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Appendix I SPE Nomenclature and Units·

Standard letter symbols for reservoir engineering and electric logging have been defined by the AI ME (Society of Petroleum Engineers). Some nonstandard terms, subscripts and nomenclature are still in use and may be encountered.

No effective standardization or metrication of units has yet occurred, and the industry uses American mixed units to a large extent, although some metric units mixed with American still may be encountered. An application of the SI metric system is found in the Journal of Petroleum Engineerinng (1985) in the issues for August (p.1415) and October p.1801.

UNITS

Volume acre-foot for large volumes barrel cubic ft cubic metre

Liquid volume barrel = 5.615 cubic ft cubic metre = (35.31) fe (Unless otherwise specified, an oil volume will be tank oil measured at 1 atmosphere and 60°F.)

* Reprinted fromlournal of Petroleum Technology, 1984, pp. 2278-2323 by permission. © SPE-AlME, 1984.

Gas volume cubic foot) measured at 1 atmosphere cubic metre) and 60°F MCF = thousands of cubic feet MMCF = millions of cubic feet (The billion is the American billion = 109 ;

the trillion is the American trillion = 1012.)

Pressure pounds force per square in (psi) atmosphere bar

Temperature degrees Fahrenheit OF degrees Rankine OR = 460 + OF degrees Kelvin K

Length pipelines - miles, feet, kilometres well depths - feet or metres

Diameters tubular diameters generally inches or centimetres feet/metres

Viscosity centipoise

Density lb mass per cubic foot kg mass per cubic metre g per cubic centimetre

257

258 PETROLEUM ENGINEERING: PRINCIPLES AND PRACTICE

Specific gravity liquids relative to water (62.4lb/ft3)

gases relative to air (0.0765Ib/ft3)

API scale for tank oil

Gas-oil ratio

Oil densities API gravity

0API = 141.5 --,----.,.-- - 131. 5 (SG)oil

standard cubic feet of gas per stock tank barrel of oil cubic metres of gas (s.c.) per cubic metre tank oil

SG = specific gravity of water = 1.0

Flow rate Recommendation for metrication and appropriate conversion factors for units are given:

liquids - barrel per day (bid) cubic metres per day (m3/d)

gases - standard cubic ft per day SCF/d, MCF/d and MSCFD/d, MMSCFD cubic metres per day (m3/d) MSCFD/d

Recommended units: conversions Quantity SI unit Industry SPE preferred

unit unit

Length m mile km metre m foot m inch mm

Area m2 sq. mile km2 acre km2 sq.ft m2

sq. inch mm2 Volume m3 m3 m3

acre foot m3 barrel m3

ft3 m3 US gallon m3

Capacity Ilength m3/m barrels/ft m3/m ft3/ft m3/m

US gall.lft m3/m Mass kg Ibmass kg

short ton Mg Temperature gradient Kim °F/ft Kim Pressure Pa atmosphere kPa

bar kPa kgf/sq. em kPa Ibf/sq. in. kPa

dyne/sq. em Pa Pressure gradient Palm Ibf/sq. in.lft kPaim Density kg/m3 Ibmlft3 kg/m3

Ibm/USgal1. kg/m3 Volume rate m3/s bid m3/d

US gall.!min m3/hr Viscosity Pa.s cP Pa.s Permeability m2 Darcy 11m2

miliiDarcy 11m2

Conversion factor

(industry ~ preferred)

1.609344 1.0

0.3048 25.4

2.589988 4.046873 x 103

0.0920304 6.4516 x 102

1.0 1.233482 x 103 1.589873 x 10.1

2.831685 x 10.2 3.785412 x 10.3 5.216119 x 10.1

9.02903404 x 10.2 1.241933 x 10.2 4.535924 x 10.1

0.9071847 1.822689

1.013250x 102 1.0 x 102

9.806650 x 101

6.894757 1 x 10.1

2.262059 x 101

1.601846 x 10-1

1 .198264 x 1 02 1.589873 x 10-1

0.2271247 1.0 x 10-3

9.869233 x 10-1

9.869233 x 10-4

SPE NOMENCLATURE AND UNITS

sPE SYMBOLS STANDARD Preface

Objectives

The primary objectives of the 1984 Symbols Standards are to combine prior standards and supplements into one publication so as to provide (1) consistency of usage and maximum ease of understanding of mathematical equations for the readers of technical papers, and (2) to codify symbols lists, rules and guides for the writers of technical papers.

