MAP
OUTPUT
IMAP
2
Tabl
e 11.1. De
fini
tion
list fo
r se
lect
ed HST3D program variables Continued
u> 00 o
IMOD
-
INDE
X OF MO
DIFI
CATI
ON FOR
ARRAY
INPUT
IMPP
TC -
INDEX
FOR
CONT
OUR
MAP
OF DE
PEND
ENT
VARI
ABLE
ARRAYS
IMPQ
W - TRUE IF S
EMI-IMPLICIT W
ELL
FLOW C
ALCULATION IS DESIRED
INZO
NE - TRUE
IF
A CELL IS CONTAINED
WITH
IN A
DEF
INED
POROUS
MEDIA
ZONE
IPAG
E - PAGE NU
MBER
FOR C
ONTO
UR M
APIP
AR
- IN
TEGE
R PA
RAME
TER
VALUE
FOR
ARRAY
INPU
TIP
ARI
- INITIAL
INTE
GER
PARAMETER
VALU
E FOR
ARRAY
INPU
TIPLOT
- INDEX
ARRA
Y ID
ENTI
FYIN
G EXCLUDED CELLS
FOR
CONTOUR
MAPS
IPMA
X -
INDEX
IN X-DIRECTION
OF CELL W
ITH
MAXI
MUM
CHANGE IN
PR
ESSU
REIP
MZ
- INDEX
OF POROUS M
EDIU
M ZO
NEIP
MZ1
- INDEX
OF FIRST
ZONE
FO
R ZONE PLOT
IPMZ
2 -
INDEX
OF LA
ST Z
ONE
FOR
ZONE
PLOT
IPRP
TC -
INDE
X OF PRINTING PRESSURE,
TEMP
ERAT
URE,
OR
SOLUTE
CONC
ENTR
AION
ARRAYS
IROW
- INDEX
OF EQ
UATI
ON NUMBER F
OR D
4 SO
LVER
ISIG
N -
INDEX
OF DIRECTION
FOR THE
WELL
RISER C
ALCULATION.
POSITIVE IS
UPW
ARDS
.ISORD
- INDEX
OF OPTIMUM
DIRECTION
FOR TW
O-LI
NE S
OR S
OLVE
RIS
UM
- SU
M OF
I,J, AND
K IN
DICE
S FO
RMIN
G A
DIAGONAL P
LANE
ITIM
E -
TIME
STEP NUMBER
ITMA
X -
INDE
X IN X-DIRECTION
OF CE
LL W
ITH
MAXIMUM
CHANGE IN T
EMPERATURE
ITNO
-
ITER
ATIO
N NUMBER IN T
WO-LINE
SOR
SOLV
ERITNOC
- ITER
ATIO
NS U
SED
FOR
SOLUTE CALCULATION
BY TWO-LINE S
OR S
OLVE
RIT
NOP
- ITER
ATIO
NS USED F
OR P
RESSURE
CALCULATION
BY T
WO-L
INE
SOR
SOLV
ERIT
NOT
- IT
ERAT
IONS
USED F
OR T
EMPERATURE CA
LCUL
ATIO
N BY
TW
O-LI
NE-S
OR S
OLVER
ITRN
-
ITERATION
COUNT
FOR
SEQUENCE OF
P,T
AND
C EQ
UATI
ON S
OLUT
ION
CYCL
ESIT
RN1
- ITER
ATIO
N COUNT
FOR
WELLBORE CALCULATION
ITRN2
- ITER
ATIO
N COUNT
FOR
WELLBORE CALCULATION
ITRN
DN -
ITER
ATIO
N CO
UNT
FOR
WELL
BORE D
ENSI
TY CA
LCUL
ATIO
NIT
RNI
- IT
ERAT
ION
COUNT
FOR
P,T
OR P
,C S
OLUT
ION
CYCLE
ITRN
P -
ITER
ATIO
N CO
UNT
FOR
P AND
WELL
BO
RE S
OLUTION
CYCLE
IUH
- INDEX
OF EQ
UATI
ON IN UP
PER
HALF OF
MATRIX
FOR
D4 S
OLVE
RIVPA
- IN
TEGE
R VA
RIAB
LY PARTITIONED
ARRA
YIW
- INDEX
OF CELL N
UMBER
IN X-DIRECTION
FOR A
WELL
IWEL
- INDEX
OF WE
LL N
UMBER
J1Z
- ZONE INDEX
J2Z
- ZO
NE INDEX
JCMAX
- INDEX
IN Y-DIRECTION
OF CE
LL W
ITH
MAXI
MUM
CHAN
GE IN
SOLUTE CONCENTRATION
JMAP1
JMAP2
JPMAX
- INDEX
IN Y-DIRECTION
OF C
ELL
WITH
MAXIMUM C
HANGE
IN PR
ESSU
REJT
MAX
- INDEX
IN Y-DIRECTION
OF CELL W
ITH
MAXI
MUM
CHAN
GE IN
TEMPERATURE
JW
- INDEX
OF CELL N
UMBER
IN Y-DIRECTION
FOR
A WE
LLK1Z
- ZONE INDEX
K2Z
- ZO
NE INDEX
KARH
C - THER
MAL
CONDUCTANCE
FACTOR F
OR H
EAT
CONDUCTION B.C.
KCMAX
- INDEX
IN Z-DIRECTION
OF CELL W
ITH
MAXI
MUM
CHANGE IN SOLUTE CONCENTRATION
Table 11.1. Definition list for selected HST3D program variables Continued
OJ
00
KLBC
KMAP
1KM
AP2
KO KOAR
KPMAX
KTHAWR
KTHF
KTHW
RKT
HXKTHXPM
KTHY
KTHYPM
KTHZ
KTHZPM
KTMAX
KXX
KYY
KZZ
LABEL
LBLDIR
LBLE
QLBW
LCBO
TWLC
ROSD
LCTO
PWLDASH
LOOT
SLE
NAX
LENA
YLENAZ
LGRE
NLI
NAGE
LIMIT
LINE
LINLIM
LOCA
IFLP
RNT
LTD
M MA MAIFC
MAPPTC
MAX IT
MAXIT1
- CO
NDUCTANCE
FACTOR F
OR L
EAKA
GE B.
C.
- WE
LL N
UMBE
R INDEX
FOR OB
SERV
ED D
ATA
- PERMEABILITY OF OU
TER AQUIFER
REGI
ON FO
R A.
I.F.
B.C.
- INDEX
IN Z-DIRECTION
OF CELL W
ITH
MAXI
MUM
CHAN
GE IN PRESSURE
- TH
ERMA
L CONDUCTIVITY OF AMBIENT
MEDIUM A
T WELL R
ISER
- TH
ERMA
L CO
NDUC
TIVI
TY OF
FLUID
- TH
ERMA
L CO
NDUC
TIVI
TY OF
WEL
L RISER
PIPE
- TH
ERMA
L CONDUCTIVITY OF FLUID
AND
PORO
US MEDIUM IN X-
DIRE
CTIO
N- TH
ERMA
L CO
NDUC
TIVI
TY OF
PO
ROUS
MEDIUM IN
X-DIRECTION
- TH
ERMA
L CONDUCTIVITY OF FL
UID
AND
PORO
US MEDIUM IN
Y-
DIRE
CTIO
N- TH
ERMA
L CO
NDUC
TIVI
TY OF PO
ROUS
MEDIUM IN
Y-DIRECTION
- TH
ERMA
L CONDUCTIVITY O
F FLUID
AND
POROUS M
EDIUM
IN Z-DIRECTION
- THERMAL
COND
UCTI
VITY
OF PO
ROUS
MEDIUM IN
Z-
DIRE
CTIO
N-
INDE
X IN Z-
DIRE
CTIO
N OF
CELL W
ITH
MAXIMUM
CHANGE IN
TEMPERATURE
- PE
RMEABILITY IN
X-DIRECTION
- PE
RMEABILITY IN
Y-DIRECTION
- PERMEABILITY IN
Z-DIRECTION
- CH
ARAC
TER
STRING FO
R LABEL
- LABEL
FOR
OPTI
MUM
DIRE
CTIO
N FO
R TWO-LINE SOR
SOLV
ER-
LABEL
FOR
SYSTEM EQ
UATI
ON NUMBER
- LE
FT S
IDE
BAND W
IDTH
OF
A4 A
RRAY
FO
R EACH EQUATION
- IN
DEX
OF BOTTOM LAYER
OF COMPLETION OF A
WELL
- TRUE IF
THE CR
OSS-
DERI
VATI
VE DI
SPER
SION
COEFFICIENTS A
RE T
O BE LU
MPED
IN
TO T
HE DIAGONAL T
ERMS
- INDEX
OF TOP
LAYER
OF COMPLETION OF A
WELL
LENGTH O
F TH
E X-
AXIS
FOR
A CONTOUR
MAP
LENGTH O
F TH
E Y-
AXIS
FOR A
CONTOUR
MAP
LENG
TH OF
THE
Z-AXIS FOR
A CONTOUR
MAP
LOGARITHM
OF T
HE REYNOLDS NU
MBER
LINE
IM
AGE
FOR
DATA INPUT
LABE
L FO
R WE
LL-B
ORE
CALCULATION
CONSTRAINTS
CHARACTER
STRING FOR TEMPORAL P
LOT
LIMIT
TO T
HE NU
MBER
OF
PRIN
TER
LINE
S FOR TE
MPOR
AL P
LOT
INDE
X FO
R LO
CATI
ON O
F TH
E AQUIFER
INFLUENCE
FUNC
TION
B.C.
INDEX
FOR
INCLUSION
OF A
NODE IN A
N ARRAY
PRINTOUT
LOGA
RITH
M OF
DI
MENS
IONL
ESS
TIME FOR
A.I.
F.CE
LL NUMBER
CELL NUMBER F
OR ASS
EMBL
YCELL N
UMBE
RS FOR AQ
UIFE
R INFLUENCE
FUNC
TION
B.C.
INDEX
FOR
OUTPUT O
F ZO
NED
CONTOUR
MAPS
OF PRESSURE,
TEMPERATURE, OR S
OLUTE
CONC
ENTR
ATIO
NMA
XIMU
M NUMBER O
F ITERATONS
FOR
TWO-LINE SO
R SO
LVER
MAXI
MUM
NUMBER O
F ITERATIONS A
LLOW
ED F
OR C
ALCULATION OF
OPTIMUM
OVER-RELAXATION
FACTOR
Table 11.1. Definition list for selected HST3D program variables Continued
u>
oo
ro
MAXI
T2 - MAXIMUM
NUMB
ER O
F IT
ERAT
IONS
ALLOWED
FOR
TWO-
LINE
SOR
SOLUTION
MAXI
TN - MA
XIMUM
NUMB
ER O
F IT
ERAT
IONS
ALLOWED
FOR
THE
SOLU
TION
CYCLE
OF TH
E TH
REE
SYSTEM EQUA
TIONS
MAXORD - MAXIMUM
ORDER
OF POLYNOMIAL A
LLOW
ED FOR
INTEGRATION
OF THE
WELL-RISER EQUATIONS
MAXPTS - MAXIMUM
NUMB
ER O
F SPATIAL
STEP
S ALLOWED
FOR
WELL-RISER C
ALCULATION
METH
-
INDEX
FOR
EXTR
APOL
ATIO
N ME
THOD S
ELECTION FOR
WELL-RISER CALCULATION
MFBC
-
CELL
NUMBERS
FOR SP
ECIF
IED
FLUX
B.
C.MF
LBL
- LA
BEL
FOR
MASS FR
ACTI
ON OR
SCALED M
ASS
FRAC
TION
MHCB
C -
CELL N
UMBERS FOR
HEAT CO
NDUC
TION
B.
C.MIJKM
- CELL NU
MBER
AT
I.J.K-1
MIJKP
- CE
LL NU
MBER
AT
I.J.
K+1
MIJM
K -
CELL
NU
MBER
AT
I.J-
l.K
MIJM
KM -
CELL
NU
MBER
AT
I.J-
l.K-
1MI
JMKP
-
CELL
NU
MBER
AT
I.J-
l.K+
1MI
JPK
- CE
LL NU
MBER
AT
I.J-
U.K
MIJP
KM -
CELL
NU
MBER
AT
I.J-
H.K-
1MI
JPKP
-
CELL N
UMBE
R AT I.
J-H.
K+1
MIMJ
K -
CELL
NU
MBER
AT
I-l.
J.K
MIMJ
KM -
CELL NU
MBER
AT
I-l.J.K-1
MIMJ
KP -
CELL
NU
MBER
AT
I-l.
J.K+
1MI
MJMK
-
CELL
NU
MBER
AT
I-l.
J-l.
KMIMJPK -
CELL
NU
MBER
AT
I-l.
J+l.
KMINUS
- '-
'MIPJK
- CE
LL NU
MBER
AT
I+l.
J.K
MIPJ
KM -
CELL
NU
MBER
AT
I+l.
J.K-
1MI
PJKP
-
CELL
NU
MBER
AT
I+l.
J.K+
lMI
PJMK
-
CELL
NU
MBER
AT
I+l.
J-l.
KMIPJPK -
CELL NU
MBER
AT
I+l.J+l.K
MKT
- CE
LL NU
MBER
AT
A WELL-DATUM LEVE
LML
BC
- CE
LL NU
MBER
S FOR
LEAK
AGE
B.C.
MOBW
- MO
BILITY FOR
AN A
QUIFER LAYER AT A WELL
BORE
MSBC
- CE
LL NUMBERS
FOR
SPEC
IFIE
D VALU
E B.
C.MT
- CE
LL NU
MBER
AT
TOP
OF REGION
MTJP
1 -
CELL N
UMBE
R AT T
OP OF
REGION AT I.
J+1
MXIT
QW - MA
XIMUM NU
MBER
DF IT
ERAT
IONS
AL
LOWE
D FOR
WELL FL
OW RA
TE CALCULATION
NAC
- CO
UNT
OF AC
TIVE
CELLS
NAIFC
- NU
MBER OF
AQUIFER
INFLUENCE
FUNC
TION
B.
C. CELLS
NCHARS -
NUMB
ER O
F CHARACTERS
NCPR
-
NUMB
ER O
F CHARACTERS T
O BE
PRINTED
FOR
ZONE PL
OTNDIM
- NU
MBER
OF
DIMENSIONS FOR
TABU
LAR
INTERPOLATION
NEHS
T -
NUMB
ER O
F EN
TRIE
S IN
THE
SATURATED
ENTH
ALPY
VS
. TE
MPER
ATUR
E TA
BLE
NFBC
- NU
MBER
OF
SPEC
IFIE
D FL
UX B.
C. CE
LLS
NFC
- CO
UNT
OF SP
ECIF
IED
FLUX CE
LLS
NGRIDX -
COLUMN NU
MBER
COR
RESP
ONDI
NG TO X-GRID PO
INT
NGRI
DY -
LINE
NU
MBER
COR
RESP
ONDI
NG T
O Y-GRID POINT
NHC
- CO
UNT
OF HEAT CO
NDUC
TION
BO
UNDA
RY CE
LLS
Table 11.1. Definition list for selected HST3D program variables Continued
UJ
00
UJ
SOLUTE CONCENTRATION
TEMPERATURE
TEMPERATURE
AT MI
NIMU
M SO
LUTE
CO
NCEN
TRAT
ION
TEMPERATURE
AT MAXIMUM
SOLU
TE CO
NCEN
TRAT
ION
NHCB
C - NUMBER OF
HE
AT C
ONDU
CTIO
N B.C. CELLS
NHCN
- NUMBER O
F NODES
EXTERNAL T
O THE
REGION FO
R THE
HEAT CONDUCTION B.C. CALCULATION
NLBC
- NUMBER O
F LE
AKAG
E B.C. CELLS
NLC
- COUNT
OF LE
AKAG
E B.C. CELLS
NMAPR
- NUMBER O
F MAP
RECO
RDS
WRIT
TEN
TO D
ISC
NMPZON -
NUMBER O
F ZONES
FOR
CONTOUR
MAPS
NNOPPR -
NUMBER O
F NODES
TO BE PR
INTE
D FO
R AR
RAY
OUTPUT
NNPR
-
NUMBER O
F NODES
TO HAVE PRINTED
VALUES
NO
- NUMBER O
F OBSERVED D
ATA
POINTS
NOCV
-
NUMBER OF DA
TA P
OINTS
FOR
VISC
OSIT
Y VS,
NOTV
- NU
MBER
OF
DATA P
OINTS
FOR
VISCOSITY
VS,
NOTVO
- NUMBER O
F DA
TA PO
INTS
FO
R VI
SCOS
ITY
VS,
NOTV
1 -
NUMBER O
F DA
TA PO
INTS
FO
R VI
SCOS
ITY
VS,
NPAG
ES - NUMBER O
F PAGES
FOR
A CO
NTOU
R MAP
NPEHDT -
NUMBER O
F PO
INTS
IN
THE
ENTHALPY DEVIATION
TABL
E ALONG
THE
PRES
SURE
CO
ORDI
NATE
NPMZ
- NUMBER O
F ZONES
OF POROUS M
EDIA
PROPERTIES
NPOSNS -
NUMBER O
F CH
ARAC
TER
POSI
TION
S IN
THE
X-DIRECTION
FOR A
CONTOUR
MAP
ELEM
ENT
NPTAIF -
NUMBER O
F PO
INTS
IN
THE
TABLE
OF T
RANS
IENT
AQU
IFER
IN
FLUE
NCE
FUNCTION VS
. TIME
NPTCBC -
NUMBER O
F SP
ECIF
IED
VALUE
B.C.
CELLS
NPTSA4 -
NUMBER O
F PO
INTS
IN
THE A
4 MA
TRIX
FO
R THE
D4 SO
LVER
NPTSD4 -
NUMBER O
F PO
INTS
FO
R TH
E D4 SO
LVER
NPTSUH - NUMBER O
F PO
INTS
IN T
HE UP
PER
HALF
OF
THE EQUATION M
ATRI
X FO
R TH
E D4 S
OLVE
RNR
-
NUMBER O
F NODES
IN T
HE R-DIRECTION
NRSTTP -
NUMBER O
F RE
STAR
T RE
CORD
TIME
PLAN
ES WRITTEN
TO DISC
NSC
- NUMBER O
F SP
ECIF
IED
VALU
E B.C. CELLS
NSHU
T -
NUMBER O
F WELLS
SHUT
IN
NSTD4
- NUMBER O
F STORAGE
LOCA
TION
S RE
QUIR
ED B
Y THE
D4 S
OLVE
RNSTSOR -
NUMBER O
F ST
ORAG
E LOCATIONS
REQU
IRED
BY
THE
TWO-
LINE
SO
R SO
LVER
NTEHDT - NUMBER O
F PO
INTS
ALO
NG T
HE T
EMPERATURE CO
ORDI
NATE
IN
THE
ENTHALPY DE
VIAT
ION
TABL
ENTHPTC -
INDEX
FOR
SPECIFYING T
HAT
EVERY
NTH
CALC
ULAT
ED P, T
OR C
POINT
IS T
O BE PL
OTTE
DNTHPTO -
INDEX
FOR
SPEC
IFYI
NG T
HAT
EVERY
NTH
OBSERVED P,
T
OR C
PO
INT
IS TO
BE PL
OTTE
DNTSCHK - NUMBER O
F TIME S
TEPS BE
TWEE
N CH
ECKP
OINT
DUMPS
NTSOPT -
NUMBER O
F TIME STEPS
BETWEEN
RECA
LCUL
ATIO
N OF
THE OP
TIMU
M OV
ER-R
ELAX
ATIO
N PARAMETER
NVST
-
NUMBER O
F PO
INTS
IN
THE T
ABLE OF
GENERALIZED V
ISCO
SITY
VS
. TEMPERATURE
NWEL
- NUMBER O
F WELLS
IN T
HE REGION
NX
- NUMBER O
F NODES
IN T
HE X-DIRECTION
NXPR
- NUMBER O
F VALUES IN X-DIRECTION
FOR AR
RAY
PRINTOUT
NXY
- NU
MBER
OF
NODES
IN A
N X-
Y PL
ANE
NXYZ
-
NUMBER O
F NODES
IN T
HE SI
MULA
TION
RE
GION
, NX*NY*NZ
NY
- NUMBER O
F NODES
IN T
HE Y-DIRECTION
NYPR
-
NUMBER O
F VALUES IN
Y-DIRECTION
FOR
ARRAY
PRINTOUT
NZ
- NUMBER O
F NODES
IN T
HE Z-DIRECTION
NZPR
- NU
MBER
OF
VALUES IN Z
-DIRECTION FOR AR
RAY
PRINTOUT
NZTPHC -
NUMBER O
F NODES
FOR
THE
INITIAL
CONDITION
TEMPERATURE
PROF
ILE
OUTS
IDE
THE
REGION FO
R HEAT CONDUCTION B.C.
NZTPRO - NUMBER O
F NODES
FOR
THE
INITIAL
CONDITION
TEMPERATURE
PROFILE
IN T
HE Z-DIRECTION
Tab
le 11.1
. D
efi
nit
ion li
st
for se
lecte
d
HST
3D p
rog
ram
va
ria
ble
s C
onti
nued
OCP
LOT
- TR
UE
IF
PLO
TS
OF
OBS
ERVE
D AN
D C
ALC
ULA
TED
VAL
UES
OF
THE
DEPE
NDEN
T VA
RIA
BLES
AR
E D
ESIR
EDOH
-
'0'
OMEGA
- OVER-RELAXATION
FACTOR FO
R TWO-
LINE
SOR
SOLV
EROMOPT
- OP
TIMU
M OV
ER-R
ELAX
ATIO
N FA
CTOR
FOR T
WO-LINE
SOR
SOLV
ERORENPR -
ORIENTATION
OF T
HE AR
RAY
PRIN
TOUT
S, AREAL
OR V
ERTI
CAL
SLICE
ORFR
- ORIENTATION
OF T
HE AR
RAY
PRINTOUTS
FOR
SATU
RATE
D FRACTION OF CE
LLP
- PRESSURE
PO
- REFERENCE
PRESSURE FOR
DENSITY
POO
- PRESSURE A
T THE
END
OF A
WELL
RISE
R, IN
ITIA
L VALUE
POH
- REFERENCE
PRESSURE FO
R ENTHALPY
PI
- '.!' FORMAT
P2
- '.2' FORMAT
P4
- '.
4' FORMAT
P5
- '.
5' FORMAT
PAAT
M - ATMOSPHERIC
PRESSURE IN
ABSOLUTE
UNIT
SPAEHDT -
PRESSURE VALUES (ABSOLUTE) FOR
ENTH
ALPY
DE
VIAT
ION
TABLE
PAIF
-
PRES
SURE
OU
TSID
E TH
E REGION FOR
A.I.F.B.C.
PAR
- PARAMETER
VALUE
FOR
ARRAY
INPU
TPA
RA
- PA
RAME
TER
VALUE
FOR
ARRA
Y INPU
T ..
PARB
-
PARA
METE
R VALUE
FOR
ARRAY
INPU
T oo
PARC
-
PARA
METE
R VALUE
FOR
ARRAY
INPU
T **
PCS
- PRESSURE CALCULATED IN A
WELL
AT LAND S
URFA
CE FOR TE
MPOR
AL PL
OTPCW
- PRESSURE CA
LCUL
ATED
AT
A WE
LL D
ATUM F
OR T
EMPO
RAL
PLOT
PFSLOW - TRUE IF
A
MESS
AGE
IS T
O BE PR
INTE
D WHEN T
HE FR
EE SURFACE
FALL
S BE
LOW
A CE
LL BOUNDARY
PHILBC -
PO
TENT
IOME
TRIC
HEAD
ON T
HE OT
HER
SIDE
OF AN
AQUITARD
FOR
A LEAKAGE
B.C.
PI
- '3
.141
59..
.'PINIT
- PR
ESSU
RE IN
ITIA
L CONDITION
AT A
GIV
EN ELEVATION
PLBL
- LABEL
FOR
PRES
SURE
AR
RAY
PRINTOUTS
PLOTWC -
TRUE IF
TEM
PORA
L PLOTS
OF SOLUTE CO
NCEN
TRAT
IONS
IN
WEL
LS A
RE DE
SIRE
DPLOTWP - TRUE IF
TEM
PORA
L PL
OTS
OF PR
ESSU
RES
IN W
ELLS A
RE DE
SIRE
DPLOTWT - TRUE IF
TE
MPOR
AL PLOTS
OF T
EMPE
RATU
RES
IN W
ELLS
ARE
DE
SIRE
DPLTZON -
TRUE IF
A
PLOT
OF
THE
POROUS ME
DIA
ZONES
IS DESIRED
PLUS
-
'+'
PMCH
V -
POROUS ME
DIUM
COM
PRES
SIBI
LITY
COEFFICIENT
IN HEAT EQUATION
PMCV
-
POROUS ME
DIUM
COM
PRES
SIBI
LITY
COEFFICIENT
IN FL
OW EQUATION
PMHV
-
POROUS ME
DIUM
THE
RMAL
COEFFICIENT
IN HE
AT EQUATION,
CURRENT
VALUE
PNP
- PRESSURE FO
R SP
ECIF
IED
VALUE
B.C.
POROAR -
PORO
SITY
OF
THE OU
TER
AQUI
FER
REGION FO
R A.
I.F.
B.C.
POROS
- PO
ROSI
TYPO
S - PRESSURE OB
SERV
ED IN
A W
ELL
AT T
HE LAND S
URFACE FOR TEMPORAL P
LOT
POSUP
- TRUE IF
THE VERTICAL A
XIS
OF T
HE CO
NTOU
R MAP
IS POSITIVE UPWARD
POW
- PRESSURES
OBSE
RVED
IN A
WELL
AT T
HE WELL D
ATUM
FOR T
EMPO
RAL
PLOT
PRBCF
- TRUE IF
PRINTOUT OF BO
UNDA
RY CO
NDIT
ION
FLOW RATES
IS DE
SIRE
DPR
DV
- TRUE IF
PR
INTO
UTS
OF DENSITY
AND
VISCOSITY
FIEL
DS A
RE DE
SIRE
DPRGFB
- TR
UE IF PR
INTO
UT OF GLOBAL FL
OW BALANCE
IS DE
SIRE
D
Table
11.1. Definition list for
selected HST3D program variables Continued
PRIB
CF -
PRIN
TOUT
IN
TERV
AL FOR
BOUN
DARY CONDITION
FLOW
RATES
PRID
V -
PRIN
TOUT
IN
TERV
AL FOR
DENS
ITY
AND
VISCOSITY
FIELDS
PRIGFB -
PRINTOUT INTERVAL F
OR G
LOBA
L FLOW B
ALANCE
PRIK
D -
PRIN
TOUT
IN
TERV
AL FOR
COND
UCTANC
ES A
ND D
ISPE
RSIO
N CO
EFFI
CIEN
TSPRIMAP -
PRINTOUT IN
TERV
AL FOR
ZONED
CONT
OUR
MAPS
PRIPTC -
PRIN
TOUT
INTERVAL F
OR P
RESSURE, TEMPERATURE, AN
D SOLUTE M
ASS
FRACTION FIELDS
PRISLM -
PRIN
TOUT
IN
TERV
AL FOR
SOLU
TION M
ETHO
D INFORMATION
PRIVEL -
PRIN
TOUT
IN
TERV
AL FO
R VE
LOCI
TY FIELD
PRIWEL -
PRIN
TOUT
INTERVAL FO
R WELL INFORMATION
PRKD
- TRUE IF
PR
INTO
UTS
OF CO
NDUC
TANC
ES A
ND D
ISPERSION
COEF
FICI
ENTS
ARE
DE
SIRE
DPR
PTC
- TRUE IF PRINTOUTS
OF DE
PEND
ENT
VARIABLES
P,T
OR C
ARE
DESIRED
PRSL
M - TRUE IF PRINTOUT O
F SOLUTION METHOD INFORMATION
IS DE
SIRE
DPRTBC
- TRUE IF PR
INTO
UT O
F BOUNDARY CONDITION
FLOW
RATES
IS DESIRED
PRTCCM - TR
UE IF PRINTOUT O
F ME
SSAG
E OF
FREE-SURFACE B.C. BE
COMI
NG CONFINED IS DESIRED
PRTCHR -
CHARACTER
STRING FO
R PR
INTO
UT O
F CO
NTOU
R MA
PSPRTDV
- TRUE IF
PRINTOUT O
F DE
NSIT
Y AN
D VISCOSITY
FIELDS IS
DESIRED
PRTFP
- TRUE IF
PRINTOUT O
F FL
UID
PARAMETERS IS
DESIRED
PRTIC
- TRUE IF
PRINTOUT O
F INITIAL
CONDITIONS IS DE
SIRE
DPRTMPD -
TR
UE IF
PR
INTO
UT O
F CO
NTOU
R MAP
PARAMETERS IS DE
SIRE
D u>
PRTPMP - TRUE IF
PRINTOUT O
F POROUS ME
DIA
PROPERTIES IS DE
SIRE
D »
PRTRE
- TR
UE IF
PR
INTO
UT O
F READ EC
HO FOR
ARRA
Y IN
PUT
IS DESIRED
PRTSLM - TRUE IF PRINTOUT O
F SOLUTION METHOD PARAMETERS IS DE
SIRE
DPRTWEL - TR
UE IF
PR
INTO
UT O
F WE
LL B
ORE
INFORMATION
IS DE
SIRE
DPRVEL
- TRUE IF
PRINTOUT O
F VELOCITY FI
ELD
IS DE
SIRE
DPRWEL
- TR
UE O
F PRINTOUT O
F WE
LL B
ORE
INFORMATION
IS DE
SIRE
DPSBC
- PR
ESSU
RE FO
R SP
ECIF
IED
VALUE
B.C.
PSLB
L -
LABE
L FOR
WELL PRESSURE A
T LA
ND S
URFACE FO
R TE
MPOR
AL PL
OTS
PSMA
X - MAXIMUM
PRES
SURE
AT
LAND
SURFACE FO
R SC
ALIN
G TEMPORAL PL
OTS
PSMIN
- MI
NIMU
M PR
ESSU
RE AT LA
ND S
URFACE FOR
SCALING
TEMPORAL PLOTS
PU
- TR
ANSI
ENT
AQUI
FER
INFLUENCE
FUNC
TION
DI
MENS
IONL
ESS
PRESSURE RESPONSE T
O A
UNIT
DIM
ENSI
ONLE
SS W
ITHD
RAWA
L FLOW-RATE
CHANGE
PV
- PORE VOLUME,
CURR
ENT
VALUE
PVK
- PO
RE VOLUME W
EIGH
TED
SORP
TION PARAMETER, CURRENT
VALUE
PWCELL -
PR
ESSU
RE IN
THE CELL A
T THE
UPPE
RMOS
T CO
MPLE
TION
LE
VEL
OF A
WEL
LPW
KT
- PRESSURE IN
A W
ELL
AT T
HE W
ELL
DATU
MPWKTS
- SP
ECIF
IED
LIMITING PRESSURE IN A
WELL
AT T
HE W
ELL
DATUM
PWLB
L -
LABE
L FOR
WELL PR
ESSU
RE A
T WELL
DAT
UM FOR
TEMP
ORAL
PLOTS
PWMA
X - MA
XIMU
M PRESSURE A
T WELL D
ATUM
FOR
SCAL
ING
TEMPORAL P
LOTS
PWMIN-
- MI
NIMU
M PR
ESSU
RE AT W
ELL
DATU
M FO
R SCALING
TEMPORAL PLOT
PWREND -
PRESSURE AT
THE
EN
D OF
A W
ELL
RISER
PIPE
PWRK
- PRESSURE IN A
WEL
L RISER
AT A
GIV
EN LEVEL
PWSUR
- PRESSURE IN
A W
ELL
AT T
HE LA
ND S
URFACE
PWSU
RS - SP
ECIF
IED
LIMI
TING
PR
ESSU
RE IN
A W
ELL
AT T
HE LA
ND S
URFACE
QDVSBC -
FLOW RA
TE FO
R THE
DEPE
NDEN
T VARIABLE AT
A S
ECIF
IED
VALU
E B.C. CELL
QFAC
- BI
-LIN
EAR
INTERPOLATION
FACT
OR F
OR C
ONTOUR M
APS
QFAIF
- VO
LUME
TRIC
FLOW
RATE
FOR
A.I.F.B.C.
Tab
le 11.1. De
fini
tion
li
st for
selected HST3D program variables Continued
QFBC
- FL
UID
FLOW
RATE A
T ANY
B.C. CE
LLQFBCV
- VO
LUME
TRIC
FLUID
FLOW
RATE
FOR
SPECIFIED
FLUX
B.C.
QFFX
- FLUID
FLUX IN
X-DIRECTION
QFFY
-
FLUID
FLUX
IN
Y-DIRECTION
QFFZ
- FL
UID
FLUX
IN Z-DIRECTION
QFLBC
- FLUID
MASS FL
OW R
ATE
FOR
LEAK
AGE
B.C.
QFSB
C - VO
LUME
TRIC
FLUID
FLOW
RATE
FOR
SPECIFIED
VALUE
B.C.
QHAIF
- HEAT F
LOW
RATE FO
R A.
I.F.
B.C.
QHBC
- HEAT F
LOW
RATE A
T ANY
B.C. CELL
QHCBC
- HE
AT F
LOW
RATE FOR
HEAT
CON
DUCT
ION
B.C.
QHFAC
- HEAT
FLOW
RATE FACTOR F
OR W
ELL
RISE
RQHFBC
- HEAT FL
OW RATE FO
R SP
ECIF
IED
FLUX B
.C.
QHFX
- SPECIFIED
HEAT F
LUX
IN T
HE X-DIRECTION
QHFY
- SPECIFIED
HEAT F
LUX
IN T
HE Y-DIRECTION
QHFZ
- SPECIFIED
HEAT F
LUX
IN T
HE Z-DIRECTION
QHLB
C - HEAT F
LOW
RATE A
T LE
AKAG
E B.
C.QH
LYR
- HEAT F
LOW
RATE FROM A
WEL
L TO
AN
AQUI
FER
LAYE
RQH
SBC
- HE
AT F
LOW
RATE A
T A
SPEC
IFIE
D VA
LUE
B.C.
QHSBC
- HE
AT FL
OW RA
TE A
T A
SPEC
IFIE
D PRESSURE B.C.
QHW
- HEAT FL
OW RATE FROM A
WELL
TO T
HE A
QUIF
ERQHWRK
- HE
AT F
LOW
RATE
IN
A W
ELL
RISE
R AT
A G
IVEN
LE
VEL
QLIM
- LI
MITI
NG FLOW R
ATE
FOR
RIVE
R LE
AKAG
EQN
-
FLOW
RATE AT
TIM
E LEVEL
NQN
P -
FLOW R
ATE
AT T
IME
LEVEL
N+l
QSAIF
- SOLUTE FLOW R
ATE
AT A
N A.I.F.B.C.
QSBC
- SOLUTE FLOW R
ATE
AT A
NY B
.C.
CELL
QSFBC
- SOLUTE FLOW R
ATE
AT A
SPE
CIFI
ED FLUX B.C.
QSFX
- SP
ECIF
IED
SOLUTE FL
UX IN
THE
X-DIRECTION
QSFY
- SP
ECIF
IED
SOLUTE FL
UX IN
THE Y-
DIRE
CTIO
NQS
FZ
- SP
ECIF
IED
SOLUTE FLUX IN
THE
Z-DIRECTION
QSLBC
- SOLUTE FLOW R
ATE
AT A
LE
AKAG
E B.C.
QSLYR
- SOLUTE FLOW R
ATE
FROM A
WELL
TO A
N AQ
UIFE
R LAYER
QSSBC
- SOLUTE FLOW RA
TE FOR
A SPECIFIED
VALU
E B.C.
QSW
- SOLUTE FLOW R
ATE
FROM
A W
ELL
TO T
HE A
QUIF
ERQWAV
- AV
ERAG
E FLOW R
ATE
FROM A WEL
L TO
AN
AQUI
FER
LAYER OV
ER A TIM
E STEP
QWLY
R -
FLUID
FLOW R
ATE
FROM
A W
ELL
TO A
N AQ
UIFE
R LA
YER
QWM
- FL
UID
MASS FL
OW R
ATE
FROM
A W
ELL
TO T
HE A
QUIF
ERQW
N -
FLUID
FLOW R
ATE
FROM
A W
ELL
TO T
HE A
QUIF
ER AT
TIME LE
VEL
NQWNP
- FLUID
FLOW
RATE O
F A
WELL A
T TIME LE
VEL
N+l
QWR
- FLUID
FLOW RA
TE IN
A W
ELL
RISE
RQWV
- VO
LUME
TRIC
FLUID
FLOW
RATE
FROM A
WELL
TO T
HE A
QUIF
ERRB
W -
RIGHT-HAND B
AND
WIDTH
FOR
EACH
EQUATION OF
THE A
4 MA
TRIX
RCPP
M -
HEAT
CAPACITY O
F TH
E PO
ROUS
ME
DIUM
PER U
NIT
VOLUME
RDAI
F - TRUE IF
AQU
IFER
INFLUENCE
B.C. INFORMATION
IS T
O BE
READ
RDCALC - TR
UE IF
CALCULATION
INFORMATION
IS T
O BE RE
AD
Tab
le 11.1
. D
efi
nit
ion li
st
for se
lecte
d
HST
3D p
rog
ram
va
ria
ble
s C
onti
nued
OJ oo
RDEC
HO -
TRUE
IF
A
READ-ECHO
FILE IS
TO
BE
WR
ITTE
NRD
FLXH
- TR
UE IF
HE
AT FLUX
DATA A
RE TO BE
READ
RDFL
XQ - TR
UE IF
FL
UID
FLUX DA
TA A
RE TO
BE
READ
RDFLXS - TRUE IF
SOLUTE FLUX DA
TA A
RE TO
BE
RE
ADRDLBC
- TR
UE IF
LE
AKAG
E B.C. DA
TA A
RE TO BE
RE
ADRD
MPDT
- TR
UE IF
CONTOUR
MAP
INFORMATION
IS TO BE
READ
RDPL
TP - TRUE IF
IN
FORM
ATIO
N FOR
PRES
SURE
PLOTS
IS TO
BE
RE
ADRD
SCBC
- TR
UE IF
SPECIFIED
SOLUTE CO
NCENTRATION
B.C.
DA
TA A
RE TO BE
RE
ADRD
SPBC
- TR
UE IF
SPECIFIED
PRES
SURE
B.
C. DATA A
RE TO BE
RE
ADRD
STBC
- TR
UE IF
SPECIFIED
TEMP
ERAT
URE
B.C.
DATA A
RE TO BE
RE
ADRD
VAIF
- TR
UE IF
A.I
.F.B
.C.
GEOMETRIC
FACTORS
ARE
TO BE
RE
ADRD
WDEF
- TR
UE IF
WELL DEFINITION INFORM
ATION
IS TO
BE
READ
RDWF
LO - TRUE IF
WELL FLOW RATE DATA A
RE TO
BE
READ
RDWHD
- TR
UE IF
WELL-HEAD
DATA
AT
LAND
SUR
FACE
ARE
TO BE
READ
REN
- RE
YNOLDS NUMBER FOR
FLOW IN
A
WELL
RI
SER
OR W
ELL
BORE
REST
RT - TR
UE IF
TH
IS IS
A RESTART
RUN
RF
- RI
GHT-HAND-SIDE
VECTOR FOR
THE
FLOW
EQ
UATI
ONRH
- RI
GHT-HAND-SIDE
VECTOR FOR
THE
HEAT EQ
UATI
ONRH1
- RI
GHT-HAND-SIDE
VECTOR A
UGMENTED W
ITH
CROS
S-DI
SPER
SIVE
FLUX TE
RMS
RHS
- RI
GHT-HAND-SIDE
VECTOR FOR
THE
SYSTEM EQUATIONS
RHSS
BC - RI
GHT-HAND-SIDE
VECTOR FO
R THE
SPECIFIED
VALU
E B.