Structure of lists

The 1984 Symbol Standards are a consolidation of the 1956 Standard and all later supplements. Some of the cross-grouping and obsolete quantities have been eliminated. The complete symbols list is given in four different forms as follows:

A. Symbols alphabetized by physical quantity,

B. Subscripts alphabetized by physical quantity,

C. Symbols alphabetized by symbols,

D. Subscripts alphabetized by symbols.

The names or labels for the quantities are for identification only and are not intended as definitions. Defining equations are given in a few cases where further identifications may be needed. For the present, the specification of units and conditions of measurement is left to the user.

For convenience in dimensional checking of equations, a column has been included giving the dimensions of each quantity in terms of mass, length, time, temperature and electrical charge (m, L, t, T, q). The term various also appears in this column for several symbols. This terminology permits maximum flexibility for quantities that may require different dimensions in different problems. Examples are symbols: (1) m for slope of a line (two variables of any dimensions can be related); (2) C for concentration (dimensions might be m/L3 ,

dimensionless or other); (3) F (factor) when it represents ratio (dimensions might be L3/m, m, dimensionless or other). This flexibility in dimensions permits desirable shortening of the symbols list.

Additional standard symbols

The extraordinary growth in all phases of petroleum and computer technology has necessitated the adoption of additional standard symbols, since the

259

original standards were published in 1956 following five years of intensive development. Additions resulted from requests from members and from editorial reviews of the numerous papers submitted to SPE for publication.

Principles of symbols selection

Once the original reservoir Symbols Standard was established in 1956, the principles employed in the selection of additional symbols have been as follows:

A. (1) Use single letters only for the main letter symbols. This is the universal practice of the American National Standards Institute (ANSI), the International Organization for Standardization (ISO) and the International Union of Pure and Applied Physics (IUP AP) in more than 20 formal Standards adopted by them for letter symbols employed in mathematical equations. (2) Make available single and multiple subscripts to the main letter symbols to the extent necessary for clarity.

Multiple letters such as abbreviations are prohibited for use as the main symbol (kernel) for a quantity. A few exceptions are some traditional mathematical symbols such as log, In and lim. Thus quantities that are sometimes represented by abbreviations in textual material, tables or graphs are required in the SPE Symbols Standards to have single-letter kernels. Examples are: gas-oil ratio (GOR), bottomhole pressure (BHP), spontaneous potential (SP), static SP (SSP), which, respectively, have the following SPE Standard symbols: R,pbh,

Esp, Essp. . B. Adopt the letter symbols of original or prior

author usage, where not in conflict with principles C and D below.

C. Adopt letter symbols consistent or parallel with the existing SPE Standard, minimizing conflicts with that Standard.

D. Where pertinent, adopt the symbols already standardized by such authorities as ANSI, ISO, or IUPAP (see A); minimize conflicts with these Standards.

E. Limit the list principally to basic quantities, avoiding symbols and subscripts for combinations, reciprocals, special conditions, etc.

F. Use initial letters of materials, phase, processes, etc., for symbols and subscripts, as being suggestive and easily remembered.

G. Choose symbols that can be readily handwritten, typed, and printed.


Principles of letter symbol standardization A. Requirements for Published Quantity.

Each published letter symbol should be:

1. Standard, where possible. In the use of published symbols, authors of technical works (including textbooks) are urged to adopt the symbols in this and other current standard lists and to conform to the principles stated here. An author should give a table of the symbols used and their respective interpretations, or else refer to a standard list as a source for symbols used but not explained. For work in a specialized or developing field, an author may need symbols in addition to those already contained in standard lists. In such a case the author should be careful to select simple suggestive symbols that avoid conflict in the given field and in other closely related special fields. Except in this situation, the author should not introduce new symbols or depart from currently accepted notation.

2. Clear in reference. One should not assign to a given symbol different meanings in such a manner as to make its interpretation in a given context ambiguous. Conflicts must be avoided. Often a listed alternative symbol or a modifying subscript is available and should be adopted. Except in brief reports, any symbol not familiar to the reading public should have its meaning defined in the text. The units should be indicated whenever necessary.

3. Easily identified. Because of the many numerals, letters and signs that are similar in appearance, a writer should be careful in ca!ling for separate symbols that in published form might be confused by the reader. For example, many letters in the Greek alphabet (lower case and capital) are practically indistinguishable from English letters; the zero is easily mistaken for a capital O.

4. Economical in publication. One should try to keep at a minimum the cost of publishing symbols. In particular: (1) Notations which call for handsetting of movable type should be rejected in favour of forms adapted to modern mechanical methods of composition. (2) No one work should use a great variety of types and special characters. (3) Handwriting of inserted symbols, in copy largely typewritten and to be reproduced in facsimile, should not be excessive. (4) Often a complicated expression appears as a compo-

nent part of a complex mathematical formula - for example, as an exponent of a given base. Instead, one may introduce locally, a single non-conflicting letter to stand for such a complicated component. An explanatory definition should then appear in the immediate context.