C. NODES
RHSW
- RI
GHT-HAND-SIDE
VECT
OR FO
R THE
WELL-BORE
NODES
FOR
CYLINDRICAL
COORDINATE SYSTEM
RIOA
R -
RADIUS OF
THE
APPROXIMATE
BOUNDA
RY BE
TWEE
N THE
INNE
R AND
OUTER
AQUI
FER
REGI
ONS
FOR
A.I.F.B.C.
RM
- RA
DII
OF CELL B
OUNDARIES
IN THE
R-DIRECTION
FOR
THE
CYLINDRICAL
COORDINATE SYSTEM
RORW
2 -
EQUI
VALE
NT C
ELL
RADIUS DIVIDE
D BY
THE
WELL
RADIUS,
QUAN
TITY
SQ
UARE
DRPRN
- '(
'RS
-
RIGHT-HAND-SIDE
VECTOR FOR
THE
SOLUTE EQ
UATI
ONRS1
- RI
GHT-HAND-SIDE
VECT
OR A
UGME
NTED W
ITH
CROS
S-DI
SPER
SIVE
FLUX TE
RMS
SAVL
DO - TR
UE IF
ONLY TH
E LA
ST RESTART
OR CHECKPOINT DU
MP IS TO BE
SAVED
SCAL
MF - TR
UE IF
A
SCALED M
ASS
FRAC
TION IS T
O BE
USED FOR
INPU
T AND
OUTPUT
SDEC
AY - AM
OUNT
OF
SOLUTE DECAYED
DURING A
TIME ST
EPSH
RES
- RE
SIDUAL ERROR
IN TH
E HEAT EQ
UATI
ON FO
R CU
RREN
T TIME ST
EPSH
RESF
-
FRAC
TION
AL RE
SIDU
AL ER
ROR
IN THE
HEAT EQ
UATI
ON FOR
THE
CURENT T
IME
STEP
SIR
- SO
LUTE IN
THE
REGION
SIRO
- IN
ITIA
L SOLUTE IN
THE
REGION
SIRN
- SO
LUTE IN
THE REGION A
T TIME LEVEL
NSL
METH
-
INDE
X FOR
SELECTION
OF EQ
UATION
SO
LUTI
ON METHOD
SMCA
LC - TR
UE IF
AN A
BBRE
VIAT
ED CA
PACI
TANC
E-CO
EFFI
CIEN
T CALCULATION
IS TO BE
DO
NESO
LUTE
- TR
UE IF
SOLUTE TR
ANSP
ORT
IS BE
ING
SIMULATED
SOLVE
- TRUE IF
THE
TWO-LINE-SOR SOLVER IS TO SO
LVE
THE
EQUATIONS
SPRA
D - SP
ECTRAL RADIUS OF
THE
EQUA
TION
COEFFICIENT
MATRIX
SRES
- RE
SIDUAL ERROR
IN THE
FLOW EQUA
TION
FO
R THE
CURR
ENT
TIME
ST
EPSR
ESF
- FR
ACTIONAL RESIDUAL ER
ROR
IN THE
FLOW
EQ
UATI
ON FOR
THE
CURR
ENT
TIME STEP
SSRES
- RE
SIDUAL ER
ROR
IN THE
SOLUTE EQ
UATI
ON FOR
THE
CURR
ENT
TIME
STEP
SSRE
SF -
FRAC
TION
AL RE
SIDU
AL ER
ROR
IN THE
SOLUTE EQUATION FOR
THE
CURR
ENT
TIME
STEP
Tabl
e 11.1. Definition list for
selected HST3D program variables Continued
u> 00 oo
STOT
FI -
FLUID
INPUT
TO T
HE REGION D
URIN
G THE
CURR
ENT
TIME STEP
STOTFP -
FLUID
PRODUCED FR
OM T
HE REGION DURING T
HE CURRENT
TIME
STEP
STOT
HI -
HEAT INPUT
TO T
HE REGION DURING T
HE CU
RREN
T TIME STEP
STOTHP -
HEAT PRODUCED FROM T
HE REGION DURING T
HE CURRENT
TIME STEP
STOT
SI - SOLUTE INPUT
TO T
HE REGION D
URING
THE
CURRENT
TIME STEP
STOTSP - SOLUTE PRODUCED F
ROM
THE
REGION DURING T
HE CU
RREN
T TI
ME STEP
SUMMOB - SUM
OF A
LL W
ELL
MOBI
LITI
ES FO
R A
GIVEN
WELL
SUMW
I - SUM
OF A
LL W
ELL
INDI
CES
FOR
A GI
VEN
WELL
SVBC
- TR
UE IF A
SPECIFIED V
ALUE B.C. IS A
T TH
IS CE
LLSX
X -
FLUID
MASS
FLOW R
ATE
IN T
HE X-DIRECTION
SXXM
- FLUID
MASS
FLOW R
ATE
IN X-DIRECTION
BETW
EEN
CELL
AT
X(I-
l) AND
X(I)
SXXP
-
FLUID
MASS
FLOW R
ATE
IN X-DIRECTION
BETW
EEN
CELL
AT
X(I)
AN
D X(
I+1)
SYMI
D - CHARACTER
SYMBOL F
OR C
ONTO
UR M
AP BOUNDARIES A
ND N
ODES
SYY
- FLUID
MASS
FLOW R
ATE
IN T
HE Y-DIRECTION
SYYM
- FLUID
MASS
FLOW R
ATE
IN Y-DIRECTION
BETWEEN
CELL A
T Y(
J-l)
AND
Y(J)
SYYP
- FLUID
MASS
FLOW R
ATE
IN Y-DIRECTION
BETWEEN
CELL
AT
Y(J)
AN
D Y(J+1)
SZZ
- FL
UID
MASS
FL
OW RA
TE IN T
HE Z-DIRECTION
SZZM
- FLUID
MASS
FLOW R
ATE
IN Z-DIRECTION
BETWEEN
CELL A
T Z(
K-l)
AN
D Z(K)
SZZP
- FL
UID
MASS
FL
OW R
ATE
IN Z
-DIRECTION B
ETWE
EN CE
LL A
T Z(
K) AN
D Z(
K+1)
SZZW
- FLUID
MASS
FLOW R
ATE
UP T
HE W
ELL
BORE
T - TEMPERATURE
TO
- REFERENCE
TEMPERATURE
FOR
DENS
ITY
TO
- REFERENCE
TEMPERATURE
AT W
HICH DENSITY
DATA
ARE GIVEN
TOO
- TEMPERATURE
AT T
HE EN
D OF
A W
ELL
RISE
R, INITIAL
VALUE
TOH
- REFERENCE
TEMPERATURE
FOR
ENTH
ALPY
AND
VISCOSITY
TABW
R - TEMPERATURE
IN T
HE A
MBIE
NT M
EDIU
M AT
THE
BOTTOM O
F A
WELL
RISER
TAIF
- TEMPERATURE
IN T
HE OUTER
AQUI
FER
REGION FOR
A.I.F.B.C.
TAMB
K - TEMPERATURE
IN T
HE A
MBIE
NT M
EDIU
M AT A
GIVEN LE
VEL ALONG
THE
WELL R
ISER
TATW
R - TEMPERATURE
IN T
HE A
MBIE
NT M
EDIU
M AT T
HE T
OP OF
A W
ELL
RISE
RTC
- TIME V
ALUES
FOR
CALC
ULAT
ED V
ARIA
BLES
AT
A WELL
TCS
- TEMPERATURE
CALCULATED IN A
WEL
L AT LA
ND S
URFA
CE FOR TEMPORAL P
LOT
TCW
- TEMPERATURE
CALCULATED A
T A WE
LL D
ATUM F
OR T
EMPORAL
PLOT
TDEH
IR -
CUMULATIVE CHANGE IN EN
THAL
PY IN T
HE REGION
TDFI
R - CUMULATIVE CHANGE IN FLUID
IN T
HE REGION
TDSI
R - CU
MULA
TIVE
CH
ANGE
IN
SOLUTE
IN T
HE REGION
TDX
- DI
SPER
SIVE
CONDUCTANCE
IN X
-DIRECTION
TDXY
- CR
OSS-
DISP
ERSI
VE C
ONDUCTANCE
TDXZ
- CR
OSS-
DISP
ERSI
VE C
ONDUCTANCE
TOY
- DI
SPER
SIVE
CONDUCTANCE
IN Y-DIRECTION
TDYX
- CR
OSS-
DISP
ERSI
VE C
ONDUCTANCE
TDYZ
- CROS
S-DI
SPER
SIVE
CONDUCTANCE
TDZ
- DI
SPER
SIVE
CONDUCTANCE
IN Z
-DIRECTION
TDZX
- CR
OSS-
DISP
ERSI
VE C
ONDUCTANCE
TDZY
- CR
OSS-
DISP
ERSI
VE CONDUCTANCE
TEHD
T - TEMPERATURE
VALUES FO
R THE
TABL
E OF
EN
THAL
PY DEVIATION
Tabl
e 11.1. Definition list fo
r selected HST3D program variables Co
ntin
ued
OJ
00
TEHST
- TEMPERATURE
VALUES FO
R THE
TABL
E OF
EN
THAL
PY A
T SA
TURA
TION
TFLX
- TEMPERATURE
FOR
INFL
OW A
T A
SPECIFIED
FLUX B.C.
TFRE
S - CUMULATIVE RE
SIDU
AL ER
ROR
IN THE
FLOW EQUATION
TFRESF -
FRAC
TION
AL C
UMULATIVE
RESIDUAL ERROR
IN T
HE FLOW EQUATION
TFW
- CONDUCTANCE
IN WELL BORE FO
R CYLINDRICAL
SYST
EMTF
X -
FLUI
D CONDUCTANCE
IN X-DIRECTION
TFY
- FLUID
CONDUCTANCE
IN Y-DIRECTION
TFZ
- FL
UID
CONDUCTANCE
IN Z-DIRECTION
THCBC
- TEMPERATURE
PROFILE
FOR
FIRS
T PROBLEM
FOR
HEAT CO
NDUC
TION
B.C.
THETXZ - ANGLE
BETW
EEN
X-AX
IS A
ND G
RAVITATIONAL V
ECTO
RTHETYZ - ANGLE
BETWEEN
Y-AXIS A
ND GRAVITATIONAL
VECTOR
THETZZ - ANGLE
BETWEEN
Z-AXIS AN
D GRAVITATIONAL
VECTOR
THRES
- CU
MULA
TIVE
RE
SIDU
AL ERROR
IN TH
E HEAT EQUATION
THRESF -
FRAC
TION
AL C
UMULATIVE
RESI
DUAL
ER
ROR
IN T
HE HE
AT E
QUATION
THRU
- TR
UE IF T
HIS
IS T
HE END
OF TH
E SI
MULA
TION
THX
- TH
ERMA
L CONDUCTANCE
IN X-DIRECTION
THXY
- CR
OSS-
DISP
ERSI
VE TH
ERMA
L CONDUCTANCE
THXZ
- CROSS-DISPERSIVE TH
ERMA
L CONDUCTANCE
THY
- TH
ERMA
L CONDUCTANCE
IN Y-DIRECTION
THYX
- CROS
S-DI
SPER
SIVE
TH
ERMA
L CONDUCTANCE
THYZ
- CROS
S-DI
SPER
SIVE
TH
ERMA
L CONDUCTANCE
THZ
- TH
ERMA
L CONDUCTANCE
IN Z-DIRECTION
THZX
- CROS
S-DI
SPER
SIVE
TH
ERMA
L CONDUCTANCE
THZY
- CR
OSS-
DISP
ERSI
VE T
HERM
AL C
ONDUCTANCE
TILT
- TR
UE IF T
HE CO
ORDI
NATE
SY
STEM
IS
TILTED SO
THAT
THE
GRAV
ITAT
IONA
L VECTOR D
OES
NOT
POIN
T IN T
HE NEGATIVE Z-DIRECTION
TIMCHG - TI
ME AT
WHICH N
EW TRANSIENT
DATA
ARE
TO
BE RE
ADTIMDAY -
TIME IN
DAYS
TIME
- TI
ME VALUE
TIME
D - DI
MENS
IONL
ESS
TIME
TIMEDN - DI
MENS
IONL
ESS
TIME AT T
IME
LEVE
L N
TIMRST -
TIME
AT W
HICH A
RES
TART
RE
CORD
IS
TO
BE
WRITTEN
TITLE
- TI
TLE
FOR
THE
SIMULATION RU
NTITLED - TI
TLE
FOR
THE
ORIG
INAL
SIM
ULAT
ION
THAT
IS
BE
ING
RESTARTED
TLBC
- TEMPERATURE
AT THE
OTHER
SIDE OF AN
CONFINING
LAYER
FOR
A LE
AKAG
E B.
C.TLBL
- LABEL
FOR
TEMPERATURE
FOR
ARRA
Y PRINTOUTS
TM1
- CONDUCTANCE
COEFFICIENT
VECT
OR F
OR T
WO-LINE
SOR
SOLV
ERTM
2 -
CONDUCTANCE
COEFFICIENT
VECT
OR FO
R TW
O-LI
NE SOR
SOLV
ERTMLBL
- LABEL
FOR
TIME
FO
R TE
MPOR
AL PLOTS
TNP
- TEMPERATURE
FOR
SPEC
IFIE
D VA
LUE
B.C.
TO
- TIME VALUES FOR
OBSE
RVED
VAR
IABL
ES IN
A
WELL
FOR
TEMPORAL PL
OTS
TOL
- TO
LERA
NCE
FOR
AN ITERATIVE
CALC
ULAT
ION
TOLDLN - TO
LERA
NCE
ON DENSITY
CHAN
GES
FOR
CONVERGENCE
OF TH
E SO
LUTI
ON CYCLE
OF THE
THRE
E SY
STEM
EQ
UATI
ONS
TOLDNC - TOLERANCE
ON DENSITY
CHAN
GES
DUE
TO S
OLUTE
CONC
ENTR
ATIO
N CHANGES
FOR
THE
SOLU
TION
CY
CLE
OF T
HE FL
OW A
ND S
OLUT
E EQUATIONS
TOLDNT - TOLERANCE
ON DENSITY
CHAN
GES
DUE
TO T
EMPERATURE CHANGES
FOR
THE
SOLUTION CYCLE
OF THE
FLOW A
ND HE
AT EQUATIONS
TOLDPW - TO
LERA
NCE
ON PRESSURE CHANGES
FOR
THE
WELL BORE CALCULATION
Tabl
e 11.1. Definition li
st fo
r selected HST3D program variables Co
ntin
ued
TOLFPW - TO
LERA
NCE
ON FR
ACTI
ONAL
PRE
SSUR
E CH
ANGE
S FOR
THE
WELL
-BOR
E CALCULATION
TOLQ
W - TO
LERA
NCE
ON FLOW R
ATE
CHAN
GES
FOR
THE
WELL-BORE
CALCULATION
TOS
- TEMP
ERAT
URES
OB
SERV
ED IN A
WELL
AT T
HE LA
ND SU
RFAC
E FOR
TEMP
ORAL
PLOT
TOTF
I - CU
MULA
TIVE
FLUID
INPUT
TO T
HE REGION
TOTF
P -
CUMULATIVE FLUID
PRODUCED FROM T
HE REGION
TOTH
I -
CUMULATIVE HEAT IN
PUT
TO T
HE REGION
TOTH
P - CU
MULA
TIVE
HEAT P
RODU
CED
FROM T
HE REGION
TOTS
I -
CUMULATIVE SO
LUTE
INPUT
TO T
HE REGION
TOTS
P -
CUMULATIVE SOLUTE PRODUCED FROM T
HE REGION
TOTW
FI -
CUMULATIVE FLUID
INJECTED B
Y TH
E WELLS
TOTWFP -
CUMULATIVE FLUID
PRODUCED B
Y TH
E WE
LLS
TOTW
HI - CU
MULA
TIVE
HE
AT IN
JECT
ED BY TH
E WE
LLS
TOTWHP -
CUMU
LATI
VE HE
AT P
RODU
CED
BY TH
E WE
LLS
TOTW
SI - CU
MULA
TIVE
SO
LUTE
IN
JECT
ED BY TH
E WELLS
TOTWSP -
CUMULATIVE SOLUTE PRODUCED BY T
HE WELLS
TOW
- TE
MPER
ATUR
ES OBSERVED IN A
WELL
AT T
HE WELL D
ATUM
FOR
TEMP
ORAL
PLO
TTP
1 - CONDUCTANCE
COEFFICIENT
VECT
OR FO
R TW
O-LI
NE SOR
SOLV
ERTP2
- CONDUCTANCE
COEFFICIENT
VECT
OR F
OR TWO-LINE
SOR
SOLV
ERTPHCBC - TEMPERATURE
PROF
ILE
FOR
SECOND PROBLEM
FOR
HEAT C
ONDU
CTIO
N B.C.
TQFAIF - CUMULATIVE FLUID
INPU
T FROM A
.I.F.B.C.
TQFF
BC - CU
MULA
TIVE
FLUID
INPUT
FROM SP
ECIF
IED
FLUX B
.C.
TQFINJ - TO
TAL
FLUID
INJE
CTIO
N RATE FOR AL
L WE
LLS
TQFL
BC - CU
MULA
TIVE
FL
UID
INPU
T FROM LE
AKAG
E B.C.
TQFPRO -
TO
TAL
FLUID
PRODUCTION RA
TE FROM A
LL W
ELLS
TQFSBC -
CUMULATIVE FL
UID
INPU
T FROM SP
ECIF
IED
VALUE
B.C.
TQHAIF - CUMULATIVE HEAT IN
PUT
FROM A
.I.F.B.C.
TQHFBC -
CUMULATIVE HEAT IN
PUT
FROM
SPE
CIFI
ED F
LUX
B.C.
TQHHBC - CU
MULA
TIVE
HE
AT IN
PUT
FROM H
EAT
CONDUCTION B.C.
TQHINJ - TO
TAL
HEAT
INJECTION
RATE FROM A
LL W
ELLS
TQHLBC -
CUMULATIVE HEAT INPUT
FROM LEAKAGE
B.C.
TQHPRO - TOTAL
HEAT PRODUCTION RATE FROM A
LL W
ELLS
TQHSBC - CU
MULA
TIVE
HEAT IN
PUT
FROM
SPE
CIFI
ED V
ALUE B.C.
TQSAIF -
CUMULATIVE SO
LUTE
IN
PUT
FROM A
.I.F.B.C.
TQSFBC -
CUMU
LATI
VE SO
LUTE
IN
PUT
FROM S
PECI
FIED
FLU
X B.C.
TQSINJ - TO
TAL
SOLUTE INJECTION
RATE FROM A
LL W
ELLS
TQSL
BC -
CUMULATIVE SO
LUTE
IN
PUT
FROM LEAKAGE
B.C.
TQSPRO - TO
TAL
SOLUTE PRODUCTION RATE FR
OM A
LL W
ELLS
TQSSBC - CU
MULA
TIVE
SOLUTE INPUT
FROM S
PECI
FIED
VALUE B.C.
TRVI
S -
REFERENCE
TEMPERATURE
AT W
HICH
VISCOSITY DATA A
RE GI
VEN
TSBC
- TEMPERATURE
FOR
INFL
OW A
T A
SPECIFIED
PRESSURE B.C.
TSLB
L -
LABE
L FOR
WELL T
EMPERATURE AT
LAND S
URFACE FOR
TEMP
ORAL
PLOTS
TSMAX
- MAXIMUM
TEMPERATURE
AT LAND SU
RFAC
E FO
R SCALING
TEMPORAL PLOTS
TSMIN
- MINI
MUM
TEMPERATURE
AT LA
ND SU
RFAC
E FO
R SCALING
TEMPORAL PLOTS
TSRES
- CU
MULA
TIVE
RESIDUAL E
RROR
IN T
HE SOLUTE EQ
UATI
ONTSRESF -
FRAC
TION
AL C
UMUL
ATIV
E ER
ROR
IN T
HE S
OLUTE
EQUATION
Table 11.1. Definition list for selected HST3D program variables Continued
TSX
- SOLUTE CO
NDUC
TANC
E IN X-DIRECTION
TSXY
- CROS
S-DI
SPER
SIVE
SOLUTE CONDUCTANCE
TSXZ
- CROS
S-DI
SPER
SIVE
SOLUTE CONDUCTANCE
TSY
- SOLUTE CO
NDUC
TANC
E IN Y-DIRECTION
TSYX
- CROS
S-DI
SPER
SIVE
SOLUTE CONDUCTANCE
TSYZ
- CROS
S-DI
SPER
SIVE
SOLUTE CONDUCTANCE
TSZ
- SOLUTE CONDUCTANCE
IN Z-DIRECTION
TSZX
- CROS
S-DI
SPER
SIVE
SOLUTE CONDUCTANCE
TSZY
- CROS
S-DI
SPER
SIVE
SOLUTE CONDUCTANCE
TVD
- TEMPERATURE
VS.
DEPT
H VALUES FO
R IN
ITIA
L CONDITION
TVFO
- TEMPERATURE
VALUES FOR
VISC
OSIT
Y VS
. TEMPERATURE
DATA
AT
MINIMUM
SOLU
TE CO
NCEN
TRAT
ION
TVF1
- TEMPERATURE
VALUES FO
R VISCOSITY
VS.
TEMPERATURE
DATA A
T MA
XIMU
M SOLUTE CO
NCEN
TRAT
ION
TVZHC
- TEMPERATURE
VS.
DISTANCE OUTWARD
FROM
HEA
T CO
NDUC
TION
B.C. FO
R INITIAL
COND
ITIO
NTWKT
- TEMPERATURE
IN A
WELL
AT THE
WELL D
ATUM
TWLB
L -
LABEL
FOR
WELL
TEMPERATURE A
T WELL D
ATUM FO
R TEMPORAL PLOTS
TWMAX
- MA
XIMU
M TEMPERATURE
AT W
ELL
DATU
M FO
R SCALING
TEMPORAL PL
OTS
TWMI
N - MI
NIMU
M TEMPERATURE
AT WE
LL D
ATUM
FO
R SCALING
TEMP
ORAL
PLOTS
TWOPI
- '6
.28.
..'
TWREND - TEMPERATURE
AT T
HE EN
D OF
A W
ELL
RISE
R PI
PETW
RK
- TEMPERATURE
IN A
WEL
L RI
SER
AT A
GIVEN LEVEL
TWSRKT - TEMPERATURE
AT LA
ND S
URFACE OR
AT
WELL D
ATUM
TWSU
R - TEMPERATURE
IN A
WELL
AT T
HE LAND S
URFACE
TX
- FLUID
COND
UCTA
NCE
FACTOR IN T
HE X-
DIRE
CTIO
NTY
-
FLUID
CONDUCTANCE
FACTOR IN
THE Y-
DIRE
CTIO
NTZ
-
FLUI
D CONDUCTANCE
FACTOR IN T
HE Z-DIRECTION
THE
UNDE
FINE
D 'U
1 VARIABLES
ARE
USED FO
R TE
MPOR
ARY
STOR
AGE
UCROSC -
CROS
S-DI
SPER
SIVE
SOLUTE FL
UX
UCROST - CR
OSS-
DISP
ERSI
VE H
EAT
FLUX
UNIGRX - TRUE IF
A U
NIFORM G
RID
IN T
HE X-
DIRE
CTIO
N IS
DESIRED
UNIGRY - TRUE IF A
UNI
FORM
GRI
D IN T
HE Y-
DIRE
CTIO
N IS DESIRED
UNIGRZ - TRUE IF
A U
NIFO
RM G
RID
IN T
HE Z-
DIRE
CTIO
N IS
DE
SIRE
D UNITEP -
UNIT
FO
R EN
ERGY
PE
R UNIT M
ASS
UNIT
H -
UNIT
FOR
HEAT
UNITHF -
UNIT F
OR H
EAT
FLOW
RATE
UNITL
- UN
IT FOR
LENG
TH
UNITM
- UN
IT FO
R MA
SS
UNITP
- UNIT FOR
PRESSURE
UNIT
T -
UNIT
FOR
TEMPERATURE
UNITTM -
UNIT FOR
TIME
UNITVS -
UNIT
FOR
VISCOSITY
VA
- SY
STEM
EQ
UATI
ON COEFFICIENT
MATR
IX
VAIF
C - GE
OMET
RIC
FACTOR F
OR A
.I.F.B.C.
VAR
- VA
RIAB
LE FOR AR
RAY
INPU
TVASBC
- SY
STEM
EQ
UATI
ON COEFFICIENT
MATR
IX FO
R NODES
WITH
SPECIFIED B
.C.
VAW
- SY
STEM
EQ
UATI
ON COEFFICIENT
MATR
IX FO
R NO
DES
ALONG
WELL
BORE IN CYLINDRICAL
COORDINATES
Tabl
e 11.1. De
fini
tion
li
st for
sele
cted
HST3D program variables Co
ntin
ued
OJ vo
VDAT
A - VI
SCOS
ITY
DATA
VELWRK - VE
LOCI
TY OF
FLO
W IN
A W
ELL
RISE
R AT
A G
IVEN LEVEL
VIS
- VI
SCOS
ITY
VISCTR - VI
SCOS
ITY
VS.
SOLUTE CO
NCEN
TRAT
ION
DATA AT
REFERENCE
TEMPERATURE
VISLBC -
VI
SCOS
ITY
AT O
THER S
IDE
OF CO
NFIN
ING
LAYER
FOR
LEAKAGE
B.C.
VISO
AR -
VI
SCOS
ITY
IN OUTER
AQUI
FER
REGION FOR A.
I.F.
B.C.
VISTFO - VI
SCOS
ITY
VS.
TEMPERATURE
DATA
AT
MINIMUM
SOLUTE CO
NCEN
TRAT
ION
VISTF1 - VI
SCOS
ITY
VS.
TEMPERATURE
DATA A
T MA
XIMU
M SO
LUTE
CO
NCEN
TRAT
ION
VPA
- VARIABLY PARTITIONED
ARRAY
VREF
- REFERENCE
VISCOSITY
VSTLOG -
LOGARITHM
OF V
ISCOSITY
VXX
- INTERSTITIAL V
ELOC
ITY
IN T
HE X-
DIRE
CTIO
NVY
Y -
INTERSTITIAL V
ELOCITY
IN T
HE Y-
DIRE
CTIO
NVZ
Z -
INTE
RSTI
TIAL
VELOCITY
IN TH
E Z-
DIRE
CTIO
NWO
- MI
NIMU
M MASS FR
ACTI
ON FO
R SCAL
ING
Wl
- MAXIMUM
MASS FR
ACTI
ON FO
R SCAL
ING
WBOD
- WE
LL-B
ORE
OUTE
R DIAMETER
WCAI
F -
CUMU
LATI
VE IN
FLOW
AT
AQUI
FER
INFL
UENC
E FU
NCTI
ON B.C.
WCF
- WE
LL C
OMPLETION
FACTOR F
OR A
GIVEN LAYER
WCLBL1 -
LABEL
DESCRIBING W
ELL
CALCULATION
TYPE
WCLBL2 -
LABEL
DESC
RIBI
NG W
ELL-
FLOW
ALLOCATION
METHOD
WFICUM -
CUMULATIVE FLUID
INJE
CTED
BY A
WEL
LWFPCUM -
CUMULATIVE FLUID
PRODUCED B
Y A
WELL
WHICUM -
CUMU
LATI
VE HEAT INJECTED BY
A
WELL
WHPCUM -
CUMU
LATI
VE HEAT P
RODUCED
BY A
WEL
LWI
- WELL INDEX
WIDLBL -
WE
LL IDENTIFICATION LABEL
FOR
TEMP
ORAL
PLO
TWQMETH -
INDE
X OF
WELL-FLOW
CALCULATIO
N METHOD
WRANGL -
WELL-RISER A
NGLE
WITH
THE
GRAVITATIONAL
VECT
ORWRCALC -
TR
UE IF WELL-RISER C
ALCULATIONS
ARE
TO BE PERFORMED
WRID
- WELL-RISER P
IPE
INSI
DE DI
AMETER
WRID
T - WELL-RISER P
IPE
INSI
DE DI
AMET
ER FO
R A
GIVEN
WELL
WRISL
- WE
LL-R
ISER
PI
PE LE
NGTH
WRRUF
- WE
LL-R
ISER
PI
PE ROUGHNESS
PARA
METE
RWSICUM -
CUMU
LATI
VE SO
LUTE
IN
JECT
ED BY A
WEL
LWSPCUM -
CUMULATIVE S
OLUTE
PRODUCED BY A
WELL
WT
- WEIGHT FACTOR F
OR S
PATI
AL D
ISCR
ETIZ
ATIO
NX
- X-
COOR
DINA
TE NO
DE LO
CATI
ONS
XC
- X-
COOR
DINA
TE LO
CATI
ON OF
CA
LCUL
ATED
DATA
FOR
TEMP
ORAL
PL
OTXI
- DI
MENS
IONL
ESS
TIME PARAMETER
FOR
HEAT T
RANS
FER
FROM W
ELL
RISE
RXL
BL
- LABEL
FOR
X-AX
IS FO
R TE
MPOR
AL PLOTS
XO
- X-
COOR
DINA
TE LO
CATI
ON OF OB
SERV
ED DA
TA FO
R TE
MPOR
AL PLOTS
XX
- SOLUTION VECTOR F
ROM
TWO-LINE SOR
SOLVER
XXN
- NE
W SOLUTION VECTOR F
ROM
TWO-
LINE
SO
R SOLVER
Y -
Y-COORDINATE NO
DE LOCATIONS
Table 11.1. Definition li
st for selected HST3D program variables Continued
YC
- Y-
COOR
DINA
TE LO
CATI
ONS
OF CALCULATED D
ATA
FOR TE
MPOR
AL P
LOTS
YLBL
- LA
BEL
FOR
Y-AXIS FOR TE
MPOR
AL P
LOTS
YO
- Y-
COOR
DINA
TE LO
CATI
ON O
F OB
SERV
ED D
ATA
FOR TEMPORAL P
LOTS
YPOSUP - TR
UE IF THE
Y-AXIS IS
POSITIVE UPWARD FOR MAPS
YY
- DEPENDENT
VARIABLE V
ECTO
R FO
R WE
LL R
ISER
INTEGRATION
Z - Z-
COORDINATE NO
DE LO
CATI
ONS
ZCHARS - CH
ARAC
TER ARRAY
FOR
ZEBRA-STRIPED
CONT
OUR
MAPS
ZEBR
A - TR
UE IF ZO
NED
CONT
OUR
MAPS A
RE T
O BE ZEBRA
STRI
PED
WITH A
LTERNATING S
YMBO
L AND
BLAN
K ZONES
ZELB
C -
ELEVATION
OF T
HE O
UTER S
URFA
CE O
F A
CONF
ININ
G LA
YER
FOR
A LE
AKAG
E B.C.
ZHCBC
- NODE LOCATIONS
OUTSIDE
THE
REGION IN A
NORMAL
DIRE
CTIO
N TO
A H
EAT
CONDUCTION BO
UNDA
RY FACE FO
R HEAT CONDUCTION B.C.
ZPINIT - Z-
COOR
DINA
TE LO
CATI
ON O
F SPECIFIED
INITIAL
PRES
SURE
FO
R HYDROSTATIC
INIT
IAL
CONDITIONS
ZPOSUP -
TRUE IF T
HE Z
-AXIS
IS POSITIVE U
PWARD
FOR
MAPS
ZT
- Z-
COOR
DINA
TE LOCATIONS
OF T
EMPERATURE PR
OFIL
E DATA FOR
INIT
IAL
CONDITIONS
ZTHC
- LO
CATI
ONS
ALON
G THE
OUTW
ARD
NORMAL T
O HE
AT-C
ONDU
CTIO
N BO
UNDA
RY FACES
OF T
EMPERATURE PROFILE
DATA
FOR
INITIAL
CONDITIONS
ZWK
- LO
CATI
ON A
LONG A
WELL-RISER
PIPE
ZWKT
- Z-
COOR
DINA
TE LO
CATI
ON O
F A
WELL
DAT
UM
OJ vo to
11.2 CROSS-REFERENCE LIST OF VARIABLES
The following cross-reference list (table 11.2) shows in which sub
programs each variable appears. Actual line numbers within each subprogram
are not provided; however, every FORTRAN compiler can provide a local cross-
reference map for a given subprogram. The first column contains the variable
names and the second column lists the subprograms that employ each variable.
The third column gives the variable type and the dimension, if an array.
Some variables are scalars in some subprograms and arrays in others; however,
the definitions are the same.
394
Table
11.2 Cross-reference li
st o
f variables
LO
Vari
able
name
A AO Al A1HC
A2 A2HC
A3HC
A4 AA1
AA2
AA3
AA4
Refe
ren
cing
prog
rams
MAP2
D
MAP2D
BSOD
EIN
TERP
MAP2D
APLYBC
INIT
2
BSOD
EIN
TERP
APLYBC
INIT
2
APLYBC
INIT
2
D4DE
S
APLYBC
APLYBC
APLYBC
APLYBC
Variable
type
REAL
*8 DIMENSIONC*,*)
REAL*8
REAL*8
REAL*8
REAL
*8
REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL*8
REAL*8
REAL
*8 DI
MENS
IONC
*)REAL*8 DI
MENS
IONC
*)
REAL*8 DI
MENS
IONC
*)RE
AL*8
DI
MENS
IONC
*)
REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL*8 DI
MENS
IONC
*)
Refer-
Vari
able
encing
name
programs
AAIF
APLYBC
ASEMBL
SUMCAL
ABOAR
HST3D
APLYBC
DUMP
ETOM
1IN
IT2
READ1
READ2
WRITE2
ABPM
ETOM
1IN
IT2
READ2
WRITE2
ACHR
MAP2D
ALBC
APLYBC
ASEM
BLSUMCAL
ALLOUT
ERROR2
ALPHL
COEFF
ETOM1
READ2
WRITE2
Variable
type
REAL
*8 DIMENSIONC*)
REAL
*8 DIMENSIONC*)
REAL
*8 DIMENSIONC*)
REAL*8
REAL
*8RE
AL*8
REAL*8
REAL
*8RE
AL*8
REAL
*8RE
AL*8
REAL
*8 DI
MENS
IONC
*)REAL*8 DI
MENS
IONC
*)RE
AL*8
DIMENSIONS)
REAL
*8 DIMENSIONC*)
REAL
*8
REAL
*8 DIMENSIONC*)
REAL
*8 DIMENSIONC*)
REAL
*8 DIMENSIONC*)
LOGI
CAL*
4
REAL*8 DI
MENS
IONC
*)REAL*8 DI
MENS
ION^
*)REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
Tabl
e 11
.2--
Cros
s-re
fere
nce
list of
variables--Continued
Variable
name
AMAX
AMAXN
AMIN
AMINN
AMN
AMX
ANGOAR
Refer
encing
prog
rams
HST3D
ETOM
2IN
IT3
MAP2D
READS
WRITES
WRIT
ES
MAP2D
HST3D
ETOM2
INIT
3MAP2D
READ
SWRITES
WRIT
ES
MAP2D
MAP2D
MAP2D
HST3D
APLYBC
DUMP
ETOM
1IN
IT2
READ
1RE
AD2
WRITE2
Vari
able
ty
pe
REAL
*8 DI
MENS
ION (3
)RE
AL*8
DIMENSION(S)
REAL
*8 DI
MENS
ION (3
)RE
AL*8
REAL*8 DIMENSION(S)
REAL*8 DIMENSION(S)
REAL*8 DIMENSION(S)
REAL*8
REAL
*8 DIMENSION (3
)REAL*8 DI
MENS
ION (3
) REAL*8 DIMENSION (3
)REAL*8
REAL*8 DI
MENS
ION(
S)REAL*8 DIMENSION (3
)REAL*8 DI
MENS
ION(
S)
REAL*8
REALMS
REAL*8
REAL*8
REALMS
REAL
*8REAL*8
REAL*8
REAL*8
REALMS
REAL*8
Variable
name
APLOT
APLOT1
APLOT2
APLOT3
APLO
T4
APRNT
ARGR
ID
ARRAY
ARWB
ARX
ARXBC
ARXF
BC
Refe
r
enci
ng
programs
MAP2D
MAP2D
MAP2D
MAP2D
MAP2D
PRNTAR
WRITE2
WRITES
WRIT
ES
HST3D
INIT
2READ2
WRITE2
PRNTAR
WELL
SS
COEF
FIN
IT2
INIT
2
INIT
2IN
IT3
Vari
able
type
REAL
*8 DIMENSION (*
,*)
REAL*8
REAL*8
REAL*8
REALMS
REALMS DIMENSION(IO)
REALMS DIMENSIONC*)
REAL*8 DI
MENS
ION(
-V)
REAL
*8 DI
MENS
IONC
*)
LOGI
CAL*
4LOGICAL*4
LOGICAL*4
LOGICAL*4
REAL*8 DI
MENS
ION (*)
REALMS
REAL
*8 DIMENSIONC*)
REALMS DI
MENS
IONC
*)
REAL*8 DIMENSION^)
REAL*8 DIMENSION^)
REAL
*8 DI
MENS
ION^
*)
Tabl
e 11.2--Cross-reference
list
of
variables Continued
Vari
able
na
me
ARY
ARYBC
ARYFBC
ARZ
ARZBC
ARZFBC
AST
AUTOTS
BO Bl
Refe
r
enci
ng
prog
rams
COEF
FIN
IT2
INIT
2
INIT
2 IN
IT3
COEF
F IN
IT2
INIT
2
INIT
2 IN
IT3
PLOT
ZONP
LT
HST3
DCO
EFF
ERRO
RSET
OM2
INIT
3READ3
WRITES
BSOD
E
BSOD
EWFDYDZ
Variable
type
REAL
*8 DI
MENS
ION S)
REAL
*8 DIMENSIONS)
REAL*8 DIMENSIONS)
REAL*8 DI
MENS
ION (*
) REAL*8 DIMENSIONS)
REAL*8 DI
MENS
ION (*
) REAL*8 DI
MENS
ION (*)
REAL*8 DIMENSIONS)
REAL*8 DIMENSIONS)
REAL*8 DIMENSIONS)
CHAR
ACTE
R*!
CHAR
ACTE
R*!
LOGICAL*4
LOGI
CAL*4
LOGI
CAL*4
LOGICAL*4
LOGI
CAL*4
LOGI
CAL*4
LOGICAL*4
REAL
*8
REAL*8
REAL*8
Refe
r-
Vari
able
en
cing
na
me
prog
rams
BAIF
AP
LYBC
ASEMBL
SUMC
AL
BBAIF
HST3D
APLYBC
BLOC
KDAT
ADU
MP
READ1
READ2
WRITE2
BBLBC
APLYBC
ASEMBL
INIT
2SU
MCAL
WRITE2
BETA
APLYBC
BLANK
MAP2D
PLOT
PRNTAR
WRITES
ZONPLT
BLANKL
PLOT
BLBC
APLYBC
ASEMBL
SUMCAL
Variable
type
REAL
*8 DIMENSIONS)
REAL
*8 DIMENSIONS)
REAL
*8 DIMENSIONS)
REAL
*8 DIMENSIONS: 3)
REAL
*8 DIMENSION (0
:3)
REAL
*8 DIMENSION (0
:3)
REAL
*8 DIMENSION(0:3)
REAL
*8 DIMENSION (0
:3)
REAL
*8 DI
MENS
ION (0
:3)
REAL
*8 DIMENSION(0:3)
REAL
*8 DI
MENS
ION (*)
REAL
*8 DIMENSIONS)
REAL
*8 DIMENSIONS)
REAL
MS DIMENSIONS)
REAL
*8 DIMENSION(*)
REAL
*8 DIMENSION(IO)
CHARACTER*!