B. Secondary symbols. Subscripts and superscripts are widely used and for a variety of conventional purposes. For example, a subscript may indicate: (1) the place of a term in a sequence or matrix; (2) a designated state, point, part, or time, or system of units; (3) the constancy of one independent physical quantity among others on which a given quantity depends for its value; (4) a variable with respect to which the given quantity is a derivative. Likewise, for example, a superscript may indicate: (1) the exponent for a power, (2) a distinguishing label, (3) a unit, or (4) a tensor index. The intended sense must be clear in each case. Several subscripts or superscripts sometimes separated by commas may be attached to a single letter. A symbol with a superscript such as prime (') or second ("), or a tensor index, should be enclosed in parentheses, braces or brackets before an exponent is attached. So far as logical clarity permits, one should avoid attaching subscripts and superscripts to subscripts and superscripts. Abbreviations, themselves standardized, may appear among subscripts. A conventional sign, or abbreviation, indicating the adopted unit may be attached to a letter symbol, or corresponding numeral. Reference marks, such as numbers in distinctive type, may be attached to words and abbreviations, but not to letter symbols.

C. Multiple subscript-position order. The wide variety and complexity of subject matter covered in the petroleum literature make it impossible to avoid use of multiple subscripts with many symbols. To make such usage less confusing, the following guides were employed for the order of appearance of the individual letters in multiple subscripts in the symbols list. Use of the same rules is recommended when it becomes necessary to establish a multiple subscript notation that has not been included in this list.

1. When the subscript r for 'relative' is used, it should appear first in subscript order. Examples: K r01· K rg.

2. When the subscript i for 'injection' or


'injected' or 'irreducible' is used, it should appear first in subscript order (but after r for 'relative'). Examples: Big, formation volume factor of injected gas; Cig, compressibility of injected gas.

3. Except for Cases 1 and 2 above (and symbols Kh and Lv), phase, composition and system subscripts should generally appear first in subscript order. Examples: Bgi,

initial or original gas formation volume factor; Boi , initial or original oil formation volume factor; CO,i' initial or original oxygen concentration; B li , initial or original total system formation volume factor; PsE, density of solid particles making up experimental pack; also FaH G Lp' Gwgp, G Fi'

4. Abbreviation subscripts (such as 'ext', 'lim', 'max', 'min'), when applied to a symbol already subscripted, should appear last in subscript order and require that the basic symbol and its initial subscript(s) be first enclosed in parentheses. Examples: (ia)max, (Shr)min'

5. Except for Case 4 above, numerical subscripts should appear last in subscript order. Examples: qoD3, dimensionless oil production rate during time period 3; PR2, reservoir pressure at time 2; (ial)max, maximum air injection rate during time period 1.

6. Except for Cases 4 and 5 above, subscript D for 'dimensionless' should usually appear last in subscript order. Examples: PID; qoD; (qoD3)max'

7. Except for Cases 4, 5 and 6 above, the following subscripts should usually appear last in subscript order: regions such as bank, burned, depleted, front, swept, unburned (b, b, d, f, s, u); separation, differential and flash (d, f); individual component identification (i orQI other). Examples: EDb; Rsf, npJ-

D. Typography. Letter symbols for physical quantities, and other subscripts and superscripts, whether upper case, lower case, or in small capitals, when appearing as light-face letters of the English alphabet, are printed in italic (sloping) type. Arabic numerals, and letters or other alphabets used in mathematical expressions, are normally printed in vertical type. When a special alphabet is required, boldface type is to be preferred to German, Gothic, or script type. In material to be reproduced in facsimile, from copy largely typewritten, letters that would be boldface in print may be indicated to be such by special underscoring, while the

261

few distinct letters used from other alphabets, if carefully made, should be self-explanatory. It is important to select a type face that has italic forms, and clearly distinguished upper case, lower case and small capitals. Only type faces with serifs are recommended.

E. Remarks. Quantity symbols may be used in mathematical expressions in any way consistent with good mathematical usage. The product of two quantities is indicated by writing abo The quotient may be indicated by writing

a -,alb or ab-1

b

If more than one solidus is used in any algebraic term, parentheses must be inserted to remove any ambiguity. Thus, one may write (a/b)/c, or a/bc, but not alb/c.

F. Special notes. Observe the following:

1. When the mobilities involved are on opposite sides of an interface, the mobility ratio will be defined as the ratio of the displacing phase mobility to the displaced phase mobility, or the ratio of the upstream mobility to the downstream mobility.