CHARACTER*!
CHARACTER*!
CHAR
ACTE
R*!
1CHARACTER*!
CHAR
ACTE
R*51
REAL
*8 DIMENSIONS)
REAL*8 DIMENSIONS)
REAL
*8 DIMENSION(*)
B2WFDYDZ
REAL*8
Tabl
e 11.2 Cross-reference list o
f va
riab
les
Cont
inued
LO
vo
00
Variable
name
BOAR
BP BT BV BVO
Refe
r
encing
programs
HST3D
APLYBC
DUMP
ETOM
1IN
IT2
READ
1RE
AD2
WRIT
E2
HST3D
DUMP
ETOM1
INIT2
READ1
READ
2 WR
ITE2
HST3D
DUMP
ETOM1
INIT2
READ1
READ2
WRIT
E2
VSINIT
HST3
DDU
MP
INIT
2RE
AD1
VISC
OS
Vari
able
ty
pe
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REALMS
REAL
*8
Refer-
Variable
encing
name
prog
rams
BV1
HST3D
DUMP
INIT
2READ1
VISCOS
C APLYBC
ASEM
BLCALCC
COEFF
CRSD
SP
INIT
2 IT
ER
READ2
SUMCAL
VISCOS
WBBAL
WELLSS
WRIT
E2
WRIT
ES
ZONPLT
COO
HST3D
WBBAL
WELLSS
WELRIS
WFDYDZ
Cl
ZONP
LT
Vari
able
ty
pe
REAL*8
REAL*8
REAL*8
REAL
*8REAL*8
REAL*8 DI
MENS
ION(
*)REAL*8 DIMENSIONS)
REAL*8
REAL*8 DIMENSION (*)
REAL*8 DIMENSION (*
) REAL*8 DI
MENS
ION(
*)
REAL*8 DIMENSIONS)
REAL*8 DIMENSION (*)
REAL*8 DIMENSIONS)
REAL*8
REAL*8 DIMENSIONS)
REAL*8 D
IMEN
SION
(*)
REAL*8 DIMENSIONS)
REAL*8 DIMENSIONS)
REAL
*8
REAL«8
REAL
*8REAL*8
REAL*8
REAL*8
REALMS
Tabl
e 11.2 Cross-reference li
st of
var
iabl
es Continued
Refe
r-
Vari
able
en
cing
name
programs
Cll
HST3D
ASEMBL
CALC
CWFDYDZ
C12
HST3D
ASEMBL
CALC
CWF
DYDZ
C13
HST3
DASEMBL
CALC
Cvo
C2
ZONPLT
vo
C21
HST3D
ASEMBL
CALC
CWFDYDZ
C22
HST3D
ASEMBL
CALC
CWFDYDZ
C23
HST3D
ASEMBL
CALC
C
C24
HST3
DASEMBL
CALC
C
Variable
type
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8
REAL*8
REAL*8
REAL*8
REAL
*8
REAL
*8REAL*8
REAL*8
REAL
*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
Refer-
Variable
encing
name
pr
ogra
ms
C31
HST3D
ASEM
BLCALCC
C32
HST3D
ASEM
BLCALCC
C33
HST3D
ASEM
BLCALCC
C34
HST3D
ASEM
BLCALCC
C35
HST3D
ASEMBL
CALCC
CAIF
APLYBC
ASEM
BLIN
IT3
SUMCAL
CC24
AS
EMBL
CC34
ASEM
BL
CC35
AS
EMBL
Vari
able
type
REAL
*8REAL*8
REAL
*8
REAL
*8REAL*8
REAL*8
REAL*8
» REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL*8 DI
MENS
IONC
*)
REAL*8 DI
MENS
IONC
*)
REAL*8 DI
MENS
IONC
*)
REAL*8 DI
MENS
IONC
*)
Tabl
e 11
.2 C
ross
-ref
eren
ce li
st of
var
iabl
es C
ontinu
ed
o
o
Vari
able
na
me
CCLBL
CCW
CFLX
CHAPRT
CHAR
C
CHAR
S
CHK1
CHKPTD
CHU3
CHU4
CHU5
CHU6
CI
Refe
r
enci
ng
prog
rams
PLOT
OC
PLOT
OC
APLYBC
INIT
3SU
MCAL
WRITE3
WRITES
WRIT
ES
READ
!
MAP2D
WRITES
HST3D
CLOS
EDUMP
READ
3
WRITES
WRITES
WRITES
WRIT
ES
D4DE
SORDER
Vari
able
Va
riab
le
type
na
me
CHAR
ACTE
R*50
CIBC
REAL
*8 DI
MENS
IONC
*)
REAL
*8 DI
MENS
IONC
*)RE
AL*8
DIMENSIONC*)
REAL
*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL
*8 DIMENSIONC*)
CHAR
ACTE
R*12
DIMENSIONC 10)
CHARACTER*!
CHARACTER*!
DIME
NSIO
N CO
: 31
) CI
BC1
CHAR
ACTE
R*2
CIBC
2
LOGICAL*4
CICALL
LOGI
CAL*
4LO
GICAL*
4 CL
BCLO
GICAL*
4
CHAR
ACTE
R* 12
CHARACTER*8
CLIN
ECH
ARAC
TER*
8CM
AXCH
ARAC
TER*
8CMIN
INTEGER*4
DIME
NSIO
NC 6,*)
INTEGER*4
DIME
NSIO
NC6,
*)
CMX
Refe
r
encing
programs
APLYBC
ASEMBL
ERROR2
ERRORS
ETOM
1INIT2
INIT3
SBCFLO
SUMC
ALWB
CFLO
WRITE2
WRITES
WRITES
SOR2
L
SOR2L
IREW
I
APLY
BCASEMBL
INIT3
SUMCAL
WRITES
MAP2D
PLOTOC
PLOTOC
ASEMBL
Variable
type
CHAR
ACTE
R*9
CHARACTER*9
CHARACTER*9
CHAR
ACTE
R*9
CHARACTER*9
CHAR
ACTE
R*9
CHARACTER*9
CHARACTER*9
CHAR
ACTE
R*9
CHARACTER*9
CHARACTER*9
CHARACTER*9
CHARACTER*9
CHAR
ACTE
R*9
CHAR
ACTE
R*9
CHAR
ACTE
R*!
REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL
*8 DIMENSIONC*)
REAL*8
REAL*8
REAL*8
REAL
*8
Tabl
e 11.2 C
ross
-ref
eren
ce li
st o
f va
riab
les
Cont
inued
Variable
name
CMY
CMZ
CN3
CNP
CNV
CNVD
CNVDFI
Refe
r
enci
ng
prog
rams
ASEM
BL
ASEMBL
PRNTAR
CALC
CRE
AD3
ETOM
1PRNTAR
WRITE2
WRITES
WRIT
ES
ETOM
1ET
OM2
READ3
HST3D
DUMP
INIT
1PL
OTOC
READ
1WRITE2
WRITE3
WRITE4
WRIT
ES
Vari
able
type
REAL*8
REAL*8
CHARACTER*2
REAL*8
REAL*8 DIMENSION (*)
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
Refer-
Vari
able
encing
name
programs
CNVDI
HST3D
DUMP
INIT
1PLOTOC
READ1
WRITE2
WRIT
E3WR
ITE4
WRITES
CNVE
ETOM2
CNVE
PI
HST3D
DUMP
INIT
1RE
AD1
WRITE3
CNVFF
ETOM2
READ3
CNVGZ
READ3
CNVHC
ETOM
1ETOM2
Vari
able
type
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
Table 11.2 Cross-reference
list o
f variables Continued
o
ro
Vari
able
name
CNVH
CI
CNVHF
CNVHFI
CNVHI
Refer
encing
programs
HST3
DDU
MPIN
IT1
PLOTOC
READ
1WR
ITE2
WRITES
WRITE4
WRIT
ES
ETOM2
READS
HST3
DDUMP
INIT1
PLOT
OCRE
AD1
WRIT
E2WR
ITES
WRIT
E4WR
ITES
HST3D
DUMP
INIT1
PLOT
OC
READ1
WRITE2
WRIT
ES
WRIT
E4
WRIT
ES
Variab
le
type
REAL*8
REAL
*8RE
AL*8
REAL
*8REAL*8
REAL
*8RE
AL*8
REAL
*8REAL*8
REAL*8
REAL
*8
REAL
*8REAL*8
REAL
*8RE
AL*8
REAL*8
REAL
*8REAL*8
REAL*8
REAL
*8
REAL
*8RE
AL*8
RE
ALMS
REAL
*8
REAL
*8
REAL
*8
REAL
*8
REAL
*8
REAL
*8
Refe
r-
Vari
able
en
cing
name
programs
CNVHTC
ETOM
1ETOM2
CNVH
TI
WRIT
E2
CNVL
ETOM
1RE
ADS
CNVL
2 ETOM1
ETOM2
READS
CNVL
2I
HST3
DDU
MPINIT1
PLOT
OCREAD1
WRIT
E2WR
ITES
WRIT
E4WRITES
CNVL
3 ET
OM1
ETOM2
CNVL
3I
HST3
D DU
MP
INIT
1 PL
OTOC
READ1
WRIT
E2
WRIT
ES
WRITE4
WRITES
Vari
able
type
REAL
*8REAL*8
REAL*8
REAL
*8REAL*8
REAL
*8REAL*8
REAL
*8
REAL*8
REAL*8
REAL
*8RE
AL*8
REAL
*8REAL*8
REAL*8
REAL
*8RE
AL*8
REAL
*8REAL*8
REAL*8
REAL
*8
REAL
*8
REAL
*8
REAL
*8
REAL
*8
REAL
*8
REAL
*8REAL*8
Tabl
e 11.2 Cross-reference list of variables Continued
Variable
name
CNVLI
CNVM
FI
CNVMI
Refe
r
enci
ng
prog
rams
HST3D
DUMP
INIT
1PL
OTOC
READ
1WRITE2
WRIT
E3WRITE4
WRIT
ES
HST3D
DUMP
INIT
1PL
OTOC
READ
1WR
ITE2
WRITE3
WRITE4
WRIT
ES
HST3D
DUMP
.IN
IT1
PLOT
OCRE
AD1
WRITE2
WRIT
E3WRITE4
WRIT
ES
Vari
able
ty
pe
REAL
*8REAL*8
REAL*8
REALMS
REALMS
REAL*8
REAL*8
REALMS
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8REALMS
REALMS
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
Refe
r-
Vari
able
en
cing
na
me
programs
CNVP
ET
OM1
ETOM2
READ
3
CNVP
I HST3D
DUMP
INIT
1PLOTOC
READ1
WRITE2
WRITES
WRITE4
WRITES
CNVSF
ETOM2
READ3
CNVT
1 ETOM1
ETOM2
READ3
CNVT
1I
HST3D
DUMP
INIT
1PLOTOC
READ
1WRITE2
WRITE3
WRITE4
WRITES
Vari
able
type
REAL
*8RE
AL*8
REAL
MS
REAL
*8REALMS
REAL
*8RE
AL*8
REAL
*8REAL*8
REAL
*8REAL*8
REAL
*8
REAL
*8RE
AL*8
REAL*8
REAL
*8RE
AL*8
REAL*8
REAL
*8REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8
Tabl
e 11
.2 C
ross
-ref
eren
ce li
st o
f variables Continued
Variable
name
CNVT
2
CNVT
2I
CNVT
CI
CNVT
HC
CNVT
M
Refe
r
encing
prog
rams
ETOM
1ET
OM2
READ3
HST3D
DUMP
INIT
1PL
OTOC
READ
1WRITE2
WRITES
WRITE4
WRITES
HST3D
DUMP
INIT
1PL
OTOC
READ
1WRITE2
WRITE3
WRITE4
WRITES
ETOM
1ETOM2
ETOM
1ET
OM2
READ
1
Vari
able
ty
pe
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REALMS
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REALMS
REALMS
REAL*8
REAL-8
REAL
-8
Refer-
Variable
encing
name
pr
ogra
ms
CNVT
MI
HST3D
DUMP
INIT
1PLOTOC
READ1
WRIT
E2WRITE3
WRITE4
WRITES
CNVU
UI
WRIT
E4
CNVW
ETOM
1READ3
CNWLI
HST3D
DUMP
INIT
1PLOTOC
READ1
WRIT
E2WR
ITE3
WRITE4
WRITES
CNWSI
HST3D
DUMP
INIT
1PLOTOC
READ
1WRITE2
WRITE3
WRITE4
WRITES
Variable
type
REAL
*8REAL*8
REAL
*8REAL
*8REAL
*8REAL*8
REAL
*8REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8REAL
*8REAL*8
REAL*8
REAL
*8REAL*8
REAL*8
REAL*8
REAL
-8REAL*8
REAL*8
REAL*8
REAL
*8REAL
*8REAL*8
REALMS
REAL*8
Tabl
e 11
.2 C
ross
-ref
eren
ce list of
var
iabl
es C
ontinued
Variable
name
COLS
COMOPT
CONL
BL
CONVC
CONV
P
g
CONVRG
Ln
CONV
T
COW
CPAR
CPARI
Refe
r
enci
ng
programs
MAP2
D
ITER
L2SO
R
WRIT
ES
HST3D
ITER
HST3
DITER
BSOD
E
HST3
DITER
PLOT
OC
IREW
I
IREW
I
Vari
able
ty
pe
REAL*8
LOGICAL*4
LOGI
CAL*
4
CHAR
ACTE
R*20
LOGICAL*4
LOGIC AL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICA
L*4
LOGICAL*4
REAL*8 DI
MENS
ION (*)
CHAR
ACTE
R*9
CHAR
ACTE
R*6
Refe
r-
Variable
enci
ng
name
programs
CPF
HST3D
APLYBC
ASEMBL
CALC
CCOEFF
CRSD
SPDUMP
ETOM
1IN
IT2
READ1
READ
2SU
MCAL
WELLSS
WELR
ISWFDYDZ
WRIT
E2WR
ITES
CPX
ASEMBL
CPY
ASEM
BL
CPZ
ASEMBL
Vari
able
type
REAL*8
REAL
*8REAL*8
REAL*8
REAL
*8RE
AL*8
REAL*8
REAL
MSRE
ALMS
REAL*8
REAL*8
REAL*8
REAL*8
REAL
MSREAL*8
REAL
*8RE
AL*8
REAL
-8
REAL
-8
REAL
*8
Tabl
e 11.2 Cross-reference list of
var
iabl
es--
Cont
inue
d
Variable
name
CSBC
CVIS
CWKT
Refe
r
enci
ng
prog
rams
ASEMBL
INIT
3SU
MCAL
WRITES
HST3D
DUMP
ETOM
1IN
IT2
READ
1RE
AD2
VISCOS
WRITE2
ASEMBL
READS
WBBAL
WELLSS
WRITES
WRIT
ES
Vari
able
ty
pe
REAL
*8 DIMENSIONC*)
REAL*8 DI
MENS
IONC
*)REAL*8 DI
MENS
IONC
*)REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC 10)
REAL*8 DI
MENS
ION CI
O)REAL*8 DI
MENS
IONC
10)
REAL*8 DIMENSIONC10)
REAL*8 DI
MENS
IONC
10)
REAL*8 DI
MENS
IONC
10)
REAL*8 DIMENSIONC10)
REAL*8 DI
MENS
IONC
10)
REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL*8 DI
MENS
IONC
*)REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
Refer-
Variable
enci
ng
name
prog
rams
CYLIND
HST3D
ASEMBL
CLOS
ECOEFF
DUMP
ERRO
R2ERRORS
ETOM1
INIT
1INIT2
INIT3
IREW
IIT
ERL2SOR
PLOTOC
READ
1READ2
READS
REWI
REWI3
SUMCAL
WBBAL
WELL
SSWR
ITE1
WRITE2
WRIT
ESWR
ITE4
WRITES
ZONPLT
Variable
type
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGI
CAL*
4LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGI
CAL*
4LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGI
CAL*
4LOGICAL*4
LOGI
CAL*
4LO
GICA
L*4
LOGI
CAL*
4LOGICAL*4
LOGI
CAL*
4LO
GICA
L*4
LOGICAL*4
LOGI
CAL*
4LOGICAL*4
LOGI
CAL*
4LOGICAL*4
LOGICAL*4
LOGICAL*4
Tabl
e 11.2 Cross-reference list of
variables Continued
Variable
name
D DAMWRC
DASHES
DBKD
DC DCMAX
Refe
r
enci
ng
programs
SOR2
L
HST3D
DUMP
INIT
2RE
AD1
READ
2WE
LLSS
WRIT
E2
WRIT
ES
INIT
2RE
AD2
WRITE2
ASEMBL
CALC
CCR
SDSP
ITER
SUMC
AL
HST3D
COEF
FITER
SUMC
ALWR
ITES
Vari
able
ty
pe
REAL*8 DIMENSION^)
REAL*8
REAL*8
REALMS
REAL
MSREAL*8
REAL*8
REAL
*8
CHAR
ACTE
R*50
REAL*8 DIMENSION^)
REALMS DIMENSION (*)
REAL
*8 DIMENSION^)
REAL*8 DIMENSION^)
REAL*8
REAL*8 DIMENSION^)
REAL
MS DIMENSION(*)
REAL*8 DI
MENS
ION (*
)
REAL-8
REAL*8
REALMS
REAL*8
REAL-8
Refer-
Vari
able
encing
name
pr
ogra
ms
DCTAS
HST3D
COEFF
ERRORS
ETOM2
INIT
3READ3
WRITE3
DDNMAX
HST3D
SUMCAL
WRITES
DDV
SBCF
LOWBCFLO
DECL
AM
HST3
DAS
EMBL
CALCC
COEFF
DUMP
ETOM
1INIT2
INIT3
READ1
READ2
READ3
SUMCAL
VISCOS
WBBAL
WELLSS
WRITE2
WRITES
WRITES
Vari
able
type
REAL
*8REAL*8
REALMS
REAL*8
REALMS
REAL
*8RE
AL*8
REAL*8
REALMS
REAL*8
REAL*8 DI
MENS
IONC
*)REALMS DIMENSION^)
REAL*8
REAL*8
REAL*8
REALMS
REAL
*8REAL*8
REAL*8
REAL-8
REAL*8
REAL
-8RE
AL*8
REAL
*8RE
AL*8
REAL
*8RE
AL-8
REAL
-8RE
AL-8
REALMS
Tabl
e 11
.2 C
ross
-ref
eren
ce list o
f variables Continued
O
OO
Vari
able
na
me
DEHIR
DELA
DELAN
DELAP
DELT
IM
DELX
DELY
Refe
r
enci
ng
programs
HST3
DSUMCAL
WRIT
ES
MAP2D
MAP2
D
MAP2D
HST3
DAP
LYBC
CALCC
COEFF
DUMP
ETOM
2IN
IT2
INIT3
READ1
READ
3SU
MCAL
WELLSS
WRITES
WRIT
E4WRITES
INIT
2
INIT2
PLOT
Vari
able
ty
pe
REAL
*8RE
ALMS
REAL
*8
REAL*8
REAL
*8
REAL
*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8RE
AL*8
REAL
*8RE
AL*8
REAL
MSRE
AL*8
REAL
*8RE
AL*8
REAL
*8
REAL
*8
REAL
*8REAL*8
Refe
r-
Vari
able
en
cing
na
me
prog
rams
DEN
APLYBC
ASEMBL
COEF
FIN
IT2
SUMCAL
WBBA
LWELLSS
WRIT
E2WR
ITES
DENO
HST3
DCALCC
DUMP
INIT2
ITER
READ
1SU
MCAL
WBBA
LWE
LLSS
WFDY
DZ
DENC
HST3D
CALC
CDU
MPIN
IT2
ITER
READ
1SU
MCAL
WBBA
LWE
LLSS
WFDYDZ
Vari
able
ty
pe
REAL
*8 DIMENSIONS)
REAL
*8 DIMENSION^)
REAL*8 DIMENSIONC*)
REAL
*8 DIMENSIONC*)
REAL
*8 DIMENSIONS)
REAL
*8 DIMENSIONC*)
REAL*8 D
IMENSIONC*)
REAL
*8 D
IMENSIONC*)
REAL*8 D
IMENSIONC*)
REAL
*8REAL*8
REAL
*8RE
AL*8
REAL*8
REAL*8
REAL*8
REAL
*8RE
AL*8
REAL*8
REAL
*8REAL*8
REAL
*8RE
AL*8
REAL
*8REAL*8
REAL*8
REAL*8
REAL
*8RE
AL*8
DELZ
INIT2
REAL
*8DE
NCHC
ITER
REAL
*8
Table
11.2
--Cr
oss-
refe
renc
e li
st of
var
iabl
es--
Cont
inue
d
Vari
able
name
DENC
HT
DENFO
DENF1
DENF
BC
DENG
L
DENL
BC
Refe
r
encing
programs
ITER
HST3D
DUMP
ETOM1
INIT2
READ1
READ
2WR
ITE2
HST3
DDUMP
ETOM1
INIT
2READ1
READ
2WR
ITE2
APLYBC
INIT
3SU
MCAL
WRIT
E3WR
ITES
WELL
SS
APLY
BCAS
EMBL
INIT3
SUMC
ALWRITE3
Variable
type
REAL*8
REAL*8
REAL
*8REAL*8
REAL
*8RE
ALMS
REAL
*8RE
AL*8
REAL
*8RE
AL*8
REAL
*8REAL*8
REAL
*8RE
AL*8
REAL*8
REAL
*8 DIMENSION^)
REAL
*8 DIMENSIONS)
REAL*8 DI
MENS
IONC
*)RE
AL*8
DI
MENS
IONC
*)RE
AL*8
DI
MENS
IONC
*)
REAL*8
REAL
*8 DIMENSION (*
)REAL*8 DIMENSIONC*)
REAL
*8 DI
MENS
ION (*)
REAL
*8 DI
MENS
IONC
*)REAL*8 DI
MENS
IONC
*)
Refer-
Variable
encing
name
programs
DENMAX
SUMC
AL
DENN
CALCC
DENN
P CA
LCC
DENO
AR
APLYBC
ASEMBL
ETOM
1INIT3
SUMC
AL
DENP
HST3
DCA
LCC
DUMP
INIT
2IT
ERRE
AD1
SUMC
ALWB
BAL
WELLSS
WFDYDZ
DENT
HS
T3D
CALC
CDU
MPIN
IT2
ITER
READ1
SUMC
ALWB
BAL
WELL
SSWFDYDZ
Variable
type
REAL
*8
REAL
*8
REAL
MS
REAL
*8 DI
MENS
IONC
*)RE
AL*8
DIMENSIONC*)
REAL
*8RE
AL*8
DIMENSIONC*)
REAL*8 DI
MENS
IONC
*)
REAL
*8RE
AL*8
REAL
*8RE
AL*8
REAL
*8REAL*8
REAL
*8RE
AL*8
REAL
*8REAL*8
REAL
*8RE
AL*8
REAL
*8RE
AL*8
REAL
*8REAL
*8RE
AL*8
REAL
*8RE
AL*8
REAL
*8
Tabl
e 11.2 Cross-reference li
st of variables Continued
Variable
name
DENW
DENWKT
DENW
RK
DET
DFIR
DM miTFST
Refe
r
encing
prog
rams
WELLSS
ASEM
BLWBBAL
WELLSS
HST3D
WELRIS
WFDYDZ
WFDYDZ
HST3D
SUMC
ALWR
ITES
HST3D
ASEMBL
COEF
F DU
MPET
OM1
INIT
2 IN
IT3
READ
1RE
AD2
READ
3SU
MCAL
VISCOS
WBBAL
WELL
SSWR
ITE2
WRIT
E3WR
ITES
UFT.
T.SS
Variable
type
REAL*8 DIMENSION (*
)
REAL
*8RE
AL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8
REAL
*8REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8REAL*8
REAL*8
REAL*8
REALMS
REAL*8
RFAT.*ft
Refer-
Vari
able
encing
name
prog
rams
DOTS
CLOSE
REWI
REWI3
WRIT
E2WRITES
WRITES
DP
ASEM
BLCALCC
ITER
SUMCAL
WBBAL
WRITES
DPMAX
HST3D
COEFF
ITER
SUMCAL
WRITES
DPTAS
HST3D
COEFF
ERROR3
ETOM2
INIT
3READ3
WRITES
DPUDT
APLY
BC
DPWKT
ASEM
BLIT
ER
WBBAL
WRIT
ES
Variable
type
CHAR
ACTE
R*50
CHARACTER*50
CHARACTER*50
CHARACTER*50
CHARACTER*50
CHAR
ACTE
R*50
REAL*8 DIMENSION^)
REAL*8
REAL*8 DI
MENS
ION(
*)RE
AL*8
DIMENSION^)
REAL*8 DIMENSION^)
REAL*8 DIMENSION^)
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8REAL*8
REAL*8
REAL*8
REAL*8 DI
MENS
ION (*
)REAL*8 DI
MENS
ION (*)
REAL
*8 DI
MENS
ION^
')RE
AL-8
DIMENSION(*)
Tab
le
11.2
--C
ross
-ref
eren
ce li
st
of
var
iaJb
les-
-Co
nti
nu
ed
Vari
able
na
me
DQFDP
DQHBC
DQHCDT
DQHDP
DQHDT
DQHWDP
DQHWDT
DQSB
C
DQSD
C
DQSDP
DQSWDC
DQSWDP
DQWDP
DQWDPL
Refe
r
enci
ng
prog
rams
ASEMBL
ASEMBL
SUMC
AL
APLY
BCASEMBL
ITER
SUMC
AL
ASEMBL
ASEMBL
ASEMBL
ASEMBL
ASEMBL
SUMC
AL
ASEMBL
ASEMBL
ASEMBL
ASEMBL
ASEMBL
ASEMBL
ITER
WBBA
LWE
LLSS
Vari
able
type
REAL*8
REALMS
REAL*8
REAL*8 DIMENSIONS)
REALMS DIMENSIONS)
REAL*8 DIMENSIONS)
REAL*8 DIMENSIONS)
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8 DIMENSIONC*)
REAL*8 DI
MENS
IONC
*)REAL*8 DIMENSION (*
)REAL*8 DI
MENS
IONC
*)
Vari
able
na
me
DQWLYR
DSIR
DSXXM
DSXXP
DSYYM
DSYYP
DSZZM
DSZZP
DT DTAD
ZW
DTHAWR
DTHHC
Refe
r
enci
ng
prog
rams
ASEM
BL
HST3D
SUMC
ALWRITES
ASEMBL
ASEMBL
ASEMBL
ASEMBL
ASEM
BL
ASEMBL
ASEMBL
CALCC
CRSDSP
ITER
SUMCAL
HST3D
WELRIS
WFDYDZ
ETOM
1READ2
WELRIS
WRITE2
APLYBC
INIT
2
Vari
able
type
REAL
*8
REAL
*8RE
AL*8
REAL*8
REAL
*8
REAL
*8
REAL
*8
REAL
*8
REAL
*8
REAL
*8
REAL
*8 DIMENSIONC*)
REAL
*8RE
AL*8
DI
MENS
IONC
*)RE
AL*8
DI
MENS
IONC
*)RE
AL*8
DIMENSION(*)
REAL
*8RE
AL*8
REAL
*8
REAL
*8 DIMENSION^)
REAL
*8 DIMENSION(»)
REAL
*8RE
AL*8
DIMENSION^)
REAL
MS DIMENSIONS)
REAL
*8 DIMENSIONS)
Tabl
e 11
.2 C
ross
-ref
eren
ce list of variables Continued
Variable
name
DTIMMN
DTIMMX
DTMAX
DTTA
S
Refe
r
enci
ng
programs
HST3
DCO
EFF
ERRORS
ETOM2
INIT
3READ3
WRITES
HST3
DCO
EFF
ERROR3
ETOM
2IN
IT3
READ
SWRITE3
HST3
DCO
EFF
ITER
SUMC
ALWR
ITES
HST3
DCO
EFF
ERROR3
ETOM2
INIT
3READ3
WRITE3
Vari
able
ty
pe
REAL*8
REAL
*8RE
AL*8
REAL*8
REAL
*8REAL*8
REAL
*8
REAL*8
REAL
*8RE
AL*8
REAL
*8RE
AL*8
REAL
*8REAL*8
REAL
*8RE
AL*8
REAL
*8RE
AL*8
REAL
*8
REAL
*8REAL*8
REAL*8
REAL
*8RE
AL*8
REAL
*8REAL*8
Variable
name
DX DXMIN
DXPRNT
DY DYY
DYYN
DZ DZCH
NG
DZMI
N
Refe
r
enci
ng
prog
rams
ZONPLT
PLOT
PLOT
ZONPLT
BSODE
WELR
ISWFDYDZ
BSOD
E
ASEM
BLBS
ODE
CALC
C
BSODE
HST3D
BSODE
DUMP
ETOM
1IN
IT2
READ
1RE
AD2
WELR
IS
Variable
type
REAL
*8
REAL
*8
REAL
*8
REAL
*8
REAL
*8 DIMENSION^)
REAL
*8 D
IMEN
SION
(2)
REAL
*8 DIMENSION^)
REAL
*8 D
IMENSION(2)
REAL
*8RE
AL*8
REAL
*8
REAL*8
REAL
*8REAL*8
REAL
*8RE
AL*8
REAL*8
REAL*8
REAL*8
REAL*8
DZW
WELRIS
REAL
*8
Tabl
e 11
.2 C
ross
-ref
eren
ce list o
f variables Contin
ued
Variable
name
EEUNIT
EH
Refe
r
enci
ng
prog
rams
HST3D
ASEMBL
CLOS
ECO
EFF
DUMP
ERRO
R2ET
OM1
INIT
1IN
IT2
INIT
3IR
EWI
PLOT
OCRE
AD1
READ
2RE
AD3
REWI
REWI
3SU
MCAL
WELLSS
WRIT
E1WR
ITE2
WRITE3
WRITE4
WRIT
ES
APLYBC
ASEMBL
COEF
FIN
IT2
SUMC
ALTO
FEP
WBBAL
WELLSS
WRITE2
WRIT
ES
Variable
type
LOGICAL**
LOGI
CAL*
*LO
GICA
L**
LOGI
CAL*
*LOGICAL**
LOGI
CAL*
*LO
GICA
L**
LOGI
CAL*
*LO
GICA
L**
LOGI
CAL*
*LOGICAL**
LOGICAL**
LOGI
CAL*
*LO
GICA
L**
LOGI
CAL*
*LO
GICA
L**
LOGICAL**
LOGI
CAL*
*LOGICAL**
LOGI
CAL*
*LO
GICA
L**
LOGI
CAL*
*LO
GICA
L**
LOGI
CAL*
*
REAL*8 DIMENSIONS)
REAL*8 DI
MENS
ION (*
)REAL*8 DIMENSION^)
REAL*8 DIMENSION (*
)REAL*8 DIMENSIONS)
REAL*8
REAL*8 DIMENSIONC*)
REAL
*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL*8 DI
MENS
IONC
*)
Refer-
Vari
able
encing
name
pr
ogra
ms
EHO
HST3D
APLYBC
ASEM
BLDU
MPINIT2
READ1
SUMCAL
WBBAL
WELL
SSWR
ITE2
WRITES
EHOO
HST3D
WBBAL
WELL
SSWELRIS
EHDT
HST3D
BLOCKDATA
DUMP
INIT
2RE
AD1
TOFEP
EHI
TOFEP
EHIR
HST3D
SUMCAL
WRITES
Variable
type
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8 DI
MENS
IONC
l*,1
0)REAL*8 DI
MENS
IONC
l*,1
0)RE
AL*8
DIMENSION(1*,10)
REAL*8 DIMENSIONCl*,10)
REAL*8 DI
MENS
IONC
l*,1
0)REAL*8 DIMENSIONCl*,10)
REAL*8
REAL*8
REAL*8
REAL*8
Tabl
e 11
.2 Cross-reference list of var
iabl
es--
Cont
inue
d
Variable
name
EHIRO
EHIRN
EHMX
EHMY
EHMZ
EHPX
EHPY
EHPZ
EHST
EHWEND
Refe
r
enci
ng
prog
rams
HST3D
APLYBC
DUMP
INIT
2RE
AD1
SUMCAL
WRIT
E2WR
ITES
SUMC
AL
ASEM
BL
ASEM
BL
ASEMBL
ASEMBL
ASEMBL
ASEMBL
HST3D
BLOCKDATA
DUMP
INIT
2RE
AD1
TOFEP
HST3D
WBBA
LWE
LLSS
WELRIS
Vari
able
ty
pe
REAL
*8RE
AL*8
REAL*8
REAL
*8REAL*8
REALMS
REAL
*8REAL*8
REAL*8
REALMS
REAL
MS
REALMS
REAL
*8
REAL*8
REAL*8
REAL*8 DIMENSION(32)
REAL*8 DIMENSION (32)
REAL-8 DI
MENS
ION (3
2)REAL*8 DIMENSION(32)
REAL*8 DIMENSION (32)
REAL
MS DIMENSION(32)
REAL
-8REALMS
REALMS
REALMS
Refe
r-
Vari
able
encing
name
programs
EHWKT
ASEMBL
WBBAL
WELLSS
WRIT
ES
EHWSUR
WBBAL
WELLSS
WRIT
ES
ELBL
PLOT
ELO
TOFEP
ENTH
TOFEP
EOD
HST3D
WELLSS
WELRIS
WFDYDZ
EODF
WELLSS
WFDYDZ
EPS
TOFEP
EPSFAC
SOR2L
EPSOMG
HST3D
DUMP
INIT
2READ1
READ2
SOR2
L
Variable
type
REAL
*8 DIMENSIONS)
REAL*8 DIMENSION^*)
REAL
*8 DIMENSIONS)
REAL
*8 DI
MENS
ION (*)
REAL*8 DIMENSIONS)
REAL
MS DIMENSIONS)
REAL
*8 DIMENSIONS)
CHAR
ACTE
R*!
REAL
*8
REAL
*8
REAL
*8RE
AL*8
REAL
*8RE
AL*8
REAL
*8RE
AL*8
REAL
*8
REAL
MS
REAL
MSRE
ALMS
REAL
*8RE
AL*8
REAL
MSRE
AL*8
Tabl
e 11.2 Cross-reference li
st o
f variables--Continued
Ul
Variable
name
EPSS
OR
EPSWR
ERRE
X
ERREXE
Refe
r
enci
ng
programs
HST3D
DUMP
INIT
2RE
AD1
READ2
SOR2
LWRITE2
HST3D
BSOD
EDU
MPIN
IT2
READ1
READ
2WE
LRIS
ERRO
R1
ERRO
R2ER
RORS
INTERP
L2SOR
READ
1 SO
R2L
VISC
OSVSINIT
HST3
D CLOSE
ITER
SUMCAL
TOFE
P WBBAL
WELLSS
WELRIS
WFDYDZ
WRIT
ES
Vari
able
ty
pe
REAL*8
REAL
*8REAL*8
REAL
*8REAL*8
REAL*8
REAL*8
REAL
*8RE
AL*8
REAL
*8REAL*8
REAL*8
REAL*8
REAL*8
LOGI
CAL*
4 LO
GICA
L*4
LOGI
CAL*
4 LO
GICA
L*4
LOGI
CAL*
4LO
GICA
L*4
LOGI
CAL*
4 LO
GICA
L*4
LOGI
CAL*
4
LOGI
CAL*
4 LO
GICA
L*4
LOGI
CAL*
4 LO
GICA
L*4
LOGI
CAL*
4 LO
GICA
L*4
LOGI
CAL*
4 LO
GICA
L*4
LOGI
CAL*
4 LO
GICA
L*4
Variable
name
ERRE
XI
EVEN
EVMA
X
EVMI
N
EX EXTRAP
F10
F12
F1AI
F
F2AI
F
F6 F7 F8
Refe
r
enci
ng
prog
rams
HST3
DCLOSE
INIT
2WRITE2
SOR2L
SOR2
L
SOR2
L
PLOT
BSODE
ZONP
LT
ZONP
LT
HST3
DAPLYBC
DUMP
INIT2
READ1
HST3
DAP
LYBC
DUMP
INIT
2 RE
AD1
ZONP
LT
ZONP
LT
ZONPLT
Vari
able
ty
pe
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
REAL
*8
REAL
*8
CHAR
ACTE
R*!