2. Abbreviated chemical formulas are used as subscripts for paraffin hydrocarbons: C1 for methane, C2 for ethane, C3 for propane ... Cn for CnH 2n +2 •

3. Complete chemical formulas are used as subscripts for other materials: CO2 for carbon dioxide, CO for carbon monoxide, O2 for oxygen, N2 for nitrogen, etc.

4. The letter R is retained for electrical resistivity in well logging usage. The symbol P is to be used in all other cases and is that preferred by ASA.

5. The letter C is retained for conductivity in well logging usage. The symbol (J is to be used in all other cases and is that preferred by ASA.

6. Dimensions: L = length, m = mass, q = electrical charge, t = time, and T = temperature.

7. Dimensionless numbers are criteria for geometric, kinematic and dynamic similarity between two systems. They are derived by one of three procedures used in methods of similarity: integral, differential, or dimensional. Examples of dimensionless numbers are Reynolds number (NRe ) and Prandtl number (Npr ). For a discussion of methods


of similarity and dimensionless numbers, see "Methods of Similarity", by R.E. Schilson, J. Pet. Tech. (August, 1964) 877.

8. The quantity x can be modified to indicate an average or mean value by an overbar, X·

Principles of computer symbol standardization

A. Symbol Structure. The computer symbols are structured from four possible parts representing respectively arithmetic mode, mathematical operators, basic quantities and subscripts, exclusive of time and space designations. Each of these parts has a defined number of characters and, when all are used in a single symbol, the total length may be ten characters. Example ten-character notations are:

XDELPRSTQQ,XDELCMPPRD

When any of the four parts are not used, the remaining characters are to be right- or leftjustified to form a string of characters without blank positions.

In practice, the combined notations will not usually exceed six characters. In those cases where the complete computer symbol does exceed six characters, and the computer language being used will not allow more than six, a shortened notation must be employed. The part of the notation representing the basic mathematical quantity (letter) symbol should be retained and the other parts of the notation shortened. Shortened symbols are no longer standard, and therefore must be defined in the text or appendix as is appropriate.

1. The first part of the notation consists of one character position to define the arithmetic mode of the complete computer symbol. It is suggested that X be used for floating point variables and I for integers. This notation position should be used only if absolutely necessary, the preferred approach being the use of a declaration within the program.

2. The second part of the notation (operator field) consists of three characters and is used for mathematical operators. The notation should suggest the operation.

3. The third part of the notation (quantity symbol field) consisting of three characters, is used to represent the basic mathematical quantity (letter) symbol. The three letter notation mnemonically denotes the quantity name as closely as possible. This part of the computer notation is thus of the nature of an

abbreviation. All three character positions must be employed.

Fixed characters are utilized in this part of the notation when heat quantities, indexes and exponents are being assigned computer symbols. When a heat quantity is denoted, H appears in the first character position, as exemplified by thermal conductivity HCN. Indexes such as resistivity index are denoted by X in the third character position. Exponents are characterized by XP in the second and third positions, such as porosity exponentMXP.

4. The fourth part of the notation (subscript field) is used to represent the subscripts of the mathematical letter symbol and normally consists of one of the three character positions. Computer symbol subscripts are normally designated by using the mathematical letter subscripts of the SPE Symbols Standard.

Though usually not required, more characters may be used when necessary for designation of multiple mathematical letter subscripts. For example, dimensionless average reservoir pressure would be denoted by PRSA VQ.

The computer subscript designation is placed immediately to the right of the quantity symbol field with no intervening space.

Dimensionless numbers are denoted by Q in the last required subscript position. A verage, maximum, minimum, extrapolated or limiting values of a quantity are denoted respectively by A V, MX, MN, XT, of LM in the first two subscript positions; additional subscripting occurs immediately to the right of these defined notations. Other than in these cases, the order of subscripting should follow the rules given in the 'Multiple Subscripts - Position Order' .

5. No binding rule is made for the notation of space and time subscripts, since the method of subscripting is often dictated by the characteristics of a particular computer. However, the vital importance of these subscripts makes it necessary to establish a standard and require an author to define any deviations. The system outlined below should be used when the subscripts are not implied by an array location or an index specified by the program logic.

The following sketch indicates the coordinate system used to denote special posi-


tion in multi-dimensional arrays. 1 (I = 1, 2, 3, ... ,NX)

This convention was adopted so that the page position of printed output obtained in a normal I, J, K sequence would correspond to position as viewed on maps as normally used in petroleum engineering. Similarly, I, K or J, K sequences would correspond to cross-sections as normally used.