REAL
*8 DIMENSION^, 11)
CHAR
ACTE
R*20
CHARACTER*20
REAL
*8RE
AL*8
REAL
*8
REAL
*8
REAL
*8
REAL
*8RE
AL*8
RE
AL*8
RE
AL*8
RE
AL*8
CHARACTER*20
CHAR
ACTE
R*20
CHARACTER*20
Tabl
e 11.2 Cross-reference li
st of
variables
Continued
Vari
able
na
me
FCJ
FDDP
FDSM
TH
FDTM
TH
FFPHL
Refe
r
enci
ng
prog
rams
WELRIS
ITER
HST3D
APLYBC
ASEMBL
COEF
FDUMP
READ
1RE
AD2
SBCFLO
SUMCAL
WBCFLO
WELLSS
WRITE2
WRIT
ES
HST3
DAPLYBC
ASEMBL
CALC
CDU
MPRE
AD1
READ
2SBCFLO
SUMC
ALWB
CFLO
WELL
SSWRITE2
WRIT
ES
WFDYDZ
Variable
type
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8
Refe
r-
Vari
able
en
cing
na
me
prog
rams
FIR
HST3D
SUMCAL
WRITES
FIRO
HST3D
APLYBC
DUMP
INIT
2READ1
SUMCAL
WRITE2
WRIT
ES
FIRN
SUMCAL
FIRVO
HST3D
APLYBC
DUMP
INIT2
READ1
SUMCAL
WRITE2
WRITES
FLO
ZONPLT
FL1
ZONPLT
FL2
ZONPLT
FL3
ZONPLT
FL4
ZONPLT
Variable
type
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
Tab
le
11
.2 C
ross
-refe
ren
ce li
st
of
var
iaJb
les
Co
nti
nu
ed
Variable
name
FL5
FL6
FLOR
EV
FLOW
FMAX
FMT
FMTL
FPR3
FRAC
FRACN
FRAC
NP
Refe
r
encing
prog
rams
20NP
LT
ZONP
LT
WBBAL
WELLSS
WELLSS
BSOD
E
ZONP
LT
ZONP
LT
WELLSS
COEF
FIN
IT2
SUMC
ALWELLSS
WRITE2
WRIT
ES
CALC
C
CALC
C
Variable
type
REAL*8
REAL*8
LOGIC AL
*4LO
GICA
L*4
LOGICAL*4
REAL*8
CHARACTER*20
CHAR
ACTE
R*20
REALMS
REAL*8 DI
MENS
IONC
*)REAL*8 DIMENSIONC*)
REAL*8
DI
MENS
IONC
*)REAL*8 DIMENSIONC*)
REAL*8 DI
MENS
IONC
*)REAL*8 DI
MENS
IONC
*)
REAL*8
REAL*8
Refer-
Vari
able
encing
name
pr
ogra
ms
FRESUR
HST3D
ASEM
BLCA
LCC
CLOS
ECOEFF
DUMP
ERROR2
ETOM
1INIT2
INIT
3IR
EWI
PLOTOC
READ
1RE
AD2
READS
REWI
SUMC
ALWELLSS
WRITE 1
WRITE2
WRITES
WRITES
FRFA
C WFDYDZ
FRFLM
WELLSS
-FRFLP
WELLSS
Vari
able
type
LOGI
CAL*
4LO
GICA
L*4
LOGI
CAL*
4LOGICAL*4
LOGI
CAL*
4LOGICAL*4
LOGI
CAL*
4LO
GICA
L*4
LOGICAL*4
LOGI
CAL*
4LO
GICA
L*4
LOGICAL*4
LOGI
CAL*
4LOGICAL*4
LOGIC AL
*4LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGI
CAL*
4
REAL
*8
REAL
*8
REAL
*8
Tabl
e 11.2 Cross-reference li
st of v
ariables Continued
Variable
name
FS FSCON
FSLOW
FTDAIF
FTXY
DM
FTXYDP
FTXZ
DM
FTXZDP
FTYX
DM
FTYX
DP
FTYZ
DM
FTYZDP
FTZX
DM
FTZXDP
Refer
enci
ng
prog
rams
INTE
RP
INIT2
SUMC
AL
INIT
2SU
MCAL
HST3D
APLYBC
DUMP
INIT
2RE
AD1
CRSDSP
CRSD
SP
CRSD
SP
CRSD
SP
CRSDSP
CRSDSP
CRSDSP
CRSD
SP
CRSDSP
CRSDSP
Variable
type
REAL*8 DIMENSION^,*)
LOGICAL*4
LOGI
CAL*
4
LOGICAL*4
LOGICAL*4
REAL*8
REAL*8
REAL*8
REAL*8
REA£*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
Refe
r-
Variable
enci
ng
name
prog
rams
FTZY
DM
CRSDSP
FTZYDP
CRSD
SP
GAMMA
APLYBC
GCOS
TH
HST3D
WELRIS
WFDYDZ
GRAV
INIT2
GX
HST3D
APLYBC
ASEM
BLCALCC
COEFF
DUMP
ERROR3
INIT
2RE
AD1
READ3
SUMCAL
WELLSS
WELRIS
Vari
able
ty
pe
REAL*8
REAL*8
REAL*8 DIMENSION(IO)
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
Table
11.2
Cro
ss-r
efer
ence
list of
var
iabl
es Continued
Vari
able
na
me
GY GZ HDPRNT
Refe
r
encing
prog
rams
HST3
DAP
LYBC
ASEMBL
CALC
CCO
EFF
DUMP
ERRO
RSIN
IT2
READ
1RE
AD3
SUMC
ALWELLSS
WELR
IS
HST3D
APLY
BCASEMBL
CALC
CCO
EFF
DUMP
ERRORS
INIT
2RE
AD1
READ
SSU
MCAL
WELLSS
WELRIS
INIT
2SU
MCAL
WRIT
E2WR
ITES
Variable
type
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL-8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8 DIMENSIONO'O
REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
Refer-
Variable
encing
name
prog
rams
HEAT
HST3D
APLYBC
ASEMBL
CALC
CCOEFF
CRSDSP
DUMP
ERROR2
ERRORS
ETOM1
ETOM2
INIT
1INIT2
INIT
3IT
ERPL
OTOC
READ1
READ2
READS
SUMCAL
VISCOS
WBBAL
WELLSS
WRITE
1WRITE2
WRITES
WRITE4
WRITES
HTCU
WELRIS
Variable
type
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGI
CAL*
4LOGICAL*4
LOGICAL*4
LOGICAL- 4
LOGICAL*4
LOGI
CAL-
4LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
REAL
*8
Tabl
e 11
.2 C
ross
-ref
eren
ce list of
variables
Continued
ho O
Refe
r-
Variab
le
enci
ng
name
pr
ogra
ms
HTCW
R ET
OM1
READ
2WELRIS
WRIT
E2
HWT
ERRO
R2ET
OM1
INIT2
READ2
Vari
able
ty
pe
REAL*8 DI
MENS
ION (*
)REAL*8 DIMENSIONS)
REAL*8
REAL
*8 DIMENSION^)
REAL*8 DIMENSIONS)
REAL
*8 DIMENSIONS)
REAL*8 DIMENSIONS)
REAL
*8 DI
MENS
ION (*)
Refe
r-
Vari
able
en
cing
name
programs
I HST3D
APLY
BCAS
EMBL
BSODE
COEF
FCR
SDSP
D4DE
SDUMP
ERRO
R 1
ERROR2
ERRO
R3ETOM1
INIT1
INIT2
INIT
3IN
TERP
IREWI
MAP2D
ORDER
PLOT
PLOT
OCPR
NTAR
READ
1READ2
READ
3RE
WIRE
WI3
SUMC
ALTO
FEP
VSINIT
WELLSS
WRITE2
WRITE3
WRIT
ESZO
NPLT
Variable
type
INTE
GER*
4INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGERS
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4IN
TEGE
R*4
Tabl
e 11.2 Cross-reference list of
variables Continued
Vari
able
na
me
11 I11Z
I12X
I12Z
HZ
12
Refe
r
encing
prog
rams
DUMP
IREW
IMAP2D
ORDER
READ
1RE
AD2
READ
3RE
WIRE
WI3
SOR2L
ZONP
LT
ZONPLT
PRNTAR
ZONPLT
COEFF
ERRO
R2IN
IT2
REAP2
WRITE2
DUMP
IREW
IMAP2D
ORDER
READ
1READ2
READ3
REWI
REWI3
SOR2L
ZONP
LT
Vari
able
ty
pe
INTE
GER*
4INTEGERS
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGER*4
INTEGE
R*4
DIMENSION(*)
CHARACTER*4
INTEGER*4
DIMENSION(*)
INTE
GER*
4 DIMENSION(*)
INTEGE
R*4
DIME
NSIO
N(*)
INTEGER*4 DIMENSION^)
INTE
GER*
4 DI
MENS
ION(
*)INTEGER*4
DIMENSION(*)
INTEGE
R*4
INTEGE
R*4
INTEGE
R*4
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGER*4
INTE
GER*
4INTEGER*4
Refer-
Vari
able
encing
name
pr
ogra
ms
I21Z
ZO
NPLT
I22Z
ZONPLT
I2Z
COEFF
ERRO
R2IN
IT2
READ2
WRITE2
13
ORDER
SOR2L
ZONPLT
I31Z
ZONPLT
I32Z
ZONPLT
IA1HC
HST3D
DUMP
INIT
1RE
AD1
IA2HC
HST3
DDUMP
INIT
1READ1
IA3HC
HST3D
DUMP
INIT1
READ1
Variable
type
INTEGER*4 DIMENSION^)
INTE
GER*
4 DIMENSION(*)
INTE
GER*
4 DIMENSION(*)
INTE
GER*
4 DIMENSION(*)
INTEGER*4 DIMENSION^)
INTEGER*4
DIMENSION(*)
INTE
GER*
4 DIMENSION(*)
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4 DI
MENS
ION(
*)
INTEGER*4
DIMENSION(*)
INTE
GER*
4INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
Tabl
e 11.2 Cross-reference li
st o
f variables Co
ntin
ued
Variable
name
IA4
IA4B
IAA1
IAA2
IAA3
IAA4
IAAIF
Refe
r
enci
ng
prog
rams
HST3D
DUMP
INIT
1IT
ERRE
AD1
D4DES
HST3D
DUMP
INIT
1RE
AD1
HST3D
DUMP
INIT
1RE
AD1
HST3D
DUMP
INIT
1RE
AD1
HST3D
DUMP
INIT
1RE
AD1
HST3D
DUMP
INIT
1IT
ERRE
AD1
Vari
able
ty
pe
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4
INTE
GER*
4INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4
INTE
GER*
4INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
Refer-
Vari
able
en
cing
na
me
programs
IABP
M HS
T3D
DUMP
INIT
1RE
AD1
IAIF
HS
T3D
APLYBC
DUMP
ERROR2
ETOM1
INIT2
READ
1READ2
WRIT
E2
IALB
C HST3D
DUMP
INIT
1IT
ERRE
AD1
IALF
L HST3D
DUMP
INIT
1INIT2
READ1
IALFT
HST3D
DUMP
INIT
1INIT2
READ1
Vari
able
ty
pe
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGER*4
INTE
GER*
4
INTE
GER*
4INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER»
4
Tabl
e 11
.2 C
ross
-ref
eren
ce li
st of
variables
Continued
K5 U)
Variable
name
IAMAP
IAPRT
IARH
C
IARX
IARX
BC
IARY
IARY
BC
IARZ
Refer
encing
programs
HST3
D
HST3
D
DUMP
INIT
1READ1
HST3D
DUMP
INIT
1READ1
HST3
D
HST3
DDU
MPIN
IT1
READ
1
HST3
D
HST3
DDU
MPINIT1
READ
1
Variable
type
INTE
GER*
4
INTE
GER*
4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4
INTE
GER*
4INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4
Refe
r-
Vari
able
encing
name
pr
ogra
ms
IAYF
BC
HST3D
DUMP
INIT1
READ
1
IAZF
BC
HST3
DDUMP
INIT
1RE
AD1
IB
SOR2
L
IBAI
F HST3D
DUMP
INIT1
ITER
READ
1
IBBL
BC
HST3D
DUMP
INIT1
ITER
READ
1
Vari
able
type
INTE
GER*
4INTEGER*4
INTE
GER*
4INTEGER*4
INTEGERS
INTEGER*4
INTEGER*4
INTE
GER*
4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
IARZBC
IAXFBC
HST3
D
HST3D
DUMP
IN
IT1
READ
1
INTE
GER*
4
INTE
GER*
4 IN
TEGE
R*4
INTEGER*4
INTE
GER*
4
Tabl
e 11
.2 C
ross
-ref
eren
ce list of
var
iabl
es Continued
NJ
Refe
r-
Variable
enci
ng
name
pr
ogra
ms
IBC
APLY
BCASEMBL
COEF
FER
ROR2
ERRO
RSET
OM1
INIT
2IN
IT3
ITER
ORDER
READ
2SB
CFLO
SOR2
LSU
MCAL
WBBA
LWE
LLSS
WRIT
E2WR
ITES
WRITE4
WRIT
ES
IBCM
AP
WRIT
ES
IBLB
C HST3D
DUMP
INIT
1IT
ERRE
AD1
Vari
able
ty
pe
INTEGER*4 DIMENSION^)
INTE
GER*
4 DIMENSION^)
INTEGERS DIMENSION^)
INTEGERS DIMENSION^)
INTE
GER*
4 DIMENSION^)
INTEGERS DIMENSION^)
INTE
GER*
4 DIMENSION^)
INTE
GER*
4 DIMENSION^)
INTEGE
R*4
DIME
NSIO
N (*)
INTEGER*4
DIMENSION(*)
INTEGERM DIMENSION(*)
INTEGER*4
DIMENSION(*)
I^TE
GER*
4 DIMENSIONC*)
INTEGERS DIMENSIONC*)
INTEGERS DI
MENS
ION (*
)IN
TEGE
R*4 DIMENSION^)
INTE
GER*
4 DIMENSION^)
INTEGER*4 DIMENSION^)
INTEGERS DIMENSIONS)
INTEGERS DIMENSIONC*)
INTE
GER*
4 DIMENSION^)
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4
Refe
r-
Variable
enci
ng
name
prog
rams
1C
HST3D
ASEM
BLDU
MPERROR2
ERRORS
ETOM1
INIT
1INIT2
INIT
3READ1
SOR2
LWRITES
WRIT
ESZONPLT
ICAI
F HST3D
DUMP
INIT
1IT
ERREAD1
I CAL
L IR
EWI
REWI
REWI3
ICC
HST3D
DUMP
ERROR2
ETOM1
INIT2
READ
1READ2
WRITE2
Vari
able
type
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGERS
INTE
GER*
4INTEGER«4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTE
GER*
4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
LOGI
CAL*
4LO
GICA
L*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGI
CAL*
4
Table
11.2
Cro
ss-r
efer
ence
list o
f variables Cont
inue
d
Ln
Vari
able
na
me
ICC24
ICC34
ICC3
5
ICCW
ICFL
X
ICH
ICHW
T
Refe
r
encing
prog
rams
HST3D
DUMP
INIT
1IT
ERREAD1
HST3D
DUMP
INIT
1IT
ERRE
AD1
HST3D
DUMP
INIT1
ITER
READ
1
HST3D
HST3D
DUMP
INIT
1IT
ERRE
AD1
ZONP
LTHST3D
DUMP
ERROR2
ETOM
1IN
IT2
READ
1RE
AD2
WRITE2
Variable
type
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGER*4
INTEGERS
INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGER*4
INTEGE
R*4
INTEGER*4
LOGI
CAL*
4LO
GICA
L*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
Refer-
Vari
able
en
cing
name
prog
rams
ICHY
DP
HST3D
DUMP
ERROR2
ETOM1
INIT2
READ
1READ2
WRITE2
ICI
HST3D
DUMP
INIT1
ITER
READ
1
ICLB
C HST3D
DUMP
INIT
1IT
ERREAD1
ICMAX
HST3D
SUMCAL
WRITES
ICNP
HST3D
ICON
D4DES
ICOW
HST3D
ICQF
LX
HST3D
Variable
type
LOGICAL*4
LOGICAL*4
LOGI
CAL*
4LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGI
CAL*
4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTE
GER*
4
INTEGER*4
INTEGERS
Table
11.2
--Cr
oss-
refe
renc
e li
st of
variables--Continued
Vari
able
na
me
ICSB
C
ICT
ICWK
T
ICXM
ICXP
ICYM
ICYP
ICZM
ICZP
Refe
r
enci
ng
prog
rams
HST3D
DUMP
INIT
1ITER
READ
1
HST3D
DUMP
ERROR2
ETOM
1IN
IT2
READ
1RE
AD2
WRITE2
HST3D
DUMP
INIT
1IT
ERRE
AD1
SUMC
AL
ASEMBL
ASEM
BL
ASEMBL
ASEMBL
ASEMBL
ASEMBL
Vari
able
type
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
LOGICAL*4
LOGI
CAL*
4LOGICAL*4
LOGI
CAL*
4LO
GICA
L*4
LOGICAL*4
LOGICAL*4
LOGI
CAL*
4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4
INTEGER*4
Refer-
Vari
able
encing
name
pr
ogra
ms
ID
HST3D
DUMP
INIT
1L2SOR
READ
1
ID4
ORDER
ID4C
ON
D4DES
ID4NO
ASEMBL
D4DES
ORDER
SBCFLO
WBCF
LO
IDBK
D HST3D
DUMP
INIT
1IT
ERRE
AD1
IDC
HST3D
DUMP
INIT
1RE
AD1
IDEN
HST3D
DUMP
INIT
1IT
ERREAD1
Vari
able
type
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGER*4
INTEGERS DIMENSION (6)
INTE
GER*
4 DI
MENS
ION(
*)IN
TEGE
R*4 DIMENSION^)
INTE
GER*
4 DIMENSION (*)
INTE
GER*
4 DIMENSION^)
INTEGER*4
DIME
NSIO
N(*)
INTE
GER*
4INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4
IDEN
WHST3D
INTEGER*4
Tab
le 1
1.2
Cro
ss-r
efer
ence
li
st
of
vari
able
s C
onti
nued
to
Variable
name
IDIA
G
IDIR
IDNF
BC
IDNL
BC
IDNO
AR
IDNU
M
IDP
Refe
r
encing
prog
rams
D4DE
SORDER
L2SO
RORDER
SOR2
L
HST3D
DUMP
INIT
1IT
ERRE
AD1
HST3D
DUMP
INIT
1IT
ERRE
AD1
HST3D
DUMP
INIT
1ITER
READ
1
PLOT
HST3D
DUMP
INIT
1RE
AD1
Vari
able
ty
pe
INTE
GER*
4 DIMENSION^)
INTEGERS DIMENSION(*)
INTE
GER*
4INTEGER*4
INTE
GER*
4
INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4INTEGER*4
Refer-
Vari
able
en
cing
na
me
prog
rams
IDPW
KT
HST3D
DUMP
INIT
1IT
ERREAD1
SUMC
AL
IDQH
DT
HST3D
DUMP
INIT
1READ1
IDQW
DP
HST3D
DUMP
INIT
1IT
ERREAD1
SUMCAL
IDRC
ON
D4DES
IDT
HST3D
DUMP
INIT
1READ1
IDTHHC
HST3D
DUMP
INIT
1READ1
Variable
type
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4 DI
MENS
ION(
6)
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
Table
11.2
Cro
ss-r
efer
ence
list o
f variables Continued
ro
oo
Variable
name
IDTH
WR
IE IE1
IE2
IEH
IEHS
UR
IEHW
KT
Refe
r
enci
ng
prog
rams
HST3
DDU
MPIN
IT1
INIT
2RE
AD1
WBBAL
WELLSS
ERRPRT
ERRP
RT
ERRPRT
HST3
DDUMP
INIT
1IT
ERRE
AD1
HST3D
DUMP
INIT
1IT
ERRE
AD1
SUMCAL
HST3D
DUMP
INIT
1IT
ERRE
AD1
SUMC
AL
Vari
able
type
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGERS
INTE
GER*
4INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER«4
INTE
GER*
4
Refe
r-
Variable
encing
name
programs
IEND
IV
HST3D
DUMP
ERROR1
INIT
1READ1
WRITE 1
IENDW
HST3D
DUMP
ERRO
R1IN
IT1
READ1
WRIT
E 1
IEQ
HST3D
ASEM
BLCA
LCC
ITER
L2SOR
SBCFLO
SOR2L
IER
IREW
IRE
WIREWI3
Vari
able
ty
pe
INTE
GER*
4INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
Tabl
e 11
.2--
Cros
s-re
fere
nce
list of
variables Continued
Vari
able
na
me
IERR
IF12
IFAC
E
IFMT
IFOR
M
IFRA
C
IG12
IHDP
RT
Refer
enci
ng
programs
HST3
DERROR1
ERROR2
ERRO
RSER
RPRT
INIT
2IREWI
ITER
READ
1RE
AD2
READ
SREWI
REWI3
SOR2L
SUMC
AL
PRNT
AR
IREW
I
PRNTAR
WRIT
E2
PRNT
AR
HST3D
PRNT
AR
HST3D
Variable
type
LOGI
CAL*
4 DIMENSION (2
00)
LOGICAL*4
DIME
NSIO
N (2
00)
LOGICAL*4
DIME
NSIO
N(20
0)LO
GICA
L*4
DIMENSION(200)
LOGI
CAL*
4 DI
MENS
ION(
200)
LOGI
CAL*
4 DI
MENS
ION(
200)
LOGI
CAL*
4 DI
MENS
ION (200)
LOGI
CAL*
4 DI
MENS
ION(
200)
LOGI
CAL*
4 DI
MENS
ION(
200)
LOGI
CAL*
4 DI
MENS
ION (2
00)
LOGICAL*4
DIME
NSIO
N(20
0)LO
GICA
L*4 DIMENSION(200)
LOGICAIM D
IMENSION (200)
LOGI
CAL*
4 DI
MENS
ION(
200)
LOGI
CAL*
4 DI
MENS
ION (200)
CHAR
ACTER*4
INTEGER*4
INTEGER*4
INTEGER*4
CHAR
ACTE
R*84
INTEGER*4
CHAR
ACTER*6
INTEGER*4
Variable
name
IHTC
R
IHWT
II III
1112
II1P1
II1Z
II2Z
113
1132
115
Refer
encing
programs
HST3
DDU
MPIN
IT1
INIT2
READ
1WB
BAL
WELL
SS
HST3
DV
ASEM
BLMA
P2D
SOR2L
PRNTAR
SOR2
L
HST3D
DUMP
INIT1
READ
1
HST3D
DUMP
INIT1
READ
1
SOR2
L
ZONPLT
PRNT
AR
Variable
type
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R«4
INTE
GER*
4INTEGER-4
INTE
GER*
4
INTE
GER-
4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4
CHAR
ACTE
R*4
INTE
GER*
4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4
INTE
GER*
4
CHARACTER*6
Tabl
e 11
.2 C
ross
-ref
eren
ce li
st of
var
iabl
es C
onti
nued
OJ o
Variable
name
IIBC
IIBCMP
IID4
IIDAG
IIFMT
IINZ
ON
IIR2
IIW
IJ1Z
Refe
r
encing
prog
rams
HST3D
DUMP
INIT
1L2
SOR
READ1
HST3
D
HST3D
DUMP
INIT
1IT
ERREAD1
HST3D
DUMP
INIT
1IT
ERRE
AD1
PRNTAR
HST3D
PRNTAR
HST3D
DUMP
INIT
1IT
ERREAD1
SUMC
AL
HST3
DDUMP
INIT
1RE
AD1
Variable
type
INTE
GER*
4INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
Refe
r-
Variable
enci
ng
name
prog
rams
IJ2Z
HST3
DDU
MPINIT1
READ
1
IJW
HST3
DDUMP
INIT1
ITER
READ
1SU
MCAL
*
IJWE
L HST3D
IK1Z
HST3D
DUMP
INIT
1READ1
IK2Z
HST3D
DUMP
INIT
1RE
AD1
IKAR
HC
HST3D
IKLB
C HST3D
DUMP
INIT
1ITER
READ
1
Vari
able
type
INTEGERS
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGERM
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGERS
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
Table
11.2
Cro
ss-r
efer
ence
list o
f variables Co
ntin
ued
U>
Vari
able
na
me
IKTAWR
IKTHX
IKTH
Y
IKTH
Z
IKTW
R
IKTXPM
IKTYPM
Refe
r
encing
programs
HST3D
DUMP
INIT
1IN
IT2
READ
1WBBAL
WELLSS
HST3D
DUMP
INIT
1RE
AD1
HST3D
DUMP
INIT
1RE
AD!
HST3D
DUMP
INIT
1RE
AD1
HST3D
DUMP
INIT
1IN
IT2
READ
1WBBAL
WELLSS
HST3D
HST3D
Variable
type
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4
INTE
GER*
4INTE
GER*
4INTE
GER*
4INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
TNTEGER*4
INTEGER*4
INTE
GER*
4INTE
GER*
4INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4
INTE
GER*
4
INTE
GER*
4
Refer-
Variable
enci
ng
name
programs
IKTZ
PM
HST3D
IKXX
HST3D
DUMP
INIT
1READ1
IKYY
HST3D
DUMP
INIT1
READ1
IKZZ
HST3D
DUMP
INIT
1READ1
ILAV
FL
HST3D
DUMP
ERRO
R1IN
IT1
READ1
WRIT
E1
ILBL
PL
OT
ILBW
IN
IT1
ILCBW
HST3D
DUMP
INIT
1ITER
READ
1SUMCAL
Variable
type
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
1NTE
G£R*
4IN
TEGE
R*4
INTE
GER*
4INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
Tabl
e 11.2 Cross-reference list of
variables
Continued
OJ
Variable
name
ILCTW
ILH
ILIVPA
ILNX
I
ILPR
T
ILVPA
IMAIFC
Refe
r
enci
ng
prog
rams
HST3D
DUMP
INIT
1IT
ERRE
AD1
SUMC
AL
D4DES
HST3D
DUMP
ERROR1
INIT
1RE
AD1
WRITE 1
WELRIS
HST3D
DUMP
INIT
1RE
AD1
HST3D
DUMP
ERROR1
INIT
1RE
AD1
WRIT
E1
HST3D
DUMP
INIT
1IT
ERRE
AD1
Vari
able
ty
pe
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
REAL
* 8
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R* 4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4
Refer-
Variable
encing
name
programs
IMAP
READ3
IMAP
1 HST3D
ERRO
R3ETOM2
INIT
3RE
AD3
WRIT
E3WR
ITES
IMAP2
HST3D
ERRO
R3ETOM2
INIT
3READ3
WRITE3
WRITES
IMAX
ORDER
IMFB
C HST3D
DUMP
INIT1
ITER
READ
1
IMHC
BC
HST3D
DUMP
INIT
1IT
ERREAD1
IMIN
ORDER
Variable
type
INTE
GER*
4
INTEGER*4
DIMENSION (3
)IN
TEGE
R*4
DIMENSION (3
)INTEGER*4
DIMENSION (3)
INTE
GER*
4 DIMENSION (3
)IN
TEGE
R*4
DIME
NSIO
N(3)
INTE
GER*
4 DIMENSION (3
)INTEGER*4
DIMENSION(3)
INTEGER*4
DIMENSION (3
)INTEGER*4
DIMENSION(3)
INTE
GER*
4 DIMENSION (3
)INTEGER*4
DIME
NSIO
N(3)
INTE
GER*
4 DIMENSION (3)
INTE
GER*
4 DIMENSION(3)
INTEGER*4
DIMENSION (3)
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4
INTE
GER*
4 *
Table
11.2
Cro
ss-r
efer
ence
li
st of
variables
Continued
e- W u>
Variable
name
IMLB
C
IMM
IMOBW
IMOD
IMPPTC
IMPQW
IMSB
C
Refe
r
enci
ng
prog
rams
HST3D
DUMP
INIT
1IT
ERRE
AD1
INIT
2
HST3D
REWI
REWI3
WRIT
ESWRITES
HST3D
DUMP
ETOM
1IN
IT2
ITER
READ
1RE
AD2
WBBAL
WELL
SSWE
LRIS
WRIT
E2WR
ITES
HST3D
DUMP
INIT
1ITER
READ
1
Variable
type
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGER*4
INTE
GER*
4
INTEGER*4
INTEGERS
INTEGE
R*4
INTE
GER*
4 DI
MENS
ION(
3)
INTEGE
R*4
INTE
GER*
4
LOGI
CAL*
4LO
GICA
L*4
LOGICAL*4
LOGI
CAL*
4LOGICAL*4
LOGI
CAL*
4LOGICAL*4
LOGICAL*4
LOGI
CAL*
4LO
GICA
L*4
LOGI
CAL*
4LOGICAL*4
INTEGER*4
INTE
GER*
4INTEGERS
INTE
GER*
4IN
TEGE
R*4
Vari
able
na
me
INCI
INCJ
INCJ
1
INCJ2
INCJ
3
INZONE
IOR
IOUT
IP IPAG
E
IPAIF
Refer
encing
programs
READ2
READ3
READ2
READ3
SOR2L
SOR2L
SOR2L
ERROR2
PRNTAR
MAP2D
HST3D
DUMP
INIT
1RE
AD1
WRIT
ES
MAP2D
HST3D
DUMP
INIT
1IT
ERREAD1
Vari
able
ty
pe
INTEGERS
INTE
GER*
4
INTEGER*4
INTEGERS
INTE
GER*
4
INTEGER*4
INTEGER* 4
DIMENSION^) LO
GICA
L*4
INTE
GER*
4
INTE
GER*
4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4
INTE
GER*
4IN
TEGE
R*4
INTEGER* 4
INTE
GER*
4IN
TEGE
R*4
Tabl
e 11.2 Cross-reference li
st o
f variables Co
ntin
ued
U)
Vari
able
name
IPAR
IPAR
I
IPCS
IPCW
IPH1
LB
IPLOT
IPMAX
IPMCHV
IPMC
V
IPMC
VK
Refe
r
enci
ng
prog
rams
IREWI
IREW
I
HST3D
HST3
D
HST3D
DUMP
INIT
1RE
AD1
MAP2D
HST3D
SUMC
ALWR
ITES
HST3D
ASEM
BLDU
MPIN
IT1
READ
1
HST3D
ASEMBL
DUMP
INIT
1RE
AD1
HST3D
ASEM
BLDUMP
INIT
1RE
AD1
Vari
able
type
INTE
GER*
* DIMENSION^)
INTE
GER*
4
INTE
GER*
*
INTE
GER*
*
INTEGER**
INTE
GER*
*INTEGER**
INTE
GER*
*
INTE
GER*
* DI
MENS
ION (*
,*)
INTE
GER*
*IN
TEGE
R**
INTE
GER*
*
INTE
GER*
*INTEGER**
INTEGER**
INTE
GER*
*INTE
GER*
*
INTE
GER*
*INTE
GER*
*INTEGER**
INTE
GER*
*INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTE
GER*
*
Refe
r-
Variable
encing
name
prog
rams
IPMHV
HST3D
ASEM
BLDUMP
INIT
1READ1
IPMZ
COEFF
ERRO
R2ET
OM1
INIT2
READ2
ZONPLT
IPMZ
1 ZONPLT
IPMZ
2 ZONPLT
IPNP
HST3D
IPOR
HST3D
DUMP
INIT
1RE
AD1
IPOS
HST3D
IPOW
HST3D
Variable
type
INTEGER**
INTE
GER*
*INTEGER**
INTEGER**
INTEGER**
INTE
GER*
*INTEGER**
INTE
GER*
*INTEGER**
INTE
GER*
*INTEGER**
INTE
GER*
*
INTE
GER*
*
INTE
GER*
*
INTEGER**
INTE
GER*
*INTEGER**
INTE
GER*
*
INTEGER**
INTEGER**
Tabl
e 11.2 Cross-reference list of
variables--
Continued
Variable
name
IPRP
TC
IPSB
C
IPT
IPV
IPVK
Refe
r
enci
ng
prog
rams
HST3D
DUMP
INIT
2RE
AD1
READ
2RE
AD3
SUMC
ALWR
ITE2
WRIT
E3WRITE4
WRIT
ES
HST3D
DUMP
INIT
1IT
ERRE
AD1
PLOT
OC
HST3D
ASEMBL
DUMP
INIT
1RE
AD1
HST3D
ASEM
BLDU
MPIN
IT1
READ
1
Variable
type
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGER*4
INTE
GER*
4
INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4
INTEGER* 4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGER*4
INTE
GER*
4IN
TEGE
R* 4
INTEGER*4
INTEGER*4
INTE
GER*
4
Refe
r-
Variable
encing
name
programs
IPWKT
HST3D
DUMP
INIT
1IT
ERRE
AD1
SUMC
AL
IPWKTS
HST3D
DUMP
INIT
1ITER
READ
1SUMCAL
IPWSRS
HST3D
DUMP
INIT
1IT
ERRE
AD1
SUMCAL
IPWS
UR
HST3D
DUMP
INIT
1IT
ERREAD1
SUMCAL
IQFA
IF
HST3D
DUMP
INIT
1ITER
READ1
Vari
able
type
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTEGER* 4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGER*4
INTEGER*4
Tabl
e 11
.2--
Cros
s-re
fere
nce
list
of var
iabl
es C
ontinued
e- OJ
Vari
able
name
IQFB
CV
IQFF
X
IQFFY
IQFF
Z
IQFL
BC
1QFS
BC
IQHAIF
IQHC
BC
IQHF
BC
Refer
encing
prog
rams
HST3D
DUMP
INIT
1RE
AD1
HST3D
HST3D
HST3D
HST3D
DUMP
INIT
1RE
AD1
HST3D
DUMP
INIT
1IT
ERRE
AD1
HST3D
DUMP
INIT
1RE
AD1
HST3D
DUMP
INIT
1RE
AD1
HST3D
DUMP
INIT
1IT
ERRE
AD1
Vari
able
ty
pe
INTE
GER*
*INTEGER**
INTE
GER*
*IN
TEGE
R**
INTE
GER*
*
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTE
GER*
*
INTEGER**
INTE
GER*
*IN
TEGE
R**
INTEGER**
INTE
GER*
*
INTE
GER*
*INTEGER**
INTEGER**
INTEGER**
INTE
GER*
*IN
TEGE
R**
INTE
GER*
*INTEGER**
INTE
GER*
*INTEGER**
INTE
GER*
*INTEGER**
INTEGER**
Vari
able
name
IQHFX
IQHFY
IQHF
Z
IQHLBC
IQHL
YR
IQHSBC
IQHW
IQSAIF
Refe
r
enci
ng
programs
HST3D
HST3D
HST3D
HST3D
DUMP
INIT1
READ
1
HSXSD
DUMP
INIT
1IT
ERREAD1
SUMCAL
HST3D
DUMP
INIT
1IT
ERRE
AD1
HST3D
DUMP
INIT
1ITER
READ
1SUMCAL
HST3D
DUMP
INIT
1READ1
Vari
able
ty
pe
INTEGER**
INTE
GER*
*
INTEGER**
INTEGER**
INTE
GER*
*INTEGER**
INTE
GER*
*
INTEGER**
INTEGER**
INTE
GER*
*INTEGER**
INTEGER**
INTE
GER*
*
INTEGER**
INTE
GER*
*INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTE
GER*
*IN
TEGE
R**
INTEGER**
INTE
GER*
*INTEGER**
INTEGER**
INTE
GER*
*INTEGER**
INTEGER**
Table
11.2--Cross-reference
list
of
variables Continued
Variable
name
IQSF
BC
IQSFX
IQSF
Y
IQSF
Z
IQSL
BC
IQSLYR
IQSSBC
IQSW
Refe
r
enci
ng
prog
rams
HST3D
DUMP
INIT
1ITER
READ
1
HST3D
HST3D
HST3D
HST3D
DUMP
INIT
1RE
AD1
HST3D
DUMP
INIT
1IT
ERRE
AD1
SUMC
AL
HST3D
DUMP
INIT
1IT
ERRE
AD1
HST3D
DUMP
INIT
1ITER
READ
1SU
MCAL
Vari
able
ty
pe
INTE
GER*
4INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4
INTEGER*4
INTEGER*4
INTE
GER*
4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGER* 4
INTE
GER*
4
INTEGER* 4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGER* 4
INTE
GER*
4
Refer-
Vari
able
encing
name
prog
rams
IQWLYR
HST3D
DUMP
INIT1
ITER
READ
1SUMCAL
IQWM
HST3D
DUMP
INIT
1ITER
READ1
SUMCAL
IQWV
HST3D
DUMP
INIT
1IT
ERREAD1
SUMCAL
IR2
PRNT
AR
IR3
PRNT
AR
IR3LBL
PRNT
AR
IR3P
PR
NTAR
IRBW
HST3D
DUMP
INIT
1ITER
READ
1
Variable
type
INTEGER*4
INTE
GER*
4INTEGER* 4
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4
INTE
GER*
4INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER* 4
INTEGER*4
INTEGER*4
INTEGER*4
CHARACTER*!