The space and time subscripts are constructed by placing a letter code (I, J, K, T) before the following symbols:

Machine Symbol

P2 P3H PI PIH MIH MI M3H M2

Definition

present location plus 2 . present location plus 3/2

present location plus I present location plus 112 present location minus 112 present location minus I present location minus 3/2 present location minus 2

Hence, the subscript for the present time t would be T, and that for subscript t-2 would be TM2.

If an array contains information corresponding to points halfway between the normally indexed points, then the convention is to shift the plus-direction elements to the node being indexed.

In the following example, the permeability at the i_lh point would be referenced as PRMIPIH(I - 1), and that for the Hl/2 point would be referenced as PRMIPIH(I). See sketch below.

i-I Ph H liz ---(0 I 0 ---I--~

1-1 PRMIPIH(I-l) I PRMIPIH(I)

B. Units. Each complete computer symbol represents a mathematical letter symbol and its associated subscripts. The mathematical letter symbol in turn designates a physical quantity. Neither the complete computer symbol nor the mathematical letter symbol implies any specific units of

263

measure. Authors are urged to familiarize themselves with the SI System of units and use them as much as practical. The choice of units (Trans. A/ME 263 (1977) 1685) and their designation is, however, left to the author.

C. Restriction to computer programs. Use of the computer symbols is restricted to the description of programming for computers. As a consequence, the computer symbols must not be used in works of portions of papers where programming is not discussed or as abbreviations in text or graphical material.

D. Character set. The computer symbols must be constructed from the 26 English letters and 10 Arabic numerical characters. Each complete computer symbol must begin with a letter and not a numeral.

The computer symbols are always represented by vertical type in printed text. English capital letters and Arabic numerals are used in hand or typewritten material.

E. Nonstandard symbols. The rules for establishing the computer symbols contained in this standard are such that quantities not covered can, in most instances, be given a notation that is compatible with it. Such additional computer symbols are, by definition, nonstandard.

Duplication of computer symbols for quantities that can occur simultaneously in an equation or computer program must be avoided. Elimination of a duplication may lead to a computer symbol that is at variance with the standard; i.e., a notation that is nonstandard.

When nonstandard computer symbols occur in a technical work, they should be clearly defined in the text or appendix, as is appropriate, and in the program.

F. Special notes. No computer symbols have been defined here for numerical quantities, functions, and arithmetic, relational, or logical operators. When employed in programs, their usage should be fully explained by comments in the program text. Some of these special cases are noted below:

1. No computer symbols to designate common or natural logarithms have been established. Rather, these functions should be designated by the notations compatible with the computer system being employed. The notation used should be defined in the paper.

2. The computer symbol for dimensionless numbers in general (unnamed dimensionless numbers) is NUMQ. Named dimen-


sionless numbers have the mnemonic title designation in the field representing the quantity and a Q in the last subscript position employed. Thus, Reynolds number is designated as REYQ. Similarly, Prandtl number could be designated as PRDQ, Grashof number as GRSQ, Graetz number as GRTQ. Any dimensionless number not contained in this standard should be defined in the paper.

3. No computer subscript notations corresponding to these mathematical letter subscripts are established. See section G.

4. No mathematical letter subscripts correspond to these computer subscripts. See section G.

G. Permissible format changes. In preparing the computer symbols it became necessary to modify the format of certain of the basic letter symbols, subscripts or symbol-subscript combinations. These changes are in accord with the General Principles of Computer Symbol Standardization. They do not imply that changes in the form of the economics, well logging and formation evaluation, reservoir engineering, or natural gas engineering letter symbols as contained elsewhere in this SPE Standard are authorized. Rather these changes are shown as a matter of record to prevent confusion and to present examples of permissible format changes in the computer symbols that may be followed when it becomes necessary to construct a computer notation not included in the list.

1. Basic symbolic subscripts of SPE Letter Symbols Standard represented by different

SPEletter Computer subscript symbol Subscript title

c CP capillary D 0 dimensionless quantity Dm OM dimensionless quantity

at condition m E EX experiment ext XT extrapolated F FU fuel lim LM limiting value m FU fuel (mass of) max MX maximum min MN minimum - PAV mean or average p

pressure pr PRO pseudo-reduced r RO reduced tD TQ dimensionless time

designation in Computer Symbols Subscript List. (Only changes in the basic subscripts are shown. Combination subscripts that contain these items are also changed accordingly.)

2. Quantities represented by single symbol in SPE Letter Symbols Standard but by symbol-subscript combination in Computer Symbols List.

SPEletter Computer Quantity symbol symbol title

G GASTI total inital gas in place in reservoir

L MOLL moles of liquid phase N NUMO dimensionless number

in general N 01 LTI initial oil in place

in reservoir u VELV volumetric velocity

(flow rate or flux, per unit area)

V M 0 LV moles of vapour phase W WTRTI initial water in place

in reservoir x MFRL mole fraction of

component in liquid phase

y MFRV mole fraction of component in vapour phase

z MFRM mole fraction of component in mixture

3. Quantities represented by symbol-subscript combination in SPE Letter Symbols Stan-dard but by a Computer Symbol Notation only.

SPEletter symbolsubscript combination

Computer symbol Quantity title

H C N thermal conductivity

4. Symbol-subscript combinations of SPE Letter Symbols Standard represented by Computer Symbol-Subscript Notation wherein subscript notations are not the same.


SPEletter symbol-subscript Computer Quantity combination symbol title

GL N G L TI initial condensate liquids in place in reservoir

GLp NGLP cumulative condensate liquids produced

NRe REya Reynolds number (dimensionless number)

Rsw GWRS gas solubility in water

5. Subscripts of SPE Letter Symbols Standard not assigned Computer Subscript Notations as a result of actions noted in 4.

SPEletter subscript

Re

sw

Subscript title

liquid produced, cumulative (usually with condensate, GLp )

Reynolds (used with Reynolds number only, NRe )

solution in water (usually with gas solubility in water, Rsw)

6. Letter operator-symbol combination of SPE Letter Symbols Standard represented by Computer Symbol Notation only.

SPEletter symbol

Computer symbol quantity Title

T A C interval transit time

Distinctions between, and descriptions of, abbreviations, computer symbols, dimensions,

letter symbols, reserve symbols,'unit abbreviations and units

Confusion often arises as to the proper distinctions between abbreviations, computer symbols, dimensions, letter symbols, reserve symbols, unit abbreviations and units used in science and engineering. The Society of Petroleum Engineers has adhered to the following descriptions:

A. Abbreviations - (for use in textual matter, tables, figures, and oral discussions) - an abbreviation is a letter or group of letters that may be used in

265

place of the full name of a quantity, unit, or other entity. Abbrevi{ltions are not acceptable in mathematical equations. SPE provides a list of preferred abbreviations in its 'Style Guide' for authors.

B. Computer Symbols - (for use in computer programs) - a computer symbol is a letter or group of letters and numerals used to represent a specific physical or mathematical quantity in the writing and execution of computer programs. One computer symbol may be employed to represent a group of quantities, properly defined. Computer symbols are not acceptable as substitutes for letter symbols in the required mathematical (equational) developments leading up to computer programs. At the present time, all SPE computer symbols employ capital letters and numerals.

C. Dimensions - dimensions identify the physical nature of or the general components making up a specific physical quantity; SPE employs the five basic dimensions of mass, length, time, temperature, and electrical charge (m, L, t, T, q). *

D. Letter symbols - (for use in mathematical equations) - a letter symbol is a single letter, modified when appropriate by one or more subscripts or superscripts, used to represent a specific physical or mathematical quantity in a mathematical equation. A single letter may be employed to represent a group of quantities, properly defined. The same letter symbol should be used consistently for the same generic quantity, or special values, being indicated by subscripts or superscripts.

E. Reserve symbols - a reserve symbol is a single letter, modified when appropriate by one or more subscripts or superscripts, which can be used as an alternate when two quantities (occurring in some specialized works) have the same standard letter symbol. These conflicts may result from use of standard SPE symbols or subscript designations that are the same for two different quantities, or use of SPE symbols that conflict with firmly established, commonly used notations and signs from the fields of mathematics, physics, and chemistry.

To avoid conflicting designations in these cases, use of reserve symbols, reserve subscripts, and reserve symbol-reserve subscript combinations is permitted, but only in cases of symbols conflict. Author preference for the reserve symbols and subscripts does not justify their use.

In making the choice as to which of two quantities should be given a reserve designation,

* Electrical charge is current times time, ISO uses: Mass (M), Length (L), Time (T), Temperature (8), Electric current (I), Amount of substance (N) and Luminous intensity (J).


an attempt should be made to retain the standard SPE symbol for the quantity appearing more frequently in the paper; otherwise, the standard SPE symbol should be retained for the more basic item (temperature, pressure, porosity, permeability, etc.).

Once a reserve designation for a quantity is employed, it must be used consistently throughout a paper. Use of an unsubscripted reserve symbol for a quantity requires use of the same reserve symbol designation when subscripting is required. Reversion to the standard SPE symbol or subscript is not permitted within a paper. For larger works, such as books, consistency within a chapter or section must be maintained.