INTE
GER*
4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGER*4
INTE
GER*
4
Tabl
e 11.2
--Cr
oss-
refe
renc
e li
st of
var
iabl
es C
ontinu
ed
00
Vari
able
na
me
IRCPPM
IRF
IRH
IRH1
IRHS
IRHSBC
Refe
r
enci
ng
prog
rams
HST3D
DUMP
INIT
1RE
AD1
HST3D
DUMP
INIT
1RE
AD1
HST3
DDU
MPIN
IT1
READ
1
HST3D
DUMP
INIT
1IT
ERRE
AD1
HST3
DDUMP
INIT
1RE
AD1
HST3D
DUMP
INIT
1IT
ERRE
AD1
Variable
type
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
^INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4
INTEGER*4
INTEGER* 4
INTE
GER*
4INTEGER*4
INTE
GER*
4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
Refe
r-
Vari
able
encing
name
programs
IRHSW
HST3D
DUMP
INIT
1IT
ERREAD1
SUMCAL
IRM
HST3D
DUMP
INIT
1READ1
IROW
D4DES
IRS
HST3D
DUMP
INIT
1READ1
IRS1
HST3D
DUMP
INIT
1IT
ERREAD1
ISIGN
HST3D
WBBAL
WELLSS
WELR
IS
ISOR
D HST3D
DUMP
L2SOR
READ1
WRITES
Vari
able
type
INTE
GER*
4INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGER* 4
INTEGER*4
INTEGER* 4
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER* 4
INTE
GER*
4
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGER*4
INTEGER* 4
INTEGER*4
INTE
GER*
4
INTEGER*4
DIME
NSIO
N (3)
INTE
GER*
4 DI
MENS
ION (3
)IN
TEGE
R*4
DIME
NSIO
N (3)
INTE
GER*
4 DI
MENS
ION (3
)INTEGER*4
DIMENSION (3)
Tabl
e 11.2 Cross-reference
list
of
variables
Continued
-fs
GJ VO
Vari
able
name
ISUM
1SXX
ISYY
ISZZ
IT ITAI
F
Refe
r
encing
programs
ORDER
HST3D
DUMP
INIT
1IT
ERRE
AD1
HST3D
DUMP
INIT
1ITER
READ
1
HST3
DDU
MPIN
IT1
ITER
READ
1
HST3D
DUMP
INIT
1RE
AD1
HST3D
DUMP
INIT
1ITER
READ
1
Vari
able
ty
pe
INTE
GER*
4
INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER* 4
INTE
GER*
4IN
TEGE
R* 4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
Refer-
Vari
able
encing
name
programs
ITBW
R HST3D
DUMP
INIT
1INIT2
READ1
WBBAL
WELL
SS
ITC
HST3D
ITCS
HST3D
ITCW
HST3D
ITFLX
HST3D
DUMP
INIT
1IT
ERREAD1
ITFW
HST3D
DUMP
INIT1
ITER
READ1
SUMCAL
ITFX
HST3D
ASEM
BLDU
MPINIT1
READ
1
Variable
type
INTE
GER*
4IN
TEGE
R* 4
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4
INTE
GER*
4
INTEGER*4
INTEGER* 4
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R* 4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
Tabl
e 11.2 Cross-reference list of
variables Continued
Vari
able
name
ITFY
ITFZ
ITHC
BC
ITHX
ITHX
Y
ITHX
Z
Refe
r
enci
ng
prog
rams
HST3D
ASEMBL
DUMP
INIT
1RE
AD1
HST3D
ASEM
BLDUMP
INIT
1RE
AD1
HST3D
DUMP
INIT
1RE
AD1
HST3D
ASEM
BLDU
MPIN
IT1
READ
1
HST3D
ASEMBL
DUMP
INIT
1RE
AD1
HST3D
ASEMBL
DUMP
INIT
1RE
AD1
Vari
able
ty
pe
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER* 4
Refer-
Variable
encing
name
programs
ITHY
HST3D
ASEM
BLDUMP
INIT1
READ
1
ITHYX
HST3D
ASEMBL
DUMP
INIT
1READ1
ITHYZ
HST3D
ASEM
BLDU
MPIN
IT1
READ1
ITHZ
HST3D
ASEM
BLDU
MPINIT1
READ1
ITHZX
HST3D
ASEM
BLDUMP
INIT1
READ1
ITHZ
Y HST3D
ASEM
BLDUMP
INIT
1READ1
Variable
type
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTEGER*4
INTEGER* 4
INTE
GER*
4INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4
Tabl
e 11.2 Cross-reference li
st of variables
Continued
c- -c-
Variable
name
ITIM
E
ITLBC
ITM1
Refe
r
enci
ng
prog
rams
HST3
DAP
LYBC
CALCC
CLOS
ECOEFF
DUMP
ERROR3
ETOM2
INIT2
INIT
3IT
ERREAD1
READ
3SU
MCAL
WBBA
LWELLSS
WRITE2
WRITE3
WRIT
E4WR
ITES
HST3
DDU
MPINIT1
ITER
READ1
HST3
DDU
MPIN
IT1
L2SOR
READ1
Variable
type
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTE
GER*
4INTEGER*4
Vari
able
na
me
ITM2
ITMA
X
ITNO
ITNO
C
ITNO
P
ITNOT
ITNP
ITO
ITOS
ITOW
Refe
r
enci
ng
prog
rams
HST3
DDU
MPIN
IT1
L2SOR
READ
1
HST3D
SUMC
ALTOFEP
WRIT
ES
SOR2
L
HST3
DSO
R2L
WRITES
HST3
DSO
R2L
WRIT
ES
HST3
DSO
R2L
WRIT
ES
HST3
D
HST3
D
HST3
D
HST3
D
Vari
able
type
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGER*4
INTE
GER*
4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTE
GER*
4
INTE
GER*
4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4
INTE
GER*
4INTEGER*4
INTE
GER*
4
INTE
GER*
4
INTEGER*4
INTE
GER*
4
INTE
GER*
4
Tabl
e 11.2 Cross-reference list of variables Continued
Vari
able
na
me
ITP1
ITP2
ITPH
BC
ITQFLX
ITRN
ITRN
1
ITRN
2
ITRN
DN
ITRN
I
ITRN
P
Refe
r
enci
ng
prog
rams
HST3D
DUMP
IN1T
1L2SOR
READ
1
HST3D
DUMP
INIT
1L2SOR
READ
1
HST3D
DUMP
INIT
1RE
AD1
HST3D
HST3D
ASEM
BLIT
ERWR
ITES
WELL
SS
WELLSS
WELLSS
ITER
ITER
Vari
able
ty
pe
INTE
GER*
4IN
TEGE
R*A
INTEGER*A
1NTEGE
R*4
INTE
GER*
4
INTEGER*4
INTEGER*4
INTEGER* 4
INTEGER*4
INTEGE
R* 4
INTEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4
INTE
GER*
4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTE
GER*
4
INTE
GER*
4
INTE
GER*
4
INTEGER*4
Refe
r-
Vari
able
encing
name
programs
ITSB
C HST3D
DUMP
INIT
1ITER
READ
1
ITSX
HST3D
ASEM
BLDUMP
INIT
1READ1
ITSX
Y HST3D
ASEMBL
DUMP
INIT
1RE
AD1
ITSXZ
HST3D
ASEM
BLDUMP
INIT
1READ1
ITSY
HST3D
ASEMBL
DUMP
INIT1
READ
1
ITSYX
HST3D
ASEM
BLDU
MPIN
IT1
READ
1
Vari
able
type
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGER*4
INTE
GER*
4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGER*4
INTEGER* 4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGER*4
INTE
GER*
4
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGERS
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4
Tabl
e 11.2 Cr
oss-
refe
renc
e list of var
iabl
es Continued
Variable
name
ITSY
Z
ITSZ
ITSZX
ITSZ
Y
ITTWR
Refer
enci
ng
programs
HST3D
ASEM
BLDUMP
INIT
1RE
AD1
HST3D
ASEM
BLDU
MPIN
IT1
READ
1
HST3D
ASEM
BLDUMP
INIT
1RE
AD1
HST3D
ASEM
BLDU
MPIN
IT1
READ
1
HST3D
DUMP
INIT
1IN
IT2
READ
1WBBAL
WELL
SS
Variable
type
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTE
GER*
4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGER*4
Refer-
Vari
able
encing
name
prog
rams
ITWKT
HST3D
DUMP
INIT1
HER
READ
1SUMCAL
ITWSUR
HST3D
DUMP
INIT1
HER
READ
1SUMCAL
ITX
HST3D
DUMP
INIT
1RE
AD1
ITY
HST3D
DUMP
INIT
1READ1
ITZ
HST3D
DUMP
INIT1
READ1
IUBB
LB
HST3D
Variable
type
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4
INTEGER*4
INTEGER*4
INTEGER* 4
INTE
GER*
4
INTEGER* 4
INTE
GER*
4INTEGER*4
INTE
GER*
4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTE
GER*
4
INTE
GER*
4
Table
11.2 Cross-reference li
st o
f variables Continued
Vari
able
name
IUCB
C
IUDNBC
IUDNLB
IUDT
HC
IUH
IUKHBC
IUKL
B
IUPHIL
IUTB
C
IUVAIF
IUVI
SL
IUZELB
IV IVA
Refe
r
enci
ng
prog
rams
HST3
D
HST3
D
HST3D
HST3
D
D*DE
S
HST3
D
HST3
D
HST3
D
HST3D
HST3D
HST3
D
HST3
D
REWI
3
HST3
DDU
MPIN
IT1
L2SOR
READ
1
Vari
able
type
INTEGER**
INTE
GER*
*
INTEGER**
INTEGER**
INTE
GER*
*
INTE
GER*
*
INTE
GER*
*
INTE
GER*
*
INTE
GER*
*
INTEGER**
INTEGER**
INTEGER**
INTE
GER*
*
INTEGER**
INTE
GER*
*INTE
GER*
*INTEGER**
INTEGER**
Refer-
Vari
able
encing
name
programs
IVAIF
HST3D
DUMP
INIT1
READ
1
IVAS
BC
HST3D
DUMP
INIT
1ITER
READ1
IVAW
HST3D
DUMP
INIT1
ITER
READ
1SUMCAL
I VIS
HST3D
DUMP
INIT
1READ1
IVPA
HST3D
DUMP
INIT
1ITER
L2SOR
READ1
SUMCAL
Variable
type
INTE
GER*
*INTEGER**
INTE
GER*
*IN
TEGE
R**
INTEGER**
INTE
GER*
*IN
TEGE
R**
INTE
GER*
*INTEGER**
INTEGER**
INTE
GER*
*INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTE
GER*
* DIMENSIONS)
INTEGER** DIMENSIONS)
INTEGER** DIMENSIONS)
INTE
GER*
* DIMENSION (*)
INTEGER** DIMENSIONS)
INTEGER**
DIMENSION (*
)INTEGER** DIMENSIONS)
Tabl
e 11.2--Cross-reference
list
of
variables
Continued
Variable
name
IVSLBC
IVXX
IVYY
IVZZ
IW IW1P
IW2P
IWAI
F
Refe
r
enci
ng
prog
rams
HST3D
DUMP
INIT
1RE
AD1
HST3
D
HST3
D
HST3
D
ASEM
BLER
ROR2
INIT
2IT
ERRE
AD2
WBBAL
WELLSS
WRITE2
WRITES
ZONPLT
WRITES
WRITES
HST3D
DUMP
INIT
1RE
AD1
Variable
type
INTEGER**
INTE
GER*
4IN
TEGE
R**
INTEGER**
INTE
GER*
*
INTE
GER*
*
INTE
GER*
*
INTEGER**
DIMENSION (*
)INTEGER**
DIME
NSIO
N (*)
INTE
GER*
* DIMENSIONS)
INTE
GER*
* DIMENSION (*)
INTE
GER*
* DI
MENS
ION (*
)INTEGER**
DIMENSION (*)
INTEGER** DIMENSION^)
INTE
GER*
* DI
MENS
ION (*
)IN
TEGE
R**
DIMENSION (*)
INTE
GER*
*
INTE
GER*
*
INTE
GER*
*
INTEGER**
INTE
GER*
*IN
TEGE
R**
INTE
GER*
*
Refer-
Variable
encing
name
pr
ogra
ms
IWEL
AS
EMBL
ERRO
R2ERROR3
ETOM
1IN
IT2
ITER
PLOT
OCREAD2
READ3
SUMCAL
WBBAL
WELL
SSWELRIS
WRIT
E2WR
ITE3
WRIT
ES
IWFICU
HST3D
DUMP
INIT
1READ1
IWFP
CU
HST3D
DUMP
INIT
1READ1
IWHI
CU
HST3D
DUMP
INIT1
READ1
Vari
able
ty
pe
INTEGER**
INTE
GER*
*IN
TEGE
R**
INTEGER**
INTEGER**
INTE
GER*
*IN
TEGE
R**
INTE
GER*
*INTEGER**
INTE
GER*
*INTEGER**
INTE
GER*
*INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTE
GER*
*INTEGER**
INTEGER**
INTEGER**
IWCF
HST3D
INTEGER**
Tabl
e 11.2 Cross-reference li
st of
var
iabl
es C
onti
nued
Vari
able
name
IWHPCU
IWI
IWID
IWOD
IWPP
IWQ1
IWQ2
Refe
r
enci
ng
programs
HST3D
DUMP
INIT
1RE
AD1
HST3D
DUMP
INIT
1ITER
READ
1SU
MCAL
HST3D
DUMP
INIT
1IN
IT2
READ
1WBBAL
WELLSS
HST3D
DUMP
INIT
1IN
IT2
READ
1WBBAL
WELL
SS
WRITES
WRITE2
WRITE2
Variable
type
INTEGER*4
INTE
GER*
4IN
TEGE
R*A
INTE
GER*
4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGER*4
INTEGE
R*4
INTEGER* 4
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4
INTE
GER*
4
Refer-
Vari
able
encing
name
programs
1WQMTH
HST3D
DUMP
INIT
1ITER
READ1
SUMCAL
IWRANG
HST3D
DUMP
INIT
1INIT2
READ1
WBBAL
WELLSS
IWRSL
HST3D
DUMP
INIT
1INIT2
READ1
WBBAL
IWRUF
HST3D
DUMP
INIT
1INIT2
READ
1WBBAL
WELL
SS
IWSICU
HST3D
DUMP
INIT
1READ1
Vari
able
type
INTEGER*4
INTEGER* 4
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTE
GER*
4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4
Tab
le
11.2
--C
ross
-ref
eren
ce li
st
of
var
iaJb
Jes-
-Conti
nued
Variable
name
IWSPCU
IX IX1M
IX1P
IX2M
IX2P
IX3M
IX3P
IXX
IXXN
Refe
r
enci
ng
prog
rams
HST3D
DUMP
INIT
1RE
AD1
HST3
DDU
MPIN
IT1
READ
1SO
R2L
SOR2
L
SOR2
L
SOR2
L
SOR2L
SOR2
L
HST3D
DUMP
INIT
1L2SOR
READ
1
HST3D
DUMP
INIT
1L2SOR
READ
1
Variable
type
INTE
GER*
*INTEGER**
INTE
GER*
4IN
TEGE
R**
INTEGER**
INTEGER**
INTE
GER*
*IN
TEGE
R**
INTEGER**
INTEGER**
INTE
GER*
*
INTEGER**
INTEGER**
INTEGER**
INTE
GER*
*INTEGER**
INTE
GER*
*INTEGER**
INTE
GER*
*
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
Refer-
Variable
encing
name
pr
ogra
ms
IY
HST3D
DUMP
INIT
1READ1
IZ
HST3D
DUMP
INIT1
ITER
READ
1
IZEL
BC
HST3D
DUMP
INIT
1ITER
READ1
IZHC
BC
HST3D
DUMP
INIT1
READ1
Variable
type
INTEGER**
INTE
GER*
*IN
TEGE
R**
INTE
GER*
*
INTE
GER*
*IN
TEGE
R**
INTE
GER*
*IN
TEGE
R**
INTE
GER*
*
INTEGER**
INTE
GER*
*INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTE
GER*
*IN
TEGE
R**
INTE
GER*
*
Tabl
e 11.2 Cross-reference li
st of
var
iabl
es C
ontinued
00
Refe
r-
Variable
enci
ng
name
programs
J AS
EMBL
BSOD
ECO
EFF
CRSD
SPD4
DES
DUMP
ERRO
R2ET
OM1
INIT
2IN
TER?
IREU
IMAP2D
ORDER
READ
1RE
AD2
READ
3RE
WIRE
WI3
SUMC
ALVSINIT
WRITES
ZONPLT
Jl
D4DES
IREW
IMAP2D
READ
2RE
AD3
REWI
REWI
3ZO
NPLT
Vari
able
ty
pe
INTE
GER*
4INTEGER*4
INTE
GER*
4INTEGER*4
INTEGERS
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGERS
INTEGER*4
INTEGER* 4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4INTEGERS
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGERS
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4INTEGERS
Refe
r-
Variable
encing
name
programs
J1Z
COEFF
ERROR2
INIT
2RE
AD2
WRIT
E2
J2
D4DES
IREW
IMAP2D
READ
2READ3
REWI
REWI
3ZONPLT
J2Z
COEFF
ERRO
R2INIT2
READ
2WRITE2
J4
D4DES
JBOT
MAP2D
JC
ERROR2
INIT2
MAP2D
JCMAX
HST3D
SUMCAL
WRIT
ES
Vari
able
ty
pe
INTEGER*4 DIMENSION^)
INTEGER*4
DIMENSION (*)
INTEGERS DIMENSION (*
)INTEGER*4 DIMENSION^)
INTEGERS DIMENSION (*)
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4
INTEGER*4
DIMENSION (*)
INTEGER*4
DIMENSION(*)
INTEGERS DIMENSION (*
)INTEGER*4
DIMENSION (*
)INTEGERS DIMENSION(*)
INTE
GER*
4
INTE
GER*
4
INTEGER* 4
INTEGERS
INTE
GER*
4
INTE
GER*
4INTEGER*4
INTEGER*4
Tabl
e 11
.2 C
ross
-ref
eren
ce 2i
st o
f variables Cont
inue
d
Variable
name
JHVSV
JHVSV1
JI JIFMT
JINC
JJ JJ2
JL JMAP
1
JMAP2
JODD
JPMAX
Refe
r
encing
prog
rams
BSOD
E
BSODE
ERROR2
PRNT
AR
MAP2D
D4DES
D4DES
PLOT
HST3D
ERRORS
ETOM
2 IN
IT3
READ
3 WRITE3
WRITES
HST3D
ERROR3
ETOM
2 IN
IT3
READ
3 WRITE3
WRIT
ES
BSODE
HST3D
SUMC
ALWRITES
Vari
able
type
INTEGER*4
INTE
GER*
4
INTEGER*4
INTE
GER*
4
INTE
GER*
4
INTE
GER*
4
INTE
GER*
4
INTE
GER*
4
INTE
GER*
4 DI
MENS
ION (3
)IN
TEGE
R*4
DIME
NSIO
N (3
)IN
TEGE
R*4
DIMENSION (3
) IN
TEGE
R*4
DIME
NSIO
N (3
) INTEGER*4
DIMENSION (3
) INTEGERS DIMENSION (3
) IN
TEGE
R*4
DIMENSION (3
)
INTEGER*4
DIME
NSIO
N (3
) INTEGERS DI
MENS
ION(
3)
INTE
GER*
4 DI
MENS
ION(
3)
INTE
GER*
4 DIMENSION (3)
INTE
GER*
4 DI
MENS
ION (3
) IN
TEGE
R*4
DIME
NSIO
N (3)
INTEGER*4
DIME
NSIO
N(3)
INTE
GER*
4
INTEGER*4
INTEGERS
INTE
GER*
4
Refe
r-
Variable
enci
ng
name
programs
JPRPTC
WRIT
E2WR
ITES
JPT
PLOTOC
JSTART
BSODE
WELRIS
JTIME
HST3D
COEFF
INIT3
JTMAX
HST3D
SUMCAL
WRIT
ES
JTOP
MAP2D
JW
ASEM
BL
ERROR2
INIT2
ITER
READ2
WBBAL
WELL
SS
WRIT
E2
WRITES
JWELL
WELLSS
Vari
able
ty
pe
INTEGERS
INTE
GER*
4
INTE
GER*
4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGERS
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGER*4
INTEGER*4
DIMENSION (*)
INTEGERS DIMENSION (*
) INTEGER*4
DIMENSION(*)
INTE
GER*
4 DIMENSION (*)
INTEGER*4
DIMENSION (*)
INTEGER*4
DIMENSION(*)
INTEGER*4
DIME
NSIO
N(*)
INTEGER*4
DIMENSION(*)
INTE
GER*
4 DIMENSION (*)
INTE
GER*
4 DIMENSION(*)
Tabl
e 11.2 Cross-reference li
st of
variables Continued
-O
Ui o
Refe
r-
Variab
le
enci
ng
name
programs
K APLYBC
ASEMBL
BSODE
CALC
CCO
EFF
CRSD
SPDU
MPERROR2
ETOM
1INIT2
IREW
IIT
ERMAP2D
ORDER
READ1
READ
2RE
WIREWI3
SUMC
ALVS
INIT
WBBAL
WBCFLO
WELL
SSWE
LRIS
WRIT
E2WRITES
Kl
INIT
2IR
EWI
MAP2
DREWI
REWI 3
WRITES
Vari
able
type
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTE
GER*
*INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTE
GER*
*IN
TEGE
R**
INTE
GER*
*IN
TEGE
R**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
Refe
r-
Vari
able
en
cing
name
programs
K1Z
COEFF
ERRO
R2IN
IT2
READ
2WR
ITE2
K2
IREWI
MAP2
DRE
WIRE
WI3
K2Z
COEFF
ERRO
R2INIT2
READ
2WRITE2
KARH
C AP
LYBC
INIT2
KG
PLOT
KCMA
X HS
T3D
SUMC
ALWR
ITES
KF
INIT2
KFLA
G BS
ODE
WELRIS
KING
INIT2
KK
MAP2
D
Variable
type
INTE
GER*
* DIMENSION^)
INTE
GER*
* DI
MENS
ION (*)
INTEGER** DIMENSION^)
INTEGER**
DIME
NSIO
N (*
)INTEGER** DIMENSION^)
INTE
GER*
*IN
TEGE
R**
INTE
GER*
*IN
TEGE
R**
INTE
GER*
* DIMENSIONS)
INTE
GER*
* DIMENSIONS)
INTE
GER*
* DIMENSIONS)
INTE
GER*
* DIMENSIONS)
INTEGER** DIMENSIONS)
REAL
*8 DI
MENS
ION (*
)RE
AL*8
DIMENSIONS)
INTE
GER*
*
INTE
GER*
*IN
TEGE
R**
INTE
GER*
*
INTEGER**
INTE
GER*
*IN
TEGE
R**
INTE
GER*
*
INTE
GER*
*
Table
11.2 Cross-reference list of
variables
Continued
Variable
name
KL KLBC
KMAP
1
KMAP2
KMAX
KO KOAR
Refe
r
enci
ng
programs
INIT
2
APLYBC
INIT
2WRITE2
HST3D
ERRO
R3ET
OM2
1NIT
3RE
AD3
WRITES
WRITES
HST3D
ERRO
R3ET
OM2
INIT
3RE
ADS
WRITES
WRITES
WELR
IS
PLOT
HST3D
APLY
BCDUMP
ETOM
1IN
IT2
READ
1RE
AD2
WRITE2
Vari
able
type
INTE
GER*
4
REAL
*8 DI
MENS
ION (*)
REAL
*8 DI
MENS
ION (*)
REAL*8 DIMENSION (*)
INTEGER*4
DIME
NSIO
N (3
)IN
TEGE
R*4
DIME
NSIO
N (3)
INTEGER*4
DIMENSION(3)
INTEGE
R*4
DIME
NSIO
N (3
)IN
TEGE
R*4
DIME
NSIO
N (3
)IN
TEGE
R*4
DIME
NSIO
N (3)
INTEGER*4
DIMENSION (3)
INTEGER*4 DIMENSION (3)
INTEGER*4
DIME
NSIO
N(3)
INTEGER*4
DIME
NSIO
N (3)
INTEGE
R*4
DIME
NSIO
N (3
)IN
TEGE
R*4
DIMENSION (3
)INTEGER*4
DIMENSION(3)
INTE
GER*
4 DIMENSION(3)
INTE
GER*
4
INTEGER*4
REAL*8
REAL
*8REAL*8
REAL*8
REAL*8
REAL
*8REAL*8
REAL* 8
Refer-
Vari
able
encing
name
pr
ogra
ms
KPMAX
HST3D
SUMCAL
WRIT
ES
KTHA
WR
ETOM
1READ2
WELRIS
KTHF
HST3D
DUMP
ETOM
1INIT2
READ
1RE
AD2
WRITE2
KTHWR
ETOM
1READ2
WELR
IS
KTHX
COEFF
ETOM1
INIT2
KTHX
PM
INIT
2READ2
WRIT
E2
KTHY
COEFF
ETOM
1IN
IT2
Vari
able
type
INTEGER*4
INTEGER*4
INTEGER* 4
INTEGER*4
DIMENSION(*)
REAL*8 DIMENSION^)
REAL
*8
REAL
*8RE
AL*8
REAL
*8REAL*8
REAL
*8RE
AL*8
REAL* 8
REAL* 8 DIMENSION (*)
REAL*8 DIMENSION (*)
REAL
* 8
REAL*8 DIMENSION (*
)REAL*8 DI
MENS
ION(
*)REAL*8 DIMENSION (*)
REAL
*8 DIMENSION (*
)REAL*8 DIMENSION (*)
REAL
*8 DIMENSION (*
)
REAL*8 DIMENSION (*)
REAL
*8 DIMENSION^)
REAL*8 DIMENSION (*)
Tabl
e 11.2--Cross-reference
list
of
vari
able
s C
ontinued
CO
Vari
able
name
KTHY
PM
KTHZ
KTHZ
PM
KTMAX
KWEL
KXX
KYY
KZZ
Refe
r
enci
ng
programs
INIT
2RE
AD2
WRIT
E2
COEFF
ETOM
1IN
IT2
INIT
2RE
A02
WRITE2
HST3D
SUMC
ALWRITES
PLOT
OC
ETOM
1IN
IT2
REA0
2WRITE2
ETOM
1IN
IT2
READ
2WRITE2
ETOM
1IN
IT2
READ
2WRITE2
Vari
able
ty
pe
REAL
*8 DI
MENS
IONC
*)REAL*8 DI
MENS
IONC
*)REAL*8 DI
MENS
IONC
*)
REAL*8 DI
MENS
IONC
*)REAL*8 DIMENSIONC*)
REAL*8 DI
MENS
IONC
*)
REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL*8 DI
MENS
IONC
*)
INTEGER*4
INTE
GER*
AIN
TEGE
R*4
INTE
GER*
4
REAL*8 DI
MENS
IONC
*)REAL*8 DIMENSIONC*)
REAL*8 DI
MENS
IONC
*)REAL*8 DI
MENS
IONC
*)
REAL*8 DI
MENS
IONC
*)REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL
*8 DI
MENS
IONC
*)
REAL*8 DIMENSIONC*)
REAL*8 DI
MENS
IONC
*)REAL*8 DI
MENS
IONC
*)REAL*8 DI
MENS
IONC
*)
Refe
r-
Variable
enci
ng
name
pr
ogra
ms
L AP
LYBC
ASEMBL
BSODE
DUMP
ERRO
R2ERRORS
INIT
2IN
IT3
ORDER
PLOT
READ
1RE
AD2
SBCFLO
SUMCAL
WBCF
LOWRITE2
WRITES
WRITES
ZONPLT
LI
ERRO
R2IN
IT2
ZONP
LT
L2
ERROR3
INIT2
SOR2L
ZONPLT
L3
D4DES
Vari
able
type
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER* 4
INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTEGER* 4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4
INTEGER*4
Tabl
e 11
.2--
Cros
s-re
fere
nce
2ist
of
variables
Continued
ui U)
Variable
name
LABE
L
LBLDIR
LBLEQ
LBW
LCBOTW
Refer
enci
ng
programs
REWI
REWI
3WR
ITE2
ZONP
LT
SOR2
LWRITES
L2SO
RSOR2L
ORDE
R
ASEMBL
ERRO
R2INIT2
ITER
READ
2WBBAL
WBCF
LOWE
LLSS
WRITE2
WRIT
ES
Variable
Vari
able
ty
pe
name
CHARACTER*13 DI
MENS
ION (5
) LC
ROSD
CHAR
ACTE
R* 10 DI
MENS
ION (3)
CHAR
ACTE
R*20
CHAR
ACTE
R*4
CHAR
ACTE
R*!
DIME
NSIO
N (3)
CHAR
ACTE
R*!
DIME
NSIO
N (3)
CHAR
ACTE
R*10
DI
MENS
ION(
3)CH
ARACTER* 10 DI
MENS
ION (3
)
INTE
GER*
4 DI
MENS
ION (*)
INTEGER*4
DIME
NSIO
N (*)
INTE
GER*
4 DI
MENS
ION (*)
INTEGER*4
DIME
NSIO
N (*)
INTE
GER*
4 DI
MENS
ION (*)
INTEGER*4
DIME
NSIO
N (*
) LC
TOPW
INTEGER*4
DIME
NSIO
N (*
)INTEGER*4
DIME
NSIO
N (*)
INTE
GER*
4 DI
MENS
ION (*)
INTEGER*4
DIME
NSIO
N (*)
INTE
GER*
4 DI
MENS
ION (*)
Refe
r
encing
programs
HST3D
ASEM
BLCOEFF
DUMP
ERRO
R!INIT1
INIT2
ITER
READ
!RE
AD2
SBCF
LOWBCFLO
WRIT
E!WR
ITE2
WRITE4
WRITES
ASEMBL
ERROR2
INIT2
ITER
READ
2WBBAL
WBCF
LOWE
LLSS
WRITE2
WRIT
ES
Variable
type
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGI
CAL*
4LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
INTE
GER*
4 DI
MENS
ION (*)
INTE
GER*
4 DI
MENS
ION (*)
INTE
GER*
4 DI
MENS
ION (*)
INTE
GER*
4 DI
MENS
ION (*)
INTE
GER*
4 DI
MENS
ION (*)
INTE
GER*
4 DIMENSION(*)
INTEGER*4
DIME
NSIO
N (*)
INTE
GER*
4 DI
MENS
ION (*)
INTE
GER*
4 DIMENSION^)
INTE
GER*
4 DIMENSION(*)
Tab
le
11.2
--C
ross
-ref
eren
ce li
st
of
vari
ab
les
Co
nti
nu
ed
Vari
able
na
me
LDASH
LDOT
S
LENAX
LENAY
LENA
Z
LGREN
L IMAG
E
LIMIT
LINE
Refe
r
enci
ng
prog
rams
WRITES
CLOSE
REW1
REWI3
WRITE2
WRITES
WRITES
HST3D
MAP2D
READ
3WRITES
WRITE5
ZONPLT
HST3D
MAP2D
READ
3WR
ITE3
WRITES
HST3D
READ
3WRITE3
WRITES
WELL
SSWF
DYDZ
READ
1
WRITE3
PLOT
Vari
able
ty
pe
CHARACTER*1SO
CHAR
ACTER* 130
CHAR
ACTER* 130
CHAR
ACTER* 120
CHAR
ACTER* 130
CHAR
ACTER* 130
CHARACTER* ISO
REAL
* 8
REAL*8
REAL
* 8
REAL*8
REAL
*8RE
AL*8
REAL
* 8
REAL
*8RE
AL*8
REAL*8
REAL
*8
REAL
*8RE
AL*8
REAL*8
REAL
* 8
REAL
*8RE
AL*8
CHAR
ACTE
R*80
CHARACTER*4
CHARACTER*101
Refe
r-
Vari
able
en
cing
na
me
prog
rams
LINL
IM
PLOT
LL
APLYBC
INIT
2
LLL
APLY
BC
LN
MAP2D
LOCAIF
HST3D
APLYBC
DUMP
ERRO
R2ET
OM1
INIT2
READ
1RE
AD2
WRITE2
LPRNT
PRNT
ARWRITE2
WRITE3
WRITE4
WRIT
ES
LRBC
ETOM
1
LTD
APLY
BC
LXL
MAP2D
Vari
able
type
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTE
GER*
4 DIMENSION(*)
INTEGER* 4 DI
MENS
ION(
*)INTEGER*4 DIMENSION^)
INTEGER*4
DIME
NSIO
N(*)
INTEGER*4
DIMENSION(*)
INTEGER*4
REAL*8
INTEGER*4
Table
11.2 Cross-reference list o
f variables Contin
ued
Ln
Ln
Refe
r-
Vari
able
encing
name
pr
ogra
ms
LXR
MAP2D
M
APLYBC
ASEM
BLBSODE
COEFF
CRSD
SPD4DES
DUMP
ERROR2
ERRO
R3ET
OM1
ETOM
2IN
IT2
INIT
3IR
EWI
ITER
L2SOR
ORDER
PRNT
ARRE
AD1
READ2
READS
REWI
REWI
3SBCFLO
SOR2
LSUMCAL
WBBAL
WBCF
LOWE
LLSS
WRITE2
WRITE3
WRITE4
WRITES
Vari
able
ty
pe
INTE
GER*
4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
1NTE
GER*
4INTEGERS
INTE
GER*
4INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGER*4
INTE
GER*
4INTEGERS
INTE
GER*
4INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGER*4
Refer-
Variable
encing
name
prog
rams
Ml
ORDER
REWI
REWI3
SOR2L
WELL
SS
M2
BSODE
REWI
REWI3
SOR2L
M3
SUMCAL
MA
ASEMBL
SBCFLO
WBCFLO
MAIFC
APLY
BCASEMBL
ERROR3
INIT
2IN
IT3
SUMCAL
WRIT
E2WRITES
MAPPTC
HST3D
ERROR3
READ
3WRITES
WRITES
MAXDXX
SOR2L
MAXIT
SOR2L
Variable
type
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4
INTEGER*4
DIMENSION (*)
INTE
GER*
4 DIMENSION(*)
INTEGER*4
DIMENSION (*)
INTE
GER*
4 DIMENSION (*
)INTEGER*4
DIMENSION (*)
INTEGERS DI
MENS
ION(
*)INTEGER*4
DIMENSION (*)
INTEGER*4 DIMENSION^)
INTE
GER*
4INTEGER*4
INTEGER*4
INTEGER*4
1NTEGER*4
REAL*8
INTEGER*4
Tabl
e 11.2 Cross-reference 2i
st of variables Continued
Vari
able
na
me
MAXIT1
MAXI
T2
MAXI
TN
MAXO
RD
MAXP
TS
MAXXX
MD4
Refe
r
enci
ng
prog
rams
HST3
DDUMP
INIT
2RE
AD1
READ
2SO
R2L
HST3D
DUMP
INIT
2RE
AD1
READ
2SO
R2L
HST3D
DUMP
INIT
2IT
ERRE
AD1
READ
2WRITE2
HST3
DBS
ODE
WELRIS
HST3D
BSOD
EWELRIS
SOR2
L
D4DE
SORDER
Vari
able
type
INTE
GER*
4INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTE
GER*
4
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R* 4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4REAL*8
INTE
GER*
4INTEGER*4
Refer-
Variable
encing
name
pr
ogra
ms
METH
HST3D
BSODE
WELR
IS
MFBC
APLYBC
ASEMBL
ERROR3
INIT
2IN
IT3
SUMCAL
WRIT
E2WR
ITE3
WRIT
ES
MFLBL
PLOT
OCWR
ITE2
WRIT
E3WR
ITES
MHCBC
APLY
BCAS
EMBL
INIT
2SUMCAL
WRITE2
WRIT
ES
MIJKM
HST3D
ASEMBL
COEFF
CRSDSP
INIT
2SBCFLO
WBBAL
WBCFLO
WELLSS
Variable
type
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4
INTE
GER*
4 DIMENSION (*)
INTE
GER*
4 DI
MENS
ION (*
)IN
TEGE
R* 4 DIMENSION (*
)IN
TEGE
R* 4 DIMENSION (*
)INTEGER*4
DIMENSION(*)
INTE
GER*
4 DI
MENS
ION(
*)INTEGER*4 DIMENSION^)
INTEGER*4
DIMENSION (*
)INTEGER*4
DIMENSION(*)
CHARACTER* 12
CHARACTER*12
CHARACTER* 12
CHARACTER* 12
INTE
GER*
4 DIMENSION (*
)INTEGER*4
DIMENSION (*
)INTEGER*4
DIMENSION (*
)IN
TEGE
R*4
DIMENSION (*
)IN
TEGE
R*4
DIMENSION (*)
INTEGER*4
DIMENSION (*
)
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGER* 4
INTE
GER*
4
Table
11.2--Cross-reference
list of v
ariables
Continued
Variable
name
M1JKP
MIJMK
MIJM
KM
MIJM
KP
MIJPK
MIJP
KM
MIJPKP
Refe
r
enci
ng
prog
rams
HST3D
ASEM
BLCOEFF
CRSDSP
SBCFLO
WBBAL
WBCF
LOWELLSS
HST3D
ASEM
BLCOEFF
CRSDSP
INIT
2SBCFLO
WBCF
LO
CRSDSP
CRSDSP
HST3D
ASEM
BLCOEFF
CRSDSP
SBCFLO
WBCF
LO
CRSDSP
CRSDSP
Vari
able
ty
pe
INTE
GER*
*INTEGER**
INTE
GER*
*IN
TEGE
R**
INTE
GER*
*IN
TEGE
R**
INTE
GER*
*INTEGER**
INTE
GER*
*IN
TEGE
R**
INTE
GER*
*INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTE
GER*
*
INTEGER**
INTE
GER*
*INTEGER**
INTEGER**
INTE
GER*
*IN
TEGE
R**
INTE
GER*
*
INTEGER**
INTEGER**
Vari
able
name
MIMJK
MIMJKM
MIMJKP
MIMJMK
MIMJPK
MINUS
MIPJK
MIPJKM
MIPJKP
MIPJMK
MIPJPK
Refer
encing
prog
rams
HST3D
ASEM
BLCRSDSP
SBCFLO
WBCF
LO
CRSDSP
CRSD
SP
CRSDSP
CRSDSP
PLOT
HST3D
ASEM
BLCRSDSP
SBCFLO
WBCF
LO
CRSD
SP
CRSDSP
CRSDSP
CRSDSP
Variable
type
INTEGER**
INTE
GER*
*INTEGER**
INTE
GER*
*INTEGER**
INTE
GER*
*
INTE
GER*
*
INTEGER**
INTEGER**
CHAR
ACTE
R*!
INTEGER**
INTE
GER*
*IN
TEGE
R**
INTE
GER*
*INTEGER**
INTEGER**
INTE
GER*
*
INTEGER**
INTEGER**
Table
11.2
Cro
ss-r
efer
ence
list o
f va
riab
les
Continued
Ui
00
Variable
name
MK MKT
ML MLBC
MM MNEXT
MOBW
MSBC
Refe
r
enci
ng
programs
INIT
2
WBBA
LWE
LLSS
WRIT
ES
INIT2
APLY
BCASEMBL
ERROR2
INIT2
INIT3
SUMC
ALWR
ITE2
WRITE3
WRITES
ASEMBL
INIT2
ITER
WBBA
LWE
LLSS
WRIT
ES
BSOD
E
WELL
SS
ASEM
BLIN
IT2
INIT
3SBCFLO
SUMC
ALWR
ITE2
WRIT
E3WRITES
Variable
type
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4
INTE
GER*
4
INTEGER*4
DIME
NSIO
N (*
)INTEGER*4 DI
MENS
ION (*)
INTEGER*4
DIME
NSIO
N (*
)INTEGER*4
DIME
NSIO
N (*
)INTEGER*4
DIME
NSIO
N (*
)INTEGER*4
DIMENSION(*)
INTEGER*4
DIME
NSIO
N (*
)INTEGER*4
DIME
NSIO
N (*)
INTEGER*4
DIME
NSIO
N (*)
INTEGER*4
INTEGER*4
DIME
NSIO
N (8)
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTE
GER*
4
REAL*8 D
IMENSIONC*)
INTE
GER*
4 DI
MENS
ION (*
)INTEGER*4
DIME
NSIO
N (*
)IN
TEGE
R*4
DIMENSIONC*)
INTEGER*4
DIME
NSIO
N (*)
INTEGER*4
DIMENSION(*)
INTEGER*4
DIME
NSIO
N (*)
INTE
GER*
4 DI
MENS
IONC
*)IN
TEGE
R*4
DIME
NSIO
NC*)
Variable
name
MT MTJP
1
MTWO
MWEL
MXITQW
N Nl N2 N3 NA NA1
NA2
NAG
Refer
enci
ng
programs
COEFF
INIT2
SUMCAL
COEFF
BSOD
E
INIT2
HST3
DDU
MPET
OM1
INIT
2RE
AD1
READ
2WE
LLSS
WRITE2
MAP2
D
PRNTAR
ZONP
LT
PRNTAR
ZONP
LT
PRNTAR
ZONPLT
MAP2
D
PRNT
AR
PRNTAR
ERRO
R2
Vari
able
type
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4
INTE
GER*
4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4
CHARACTER*6
CHAR
ACTE
R*2
INTE
GER*
4
Table
11.2--Cross-reference
list of variables Continued
Ul
Variable
name
NAIF
C
NC NCHARS
NCHP
NCHP
L
NCHP
R
NCPR
Refe
r
enci
ng
programs
HST3
DAPLYBC
ASEMBL
DUMP
ERRO
R 1
ERROR2
ERRO
RSET
OM1
ETOM
2IN
IT1
INIT2
INIT3
ITER
READ1
READ
2RE
AD3
SUMCAL
WRIT
E1WRITE2
WRIT
ESWR
ITES
PLOT
PLOT
OC
MAP2D
MAP2D
ZONP
LT
MAP2D
MAP2D
ZONPLT
Vari
able
ty
pe
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4
INTE
GER*
4
INTE
GER*
4
Refer-
Vari
able
en
cing
na
me
programs
NDEL
A MAP2D
NDIM
INTE
RPPR
NTAR
NEHS
T HS
T3D
BLOCKDATA
DUMP
INIT2
READ
1TO
FEP
'
NFBC
HST3
DAPLYBC
ASEMBL
DUMP
ERRO
R1ERROR2
ERRO
R3ET
OM1
ETOM
2IN
IT1
INIT2
INIT3
ITER
READ
1RE
AD2
READ
3SU
MCAL
WRIT
E 1
WRIT
E2WR
ITES
WRIT
ES
NFC
ERRO
R2
Vari
able
type
INTE
GER*
4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R* 4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
Tabl
e 11
.2 C
ross
-ref
eren
ce li
st o
f va
riab
les
Cont
inue
d
Vari
able
name
NGRI
DX
NGRI
DY
NHC
NHCBC
Refe
r
enci
ng
prog
rams
MAP2D
MAP2D
ERRO
R2
HST3
DAP
LYBC
ASEM
BLDUMP
ERROR2
ERROR3
ETOH
1ET
OM2
INIT
1IN
IT2
INIT
3HER
READ
1RE
AD2
READ3
SUMC
ALWRITE1
WRITE2
WRIT
E3WRITES
Variable
type
INTE
GER*
4 DIMENSION(SO)
INTE
GER*
4 DIMENSION (50)
INTEGER**
INTE
GER*
*INTEGER**
INTEGER**
INTE
GER*
*IN
TEGE
R**
INTE
GER*
*IN
TEGE
R**
INTEGER**
INTE
GER*
*IN
TEGE
R**
INTE
GER*
*IN
TEGE
R**
INTEGER**
INTEGE
R**
INTE
GER*
*IN
TEGE
R**
INTEGER**
INTE
GER*
*IN
TEGE
R**
INTEGER**
Refer-
Vari
able
encing
name
pr
ogra
ms
NHCN
HST3D
APLY
BCDU
MPERROR1
ERRO
R2ETOM1
INIT
1INIT2
READ1
READ2
WRITE 1
WRITE2
NL
ZONPLT
Variable
. ty
pe
INTE
GER*
*IN
TEGE
R**
INTE
GER*
*IN
TEGE
R**
INTEGER**
INTE
GER*
*INTEGER**
INTE
GER*
*INTEGER**
INTEGER**
INTE
GER*
*INTEGER**
INTEGER**
Tabl
e 11.2 Cross-reference li
st o
f variables Cont
inue
d
Variable
name
NLBC
NLC
NLP
NMAPR
Refe
r
enci
ng
prog
rams
HST3D
APLY
BCAS
EMBL
DUMP
ERROR1
ERROR2
ERRO
RSET
OM1
ETOM
2IN
IT1
INIT
2IN
IT3
ITER
READ
1RE
AD2
READ
3SU
MCAL
WRITE1
WRIT
E2WRITES
WRIT
ES
ERRO
R2
PLOT
ZONP
LT
HST3D
CLOS
EDU
MPIN
IT2
READ
1
Vari
able
ty
pe
INTE
GER*
4IN
TEGE
R* 4
INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4IN
TEGE
R* 4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTE
GER*
4
INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
Refer-
Variable
encing
name
pr
ogra
ms
NMPZON
HST3D
1NIT
3MAP2D
READ3
WRIT
ESWRITES
NN3
ZONP
LT
NNC
D4DES
NNOPPR
PRNTAR
NNOUT
MAP2D
NNPR
PR
NTAR
NO
PLOT
PLOTOC
NOCV
HST3D
DUMP
ERROR2
ETOM1
INIT
2READ1
READ2
VISCOS
WRIT
E2
NOTV
VSINIT
Vari
able
type
INTE
GER*
4 DI
MENS
ION (3)
INTEGER*4
DIMENSION(3)
INTE
GER*
4INTEGER*4
DIME
NSIO
N(3)
INTE
GER*
4 DIMENSION (3
)INTEGER*4
DIME
NSIO
N(3)
INTE
GER*
4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER* 4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGER*4
INTE
GER*
4
INTEGER*4
Tab
le
11.2
--C
ross
-ref
eren
ce li
st
of
var
iaJb
Ies-
-Conti
nued
N>
Variable
name
NOTVO
NOTV
1
NP NPAG
ES
NPAIF
NPCX
NPCY
NPEH
DT
Refe
r
enci
ng
prog
rams
HST3D
DUMP
ERRO
R2ET
OM1
INIT
2RE
AD1
READ
2VI
SCOS
WRITE2
HST3D
DUMP
ERROR2
ETOM
1IN
IT2
READ
1RE
AD2
VISCOS
WRIT
E2
ZONPLT
MAP2D
APLY
BC
ZONPLT
ZONPLT
HST3D
BLOCKDATA
DUMP
INIT
2RE
AD1
TOFE
P
Variable
type
INTE
GER*
4INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGERS
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4
INTE
GER*
4
1NTEOER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGER*4
Refe
r-
Vari
able
en
cing
na
me
programs
NPMZ
HST3D
COEFF
DUMP
ERRO
R1ERROR2
ETOM
1INIT1
INIT2
READ
1READ2
WRITE 1
WRITE2
ZONP
LT
NPOSNS
MAP2D
NPR2
PRNT
AR
NPR3
PR
NTAR
NPTAIF
HST3D
DUMP
ERROR2
ETOM
1INIT2
READ1
READ2
WRITE2
Variable
type
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4
INTEGERS
INTE
GER*
4
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
Tabl
e 11
.2--
Cros
s-re
fere
nce
list of
var
iabl
es C
onti
nued
to
Variable
name
NPTC
BC
NPTS
A4
Refe
r
enci
ng
prog
rams
HST3D
APLY
BCAS
EMBL
DUMP
ERRO
R1ER
ROR2
ERRO
R3ET
OM1
ETOM
2IN
IT1
INIT
2IN
IT3
ITER
READ
1RE
AD2
READS
SBCFLO
SUMCAL
WRITE1
URIT
E2WR
ITE3
WRITES
HST3D
D4DES
DUMP
INIT
1ORDER
READ
1WRITE1
Variable
type
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGERS
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTE
GER*
4
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
Refer-
Variable
encing
name
programs
NPTSD4
HST3D
D4DES
DUMP
INIT1
ORDER
READ1
WRITE1
NPTS
UH
HST3D
ASEM
BLD4DES
DUMP
INIT1
ORDER
READ
1SBCFLO
WBCF
LOWRITE1
NR
ERRO
R2INIT2
READ2
WRITE2
NROWS
MAP2D
NRP
ZONPLT
NRPR
ZONP
LT
Vari
able
ty
pe
INTE
GER*
4INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4
INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGER*4
INTEGER*4
Tabl
e 11.2 Cross-reference li
st o
f va
riab
les
Cont
inue
d
Vari
able
name
NRST
TP
NS NSC
NSHUT
NSTD
4
NSTS
OR
NTEH
DT
Refe
r
encing
prog
rams
HST3D
CLOSE
DUMP
INIT
2RE
AD1
ZONPLT
ERRO
R2
WELL
SS
HST3D
DUMP
INIT
1RE
AD1
WRIT
E1
HST3D
DUMP
INIT
1RE
AD1
WRITE1
HST3D
BLOC
KDAT
ADUMP
INIT
2RE
AD1
TOFEP
Vari
able
type
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGE
R*4
INTEGER*4
INTE
GER*
4
INTE
GER*
4
INTEGE
R*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGER*4
INTEGE
R*4
INTE
GER*
4INTEGER*4
1NTE
GER*
4INTEGER*4
INTEGE
R*4
INTE
GER*
4INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTE
GER*
4
Refer-
Vari
able
encing
name
pr
ogra
ms
NTHP
TO
PLOT
OC
NTSCHK
HST3D
CLOSE
DUMP
READ3
NTSOPT
HST3D
DUMP
INIT2
ITER
READ1
READ2
SOR2L
WRIT
E2
NVST
VSINIT
Vari
able
type
INTE
GER*
4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
NTHP
TCPLOTOC
INTEGE
R*4
Tabl
e 11.2 Cross-reference li
st of
variables Continued
Refe
r-
Vari
able
en
cing
na
me
prog
rams
NWEL
HST3D
ASEMBL
DUMP
ERRO
R2ERRORS
ETOM
1ET
OM2
INIT
1IN
IT2
INIT
3IT
ERRE
AD1
READ
2READ3
SUMCAL
WBBAL
WELLSS
WRIT
E1WRITE2
WRITE3
WRIT
ES
Variable
type
INTE
GER*
*INTEGER**
INTEGER**
INTE
GER*
*INTEGER**
INTE
GER*
*INTEGER**
INTEGER**
INTEGER**
INTE
GER*
*INTEGER**
INTE
GER*
*IN
TEGE
R**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTE
GER*
*
Refe
r-
Vari
able
encing
name
pr
ogra
ms
NX
HST3D
APLY
BCASEMBL
COEFF
CRSDSP
D4DES
DUMP
ERROR1
ERROR2
ETOM1
ETOM2
INIT
1IN
IT2
INIT3
INTERP
IREWI
ITER
MAP2D
ORDER
PLOTOC
PRNT
ARRE
AD1
READ2
READ3
REWI
REWI3
SBCF
LOSOR2L
SUMCAL
WBBAL
WBCF
LOWELLSS
WRITE1
WRITE2
WRIT
E3WRITE*
WRITES
ZONP
LT
Variable
type
INTEGER**
INTEGER**
INTEGER**
INTE
GER*
*INTEGER**
INTEGER**
INTE
GER*
*IN
TEGE
R**
INTEGER**
INTE
GER*
*INTEGER**
INTE
GER*
*IN
TEGE
R**
INTE
GER*
*INTEGER**
INTE
GER*
*INTEGER**
INTE
GER*
*INTEGER**
INTE
GER*
*IN
TEGE
R**
INTE
GER*
*INTEGER**
INTE
GER*
*INTEGER**
INTEGER**
INTE
GER*
*INTEGER**
INTE
GER*
*IN
TEGE
R**
INTEGER**
INTE
GER*
*IN
TEGE
R**
INTEGER**
INTE
GER*
*INTEGER**
INTE
GER*
*INTEGER**
Tabl
e 11.2 Cross-reference li
st of
variables Continued
Variable
name
NX1
NX2
NX3
NXPR
NXX
Refe
r
enci
ng
programs
ORDER
SOR2L
ZONPLT
ORDER
SOR2L
ZONPLT
ORDER
SOR2
L
PRNT
AR
INIT
2TOFEP
VISCOS
Variable
type
INTE
GER*
*IN
TEGE
R**
INTE
GER*
*
INTE
GER*
*INTEGER**
INTEGER**
INTEGER**
INTE
GER*
*
INTE
GER*
*
INTE
GER*
*INTEGER**
INTE
GER*
*
Refer-
Variable
encing
name
programs
NXY
HST3D
APLYBC
ASEMBL
COEFF
CRSD
SPD4DES
DUMP
ERRO
R1ERROR2
ETOM1
ETOM2
INIT1
INIT2
INIT3
IREW
IIT
ERORDER
PLOT
OCPRNTAR
READ
1READ2
READ3
REWI
REWI3
SBCFLO
SOR2L
SUMCAL
WBBAL
WBCFLO
WELLSS
WRITE 1
WRITE2
WRIT
E3WRITE*
WRITES
Vari
able
ty
pe
INTE
GER*
*IN
TEGE
R**
INTEGER**
INTEGER**
INTEGER**
INTE
GER*
*IN
TEGE
R**
INTE
GER*
*IN
TEGE
R**
INTE
GER*
*IN
TEGE
R**
INTE
GER*
*INTEGER**
INTE
GER*
*IN
TEGE
R**
INTEGER**
INTEGER**
INTE
GER*
*IN
TEGE
R**
INTE
GER*
*IN
TEGE
R**
INTEGER**
INTE
GER*
*INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTE
GER*
*INTEGER**
INTEGER**
INTEGER**
INTE
GER*
*IN
TEGE
R**
INTEGER**
INTE
GER*
*
Tabl
e 11.2 Cross-reference list of variables
Continued
Refe
r-
Vari
able
encing
name
programs
NXYZ
HST3D
APLY
BCAS
EMBL
COEFF
D4DES
DUMP
ERRO
R1ERROR2
ETOM
1ET
OM2
INIT
1IN
IT2
INIT
3IR
EWI
ITER
L2SOR
ORDER
PLOT
OCPR
NTAR
READ
1READ2
READ
3RE
WIREWI3
SOR2
LSUMCAL
WBBAL
UELL
SSWRITE 1
WRITE2
WRIT
ESWRITE4
WRIT
ES
Vari
able
ty
pe
INTEGER**
INTEGER**
INTE
GER*
*IN
TEGE
R**
INTEGER**
INTE
GER*
*IN
TEGE
R**
INTE
GER*
*INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTE
GER*
*INTEGER**
INTEGER**
INTEGER**
INTE
GER*
*INTEGER**
INTEGER**
INTE
GER*
*INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTE
GER*
*IN
TEGE
R**
INTEGER**
INTE
GER*
*INTEGER**
INTEGER**
INTE
GER*
*IN
TEGE
R**
INTEGER**
Refe
r-
Vari
able
en
cing
na
me
prog
rams
NY
HST3D
APLY
BCASEMBL
COEFF
DUMP
ERROR1
ERROR2
ETOM1
INIT1
INIT2
INIT3
INTERP
IREW
IITER
MAP2D
ORDER
PRNTAR
READ1
READ2
READ3
REWI
REWI3
SOR2L
SUMCAL
WBBAL
WELL
SSWRITE1
WRIT
E2WRITE5
ZONP
LT
NY1
ZONPLT
NY2
ZONP
LT
Vari
able
type
INTEGER**
INTEGER**
INTEGER**
INTE
GER*
*IN
TEGE
R**
INTE
GER*
*INTEGER**
INTE
GER*
*INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTE
GER*
*IN
TEGE
R**
INTE
GER*
*INTEGER**
INTEGER**
INTEGER**
INTE
GER*
*INTEGER**
INTEGER**
INTE
GER*
*INTEGER**
INTEGER**
INTE
GER*
*INTEGER**
INTEGER**
INTEGER**
INTE
GER*
*
Table
11.2 Cross-reference li
st of
variables
Continued
00
Vari
able
name
NYPR
NZ NZPR
Refe
r
enci
ng
programs
PRNT
AR
HST3D
APLY
BCAS
EMBL
CALC
CCOEFF
DUMP
ERRO
R1ERROR2
ETOM
1IN
IT1
INIT
2INIT3
IREWI
ITER
ORDER
PRNT
ARREAD1
READ
2READ3
REWI
REWI3
SOR2L
SUMC
ALWB
BAL
WELL
S S
WRITE 1
WRIT
E2WRITES
PRNTAR
Variable
type
INTEGER**
INTEGER**
INTE
GER*
*INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTE
GER*
*INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTE
GER*
*INTEGER**
INTE
GER*
*INTEGER**
INTEGER**
INTE
GER*
*IN
TEGE
R**
INTEGER**
INTEGER**
INTEGER**
INTE
GER*
*INTEGER**
INTEGER**
Refer-
Variable
enci
ng
name
pr
ogra
ms
NZTP
HC
HST3D
DUMP
ETOM
1INIT2
READ
1RE
AD2
WRIT
E2
NZTPRO
HST3
DDUMP
ETOM
1INIT2
READ1
READ2
WRITE2
OCPL
OT
HST3D
CLOSE
DUMP
ERRO
R3RE
AD1
READ2
READ3
SOR2
LWE
LLS S
WELR
ISWR
ITE2
WRITE3
WRIT
ES
ODD
ORDE
R
OH
PLOT
Vari
able
ty
pe
INTE
GER*
*IN
TEGE
R**
INTEGER**
INTE
GER*
*INTEGER**
INTE
GER*
*INTEGER**
INTEGER**
INTEGER**
INTEGER**
INTE
GER*
*INTEGER**
INTE
GER*
*INTEGER**
LOGI
CAL*
*LO
GICA
L**
LOGICAL**
LOGI
CAL*
*LOGICAL**
LOGI
CAL*
*LOGICAL**
LOGICAL**
LOGI
CAL*
*LO
GICA
L**
LOGICAL**
LOGICAL**
LOGI
CAL*
*
LOGI
CAL*
*
CHAR
ACTE
R*!
Tabl
e 11
.2 C
ross
-ref
eren
ce li
st o
f variables Continued
v£>
Variable
name
OMEG
A
OMGMAX
OMGMIN
OMOP
T
ORENPR
ORFR
Refe
r
enci
ng
programs
L2SOR
SOR2
L
SOR2
L
SOR2
L
HST3
DDUMP
L2SOR
READ
1
HST3
DDUMP
INIT2
PRNTAR
READ1
READ2
WRIT
E2WRITES
WRIT
E4WRITES
WRIT
ES
Variable
type
REAL
*8RE
AL*8
REAL
*8
REAL
*8
REAL
*8 DI
MENS
ION (3)
REAL
*8 D
IMEN
SION
(3)
REAL
*8 D
IMEN
SION
(3)
REAL
*8 D
IMEN
SION
(3)
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGERS
INTEGER*4
INTE
GER*
4INTEGER*4
INTE
GER*
4INTEGER*4
1NTE
GER*
4
INTEGER*4
Refer-
Vari
able
en
cing
na
me
programs
P APLYBC
ASEMBL
CALC
CCO
EFF
ETOM1
INIT
2ITER
READ
2SU
MCAL
TOFE
PWBBAL
WELL
SSWRITE2
WRITES
ZONPLT
PO
HST3
DDUMP
ETOM
1IN
IT2
READ1
READ
2SU
MCAL
WBBA
LWE
LLSS
WFDYDZ
WRITE2
WRITES
Vari
able
type
REAL
*8 DI
MENS
ION (*)
REAL
*8 DI
MENS
ION (*
)RE
AL* 8
REAL
*8 DI
MENS
ION (*
)REAL*8 DIMENSION^)
REAL
*8 D
IMENSION(*)
REAL
*8 DIMENSION(*)
REAL
*8 DI
MENS
ION (*)
REAL
*8 DIMENSIONS)
REAL
*8RE
AL*8
DI
MENS
ION (*)
REAL
*8 DI
MENS
ION (*)
REAL*8 DIMENSIONS)
REAL*8 D
IMENSION(*)
CHAR
ACTE
R*10
000
REAL
*8RE
AL*8
REAL
*8RE
AL*8
REAL
*8REAL*8
REAL
*8RE
AL*8
REAL
*8RE
AL*8
REAL
*8RE
AL*8
Tab
le
11.2
--C
ross
-ref
eren
ce li
st
of
var
iaJb
Jes-
-Co
nti
nu
ed
Vari
able
na
me
POO
POH
PI P2 PA P5
Refe
r
enci
ng
programs
HST3
DWBBAL
WELLSS
WELRIS
HST3D
APLY
BCAS
EMBL
DUMP
ETOM
1IN
IT2
READ
1RE
AD2
SUMC
ALWELLSS
WELRIS
WRITE2
PRNT
AR
PRNTAR
PRNT
AR
PRNT
AR
Vari
able
ty
pe
REAL*8
REAL*8
REAL
*8REAL*8
REAL*8
REAL
* 8
REAL*8
REAL*8
REAL*8
REAL
* 8
REAL*8
REAL
* 8
REAL*8
REAL*8
REAL*8
REAL*8
CHAR
ACTE
R*2
CHAR
ACTE
R*2
CHAR
ACTE
R*2
CHARACTER*2
Refe
r-
Vari
able
encing
name
programs
PAATM
HST3D
APLY
BCAS
EMBL
DUMP
ETOM
1INIT2
READ1
READ2
SUMC
ALTOFEP
WBBAL
WELL
SSWELRIS
WRITE2
WRITES
PAEHDT
HST3D
BLOCKDATA
DUMP
INIT
2READ1
TOFEP
PAIF
AP
LYBC
INIT2
Variable
type
REAL
*8REAL*8
REAL*8
REAL
*8REAL*8
REAL
*8RE
AL*8
REAL*8
REAL
*8RE
AL*8
REAL*8
REAL
*8REAL*8
REAL
*8REAL*8
REAL
*8 DI
MENS
ION(
IO)
REAL
*8 DIMENSION (10)
REAL
*8 DI
MENS
ION(
IO)
REAL*8 DIMENSION (1
0)RE
AL*8
DIMENSION(IO)
REAL*8 DIMENSION (10)
REAL
*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
PAR
REWI
REAL*8 DIMENSIONC*)
Tabl
e 11.2 Cross-reference li
st o
f va
riab
les-
-Con
tinu
ed
Variable
name
PARA
PARE
PARC
PCL
PCR
PCS
PCW
PFAC
PFSLOW
PHILBC
PI PINIT
Refe
r
enci
ng
prog
rams
REWI
3
REWI
3
REWI
3
WELLSS
WELLSS
PLOTOC
PLOTOC
MAP2D
SUMCAL
APLYBC
ERRO
RSIN
IT3
WRITES
APLYBC
INIT
2WELLSS
WELRIS
WFDYDZ
HST3D
DUMP
ETOM1
INIT2
READ
1RE
AD2
WRITE2
Vari
able
type
REAL*8 DI
MENS
ION (*
)
REAL*8 DIMENSION(*)
REAL*8 DIMENSION (*
)
REAL
* 8
REAL*8
REAL*8 DI
MENS
ION (*
)
REAL*8 DIMENSION (*)
REAL*8
LOGI
CAL*
4
REAL*8 DIMENSION(*)
REAL*8 DIMENSION (*)
REAL*8 DIMENSION (*
)REAL*8 DIMENSION (*)
REAL
* 8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8REAL*8
REAL*8
REAL
*8RE
AL*8
REAL*8
Variable
name
PLBL
PLOTWC
PLOTWP
PLOTWT
PLTZON
PLUS
PMCHDT
PMCHV
PMCV
Refe
r
encing
programs
WRITES
HST3D
ERROR3
PLOTOC
READ3
HST3D
ERROR3
PLOTOC
READ3
HST3D
ERROR3
PLOTOC
READ3
HST3D
DUMP
READ1
READ2
WRITE2
WRITE3
PLOT
CALCC
CALCC
INIT
2SUMCAL
CALCC
INIT
2SUMCAL
Vari
able
ty
pe
CHAR
ACTE
R*20
LOGI
CAL*
4LOGICAL*4
LOGI
CAL*
4LO
GICA
L*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGI
CAL*
4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGI
CAL*
4LOGICAL*4
LOGI
CAL*
4LOGICAL*4
LOGICAL*4
LOGICAL*4
CHARAC
TER*
!
REAL* 8
REAL*8
REAL
*8 DI
MENS
ION (*
)REAL*8 DIMENSION (*)
REAL*8
REAL*8 DIMENSION (*)
REAL*8 DIMENSIONS)
Tabl
e 11.2 Cross-reference li
st of
var
iabl
es C
onti
nued
ro
Vari
able
name
PMCV
DT
PMHV
PMHV
DT
PNP
POROAR
POROS
POS
POSU
P
POW
PPCL
Refe
r
encing
programs
CALCC
CALC
CINIT2
SUMC
AL
CALC
C
CALCC
ETOM2
INIT3
READ
3
HST3
DAP
LYBC
DUMP
ETOM
1IN
IT2
READ
1RE
AD2
WRIT
E2
COEFF
INIT
2READ2
WRIT
E2
PLOTOC
MAP2D
PLOT
OC
WELL
SS
Vari
able
ty
pe
REAL
*8
REAL
* 8
REAL
*8 D
IMEN
SION
(*)
REAL
* 8 DI
MENS
ION (*
)
REAL*8
REAL
*8RE
AL*8
DIM
ENSI
ON(*
)RE
AL*8
DIMENSION^)
REAL
*8 D
IMENSION (*)
REAL
*8RE
AL*8
REAL
*8RE
AL*8
REAL
*8RE
AL*8
REAL
* 8
REAL*8
REAL
*8 DIM
ENSI
ON (*)
REAL
*8 DIM
ENSI
ON (*)
REAL
*8 DIMENSIONS)
REAL*8 D
IMEN
SION
(*)
REAL
*8 D
IMEN
SION
(*)
LOGI
CAL*
4
REAL*8 D
IMENSIONC*)
REAL
*8
Vari
able
name
PPCR
PRBC
F
PRDV
PRES
S
PRGFB
PRIB
CF
PRIDV
PRIG
FB
PRIKD
PRIMAP
Refer
enci
ng
programs
WELLSS
HST3
DSUMCAL
WRITES
HST3
DSUMCAL
WRIT
ES
TOFEP
. HST3
DSU
MCAL
WRITES
HST3D
READ
3WRITES
HST3
DREAD3
WRITES
HST3D
READ3
WRITES
HST3
DRE
AD3
WRITE4
WRITES
HST3
DREAD3
WRITES
WRIT
ES
Vari
able
type
REAL
*8
LOGICAL*4
LOGI
CAL*
4LOGICAL*4
LOGI
CAL*
4LOGICAL*4
LOGICAL*4
REAL*8
LOGICAL*4
LOGICAL*4
LOGICAL*4
INTEGER*4
INTEGER*4
INTE
GER*
4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
INTEGER*4
INTEGER*4
INTE
GER*
*
INTEGER*4
INTEGER**
INTEGER*4
INTEGER**
INTE
GER*
4IN
TEGE
R*4
INTEGER**
INTE
GER*
4
Table
11.2
Cro
ss-r
efer
ence
li
st o
f variables Cont
inue
d
Variable
name
PRIPTC
PRIS
LM
PRIV
EL
PRIWEL
PRKD
PRNT
PRPTC
PRSLM
Refe
r
encing
prog
rams
HST3
DREADS
WRIT
ES
HST3D
READ
SWR
ITES
HST3D
READ
SWR
ITE4
WRIT
ES
HST3D
READS
WRIT
ES
WRIT
E4
WRITE3
HST3D
SUMCAL
WRIT
ES
HST3D
SUMC
ALWR
ITES
Variable
type
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGER*4
INTE
GER*
4
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTEGER*4
LOGICAL*4
LOGI
CAL*
4
LOGICA
L*4
LOGICAL*4
LOGI
CAL*
4
LOGICAL*4
LOGICA
L*4
LOGICAL*4
Refe
r-
Vari
able
encing
name
prog
rams
PRTBC
HST3D
DUMP
READ1
READ2
READ3
SOR2L
WELLSS
WELRIS
WRITE2
WRIT
E3
PRTC
CM
HST3D
DUMP
READ
1READ2
SUMC
AL
PRTCHR
MAP2D
PRTDV
HST3D
DUMP
READ1
READ2
WRIT
E2WRITE3
Variable
type
LOGICAL*4
LOGICAL*4
LOGI
CAL*
4LOGICAL*4
LOGI
CAL*
4LO
GICA
L*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGI
CAL*
4LOGICAL*4
LOGI
CAL*
4LO
GICA
L*4
LOGICAL*4
CHARACTER* 125
LOGICAL*4
LOGI
CAL*
4LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGI
CAL*
4
Tabl
e 11
.2 C
ross
-ref
eren
ce list of variables Continued
Vari
able
name
PRTFP
PRTIC
PRTM
PD
PRTP
MP
PRTRE
Refer
encing
prog
rams
HST3D
DUMP
READ
1READ2
WRIT
E2WRITE3
HST3D
DUMP
READ
1READ2
WRIT
E2WR
ITE3
HST3D
READ
3WR
ITES
WRITES
HST3D
DUMP
READ
1READ2
WRIT
E2WR
ITE3
HST3D
DUMP
IREW
IRE
AD1
READ2
REWI
REWI3
SUMCAL
Vari
able
type
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGI
CAL*
4LOGICAL*4
LOGI
CAL*
4LO
GICA
L*4
LOGICAL*4
LOGI
CAL*
4LO
GICA
L*4
LOGICAL*4
LOGI
CAL*
4
LOGICAL*4
LOGICAL*4
LOGI
CAL*
4LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
Refer-
Variable
enci
ng
name
programs
PRTS
LM
HST3D
DUMP
READ
1READ2
READ3
SOR2L
WELL
SSWE
LRIS
WRIT
E2WRITE3
PRTW
EL
HST3D
DUMP
READ1
READ2
READ3
WELL
SSWE
LRIS
WRIT
E2WRITE3
PRVE
L WRITE4
PRWE
L HST3D
SUMC
ALWRITES
PSBC
ASEMBL
INIT3
WRITE3
PSLBL
PLOT
OC
Variable
type
LOGI
CAL*
4LO
GICA
L*4
LOGI
CAL*
4L0
6ICA
L*4
LOGICAL*4
LOGICAL*4
LOGI
CAL*
4LO
GICA
L*4
LOGICAL*4
LOGICAL*4
LOGI
CAL*
4LO
GICA
L*4
LOGI
CAL*
4LO
GICA
L*4
LOGICAL*4
LOGI
CAL*
4LOGICAL*4
LOGI
CAL*
4LO
GICA
L*4
LOGI
CAL*
4
LOGICAL*4
LOGI
CAL*
4LO
GICA
L*4
REAL*8 DIMENSION (*
)REAL* 8 DIMENSION (*
)REAL*8 DIMENSIONS)
CHARACTER*50
Tabl
e 11
.2--
Cros
s-re
fere
nce
list
of
var
iabl
es Continued
Variable
name
PSMAX
PSMI
N
PTOP
PU PV PVDTN
PVK
PVKD
TN
PWCE
LL
PWKT
PWKTS
Refe
r
enci
ng
prog
rams
PLOTOC
PLOT
OC
WELL
SS
APLYBC
CALCC
COEFF
INIT
2SUMCAL
WRITE2
CALCC
CALCC
COEFF
INIT
2SU
MCAL
CALCC
WRITES
ASEM
BLER
RORS
ITER
READ
3WBBAL
WELL
SSWR
ITES
WRITES
ITER
WBBAL
WELL
SS
Vari
able
type
REAL*8
REAL*8
REAL*8
REAL*8
REAL* 8
REAL
*8 DI
MENS
ION (*
)REAL*8 DIMENSION(*)
REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL*8
REAL*8
REAL
* 8 DI
MENS
IONC
*)REAL*8 DIMENSIONC*)
REAL*8 DI
MENS
IONC
*)
REAL*8
REAL*8
REAL*8 D
IMEN
SION
C*)
REAL*8 DI
MENS
IONC
*)REAL*8 DIMENSIONC*)
REAL*8 DI
MENS
IONC
*)REAL*8 DIMENSIONC*)
REAL* 8 DI
MENS
IONC
*)REAL*8 DI
MENS
IONC
*)REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL*8 DI
MENS
IONC
*)REAL*8 DIMENSIONC*)
Variable
name
PWLBL
PWMAX
PWMIN
PWREND
PWRK
PWSUR
PWSURS
QDVS
BC
QFAC
QFAIF
QFBC
Refe
r
encing
prog
rams
PLOTOC
PLOTOC
PLOT
OC
HST3D
WBBAL
WELLSS
WELR
IS
WFDY
DZ
WBBAL
WELL
SSWRITES
ERROR3
READ3
WELLSS
WRITE3
SBCF
LO
MAP2D
SUMCAL
WRITES
APLYBC
ASEMBL
SUMCAL
Variable
type
CHAR
ACTE
R*SO
REAL
*8
REAL*8
REAL
*8REAL*8
REAL*8
REAL*8
REAL*8
REAL*8 DI
MENS
IONC
*)REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL*8 DI
MENS
IONC
*)REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL*8
REAL*8 DIMENSIONC*)
REAL*8 DI
MENS
IONC
*)
REAL*8
REAL*8
REAL*8
Tabl
e 11
.2 C
ross
-ref
eren
ce li
st o
f variables Continued
Vari
able
na
me
QFBCV
QFFX
QFFY
QFFZ
QFLBC
QFSB
C
QHAIF
QHBC
Refe
r
enci
ng
prog
rams
APLY
BCASEMBL
ERRO
RSIN
IT3
ITER
SUMC
ALWRITES
WRITES
ETOM
2IN
IT3
READ
3
ETOM
2IN
IT3
READ
3
ETOM
2IN
IT3
READ
3
SUMC
ALWRITES
ASEMBL
ITER
SUMC
ALWRITES
SUMC
ALWRITES
APLYBC
ASEMBL
Vari
able
ty
pe
REAL*8 DIMENSIONC*)
REAL*8 DIMENSION (*)
REAL*8 DI
MENS
ION (*)
REAL*8 DI
MENS
ION (*
)REAL*8 DI
MENS
ION (*)
REAL*8 DIMENSION (*
)RE
AL*8
DI
MENS
ION (*
)REAL*8 DI
MENS
ION (*
)
REAL*8 DIMENSION (*)
REAL*8 DIMENSION (*)
REAL
*8 DIMENSION (*
)
REAL
*8 DI
MENS
ION (*)
REAL
*8 DIMENSION (*
)RE
AL*8
DIMENSION (*)
REAL*8 DI
MENS
IONC
*)REAL*8 DIMENSIONC*)
REAL*8 DIMENSION(*)
REAL
*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL*8 DI
MENS
IONC
*)RE
AL*8 DI
MENS
IONC
*)REAL*8 DI
MENS
IONC
*)
REAL
* 8 DI
MENS
IONC
*)REAL*8 DIMENSIONC*)
REAL*8
REAL*8
Vari
able
na
me
QHCB
C
QHFAC
QHFBC
QHFX
QHFY
QHFZ
QHLBC
QHLYR
Refer
encing
programs
APLYBC
SUMCAL
WRITES
HST3D
WELR
ISWF
DYDZ
APLYBC
ERROR3
INIT
3SUMCAL
WRITE3
WRIT
ES
ETOM2
INIT3
READ3
ETOM2
INIT3
READ3
ETOM2
INIT3
READ3
SUMC
ALWR
ITES
WBBAL
WELLSS
WRIT
ES
Variable
type
REAL*8 DI
MENS
IONC
*)RE
AL*8
DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL*8
REAL
*8REAL* 8
REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL*8 DIMENSION^*)
REAL*8 DI
MENS
IONC
*)REAL*8 DIMENSIONC*)
REAL*8 DIMENSION^*)
REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL
*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL
*8 DI
MENS
IONC
*)
REAL*8 DI
MENS
IONC
*)RE
AL*8
DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL
*8 DIMENSIONC*)
REAL
*8 DI
MENS
IONC
*)
REAL*8 DIMENSIONC*)
REAL
*8 DI
MENS
IONC
*)REAL*8 DI
MENS
ION^
*)
Tabl
e 11
.2--
Cros
s-re
fere
nce
list
of
variables Continued
Vari
able
name
QHSB
C
QHW
QHWRK
QLIM
QN QNP
QSAI
F
QSBC
QSFB
C
Refe
r
encing
prog
rams
SUMC
ALWR
ITES
ASEM
BLSU
MCAL
WBBAL
WELLSS
WRITES
WFDY
DZ
APLY
BCAS
EMBL
SUMCAL
APLY
BCASEMBL
SUMC
AL
ASEM
BLSU
MCAL
SUMCAL
WRITES
APLY
BCASEMBL
APLY
BCERRORS
INIT
3SU
MCAL
WRITES
WRITES
Vari
able
type
REAL
*8 DI
MENS
ION (*
)REAL*8 DIMENSION (*
)
REAL
*8REAL*8 DI
MENS
ION (*)
REAL
*8 DIMENSION^)
REAL*8 DIMENSION (*)
REAL
*8 DI
MENS
ION (*)
REAL
*8
REAL
*8REAL*8
REAL
*8
REAL
*8RE
AL*8
REAL*8
REAL
*8REAL*8
REAL
*8 DIMENSION (*
)REAL*8 DI
MENS
ION (*
)
REAL
*8REAL*8
REAL
*8 DI
MENS
ION (*
)REAL
*8 DIMENSION (*)
REAL
*8 DI
MENS
ION (*
)REAL*8 DIMENSION (*)
REAL
*8 DI
MENS
ION (*)
REAL*8 DI
MENS
ION (*)
Variable
name
QSFX
QSFY
QSFZ
QSLBC
QSLYR
QSSBC
QSW
QUOT
QUOT
SV
QWAV
Refer
encing
programs
ETOM2
INIT3
READ3
ETOM2
INIT
3READ3
ETOM2
INIT
3READ3
SUMCAL
WRIT
ES
WBBAL
WELLSS
WRITES
SUMCAL
WRITES
ASEM
BLSUMCAL
WBBAL
WELLSS
WRITES
BSODE
BSODE
ASEM
BL
Vari
able
type
REAL*8 DIMENSIONS)
REAL*8 DIMENSION (*)
REAL*8 DIMENSION^)
REAL*8 DIMENSION^)
REAL*8 DIMENSION^)
REAL*8 DIMENSION (*)
REAL*8 DIMENSION (*)
REAL*8 DIMENSION(*)
REAL*8 DIMENSION (*)
REAL*8 DIMENSION (*
)REAL*8 DIMENSION (*)
REAL
*8 DI
MENS
ION (*)
REAL*8 DIMENSION^*)
REAL*8 DIMENSION (*
)
REAL*8 DIMENSION(*)
REAL*8 DI
MENS
ION(
*)
REAL*8
REAL* 8 DIMENSION (*)
REAL*8 DIMENSION^*)
REAL
*8 DIMENSION(*)
REAL
*8 DIMENSION^*)
REAL*8 DIMENSION (1
1, 2)
REAL*8
REAL
*8
Table
11.2--Cross-reference
2ist of variables Continued
00
Variable
name
QWLYR
QWM
QWN
QWNP
QWR
QWV
R RATIO
Refe
r
enci
ng
prog
rams
ASEM
BLIT
ERWBBAL
WBCF
LOWELLSS
WRITES
ASEMBL
ITER
SUMCAL
WBBAL
WELLSS
WELRIS
WRITES
ASEM
BL
ASEM
BL
HST3
DWELRIS
WFDYDZ
ASEM
BLER
ROR3
READ
3SU
MCAL
WBBAL
WELLSS
WRITES
WRITES
WELLSS
MAP2D
Vari
able
ty
pe
REAL*8 DIMENSION^)
REAL*8 DIMENSIONS)
REAL*8 DIMENSION(*)
REAL*8 DIMENSIONS)
REAL*8 DIMENSION (*)
REAL*8
DI
MENS
ION (*
)
REAL*8 DIMENSIONS)
REAL
*8 DIMENSIONS)
REAL*8 DIMENSION(*)
REAL*8
DIMENSIONS)
REAL*8 DI
MENS
ION (*
)REAL*8
REAL*8 DI
MENS
ION(
*)
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8 DIMENSIONS)
REAL*8
DIMENSION (*)
REAL*8 DIMENSION(*)
REAL*8
DI
MENS
ION (*)
REAL*8 DIMENSIONS)
REAL*8 DIMENSION (*
)RE
AL*8
DIMENSIONS)
REAL*8 DIMENSION(*)
REAL*8 DIMENSION(*)
REAL*8
Refer-
Vari
able
encing
name
programs
RBW
D4DE
SORDER
RCPPM
ETOM
1INIT2
READ2
WRITE2
RDAIF
HST3D
ERROR3
ETOM2
INIT3
READ3
WRIT
ES
RDCALC
HST3D
ERRO
R3ETOM2
INIT
3READ3
WRIT
E3
RDECHO
HST3D
CLOSE
DUMP
IREW
IPL
OTOC
READ
1READ2
READ3
REWI
Vari
able
type
INTE
GER*
4 DIMENSION (*)
INTEGER*4 DIMENSIONS)
REAL*8 DIMENSION (*)
REAL*8 DIMENSION (*)
REAL
*8 DIMENSION (*
)RE
AL*8
DI
MENS
ION (*
)
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGI
CAL*
4LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGI
CAL*
4LO
GICA
L*4
LOGICAL*4
LOGICAL*4
Tab
le
11.2
Cro
ss-r
efer
ence
li
st
of
vari
aJb
les
Con
tin
ued
VO
Variable
name
RDFL
XH
RDFL
XQ
BDFLXS
RDLBC
BDMP
DT
Refe
rencing
prog
rams
HST3
DERRORS
ETOM
2INIT3
READ3
WRITES
HST3
DERROR3
ETOM
2IN
IT3
READ3
WRIT
E3
HST3D
ERROR3
ETOM
2IN
IT3
READ3
WRITE3
HST3
DERROR3
ETOM2
INIT
3READ3
WRIT
E3
HST3D
ERROR3
ETOM
2IN
IT3
READ3
WRIT
E3
Variable
type
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGI
CAL*
4LOGICAL*4
LOGICAL*4
LOGI
CAL*
4LOGICAL*4
LOG1CAL*4
LOGI
CAL*
4LO
GICA
L*4
LOGI
CAL*
4LOGICAL*4
LOGI
CAL*
4LO
GICA
L*4
LOGICAL*4
LOGI
GAL*
4LO
GICA
L*4
LOGICAL*4
LOGI
CAL*
4LOGICAL*4
LOGI
CAL*
4LOGICAL*4
LOGICAL*4
LOGI
CAL*
4LO
GICA
L*4
LOGI
CAL*
4
Refer-
Variable
encing
name
programs
RDPL
TP
PLOT
OC
RDSC
BC
HST3D
ERRO
R3ET
OM2
INIT3
READ
3WRITE3
RDSP
BC
HST3D
ERRO
R3ETOM2
INIT3
READ
3WRITE3
RDST
BC
HST3D
ERRO
R3ETOM2
INIT3
READ
3WR
ITE3
RDVAIF
HST3D
APLYBC
DUMP
ERROR2
ETOM
1INIT2
READ1
READ2
WRIT
E2
Variable
type
LOGI
CAL*
4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGI
CAL*
4LO
GICA
L*4
LOGI
CAL*
4LO
GICA
L*4
LOGICAL*4
LOGI
CAL*
4LO
GICA
L*4
LOGI
CAL*
4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGI
CAL*
4LO
GICA
L*4
LOGI
CAL*
4LOGICAL*4
LOGI
CAL*
4LOGICAL*4
Tabl
e 11
.2 C
ross
-ref
eren
ce list of
var
iabl
es C
onti
nued
oo o
Vari
able
na
me
RDWD
EF
RDWF
LO
RDWHD
REN
REST
RT
Refe
r
encing
prog
rams
UST3D
DUMP
ETOM
1IN
IT2
ITER
READ
1RE
AD2
WBBAL
WELLSS
WELR
ISWRITE2
WRITES
HST3D
ERROR3
ETOM
2IN
IT3
READ
3WRITE3
HST3D
ERRO
R3ET
OM2
INIT
3RE
AD3
WRIT
E3
WELL
SSWF
DYDZ
HST3D
READ
1WR
ITE1
Vari
able
type
LOGI
CAL*
4LOGICAL**
LOGI
CAL*
4LO
GICA
L**
LOGICAL**
LOGICAL**
LOGICAL*4
LOGI
CAL*
*LOGICAL**
LOGICAL**
LOGICAL**
LOGI
CAL*
*
LOGICAL**
LOGICAL**
LOGI
CAL*
*LO
GICA
L**
LOGI
CAL*
*LOGICAL**
LOGI
CAL*
*LO
GICA
L**
LOGI
CAL*
*LO
GICA
L**
LOGICAL**
LOGI
CAL*
*
REAL*8
REAL*8
LOGICAL**
LOGICAL**
LOGI
CAL*
*
Refer-
Variable
encing
name
pr
ogra
ms
RF
APLY
BCAS
EMBL
COEFF
ITER
WELL
SS
RH
APLY
BCASEMBL
COEFF
ITER
WELLSS
RH1
ASEMBL
RHS
ASEMBL
D*DES
ITER
L2SOR
SOR2L
RHSSBC
ASEMBL
SBCF
LO
RHSW
ASEMBL
WBCF
LO
RIOAR
HST3D
APLYBC
DUMP
ETOM1
INIT
2READ1
READ2
WRIT
E2
Variable
type
REAL*8 DIMENSION^)
REAL*8 DIMENSION (*)
REAL*8 DI
MENS
ION(
*)REAL*8 DI
MENS
ION (*)
REAL*8 DIMENSION(*)
REAL*8 DIM
ENSI
ON (*)
REAL*8 DIMENSION(*)
REAL*8 DIMENSION (*
)RE
AL*8
DIMENSION (*
)REAL*8 DIMENSION (*
)
REAL
*8 DIMENSION(*)
REAL
*8 DIMENSION(*)
REAL*8 DI
MENS
ION (*)
REAL*8 DI
MENS
ION(
*)REAL*8 DIMENSION (*)
REAL*8 DIMENSION^)
REAL
*8 DIMENSION (*)
REAL*8 DIMENSION (*
)
REAL*8 DIMENSION (*)
REAL
*8 DIMENSION(*)
1
REAL*8
REAL*8
REAL
*8RE
AL*8
REAL
*8RE
AL*8
REAL*8
REAL
*8
Tabl
e 11.2 Cross-reference li
st o
f variables Continued
00
Vari
able
na
me
RM RORW
2
RPRN
RS RS1
SAVLDO
SCALMF
Refe
r
encing
prog
rams
INIT
2WRITE2
INIT
2
PRNT
AR
APLY
BCAS
EMBL
COEFF
ITER
WELLSS
ASEM
BL
HST3D
CLOSE
DUMP
READ3
HST3D
CLOSE
DUMP
INIT
2INIT3
IREW
IPLOTOC
READ
1READ2
READ3
REWI
SUMCAL
WRITE1
WRIT
E2WR
ITE3
WRIT
ES
Variable
type
REAL*8 DI
MENS
ION (*
)REAL*8 DI
MENS
ION (*)
REAL
*8
CHARACTER*!