The symbol nomenclature, which is a required part of each work, must contain each reserve notation that is used together with its definition.

F. Unit Abbreviations - a unit abbreviation is a letter or group of letters (for example, cm for centimeter), or in a few cases a special sign, that may be used in place of the name of a unit. The International Organization for Standardization

(ISO) and many other national and international bodies concerned with standardization emphasize the special character of these designations and rigidly prescribe the manner in which the unit abbreviations shall be developed and treated.

G. Units - units express the system of measurement used to quantify a specific physical quantity. In SPE usage, units have 'abbreviations' but do not have 'letter symbols'. Up to this time, SPE has not standardized a general system of units, nor units for individual quantities; it has signified willingness, however, to join in a future national effort to convert from the English to a metric system of units.

SPE's practices showing the above distinctions are illustrated in the table of example quantities. Authors can materially aid themselves, editors, and readers by keeping the distinctions in mind when preparing papers for SPE review. Manuscripts submitted to SPE are subject to review on these aspects before being accepted for publication.

Examples

Letter Abbrev. symbol for text, for tables, mathe-figures, matical

Quantity oral use equations

gas-oil ratio, producing GaR R gas-oil ratiO, initial Rsi

solution, initial solution GaR productivity index PI J productivity index, SPI Js

specific

* Examples only; SPE has not standardized units.

Contrasting symbol usage

SPE and certain American Standards Association, American National Standards Institute and International Organization for Standardization symbols lists do not use the same letter symbols to represent identical quantities. The variations in notations result from the application of the SPE guides in choosing symbols as detailed herein, the lack of agreement between various ASA standards, the ASA's policy of allowing several symbols to represent the same quantity in any list and the large number of quantities assigned symbols by the SPE. It is to be emphasized that the symbols contained in the SPE list are standard for use in petroleum engineering, but the symbols of other disciplines as sanctioned by the American Standards Association should be used when working outside the area of

Reserve symbol

used only in Computer case of symbol Unit symbols for Dimen- abbrev. conflict programs sions and units'

none GaR none cu ftlBBL none GORSI none cu ftlBBL

j POX L4Vm bid/psi js POXS L3 t1m b/d/psilft

petroleum production. These ASA symbol standards are published by the American Society of Mechanical Engineers, United Engineering Center, 345 East 47th Street, New York, NY 10017.

The Society Board of Directors has approved the SPE 1984 Symbols Standards, and recommends them to the membership and to the industry. All authors must include Nomenclatures in any manuscript submitted to SPE for publication.

Acknowledgement

The work done in sorting and combining the various standard lists by Schlumberger Well Services Engineering personnel in Houston, Texas and Schlumberger-Doll Research Center personnel in Ridgefield, Connecticut is gratefully acknowledged.

SPE NOMENCLATURE AND UNITS 267

A. Symbols alphabetized by physical quantity

Letter Reserve Computer Quantity Dimensions symbol SPE letter

letter symbol symbol

w z ARR Arrhenius reaction rate velocity constant L3/m k K PRM absolute permeability (fluid flow) L2 g GRV acceleration of gravity Llt2 Za MPDA acoustic impedance m/L2t v V,U VAC acoustic velocity Lit a ACT activity FaF FACAFU air/fuel ratio various ia INJA air injection rate L3/t a Fa AIR air requirement various aE FaE AIREX air requirement, unit, in laboratory experimental L3/m

run, volumes of air per unit mass of pack aR FaR AIRR air requirement, unit, in reservoir, volumes of

air per unit bulk volume of reservoir rock IJ-a 11a VISA air viscosity miLt mk AMAK amortization (annual write-off of unamortized M

investment at end of year k) A AMP amplitude various Ac AMPC amplitude, compressional wave various Ar AMPR amplitude, relative various As AMPS amplitude, shear wave various a [J,y ANG angle e [J,y ANG angle e ad ANGD angle of dip ec roYc ANGC angle, contact w angular frequency lit Kam Mam COEANI anisotropy coefficient IR INCK annual operating cash income, over year k M Gan fGan GMFAN annulus geometrical factor

(muliplier or fraction) tascript t at TACA apparent interval transit time tiL Ca Oa ECNA apparent conductivity tq2 /mL3

Pa Da DENA apparent density m/L3 rwa Rwa RADWA apparent or effective wellbore radius (includes L

effects of well damage or stimulation) <Pa fmea PORA apparent porosity Ra Pmra RESA apparent resistivity mL3tq2 Rz pz,rz RESZ apparent resistivity of the conductive fluids in mL3tq2

an invaded zone (due to fingering)