REAL
*8 DIMENSION (*
)REAL*8 DI
MENS
ION (*
)REAL*8 DI
MENS
ION (*
)REAL*8 DIMENSION (*
)REAL*8 DI
MENS
ION (*
)
REAL*8 DI
MENS
ION(
*)
LOGICAL*4
LOGI
CAL*
4LOGICAL*4
LOGI
CAL*
4
LOGI
CAL*
4LO
GICA
L*4
LOGICAL*4
LOGI
CAL*
4LOGICAL*4
LOGI
CAL*
4LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGI
CAL*
4LOGICAL*4
LOGICAL*4
LOGICAL*4
Refer-
Vari
able
encing
name
prog
rams
SDEC
AY
HST3D
SUMCAL
WRIT
ES
SHRES
HST3D
SUMCAL
WRITES
SHRESF
HST3D
SUMCAL
WRITES
SIR
HST3D
SUMCAL
WRIT
ES
SIRO
HST3D
APLYBC
DUMP
INIT
2READ1
SUMC
ALWRITE2
WRITES
SIRN
SUMCAL
Vari
able
ty
pe
REAL*8
REAL
*8REAL*8
REAL*8
REAL
*8REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8RE
AL*8
REAL
*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL
* 8
REAL
*8
Tabl
e 11.2 Cross-reference l
ist of var
iabl
es Continued
oo 10
Refer-
Vari
able
encing
name
programs
SLME
TH
HST3D
ASEM
BLDU
MPER
ROR1
INIT
1IM
IT2
ITER
READ1
READ2
SBCF
LOWB
CFLO
WRITE1
WRIT
E2WR
ITES
SMCA
LC
CALCC
Vari
able
.
type
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4INTEGER*4
INTEGER*4
INTE
GER*
4INTEGER*4
INTEGER*4
IMTEGER*4
INTE
GER*
4IN
TEGE
R*4
INTE
GER*
4IN
TEGE
R*4
1NTEGER*4
LOGICAL*4
Refe
r-
Vari
able
encing
name
pr
ogra
ms
SOLUTE
HST3D
APLYBC
ASEMBL
CALCC
COEFF
CRSD
SPDUMP
ERROR2
ERROR3
ETOM1
INIT1
INIT2
INIT3
ITER
PLOT
OCREAD1
READ2
READ3
SUMC
ALVI
SCOS
WBBAL
WELL
SSWR
ITE1
WRIT
E2WRITES
WRIT
E4WRITES
Variable
type
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGI
CAL*
4LOGICAL*4
LOGICAL*4
LOGI
CAL*
4LOGICAL*4
L06I
CAL*
4LO
GICA
L*4
LOGICAL*4
LOGI
CAL*
4LO
GICA
L*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGI
CAL*
4LO
GICA
L*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
Tabl
e 11.2 Cross-reference
list
of
variables
Continued
00 u>
Variable
name
SOLV
E
SPR
SPRA
D
SRES
SRES
F
SSRES
SSRE
SF
STOTFI
Refer
enci
ng
programs
L2SOR
SOR2
L
HST3D
L2SOR
L2SOR
SOR2
L
HST3
DSU
MCAL
WRIT
ES
HST3D
SUMCAL
WRIT
ES
HST3
DSU
MCAL
WRITES
HST3
DSU
MCAL
WRIT
ES
HST3
DAP
LYBC
SUMC
ALWR
ITES
Variable
type
LOGICAL*4
LOGICAL*4
REAL
*8 DIMENSION (3)
REAL
*8 DI
MENS
ION (3)
REAL
*8RE
AL*8
REAL*8
REAL
*8REAL*8
REAL*8
REAL
*8RE
AL*8
REAL
*8RE
AL*8
REAL
*8
REAL
*8RE
AL*8
REAL* 8
REAL*8
REAL
*8REAL*8
REAL
*8
Refe
r-
Variable
encing
name
programs
STOT
FP
HST3
DAPLYBC
SUMC
ALWR
ITES
STOTHI
HST3D
APLYBC
SUMC
ALWRITES
STOT
HP
HST3
DAPLYBC
SUMCAL
WRITES
STOT
SI
HST3D
APLYBC
SUMCAL
WRIT
ES
STOTSP
HST3
DAP
LYBC
SUMC
ALWRITES
SUM
INIT
2
SUM1
ITER
WELLSS
Vari
able
type
REAL*8
REAL* 8
REAL*8
REAL*8
REAL
*8REAL* 8
REAL
*8REAL*8
REAL*8
REAL* 8
REAL
*8REAL*8
REAL
*8REAL*8
REAL*8
REAL
*8
REAL*8
REAL
*8RE
AL*8
REAL*8
REAL*8
REAL
*8RE
AL*8
Tabl
e II
.2--
Cros
s-re
fere
nce
list
of va
riab
les Con
tinu
ed
00
Variable
name
SUM2
SUMCWI
SUMM
OB
SUMT
WI
SUMW
I
SUMXX
SUMX
Y
SVBC
SXX
SXXM
SXXP
SYMID
SYY
SYYM
SYYP
SZZ
Refe
r
encing
prog
rams
HER
WELLSS
WELL
SS
WELLSS
WELL
SS
VSIN
IT
VSIN
IT
ASEMBL
ASEM
BLCOEFF
ASEM
BL
ASEM
BL
MAP2D
ASEM
BLCOEFF
ASEM
BL
ASEM
BL
ASEM
BLCOEFF
Variable
type
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8
REAL*8
LOGICAL*4
REAL*8 DIMENSION (*
)REAL*8 DIMENSION^)
REAL
*8
REAL*8
CHARACTER*!
DIMENSION (5)
REAL
*8 DIMENSION (*
)REAL*8 DIMENSION (*)
REAL*8
REAL*8
REAL*8 DIMENSION (*)
REAL*8 DI
MENS
ION (*)
Refer-
Vari
able
encing
name
prog
rams
SZZM
AS
EMBL
SZZP
ASEM
BL
SZZW
WELL
SS
T AP
LYBC
ASEMBL
CALCC
COEFF
CRSDSP
£TOM
IIN
IT2
1TER
READ2
SUMCAL
TOFEP
VISCOS
WELLSS
WRITE2
WRITES
TO
HST3D
DUMP
ETOM
1INIT2
READ1
READ2
SUMCAL
WBBAL
WELLSS
WFDY
DZWR
ITE2
WRIT
ES
Variable
type
REAL*8
REAL*8
REAL*8
REAL*8 DIMENSION(*)
REAL*8 DIMENSION(*)
REAL*8
REAL*8 DIMENSION (*
)REAL*8 DIMENSION (*)
REAL
*8 DIMENSION(*)
REAL*8 DIMENSION (*
)RE
AL*8
DIMENSION(*)
REAL*8 DIMENSION (*)
REAL
*8 DI
MENS
ION (*
)REAL*8
REAL
*8RE
AL*8
DIMENSION (*)
REAL*8 DIMENSION (*)
REAL*8 DI
MENS
ION (*)
REAL
*8RE
AL*8
REAL
*8REAL*8
REAL*8
REAL*8
REAL
*8REAL*8
REAL
*8REAL*8
REAL
*8RE
AL*8
Tabl
e 11
.2--
Cros
s-re
fere
nce
list
of variables Continued
00
Ui
Variable
name
TOO
TOH
TA TABWR
TAIF
TAMB
I
Refer
encing
prog
rams
HST3D
WBBAL
WELLSS
WELRIS
HST3D
APLYBC
ASEM
BLDUMP
ETOM
1IN
IT2
READ1
READ
2SU
MCAL
WELL
SSWELRIS
WRIT
E2WRITES
BSODE
ETOM
1RE
AD2
WELRIS
WRITE2
APLY
BCASEMBL
INIT
3SUMCAL
HST3D
WELRIS
WFDY
DZ
Vari
able
ty
pe
REAL
*8RE
AL*8
REAL*8
REAL*8
REAL*8
REAL
*8REAL*8
REAL*8
REAL*8
REAL* 8
REAL*8
REAL
*8REAL*8
REAL* 8
REAL
*8RE
AL*8
REAL*8
REAL
*8
REAL
*8 D
IMEN
SION
(*)
REAL
*8 D
IMEN
SION
(*)
REAL
*8REAL*8 D
IMEN
SION
(*)
REAL
*8 D
IMEN
SION
(*)
REAL*8 D
IMENSION (*)
REAL
*8 D
IMEN
SION
(*)
REAL
*8 DI
MENS
ION (*
)
REAL*8
REAL*8
REAL
*8
Vari
able
na
me
TAMB
K
TATW
R
TC TCS
TCW
TDATA
TDEHIR
TDFIR
TDSI
R
TDK
TDXY
TDXZ
TDY
TDYX
TDYZ
Refe
r
encing
prog
rams
HST3D
WELRIS
WFDYDZ
ETQM
1RE
AD2
WELRIS
WRITE2
PLOT
OC
PLOT
OC
PLOT
OC
VSINIT
WRITES
WRIT
ES
WRIT
ES
COEF
F
COEF
F
COEFF
COEFF
COEF
F
COEFF
Vari
able
type
REAL*8
REAL*8
REAL
*8
REAL
*8 D
IMEN
SION
(*)
REAL
*8 D
IMEN
SION
(*)
REAL
*8RE
AL*8
DIM
ENSI
ON (*)
REAL*8 D
IMEN
SION
(*)
REAL
*8 D
IMENSIONC*)
REAL
*8 D
IMENSIONC*)
REAL
*8 D
IMENSIONC*)
REAL
*8
REAL
*8
REAL
*8
REAL
*8
REAL
*8
REAL*8
REAL*8
REAL*8
REAL
*8
Table
11.2 Cross-reference li
st of
variables Continued
00
Vari
able
na
me
TDZ
TDZX
TDZY
TEHD
T
TEHS
T
TEMP
TFLX
TFRES
Refe
r
enci
ng
prog
rams
COEF
F
COEF
F
COEFF
HST3D
BLOC
KDAT
ADUMP
INIT2
READ1
TOFE
P
HST3
DBL
OCKD
ATA
DUMP
INIT2
READ1
TOFE
P
TOFE
P
APLY
BCIN
IT3
SUMC
ALWR
ITE3
WRITES
HST3D
SUMC
AL
Variable
type
REAL
*8
REAL
*8
REAL*8
REAL
*8 D
IMEN
SION
(14
)RE
AL*8
DIM
ENSI
ON (14)
REAL
*8 D
IMEN
SION
(14
)RE
AL*8
DI
MENS
ION(
14)
REAL*8 DIM
ENSI
ON (14
)REAL*8 D
IMEN
SION
(14
)
REAL
*8 D
IMEN
SION
(32)
REAL*8 DI
MENS
ION (32)
REAL*8 DIMENSION(32)
REAL
*8 D
IMEN
SION
(32
)REAL*8 DI
MENS
ION(
32)
REAL*8 D
IMEN
SION
(32)
REAL*8
REAL*8 D
IMEN
SION
(*)
REAL*8 DIMENSION(*)
REAL*8 DI
MENS
ION (*)
REAL*8 DIMENSION^)
REAL
*8 D
IMEN
SION
(*)
REAL
*8RE
AL*8
Variable
name
TFRE
SF
TFW
TFX
TFXM
TFXP
TFY
TFYM
TFYP
TFZ
TFZM
TFZP
THCB
C
Refe
r
enci
ng
programs
HST3
DSU
MCAL
WRIT
ES
ASEM
BLWE
LLS S
COEF
FWRITE4
ASEMBL
ASEM
BL
COEFF
WRITE4
ASEMBL
ASEMBL
COEFF
WRIT
E4
ASEM
BL
ASEM
BL
APLYBC
INIT
2
Variable
type
REAL
* 8
REAL*8
REAL
*8
REAL
*8 D
IMENSION (*)
REAL*8 DI
MENS
ION (*)
REAL*8 DI
MENS
ION (*)
REAL
*8 DIMENSION^)
REAL
*8
REAL* 8
REAL*8 DIMENSION^)
REAL
*8 DI
MENS
ION (*)
REAL
*8
REAL*8
REAL*8 D
IMEN
SION
(*)
REAL
*8 DI
MENS
ION (*
)
REAL
*8
REAL
*8
REAL
*8 DIMENSION(*)
REAL*8 DIMENSION(*)
Table
11.2 Cross-reference li
st of
variables Continued
o>
Vari
able
na
me
THET
XZ
THETYZ
THETZZ
THI
THRE
S
THRE
SF
Refe
r
enci
ng
prog
rams
HST3D
DUMP
ERROR2
INIT
2RE
AD1
READ2
WRIT
E2
HST3D
DUMP
ERRO
R2INIT2
READ1
READ2
WRITE2
HST3D
DUMP
ERRO
R2INIT2
READ
1READ2
WRIT
E2
TOFEP
HST3D
SUMC
ALWR
ITES
HST3D
SUMC
ALWRITES
Vari
able
ty
pe
REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
Vari
able
na
me
THRU
THX
THXM
THXP
TEXT
THXZ
THY
THTM
THYP
THYX
THYZ
Refe
r
encing
prog
rams
HST3D
COEFF
READ3
WRIT
E4
COEFF
WRITE4
ASEMBL
ASEMBL
COEFF
CRSDSP
WRIT
EA
COEFF
CRSD
SPWR
ITE4
COEFF
WRITEA
ASEMBL
ASEMBL
COEFF
CRSDSP
WRIT
EA
COEFF
CRSD
SPWR
ITEA
Variable
type
LOGICAL*A
LOGI
CAL*
4LOGICAL*A
LOGI
CAL*
4
REAL
*8 D
IMENSIONC*)
REAL
*8 DIMENSIONC*)
REAL
*8
REAL
*8
REAL
*8 DIMENSION (*
)REAL*8 DIMENSION(*)
REAL*8 DIMENSIONC*)
REAL
*8 DIMENSIONC*)
REAL
*8 D
IMENSIONC*)
REAL
*8 DIMENSIONC*)
REAL* 8 DIMENSIONC*)
REAL*8 D
IMENSIONC*)
REAL
*8
REAL
*8
REAL
*8 D
IMENSIONC*)
REAL* 8 DI
MENS
IONC
*)REAL*8 DIMENSIONC*)
REAL*8 D
IMENSIONC*)
REAL
*8 DIM
ENSI
ONC*
)REAL*8 DIMENSIONC*)
Tabl
e 11.2 Cross-reference li
st of v
ariables
Continued
00 oo
Vari
able
name
THZ
THZM
THZP
THZX
THZY
TILT
TIMC
HG
Refe
r
encing
prog
rams
COEFF
WRIT
E4
ASEM
BL
ASEM
BL
COEFF
CRSDSP
WRIT
E4
COEFF
CRSDSP
WRIT
E4
HST3D
DUMP
ERRO
R2IN
IT2
READ
1RE
AD2
WRIT
E2
HST3D
COEFF
DUMP
ERRO
RSET
OM2
INIT
3READS
SUMC
ALWRITE
1WR
ITES
WRIT
E4WRITES
Vari
able
type
REAL*8 DIMENSION (*)
REAL
*8 D
IMEN
SION
C*)
REAL*8
REAL*8
REAL*8 DI
MENS
IONC
*)REAL*8 DIMENSIONC*)
REAL*8 D
IMENSIONC*)
REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL
*8 DIM
ENSI
ONC*
)
LOGICAL*4
LOGICAL*4
LOGI
CAL*
4LO
GICA
L*4
LOGI
CAL*
4LO
GICA
L*4
LOGI
CAL*
4
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8
Refe
r-
Vari
able
en
cing
na
me
programs
TIMDAY
WELLSS
TIME
HST3D
APLYBC
CALCC
CLOSE
COEFF
DUMP
ERRORS
ETOM2
INIT
2INIT3
ITER
READ1
READ
3SUMCAL
WBBAL
WELL
SSWE
LRIS
WRITE2
WRIT
E3WR
ITE4
WRIT
ES
TIMED
APLY
BCWELRIS
TIME
DN
APLY
BC
TIMRST
HST3D
READ1
WRITE1
Vari
able
ty
pe
REAL*8
REAL*8
REAL*8
REAL
*8REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8REAL*8
REAL*8
REAL*8
REAL
*8REAL*8
REAL*8
REAL
*8REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
Table
11.2
--Cr
oss-
refe
renc
e li
st o
f va
riab
les
Cont
inue
d
oo
Vari
able
na
me
TITL
E
TITLEO
TLBC
TLBL
TLO
TM1
TM2
TMLB
L
TNP
TO TOL
Refe
r
enci
ng
prog
rams
HST3D
DUMP
MAP2D
READ
1WRITE 1
WRITES
HST3D
READ
1WRITE 1
APLYBC
ASEM
BLIN
IT3
SUMC
ALWRITES
WRITES
TOFE
P
SOR2
L
SOR2
L
PLOTOC
CALC
CREADS
PLOTOC
PLOT
Variable
type
CHAR
ACTE
R*16
0CH
ARAC
TER*
160
CHARACTER*80
CHAR
ACTE
R* 160
CHAR
ACTE
R* 160
CHARACTER*80
CHAR
ACTE
R* 160
CHARACTER* 160
CHARACTER* 160
REAL*8 DIMENSION (*)
REAL
*8 DIMENSION (*
)RE
AL*8
DI
MENS
ION (*)
REAL
*8 DI
MENS
ION (*
)RE
AL*8
DIMENSION (*)
CHARACTER*20
REAL*8
REAL
*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
CHAR
ACTE
R* 30
REAL*8
REAL
*8 DI
MENS
IONC
*)
REAL*8 D
IMEN
SION
C*)
REAL*8
Refe
r-
Variable
enci
ng
name
pr
ogra
ms
TOLDEN
HST3D
DUMP
INIT2
ITER
READ
1RE
AD2
WRIT
E2
TOLDNC
HST3D
DUMP
INIT
2IT
ERREAD1
READ2
TOLDNT
HST3D
DUMP
INIT2
ITER
READ1
READ2
TOLD
PW
HST3D
DUMP
ETOM
1INIT2
READ
1READ2
WELLSS
WRITE2
Vari
able
ty
pe
REAL*8
REAL*8
REAL*8
REAL
*8RE
AL* 8
REAL
*8REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8REAL*8
REAL*8
REAL*8
REAL*8
Tabl
e 11
.2 C
ross
-ref
eren
ce li
st of
var
iabl
es Continued
VO
O
Variable
name
TOLF
PW
TOLQW
TOS
TOTF
I
TOTF
P
Refer
encing
programs
HST3D
DUMP
ETOM
1IN
IT2
READ
1READ2
WELLSS
WRIT
E2
HST3D
DUMP
ETOM
1IN
IT2
READ1
READ2
WELL
SSWR
ITE2
PLOTOC
HST3
DAP
LTBC
DUMP
INIT
2RE
AD1
SUMCAL
WRIT
ES
HST3D
APLY
BCDUMP
IN1T
2READ1
SUMC
ALWR
ITES
Variable
type
REAL
*8REAL*8
REAL*8
REAL
*8REAL*8
REAL
*8RE
AL*8
REAL
*8
REAL
*8REAL*8
REAL*8
REAL*8
REAL
*8RE
AL*8
REAL
*8REAL*8
REAL
*8 DIMENSION (*)
REAL* 8
REAL*8
REAL*8
REAL*8
REAL
*8RE
AL*8
REAL*8
REAL
*8RE
AL*8
REAL*8
REAL*8
REAL
*8RE
AL*8
REAL*8
Refer-
Vari
able
en
cing
na
me
prog
rams
TOTHI
HST3D
APLYBC
DUMP
INIT2
READ
1SU
MCAL
WRITES
TOTHP
HST3D
APLY
BCDQMP
INIT
2READ1
SUMC
ALWRITES
TOTSI
HST3
DAPLYBC
DUMP
INIT2
READ1
SUMCAL
WRIT
ES
TOTS
P HST3D
APLYBC
DUMP
INIT2
READ1
SUMC
ALWR
ITES
Variable
type
REAL*8
REAL*8
REAL
*8REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8REAL*8
REAL*8
REAL*8
REAL*8
Table
11.2--Cross-reference
list
of
variables Continued
Variable
name
TOTWFI
TOTW
FP
TOTW
HI
TOTWHP
Refe
r
encing
prog
rams
HST3D
APLY
BCDUMP
INIT
2RE
AD1
SUMC
ALWRITES
HST3D
APLYBC
DUMP
1NIT
2RE
AD1
SUMCAL
WRIT
ES
HST3D
APLY
BCDU
MPIN
IT2
READ
1SUMCAL
WRITES
HST3D
APLY
BCDUMP
INIT
2RE
AD1
SUMCAL
WRITES
Variable
type
REAL*8
REAL*8
REAL
*8RE
AL*8
REAL*8
REAL
*8RE
AL*8
REAL
*8RE
AL* 8
REAL
*8RE
AL*8
REAL*8
REAL
*8RE
AL*8
REAL
*8REAL*8
R£AL
*8RE
AL*8
REAL
*8RE
AL*8
REAL
*8
REAL*8
REAL*8
REAL
*8REAL*8
REAL*8
REAL
*8REAL*8
Refe
r-
Variable
encing
name
pr
ogra
ms
TOTWSI
HST3D
APLY
BCDUMP
INIT
2RE
AD1
SUMCAL
WRIT
ES
TOTWSP
HST3D
APLYBC
DUMP
INIT
2READ1
SUMCAL
WRITES
TOW
PLOTOC
TP1
SOR2L
TP2
SOR2L
TPHCBC
APLY
BC
TQFA
IF
HST3D
APLY
BCDUMP
INIT
2READ1
SUMCAL
WRIT
ES
Variable
type
REAL*8
REAL*8
REAL*8
REAL*8
R£AL*8
REAL*8
REAL
*8
REAL*8
REAL*8
R£AL
*8REAL*8
REAL*8
REAL*8
REAL*8
REAL*8 DIMENSION(*)
REAL*8 DIMENSION^)
REAL*8 DIMENSION (*
)
REAL*8 DIMENSION (*)
REAL*8
REAL*8
REAL
*8REAL*8
R£AL
*8REAL* 8
REAL*8
Tabl
e 11.2 Cross-reference 2ist of
variables
Continued
Variable
name
TQFF
BC
TQFINJ
TQFL
BC
TQFP
RO
TQFSBC
Refer
encing
prog
rams
HST3
DAP
LYBC
DUMP
INIT2
READ
1SUMCAL
WRIT
ES
HST3D
SUMCAL
WELL
SSWR
ITES
HST3D
APLYBC
DUMP
INIT
2RE
AD1
SUMCAL
WRITES
HST3D
SUMCAL
WELL
SSWRITES
HST3D
APLY
BCDU
MPIN
IT2
READ
1SUMCAL
WRITES
Vari
able
ty
pe
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8REAL*8
REAL
*8REAL
*8
REAL*8
REAL*8
REAL*8
REAL
*8REAL*8
REAL*8
REAL
*8
REAL*8
REAL
*8RE
AL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8REAL* 8
REAL
*8REAL*8
Refer-
Variable
encing
name
programs
TQHA
IF
HST3D
APLY
BCDUMP
INIT2
READ
lSU
MCAL
WRIT
ES
TQHF
BC
HST3
DAPLYBC
DUMP
INIT2
READ
lSUMCAL
WRITES
TQHH
BC
HST3
DAP
LYBC
DUMP
INIT
2READl
SUMCAL
WRITES
TQHINJ
HST3D
SUMCAL
WELLSS
WRITES
Variable
type
REAL*8
REAL
*8REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8REAL*8
REAL
*8REAL*8
REAL
*8REAL*8
REAL
*8REAL*8
REAL*8
REAL
*8RE
AL*8
REAL
*8RE
AL*8
Tab
le
11.2
--C
ross
-ref
eren
ce li
st
of
vari
ab
les
Co
nti
nu
ed
U>
Vari
able
na
me
TQHLBC
TQHP
RO
TQHSBC
TQSA
IF
TQSFBC
Refer
encing
prog
rams
HST3D
APLYBC
DUMP
INIT
2RE
AD1
SUMC
ALWRITES
HST3D
SUMCAL
WELLSS
WRITES
HST3D
APLY
BCDUMP
INIT
2RE
AD1
SUMCAL
WRITES
HST3D
APLY
BCDU
MP1N
IT2
READ
1SUMCAL
WRIT
ES
HST3D
APLY
BCDU
MPIN
IT2
READ
1SU
MCAL
WRITES
Variable
type
REAL*8
REAL
*8REAL*8
REAL*8
REAL*8
REAL
*8RE
AL*8
REAL*8
REAL
*8REAL*8
REAL
*8
REAL*8
REAL
*8RE
AL*8
REAL*8
REAL*8
REAL
*8REAL*8
REAL
*8REAL*8
REAL*8
REAL*8
REAL
*8RE
AL*8
REAL
*8
REAL*8
REAL
*8RE
AL*8
REAL*8
REAL
*8RE
AL*8
REAL*8
Refe
r-
Variable
encing
name
programs
TQSINJ
HST3D
SUMCAL
WELL
SSWRITES
TQSLBC
HST3D
APLY
BCDUMP
INIT2
READ1
SUMCAL
WRITES
TQSPRO
HST3D
SUMCAL
WELLSS
WRITES
TQSSBC
HST3D
APLY
BCDUMP
INIT2
READ
1SU
MCAL
WRIT
ES
TRVIS
HST3D
DUMP
ETOM1
READ1
READ2
VISC
OSVS
INIT
WRIT
E2
Vari
able
type
REAL*8
REAL*8
REAL* 8
REAL*8
REAL
*8RE
AL*8
REAL
*8REAL*8
REAL*8
REAL
*8REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8
REAL*8
REAL
*8REAL*8
REAL
*8REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8RE
AL*8
REAL*8
Tab
le
11
.2 C
ross
-refe
ren
ce li
st
of
vari
ab
les
Co
nti
nu
ed
Variable
name
TSBC
TSLBL
TSMAX
TSMIN
TSRE
S
TSRE
SF
TSX
TSXM
TSXP
TSXY
TSXZ
TSY
Refe
r
enci
ng
prog
rams
ASEM
BLIN
IT3
SUMC
ALWRITES
PLOTOC
PLOT
OC
PLOTOC
HST3D
SUMCAL
WRITES
HST3D
SUMC
ALWRITES
COEFF
WRITEA
ASEMBL
ASEMBL
COEF
FCR
SDSP
WRITEA
COEF
FCR
SDSP
WRITEA
COEF
FWRITEA
Vari
able
ty
pe
REAL*8 DI
MENS
ION (*
)REAL*8 DI
MENS
ION (*
)REAL*8 DIMENSION^)
REAL
* 8 DIMENSION (*)
CHARACTER*SO
REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8
REAL*8
REAL
*8REAL*8
REAL*8 DIMENSION (*)
REAL*8 DI
MENS
ION (*
)
REAL*8
REAL*8
REAL*8 DI
MENS
ION (*
)REAL*8 DI
MENS
ION (*
)REAL*8 DI
MENS
ION (*
)
REAL*8 DIMENSION (*)
REAL
*8 DI
MENS
ION (*
)REAL*8 DI
MENS
ION (*)
REAL
*8 DIMENSION (*
)REAL*8 DI
MENS
ION (*)
Vari
able
na
me
TSYM
TSYP
TSYX
TSYZ
TSZ
TSZM
TSZP
TSZX
TSZY
TVD
Refer
encing
prog
rams
ASEM
BL
ASEM
BL
COEFF
CRSD
SPWR
ITEA
COEFF
CRSD
SPWRITEA
COEF
FWRITEA
ASEMBL
ASEMBL
COEFF
CRSD
SPWRITEA
COEFF
CRSDSP
WRIT
EA
HST3D
DUMP
ETOM
1IN
IT2
READ
1READ2
WRIT
E2
Vari
able
type
REAL
*8
REAL
*8
REAL*8 DIMENSION (*)
REAL
*8 DIMENSION (*
)REAL*8 DIMENSION (*)
REAL*8 DIMENSIONS)
REAL*8 DIMENSION (*
)RE
AL*8
DIMENSION (*
)
REAL*8 D
IMEN
SION
(*)
REAL
*8 DI
MENS
ION(
*)
REAL
*8
REAL
*8
REAL*8 DIMENSION (*
)REAL*8 DIMENSION (*
)REAL*8 DI
MENS
ION (*)
REAL
*8 DIMENSION^)
REAL*8 DIMENSION (*)
REAL
*8 DIMENSIONS)
REAL*8 DIMENSION (10)
REAL
*8 DIMENSION (10)
REAL*8 DIMENSION (10)
REAL
*8 DI
MENS
ION(
IO)
REAL*8 DI
MENS
ION (10)
REAL
*8 DI
MENS
ION(
IO)
REAL*8 DIMENSION (10)
Tabl
e 11.2 Cr
oss-
refe
renc
e li
st o
f va
riab
les Continued
VO
Cn
Vari
able
na
me
TVFO
TVF1
TVZHC
IWKT
TWLBL
Refe
r
encing
prog
rams
HST3D
DUMP
ETOM
1IN
IT2
READ
1RE
AD2
VISCOS
VRITE2
HST3D
DUMP
ETOM
1IN
IT2
READ
1RE
AD2
WRITE2
HST3D
DUMP
ETOM
1IN
IT2
READ
1RE
AD2
VRIT
E2
ASEMBL
WBBAL
WELL
SSWRITES
PLOT
OC
Vari
able
ty
pe
REAL*8 DI
MENS
ION (10)
REAL
* 8 DIMENSION (1
0)REAL*8 DIMENSION(IO)
REAL*8 DI
MENS
ION (10)
REAL*8 DIMENSION(IO)
REAL*8 DI
MENS
ION (1
0)REAL*8 D
IMEN
SION
(IO)
REAL
*8 DI
MENS
ION (10)
REAL*8 DI
MENS
ION(
IO)
REAL*8 DIMENSION (10
)REAL*8 DI
MENS
ION (1
0)RE
AL*8
DIMENSION(IO)
REAL*8 DIMENSION (1
0)RE
AL*8 DIMENSION (10)
REAL*8 DI
MENS
ION (1
0)
REAL
*8 DIMENSION (5)
REAL*8 DI
MENS
ION (5)
REAL
*8 DIMENSION (5)
REAL*8 DIMENSION^)
REAL*8 D
IMEN
SION
(S)
REAL*8 DI
MENS
ION(
5)R£AL*8 DIMENSION (5)
REAL*8 DIMENSION(*)
R£AL
*8 DIMENSION^)
REAL*8 DIMENSION(*)
REAL
*8 DIMENSION^)
CHAR
ACTE
R*50
Refer-
Vari
able
encing
name
prog
rams
TWMAX
PLOT
OC
TWMIN
PLOT
OC
TWOPI
INIT2
TWREND
HST3D
WBBAL
WELL
SSWE
LRIS
TWRK
WF
DYDZ
TWSR
KT
READ
3WR
ITE3
TWSUR
WBBAL
WELL
SSWRITES
TX
COEFF
INIT2
WRIT
E2
TY
COEFF
INIT2
WRIT
E2
TZ
COEFF
IN1T2
WRIT
E2
Variable
type
REAL
*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8
REAL*8
REAL*8 DIMENSION (*)
REAL*8 DIMENSION (*
)
REAL*8 DIMENSION^)
REAL
*8 DIMENSIONS)
REAL*8 DIMENSION (*)
REAL*8 DIMENSIONS)
REAL*8 DIMENSION (*)
REAL*8 DIMENSIONC*)
REAL*8 DIMENSION (*)
REAL*8 DIMENSION(*)
REAL*8 DIMENSION (*)
REAL*8 DIMENSIONC*)
REAL*8 DIMENSION (*)
REAL
*8 DI
MENS
IONC
*)
Table
11.2
Cro
ss-r
efer
ence
list of variables Continued
Vari
able
name
UO Ul U2 U3 U4 U5 U6
Refe
r
encing
programs
BSODE
INIT2
SUMC
AL
BSOD
ECOEFF
INIT2
PLOT
SUMC
ALWE
LLSS
WRIT
E2WRITES
COEF
FSU
MCAL
WRIT
E2WR
ITES
COEF
FWRITE2
WRITES
WRIT
E2WR
ITES
WRIT
E2WRITES
WRIT
E2WR
ITES
Vari
able
ty
pe
REAL
*8RE
AL*8
REAL*8
REAL
*8RE
AL*8
REAL
*8INTEGER**
REAL
*8REAL
*8REAL
*8RE
AL*8
^ REAL
*8REAL*8
REAL
*8RE
AL*8
REAL
*8RE
AL*8
REAL
*8
REAL*8
REAL
*8
REAL
*8RE
AL*8
REAL
*8REAL* 8
Refe
r-
Variable
enci
ng
name
programs
UBBLB
ETOM
1INIT2
READ
2
UBBRB
READ
2
UC
INIT
2PLOTOC
READ3
SUMC
ALWBBAL
WELLSS
WRIT
E3
UCBC
INIT3
READ3
UCLM
WBBAL
WELL
SS
UCLP
WBBAL
WELL
SS
UCRBC
READ
3
UCROSC
ASEMBL
CRSDSP
UCRO
ST
ASEMBL
CRSD
SP
Vari
able
ty
pe
REAL
*8 DI
MENS
ION (*)
REAL*8 DIMENSION^)
REAL
*8 DIMENSION(*)
REAL
*8
REAL*8
REAL
*8REAL*8
REAL
*8RE
AL*8
REAL*8
CHARACTER* 11
REAL
*8 DIMENSIONC*)
REAL
*8 DI
MENS
IONC
*)
REAL
*8RE
AL*8
REAL
*8REAL*8
REAL
*8
REAL
*8RE
AL*8
REAL*8
REAL*8
UARB
CINIT2
REAL*8
UCTC
COEFF
REAL
*8
Tab
le
11.2
Cro
ss-r
efe
rence li
st
of
var
iaJb
les
Co
nti
nu
ed
Variable
name
UCWT
UDC
UDEL
Y
UDEN
UDENBC
UDENLB
UDNR
BC
UDPW
KT
UDT
UDTH
HC
UDTIM
Refer
enci
ng
programs
COEFF
INIT
2WE
LLSS
PLOT
COEFF
INIT
2SUMCAL
WBBAL
ETOM
2 IN
IT3
READ3
ETOM
2 IN
IT3
READ
3
READ
3
ITER
INIT
2WE
LLSS
ETOM
1 IN
IT2
READ
2 WRITE2
COEFF
Vari
able
ty
pe
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8 DIMENSIONS)
REAL*8
DIMENSIONS)
REAL*8 DIMENSIONS)
REAL*8 DIMENSION (*
) REAL*8 DIMENSIONS)
REAL*8 DIMENSIONC*)
REAL* 8
REAL* 8
REAL*8
REAL*8
REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL
*8 DI
MENS
IONC
*)
REAL*8 DIMENSIONC*)
REAL* 8
Vari
able
na
me
UDX
UDXDY
UDXDYI
UDXD
YO
UDXDZ
UDXYZ
UDXYZI
UDXY
ZO
UDY
UDYDZ
UDZ
UEH
UEHLM
UEHLP
UFRAC
UFX
Refer
encing
programs
COEFF
INIT2
INIT2
INIT2
INIT2
INIT2
INIT2
INIT2
COEFF
INIT
2
COEFF
WBBAL
WELL
SS
WBBAL
WELLSS
WBBAL
COEFF
COEFF
Vari
able
type
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8
REAL*8
REAL*8
REAL*8
REAL
*8
REAL*8
REAL
*8
REAL*8
REAL*8
REAL*8
REAL
*8
REAL
*8
Tabl
e 11.2
Cro
ss-r
efer
ence
li
st o
f va
riab
les Continued
00
Vari
able
na
me
UFY
UFZ
UGDELX
UGDELT
UGDE
LZ
UHRBC
UHWT
UJV
UKHC
BC
UKLB
UKRB
UNIGRX
UNIG
RT
Refer
encing
programs
COEFF
COEFF
INIT
2
INIT
2
INIT
2
READ3
COEFF
READ2
ETOM
1IN
IT2
READ2
ETOM
1IN
IT2
READ2
READ2
HST3D
INIT
2READ2
WRIT
E2
HST3D
1NIT
2RE
AD2
WRIT
E2
Variable
type
REAL*8
REAL*8
REAL*8
REAL* 8
REAL*8
REAL*8
REAL*8
INTE
GER*
4
REAL*8 DI
MENS
IONC
*)RE
AL* 8 DI
MENS
IONC
*)RE
AL*8 DI
MENS
IONC
*)
REAL*8
DI
MENS
IONC
*)RE
AL*8
DI
MENS
IONC
*)RE
AL*8
DIMENSIONC*)
REAL
*8
LOGICAL*4
LOGICAL*4
LOGI
CAL*
4LOGICAL*4
LOGI
CAL*
4LOGICAL*4
LOGI
CAL*
4LO
GICAL*4
Refer-
Variable
enci
ng
name
programs
UNIG
RZ
HST3D
INIT2
READ2
WRITE2
UNITE?
REWI3
WRITES
UNITH
HST3D
DUMP
INIT1
PLOT
OCRE
AD1
REWI3
WRIT
E2WR
ITES
WRITE4
WRITES
UNIT
HF
HST3D
DUMP
INIT
1PLOTOC
READ1
REWI3
WRIT
E2WR
ITES
WRITE4
WRIT
ES
Variable
type
LOGI
CAL*
4LO
GICA
L*4
LOGI
CAL*
4LO
GICA
L*4
CHARACTER*! 0
CHARACTERMO
CHAR
ACTE
R*3
CHAR
ACTE
R*3
CHARACTER*3
CHAR
ACTE
R*3
CHARACTER*3
CHAR
ACTE
R*3
CHARACTER*3
CHAR
ACTE
R*3
CHAR
ACTE
R*3
CHAR
ACTE
R*3
CHARACTER*?
CHARACTER*?
CHARACTER*?
CHARACTER*?
CHARACTER*?
CHARACTER*?
CHAR
ACTE
R*?
CHARACTER*?
CHAR
ACTE
R*?
CHAR
ACTE
R*?
Tab
le
11.2
--C
ross
-ref
eren
ce 2is
t of
vari
able
s C
onti
nued
Vari
able
na
me
UNITL
UNITM
UNITP
Refe
r
encing
prog
rams
HST3D
DUMP
INIT
1PLOTOC
READ
1RE
WI3
WRITE2
WRITE3
WRIT
E4WR
ITES
HST3D
DUMP
INIT
1PL
OTOC
READ
1REWI3
WRITE2
WRIT
E3WRITEA
WRIT
ES
HST3D
DUMP
INIT
1PLOTOC
READ
1REWI3
WRITE2
WRIT
E3WRITEA
WRIT
ES
Vari
able
type
CHAR
ACTE
R*2
CHAR
ACTE
R*2
CHARACTER*2
CHARACTER*2
CHARACTER*2
CHARACTER* 2
CHAR
ACTE
R*2
CHAR
ACTE
R*2
CHAR
ACTE
R*2
CHARACTER* 2
CHARACTER*2
CHAR
ACTE
R*2
CHAR
ACTE
R*2
CHARACTER*2
CHAR
ACTE
R*2
CHARACTER*2
CHAR
ACTE
R*2
CRARACTER*2
CHARACTER*2
CHAR
ACTE
R*2
CHARACTER*3
CHARACTER*3
CHAR
ACTE
R*3
CHARACTER*3
CHARACTER*3
CHAR
ACTE
R*3
CHAR
ACTE
R*3
CHARACTER*3
CHAR
ACTE
R*3
CHAR
ACTE
R* 3
Refe
r-
Vari
able
en
cing
na
me
prog
rams
UNITT
HST3D
DUMP
INIT
1PL
OTOC
READ
1REWI3
WRITE2
WRIT
E3WR
ITEA
WRITES
UNIT
TM
HST3D
DUMP
INIT1
PLOTOC
READ
1REWI3
WRIT
E2WRITE3
WRITEA
WRIT
ES
UNITVS
REWI3
WRITE2
WRIT
E3
UNLP
PLOT
UP
WELL
SS
UP1
READ3
WRIT
E3
Vari
able
type
CHAR
ACTE
R*!
CHAR
ACTE
R*!
CHARACTER*!
CHARACTER*!
CHAR
ACTE
R*!
CHARACTER*!
CHARACTER*!
CHAR
ACTE
R*!
CHARACTER*!
CHAR
ACTE
R*!
CHAR
ACTE
R* 3
CHARACTER*3
CHARACTER*3
CHARACTER*3
CHARACTER*3
CHAR
ACTE
R*3
CHAR
ACTE
R*3
CHARACTER*3
CHARACTER* 3
CHAR
ACTE
R*3
CHARACTER*9
CHARACTER*9
CHAR
ACTE
R* 9
INTEGER*A
REAL*8
REAL*8
CHAR
ACTE
R* 11
Table
11.2 Cross-reference list of variables Continued
Variable
name
UP2
UPABD
UPHI
LB
UPHIM
UPS
g
UPTC
o
UPW
UPWKT
UPWKTS
UQ UQCLM
UQCL
P
UQH
UQHLM
Refe
r
enci
ng
prog
rams
READ
3WR
ITE3
INIT
2
ETOM
2IN
IT3
READ
3
APLY
BC
PLOTOC
COEF
F
PLOTOC
ITER
WELL
S S
WELLSS
INIT
3RE
AD3
WRITE3
WBBAL
WELLSS
WBBAL
WELLSS
INIT
3
WBBAL
WELL
SS
Vari
able
ty
pe
REAL*8
CHARACTER* 11
REAL
*8
REAL*8 DIMENSION (*
)REAL*8 DIMENSION (*
)RE
AL*8 DIMENSION^)
REAL*8
REAL*8
REALMS
REAL
* 8
REAL*8
REAL*8
REAL*8
REAL
*8REAL*8
CHAR
ACTER* 11
REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8
REAL*8
REAL*8
Variable
name
UQHLP
UQS
UQW
UQWLM
UQWLP
UQWLYV
UQWM
UQWV
UR1
UR2
URH
URS
UT
Refe
r
encing
prog
rams
WBBAL
WELL
SS
INIT
3
WELLSS
WBBAL
WELL
SS
WBBAL
WELLSS
WBBAL
WBBAL
WELLSS
WBBAL
WELLSS
ASEM
BL
ASEM
BL
ASEMBL
ASEMBL
INIT
2PLOTOC
READ3
SUMCAL
VSIN
ITWR
ITE3
Vari
able
type
REAL
*8RE
AL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL
* 8
REAL*8
REAL*8
REAL
*8RE
AL*8
REAL*8
REAL* 8
REAL*8
REAL*8
REAL*8
REAL
*8REAL*8
REAL*8
REAL*8
CHAR
ACTE
R* 11
Table
11.2--Cross-reference
list
of
va
riab
les Continued
Variable
name
UTBC
UTLM
UTLP
UTRB
C
UTS
UTTC
UTW
UTXM
UTXP
UTYM
UTYP
UTZM
UTZP
UVAIFC
Refe
r
encing
programs
ETOM
2IN
IT3
READ
3
WBBAL
WELLSS
WELL
SS
READ
3
PLOTOC
COEFF
PLOTOC
ASEMBL
ASEM
BL
ASEM
BL
ASEM
BL
ASEM
BL
ASEM
BL
ETOM
1IN
IT2
READ
2WRITE2
Variable
type
REAL*8 DIMENSIONC*)
REAL
*8 DI
MENS
ION(
*)RE
AL*8
DIMENSIONC*)
REAL
*8RE
AL*8
REAL
*8
REAL
*8
REAL
*8
REAL
*8
REAL
*8
REAL
*8
REAL*8
REAL*8
REAL
*8
REAL
*8
REAL*8
REAL
*8 DI
MENS
IONC
*)REAL*8 DIMENSIONC*)
REAL*8 DI
MENS
IONC
*)REAL*8 DI
MENS
IONC
*)
Vari
able
na
me
UVAR
UVEL
UVFLM
UVFLP
UVIS
UVISLB
UVSR
BC
UVWLM
UVWLP
UWI
UXX1
UXX2
UYMAX
UYMIN
UZELB
Refe
r
enci
ng
programs
READ2
COEFF
WELL
SS
WELLSS
COEFF
t
ETOM2
INIT3
READ3
READ3
WELL
SS
WELL
SS
INIT
2
SOR2L
SOR2
L
PLOT
PLOT
ERROR2
ETOM1
INIT
2RE
AD2
Variable
type
REAL* 8
REAL*8
REAL
*8
REAL
*8
REAL*8
REAL*8 D
IMENSIONC*)
REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL*8
REAL*8
REAL*8
R£AL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8 DIMENSIONC*)
REAL*8 DIMENSION^*)
REAL*8 DIMENSIONC*)
REAL*8 DI
MENS
ION^
*)
Tabl
e 11.2--Cross-reference
list of variables--Continued
Variable
name
UZERB
VA VAIFC
VAR
VASBC
VAW
VDATA
VELWRK
VIS
Refe
r
enci
ng
prog
rams
READ
2
ASEM
BLD4DES
ITER
SOR2L
APLY
BCIN
IT2
REWI
REWI
3
ASEM
BLSB
CFLO
ASEM
BLWB
CFLO
VSIN
IT
WFDY
DZ
APLY
BCCOEFF
INIT
2SU
MCAL
WELLSS
WRITE2
WRITES
Vari
able
ty
pe
REAL* 8
REAL*8 DI
MENS
IONC
7,*)
REAL*8 DIMENSIONC7,*)
REAL*8 DIMENSION (7,*)
REAL*8 DIMENSIONC7,*)
REAL*8 DI
MENS
IONC
*)REAL*8 DIMENSIONC*)
REAL*8
REAL*8 DIMENSIONC3)
REAL
*8 DIMENSION (7,*)
REAL*8 DIMENSION (7,*)
REAL*8 DI
MENS
IONC
7,*)
REAL*8 DIMENSIONC7,*)
REAL
*8 DI
MENS
IONC
*)
REAL*8
REAL*8 DI
MENS
IONC
*)REAL*8 DI
MENS
IONC
*)RE
AL*8 DI
MENS
IONC
*)REAL*8 DIMENSIONC*)
REAL*8
DI
MENS
IONC
*)REAL*8 DIMENSIONC*)
REAL*8 DI
MENS
IONC
*)
Refe
r-
Vari
able
en
cing
na
me
prog
rams
VISC
TR
HST3D
DUMP
ETOM
11N
IT2
READ
1READ2
VISC
OSWRITE2
VISLBC
APLY
BCIN.IT3
WRIT
ES
VISO
AR
HST3D
APLYBC
DUMP
ETOM1
INIT
2RE
AD1
READ2
WRIT
E2
VISTFO
HST3D
DUMP
ETOM
1INIT2
READ
1READ2
VISCOS
WRIT
E2
Vari
able
type
REAL*8 DIMENSION(IO)
REAL*8 DI
MENS
ION CIO)
REAL
*8 DIMENSION CI
O)REAL*8 DI
MENS
ION CIO)
REAL
*8 DIMENSION CIO)
REAL*8 DI
MENS
ION CIO)
REAL
*8 DIMENSION CI
O)REAL*8 DI
MENS
ION CI
O)
REAL
*8 DIMENSIONC*)
REAL*8 DI
MENS
IONC
*)RE
AL*8
DI
MENS
IONC
*)
REAL
*8RE
AL*8
REAL
*8RE
AL*8
REAL*8
REAL
*8RE
AL*8
REAL
*8
REAL*8 DIMENSION CI
O)RE
AL*8
DIMENSION(IO)
REAL*8 DIMENSION CIO)
REAL*8 DI
MENS
ION CI
O)REAL*8 DIMENSION CI
O)RE
AL*8
DIMENSION CI
O)REAL*8 DIMENSION CI
O)RE
AL*8
DIMENSIONC 10)
Tab
le
11.2
Cro
ss-r
efer
ence
li
st
of
vari
aJb
les
Con
tin
ued
Vari
able
name
VIST
F1
VPA
VREF
VSTL
OG
VXX
VYY
VZZ
Refer
encing
prog
rams
HST3D
DUMP
ETOM
1IN
IT2
READ
1READ2
WRIT
E2
HST3D
ASEM
BLDU
MPIN
IT1
INIT
2ITER
L2SOR
READ
1SUMCAL
WBBAL
WELL
SS
VSIN
IT
VSIN
IT
COEFF
WRIT
E4
COEFF
WRIT
E4
COEFF
WRIT
E4
Vari
able
ty
pe
REAL*8 DIM
ENSI
ON (10)
REAL*8 DI
MENS
ION(
IO)
REAL*8 DIMENSION(IO)
REAL*8 DI
MENS
ION(
IO)
REAL*8 DI
MENS
ION (10)
REAL*8 DIM
ENSI
ON(I
O)REAL*8 DIMENSION (10)
REAL*8 DIMENSION(*)
REAL*8 DIMENSION (*)
REAL*8 DIMENSION (*)
REAL*8 DIMENSION (*)
REAL*8 DIMENSION (*)
REAL*8 DIMENSION (*)
REAL*8 DIMENSIONS)
REAL*8 DIM
ENSI
ONC*
)REAL*8 DI
MENS
IONC
*)REAL*8 DI
MENS
ION (*
)REAL*8 DI
MENS
IONC
*)
REAL
*8
REAL*8 DIM
ENSI
ON (16
)
REAL
*8 D
IMEN
SION
C*)
REAL*8 DIMENSIONC*)
REAL
*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL*8 DIMENSION (*
)REAL*8 DI
MENS
IONC
*)
Refer-
Variable
encing
name
pr
ogra
ms
WO
HST3D
DUMP
INIT
2IN
IT3
READ
1READ2
READ3
SUMCAL
VISC
OSWBBAL
WELL
SSWR
ITE2
WRIT
E3WRITES
Wl
HST3D
DUMP
INIT
2IN
IT3
READ1
READ2
READ3
VISCOS
WRITE2
WRIT
E3WRITES
WBOD
ETOM1
INIT
2READ2
WELRIS
WRITE2
Variable
type
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8 DIMENSIONC*)
REAL*8 DIMENSION (*
)REAL*8 DIMENSION (*
)RE
AL*8
REAL*8 DI
MENS
ION (*
)
Tabl
e 11.2--Cross-reference
list of
var
iabl
es--
Cont
inue
d
o
-P-
Vari
able
na
me
WCAIF
WCF
WCLBL1
WCLBL2
WFICUM
WFPCUM
WHICUM
WHPCUM
WI
Refe
r
encing
prog
rams
APLY
BCIN
IT2
SUHCAL
ERROR2
INIT
2READ2
WRITE2
WRITE2
WRIT
E2
INIT
2SUMCAL
WELL
SSWRITES
INIT
2SUMCAL
WELLSS
WRITES
INIT
2SUMCAL
WELL
SSWRITES
INIT
2SUMCAL
WELLSS
WRIT
ES
INIT
2WELLSS
WRITE2
Vari
able
Va
riab
le
type
na
me
REAL*8 DIMENSION (*
) WI
DLBL
REAL
*8 DIMENSIONC*)
REAL*8 DI
MENS
IONC
*)WQ
METH
REAL*8 DIMENSION(*)
REAL
*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL*8 DI
MENS
IONC
*)
CHARACTER*60 D
IMENSION CO: 5)
CHARACTER*50 DIMENSION CO : 2)
REAL*8 DIMENSIONC*)
REAL*8 DI
MENS
IONC
*)REAL*8 DIMENSIONC*)
REAL
*8 DI
MENS
IONC
*)WR
ANGL
REAL
*8 DIMENSIONC*)
REAL
*8 DI
MENS
IONC
*)REAL*8 DI
MENS
IONC
*)REAL*8 DI
MENS
IONC
*)
WRCA
LC
REAL*8 DIMENSIONC*)
REAL
*8 DI
MENS
IONC
*)REAL*8 DI
MENS
IONC
*)REAL*8 DIMENSIONC*)
REAL
*8 DI
MENS
IONC
*)REAL*8 DI
MENS
IONC
*)REAL*8 DIMENSIONC*)
REAL
*8 DI
MENS
IONC
*)
REAL*8 DIMENSIONC*)
REAL
*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
Refe
r
encing
prog
rams
PLOT
PLOTOC
ASEMBL
ERROR2
ERROR3
ITER
PLOTOC
READ2
READS
SUMCAL
WBBAL
WELL
SSWRITE2
WRITES
WRIT
ES
READ2
WELR
ISWRITE2
HST3D
DUMP
ETOM1
INIT2
READ1
READ2
WBBAL
WELL
SSWELRIS
WRIT
E2WRITES
Variable
type
CHARACTER*80
CHARACTER* 80
INTEGER*4
DIMENSIONC*)
INTEGER*4 DIMENSIONC*)
INTEGER*4
DIMENSIONC*)
INTEGER*4
DIMENSIONC*)
INTE
GER*
4INTEGER*4
DIME
NSIO
NC*)
INTEGER*4
DIMENSIONC*)
INTE
GER*
4 DI
MENS
IONC
*)IN
TEGE
R*4
DIMENSIONC*)
INTEGER*4 DIMENSIONC*)
INTEGER*4
DIMENSIONC*)
INTEGER*4 DIMENSIONC*)
INTE
GER*
4 DI
MENS
IONC
*)
REAL*8 DIMENSIONC*)
REAL
*8RE
AL* 8 DI
MENS
IONC
*)
LOGI
CAL*
4LO
GICA
L*4
LOGICAL*4
LOGICAL*4
LOGICAL*4
LOGI
CAL*
4LO
GICA
L*4
LOGI
CAL*
4LOG1CAL*4
LOGICAL* 4
LOGICAL*4
Table
11.2
--Cr
oss-
refe
renc
e li
st of
variables Continued
Ln O
Vari
able
name
WRID
WRIDT
WRISL
WRRU
F
WSICUM
WSPC
UM
WT WTMX
Refer
enci
ng
programs
ETOM1
READ
2VELRIS
WRIT
E2
HST3D
WELRIS
WFDYDZ
ETOM
1RE
AD2
WELLSS
WELRIS
WRITE2
ETOM1
READ2
WELR
ISWR
ITE2
INIT
2SU
MCAL
WELLSS
WRIT
ES
INIT
2SU
MCAL
WELLSS
WRITES
COEFF
ASEMBL
Variable
type
REAL*8 DI
MENS
ION (*)
REAL
* 8 DIMENSION^)
REAL
*8RE
AL*8
DIMENSIONC*)
REAL*8
REAL
*8RE
AL*8
REAL
*8 D
IMEN
SION
C*)
REAL*8 D
IMEN
SION
C*)
REAL*8 D
IMENSIONC*)
REAL*8
REAL*8 D
IMEN
SION
C*)
REAL*8
DIMENSIONC*)
REAL
*8 DIMENSIONC*)
REAL*8
REAL*8 D
IMENSIONC*)
REAL
*8 D
IMENSIONC*)
REAL*8 D
IMENSIONC*)
REAL
*8 D
IMENSIONC*)
REAL* 8 DIMENSIONC*)
REAL*8 D
IMENSIONC*)
REAL
*8 DIMENSIONC*)
REAL*8
DIMENSIONC*)
REAL*8 D
IMENSIONC*)
REAL*8
REAL*8
Variable
name
WTMY
WTMZ
WTPX
WTPY
WTPZ
X XO XI X2 XARG
XC
Refe
r
encing
programs
ASEM
BL
ASEM
BL
ASEMBL
ASEMBL
ASEMBL
COEF
FER
ROR2
ETOM
1IN
IT2
MAP2
DPL
OTREAD2
WRIT
E2WRITES
ZONPLT
INIT
2
MAP2
DZONPLT
MAP2D
ZONP
LT
INTERP
PLOT
ZONP
LT
Vari
able
ty
pe
REAL
*8
REAL*8
REAL
*8
REAL
*8
REAL
*8
REAL
*8 DIMENSIONC*)
REAL*8 D
IMENSIONC*)
REAL
*8 DIMENSIONC*)
REAL
*8 D
IMENSIONC*)
REAL
*8 D
IMENSION^*)
REAL
* 8
REAL*8 DIMENSIONC*)
REAL
*8 D
IMENSIONC*)
REAL*8 DIMENSIONC*)
REAL*8 D
IMENSIONC*)
REAL*8
REAL
*8RE
AL*8
REAL
*8REAL*8
REAL*8
REAL*8 DIMENSIONC*)
REAL
*8
Tabl
e 11
.2 C
ross
-ref
eren
ce li
st o
f variables C
ontinued
Ln O
Vari
able
na
me
XD XI XINC
XLBL
XMAX
XMIN
XO XPRNT
XS XTOT
XX XXN
XYRAT
Refe
r
encing
programs
ZONPLT
WELR
IS
PLOT
PLOT
PLOT
ZONPLT
PLOT
ZONPLT
PLOT
PLOT
INTERP
MAP2D
INIT
2SO
R2L
TOFEP
VISCOS
VSIN
IT
SOR2
L
ZONPLT
Variable
type
REAL*8
REAL*8
REAL*8
CHAR
ACTE
R*30
REAL*8
REAL*8
REAL*8
REAL
*8
REAL
* 8
DIME
NSIO
NC*)
REAL*8
REAL*8 DIMENSIONC*)
REAL
*8
REAL
*8RE
AL*8
DIMENSIONC*)
REAL*8
REAL*8
REAL*8
REAL*8 DIMENSIONC*)
REAL*8
Refer-
Vari
able
encing
name
prog
rams
Y
COEFF
ETOM
1INIT2
MAP2D
PLOT
READ2
WRIT
E2WR
ITES
ZONP
LT
YO
INIT2
Yl
MAP2D
WELL
SSWF
DYDZ
ZONPLT
Y2
MAP2D
ZONPLT
YAR6
INTERP
YC
PLOT
ZONP
LT
YD
ZONP
LT
YLBL
PLOT
YMAX
PLOT
ZONPLT
Vari
able
type
REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONS)
REAL
*8 DIMENSIONC*)
REAL*8 DI
MENS
IONC
*)RE
AL*8
DIM
ENSI
ONC*
)REAL*8 DIMENSIONC*)
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL*8
REAL
*8 DIM
ENSI
ONC*
)REAL*8
REAL*8
CHARACTER*40
REAL
*8RE
AL*8
Table
11.2 Cross-reference list o
f variables Continued
5
Vari
able
na
me
YMAX
HV
YMIN
YNHV
YNM1
HV
YO YPOS
UP
YREF
YS YTOT
YY YYERR
YYMAX
Refe
r
encing
prog
rams
BSODE
PLOT
ZONPLT
BSODE
BSODE
PLOT
WELLSS
WFDY
DZ
HST3D
READ3
WRITE3
WRIT
ES
VSIN
IT
INTE
RP
MAP2D
BSOD
EVS
INIT
WELR
ISWF
DYDZ
BSODE
WELR
IS
BSODE
WELR
IS
Vari
able
type
REAL*8 DIMENSION (2, 12)
REAL*8
REAL
*8
REAL*8 DI
MENS
ION (2, 12
)
REAL
*8 DIMENSION(2,12)
REAL*8 DIMENSION (*)
REAL*8
REAL*8
LOGI
CAL*
4LO
GICA
L*4
LOGI
CAL*
4LOGICAL*4
REAL
*8
REAL*8 DIMENSION^)
REAL*8
REAL*8 DIMENSION (2
)REAL*8
REAL
*8 D
IMENSION(2)
REAL*8 DIMENSIONS)
REAL
*8 DIMENSION (2)
REAL*8 DI
MENS
ION (2
)
REAL*8 DIMENSION (2)
REAL*8 DIM
ENSI
ON (2)
Variable
name
YYMX
SV
YYN
YYNM1
YYSA
VE
Z ZO Zl Z2 ZA ZCHARS
ZEBRA
Refer
encing
prog
rams
BSODE
BSODE
BSODE
BSODE
APLY
BCASEMBL
BSODE
COEFF
ERROR2
ETOM
1INIT2
READ2
SUMCAL
WELLSS
WRITE2
WRIT
ES
INIT
2
MAP2D
MAP2D
BSODE
MAP2D
MAP2D
WRITES
Vari
able
type
REAL*8 DI
MENS
ION(
2)
REAL
*8 DIMENSION(2)
REAL*8 DIMENSION (2
)
REAL*8 DIMENSION (2)
REAL*8 DIMENSION (*)
REAL
*8 DIMENSION (*)
REAL
* 8
REAL
*8 DIMENSION (*)
REAL*8 DIMENSION (*)
REAL*8 DIMENSION (*)
REAL*8 DIMENSION (*)
REAL*8 DIMENSION (*)
REAL*8 DIMENSION (*)
REAL*8 DIMENSION (*)
REAL*8 DIMENSION (*)
REAL*8 DIMENSION (*)
REAL*8
REAL*8
REAL
*8
REAL*8
CHAR
ACTE
R*!
DIMENSION (0
:31)
LOGICAL*4
LOGI
CAL*
4
Tab
le
11.2
--C
ross
-ref
eren
ce li
st
of
var
iaJb
2es
--C
onti
nued
o 00
Variable
name
ZELBC
ZHCBC
ZPIN
IT
ZPOSUP
Refe
r
enci
ng
prog
rams
APLYBC
ASEM
BLER
RORS
INIT
2SUMCAL
WRITE2
APLYBC
ETOM
1IN
IT2
READ
2WRITE2
HST3D
DUMP
ETOM
1IN
IT2
READ
1RE
AD2
WRITE2
HST3D
READ
3WRITES
WRITES
Vari
able
type
REAL*8 DI
MENS
IONC
*)REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL
*8 DI
MENS
IONC
*)REAL*8 DIMENSIONC*)
REAL*8 DI
MENS
IONC
*)
REAL*8 DIMENSIONC*)
REAL*8 DIMENSIONC*)
REAL
*8 DI
MENS
IONC
*)REAL*8 DI
MENS
IONC
*)RE
AL*8 D
IMEN
SION
C*)
^
REAL
* 8
REAL*8
REAL*8
REAL*8
REAL
* 8
REAL
*8REAL*8
LOGI
CAL*
4LOGICAL*4
LOGICAL*4
LOGICAL*4
Refer-
Vari
able
encing
name
programs
ZT
HST3D
DUMP
ETOM1
INIT2
READ1
READ2
WRITE2
ZTHC
HST3
DDUMP
ETOM
1IN
IT2
READ
1READ2
WRIT
E2
ZU
BSODE
ZWK
WELRIS
WFDY
DZ
ZWKT
WE
LLSS
Vari
able
type
REAL*8 DIMENSION CIO)
REAL*8 DIMENSION(IO)
REAL*8 DIMENSION CI
O)RE
AL*8
DI
MENS
IONC
10)
REAL*8 DIMENSION CIO)
REAL
*8 DIMENSION(IO)
REAL*8 DIMENSION CIO)
REAL*8 DI
MENS
IONC
5)REAL*8 DIMENSION C5
)RE
AL*8
DIMENSION C5
)REAL*8 DIMENSION C5
)RE
AL*8
DIMENSION (5)
REAL*8 DIMENSION C5
)RE
AL*8
DIMENSION (5
)
REAL
*8
REAL
*8RE
AL*8
REAL*8
11.3 CROSS-REFERENCE LIST OF COMMON BLOCKS
A cross-reference list of common blocks (table 11.3) shows in which
subprograms each named common block appears. Blank common is used only for
the two variably-partitioned arrays. Generally, the common block names relate
to the subprogram in which the variables of that common block are defined
first. All common blocks are contained in the main program.
509
Table
11.3
Cro
ss-r
efer
ence
li
st o
f co
mmon
blo
cks
Ln i O
Common
bloc
k na
me ASA
CCC
ER1
IN1A
Referencing
programs
MAIN
ASEMBL
CRSD
SP
MAIN
ASEMBL
CALC
MAIN
ERRO
R 1
ERRO
R2ER
ROR3
ERRP
RTIN
IT2
IREW
IITER
READ
!RE
AD2
READ
3RE
WIRE
VI3
SOR2
LSU
MCAL
MAIN
DUMP
INIT
1RE
AD1
Common
block
Referencing
name
prog
rams
IN1B
MAIN
DUMP
ERROR
1IN
IT1
READ1
WRIT
E1
IN1C
MAIN
DUMP
INIT
1L2SOR
READ1
IN1D
MA
INDU
MPIN
IT1
ITER
READ
1
IN1E
MA
INAS
EMBL
DUMP
INIT
1READ1
IN1F
MAIN
DUMP
INIT
1IN
IT2
READ1
Comm
on
bloc
k Re
fere
ncin
g na
me
prog
rams
IN1G
MAIN
DUMP
INIT1
ITER
READ
1
IN1H
MAIN
DUMP
INIT
1L2SOR
READ
1
IN1I
MAIN
DUMP
INIT
1READ1
IN1J
MAIN
ASEMBL
DUMP
INIT
1RE
AD1
IN1L
MAIN
DUMP
INIT
1INIT2
READ
1WB
BAL
WELLSS
Common
bloc
k Referencing
name
prog
rams
IN1M
MAIN
DUMP
INIT
1ITER
READ
1SUMCAL
IN1P
MAIN
DUMP
INIT
1RE
AD1
IN1Q
MAIN
DUMP
INIT
1ITER
READ
1
IN1S
MAIN
DUMP
INIT
1PLOTOC
READ
1WR
ITE2
WRITE3
WRIT
E A
WRIT
ES
Table
11.3 Cross-reference list of common blocks Continued
Common
block
name IN1T
IN2A
IN2B
Refe
renc
ing
prog
rams
MAIN
DUMP
INIT
1PL
OTOC
READ
1RE
WI3
WRITE2
WRITE 3
WRITE4
WRIT
ES
MAIN
APLYBC
ASEMBL
CALC
COEF
FDUMP
ERRO
R3INIT2
INIT
3READ1
READ
3SU
MCAL
WELLSS
WELRIS
MAIN
BLKDAT
DUMP
INIT2
READ
1TO
FEP
Common
Comm
on
block
Referencing
block
name
pr
ogra
ms
name
IN2BV
MAIN
IN2F
BLKDAT
DUMP
INIT
2RE
AD1
TOFEP
IM2H
IN2C
MAIN
APLYBC
ASEMBL
DUMP
INIT2
READ1
SUMCAL
WBBAL
WELLSS
WRITE2
WRITES
IN2D
MAIN
DUMP
INIT2
READ1
VISCOS
IN2E
MAIN
CALC
DUMP
IN2I
INIT
2IT
ERREAD1
SUMCAL
WBBAL
WELLSS
WFDYDZ
Referencing
prog
rams
MAIN
APLYBC
DUMP
INIT2
READ
1
MAIM
APLY
BCCA
LCCLOSE
COEFF
DUMP
ERROR3
ETOM2
INIT
2INIT3
ITER
READ1
READ3
SUMC
ALWBBAL
WELLSS
WRITE2
WRITE3
WRIT
E4WRITES
MAIN
APLYBC
DUMP
INIT2
READ1
SUMC
ALWRITE2
WRITES
Common
bloc
k Referencing
name
pr
ogra
ms
IN2L
MAIN
CLOSE
DUMP
INIT2
READ1
ITA
MAIN
ASEMBL
ITER
WRITES
L2SAV
MAIN
DUMP
L2SOR
READ1
WRITES
ORA
MAIN
ASEMBL
D4DES
DUMP
INIT
1ORDER
READ1
SBCFLO
WRITE 1
laoie
ii
.j c
;ross
-rere
rence u
se o
r co
mm
on D
IOC
KS
conti
nued
Ni
Common
block
name RD1A
RD1AC
Refe
renc
ing
programs
MAIN
APLY
BCAS
EMBL
CALC
COEF
FCRSDSP
DUMP
ERRO
R2ER
ROR3
ETOM
1ET
OM2
INIT
1IN
IT2
INIT
3IT
ERPL
OTOC
READ
1RE
AD2
READ
3SU
MCAL
VISC
OSWB
BAL
WELLSS
WRIT
E1WR
ITE2
WRIT
E3WRITE4
WRIT
ES
MAIN
DUMP
READ
1WRITE1
Comm
on
block
Referencing
name
pr
ogra
ms
RD1B
MAIN
READ
1WR
ITE1
RD1C
MAIN
APLY
BCAS
EMBL
COEF
FCRSDSP
D4DES
DUMP
ERROR
1ER
ROR2
ETOM1
ETOM2
INIT
1INIT2
INIT
3IR
EWI
ITER
ORDER
PLOT
OCPRNTAR
READ
1RE
AD2
READ3
REWI
REWI
3SB
CFLO
SOR2
LSU
MCAL
WBBAL
WELLSS
WRIT
E1WRITE2
WRITE3
WRITE4
WRIT
ES
Comm
on
block
Referencing
name
prog
rams
RD1D
MAIN
ASEM
BLCLOSE
COEFF
DUMP
ERROR2
ERROR3
ETOM
1IN
IT1
INIT2
INIT3
IREW
IIT
ERL2SOR
PLOTOC
READ
1READ2
READ3
REWI
REWI
3SUMCAL
WBBAL
WELL
SSWR
ITE1
WRITE2
WRIT
E3WRITE4
WRITES
ZONPLT
Comm
on
block
Refe
renc
ing
name
pr
ogra
ms
RD1E
MAIN
APLYBC
ASEMBL
DUMP
ERROR1
ERRO
R2ER
ROR3
ETOM
1ET
OM2
INIT
1IN
IT3
INIT
3ITER
READ
1RE
AD2
READ
3SB
CFLO
SUMC
ALWRITE1
WRIT
E2WRITE3
WRIT
ES
RD1F
MAIN
COEF
FDU
MPERROR1
ERRO
R2ETOM1
INIT
1IN
IT2
READ
1RE
AD2
WRITE1
WRIT
E2ZO
NPLT
Table
11.3--Cross-reference
list of
common blocks-"Continued
Comm
on
block
name RD1G
RD1H
RD2A
Referencing
prog
rams
MAIN
APLY
BCDU
MPER
ROR 1
ERRO
R2ET
OM1
INIT
1IN
IT2
READ
1RE
AD2
WRITE1
WRIT
E2
MAIN
ASEMBL
COEF
FDU
MPERROR 1
INIT
1IN
IT2
ITER
READ
1RE
AD2
SBCF
LOWR
ITE1
WRIT
E2WRITE4
WRIT
ES
MAIN
DUMP
ERRO
R2IN
IT2
READ
1RE
AD2
WRIT
E2
Comm
on
block
Referencing
name
programs
RD2B
MAIN
APLYBC
ASEM
BLCA
LCCO
EFF
CRSD
SPDUMP
ETOM1
INIT2
READ
1READ2
SUMCAL
WELLSS
WELRIS
WFDYDZ
WRITE2
WRITES
RD2C
MA
INDU
MPETOM1
INIT2
READ1
READ2
WRITE2
RD2D
MAIN
INIT2
READ2
WRIT
E2
Comm
on
block
Referencing
name
programs
RD2E
MA
INASEMBL
COEFF
DUMP
ETOM
1IN
IT2
INIT
3PL
OTOC
READ
1READ
2READ3
SUMC
ALVI
SCOS
WBBAL
WELL
SSWR
ITE2
WRIT
E3WR
ITES
RD2F
MAIN
DUMP
ETOM
1IN
IT2
READ
1READ
2WR
ITE2
Comm
on
block
Referencing
name
prog
rams
RD2G
MAIN
DUMP
ERRO
R2ETOM1
INIT
2READ1
READ
2VI
SCOS
WRIT
E2
RD2GV
MAIN
DUMP
ETOM1
INIT
2RE
AD1
READ
2VI
SCOS
WRITE2
RD2H
MAIN
APLY
BCDU
MPER
ROR2
ETOM
1IN
IT2
READ
1READ2
WRITE2
RD2IV
MAIN
APLY
BCBL
KDAT
DUMP
READ
1READ2
WRITE2
(J\
Comm
on
block
name RD2J
RD2K
RD2KV
Referencing
programs
MAIN
APLY
BCASEMBL
DUMP
ETOM
1IN
IT2
READ
1RE
AD2
SUMC
ALTOFEP
WBBAL
WELL
SSWE
LRIS
WFDY
DZWR
ITE2
WRIT
ES
MAIN
DUMP
ERRO
R2ET
OM1
INIT
2RE
AD1
READ
2WR
ITE2
MAIN
DUMP
ETOM
1IN
IT2
READ
1RE
AD2
WRIT
E2
Comm
on
block
Referencing
name
programs
RD2L
MAIN
DUMP
INIT
2IT
ERRE
AD1
READ
2WR
ITE2
RD2M
MAIN
CLOSE
DUMP
READ
1RE
AD2
READ
3WE
LLSS
WELR
ISWR
ITE2
WRIT
E3WR
ITES
RD2N
MAIN
DUMP
ETOM
1INIT2
ITER
READ
1RE
AD2
WBBAL
WELL
SSWE
LRIS
WRIT
E2WR
ITES
Comm
on
bloc
k Referencing
name
programs
RD2P
MAIN
DUMP
ETOM1
INIT
2READ1
READ2
WELLSS
WRIT
E2
RD2Q
MA
INDU
MPIN
IT2
ITER
READ1
READ2
WRIT
E2
RD2S
MAIN
APLYBC
ASEMBL
COEFF
DUMP
READ
1READ2
SBCFLO
SUMCAL
WELLSS
WRITE2
WRIT
ES
RD2T
MAIN
DUMP
INIT
2IT
ERREAD1
READ2
SOR2L
WRIT
E2
Comm
on
bloc
k Re
fere
ncin
g na
me
prog
rams
RD2U
MAIN
DUMP
IREW
IRE
AD1
READ2
REWI
REWI
3SU
MCAL
RD2V
MAIN
PUMP
INIT
2RE
AD1
READ2
READ3
SUMC
ALWR
ITE2
WRIT
E3WR
ITEA
WRIT
ES
RD2W
ETOM1
RD3A
MAIN
ERRO
R3ET
OM2
INIT
3READ3
WRIT
E3
RD3B
MAIN
COEF
FER
ROR3
ETOM2
INIT
3READ3
WRIT
E3
Tabl
e 11
.3 C
ross
-ref
eren
ce list of c
ommo
n bl
ocks
--Co
ntin
ued
Ul
I 1
Ln
Comm
on
block
name RD3C
RD3D
RD3E
RD3EV
RD3F
RD3G
Refe
renc
ing
programs
MAIN
READ
3WRITE4
WRIT
ES
MAIN
ERRO
R3RE
AD3
WRIT
E3WR
ITES
MAIN
CLOS
EDUMP
READ
3
MAIN
ERRO
R3ET
OM2
INIT
3RE
AD3
WRIT
E3WR
ITES
MAIN
READ
3
MAIN
COEF
FRE
AD3
WRITE4
Comm
on
Comm
on
bloc
k Re
fere
ncin
g block
name
prog
rams
na
me
RD3I
MA
IN
SCA
CLOS
ECOEFF
DUMP
ERROR3
ETOM
2IN
IT3
SCB
READ
3SUMCAL
WRIT
E 1
WRITE3
WRITE4
SCC
WRIT
ES
*
Refe
renc
ing
programs
MAIN
COEFF
ITER
SUMC
ALWR
ITES
MAIN
APLY
BCSU
MCAL
WRIT
ES
MAIN
SUMC
ALWE
LLSS
WRIT
ES
Common
block
Refe
renc
ing
name
pr
ogra
ms
SORA
MA
INSO
R2L
WRITES
WRA
MAIN
WELR
ISWFDYDZ
WRB
MAIN
BSOD
EWELRIS
WRC
MAIN
WELRIS
WFDYDZ
WSSA
MAIN
WBBAL
WELL
SSWELRIS
WFDYDZ
i*U.S. GOVERNMENT PRINTING OFFICE: 1987 774-930/65111
11.4 COMMENT FORM AND MAILING-LIST REQUEST
iIf you wish to be placed on a mailing list for revisions of the program
documentation and announcements of new releases of this program, please return
this page to:
HST3D Code Custodian
U.S. Geological Survey
Water Resources Division
Box 25046, Mail Stop 413
Denver Federal Center
Denver, Colorado 80225
Any comments on the program or documentation will be appreciated.
Name Date
Organization
Street
City_________________________State
Zip code or Country
Telephone Number ( ) _________________
517