"'" APPR apbroximately e~ual to or is approximated y (usually wit functions)

L2 A S ARA area EA 11A,eA EFFA areal efficiency (used in describing results of

model studies only); area swept in a model divided by total model reservoir area (see Ep)

ASYM asymptotically equal to Pa P a PRSA atmospheric pressure m/Lt2 Z ANM atomic number A AWT atomic weight (atomic mass, relative) m a Me< COEA attenuation coefficient IlL q Q RTEAV average flow rate or production rate L3/t

AV average or mean (overbar) - p PRSAV m/Lt2 P average pressure PR

p PRSAVR average reservoir pressure m/Lt2

 f3d DAZ azimuth of dip /.t M RAZ azimuth of reference on sonde n NGW backpressure curve exponent, gas well C CGW backpressure curve (gas well), coefficient of L3-2nt4n/m2n

n NGW backpressure curve (gas well), exponent of loga base a, logarithm f3 y BRGR bearing, relative h d,e THK bed thickness, individual L Pwj P wj PRSWF bottom hole flowing pressure m/Lt2

Pbh P BH PRSBH bottomhole pressure m/Lt2

Pwj P wj PRSWF bottom hole pressure flowing m/Lt2

Piwj P iwj PRSIWF bottomhole flowing pressure, injection well miLe P iws P iws PRSIWS bottomhole static pressure, injection well m/Lt2

Pws P ws PRSWS bottomhole pressure at any time after shut-in m/Lt2

Pw P w PRSW bottomhole pressure, general m/Lt2

Pws P ws PRSWS bottomhole pressure, static miLt 2

Pww P ww PRSWW bottomhole (well) pressure in water phase m/Lt2

Tbh 8BH TEMBH bottomhole temperature T b w WTH breadth, width, or (primarily in fracturing) L

thickness Pe P e PRSE boundary pressure, external m/Lt2

Te Re RADE boundary radius, external L Bgb Fgb FVFGB bubble-point formation volume factor, gas Bob Fob FVFOB bubble-point formation volume factor, oil Ph Ps,Ps,Pb PRSB bubble-point (saturation) pressure m/Lt2 bgb !gb,Fgb RVFGB bubble-point reciprocal gas formation volume

factor at bubble-point conditions L3 V bp Vbp VOLBP bubble-point pressure, volume at

Rsb Fgsb GORSB bubble-point solution gas-oil ratio I::J.tws I::J.tws DEL TIMWS buildup time; shut-in time

(time after well is shut in) (pressure buildup, shut-in time)

Pb Db DENB bulk density m/L3 K Kb BKM bulk modulus miLe Vb Vb VOLB bulk volume L3 V bE Vbt VOLBEX bulk volume of pack burned in experimental L3

tube run !v !Vb, V bt FRCVB bulk (total) volume, fraction of V Rb VRb VOLRB burned reservoir rock, volume of L3 Vb Vb,Ub VELB burning-zone advance rate (velocity of) Lit

C ECQ capacitance q2e/mL2 Qv Zv CEXV capacity, cation exchange, per unit pore volume QVt ZVt CEXUT capacity, cation exchange,

per unit pore volume, total miLe Pe PoPe PRSCP capillary pressure

Ci INVI capital investment, initial M Ck INVK capital investment, subsequent, in year k M C C INVT capital investments, summation of all M Ppv CFLPV cash flow, discounted M P CFL cash flow, un discounted M h INCK cash income, annual operating, over year k M I INC cash income, operating M Ia INCA cash income, operating, after taxes M h INCB cash income, operating, before taxes M Pe! Pet PRSCF casing pressure, flowing m/Lt2

Pes Pes RSCS casing pressure, static m/Lt2 Qv Zv CEXV cation exchange capacity per unit pore volume QVt ZVt CEXUT cation exchange capacity per unit pore volume,

total m MXP cementation (porosity) exponent (in an empirical

relation between F Rand <j» Q q CHG charge (current times time) q Kani Mani COEANI coefficient, anisotropy ex M", COEA coefficient, attenuation IlL h hh,hT HTCC coefficient, convective heat transfer m/eT D /L,a DFN coefficient, diffusion L2/t Ke MoKee COEC coefficient, electrochemical mL2/t2q KR MRa,C COER coefficient, formation resistivity factor

(FR<j>m) K KSP coefficient in the equation of the electro- me/t2q

chemical component of the SP (spontaneous electromotive force)

L3-2nt4n/m2n C CGW coefficient of gas-well backpressure curve V VT, Ve HTCU coefficient heat transfer, over-all m/eT I IT, Ie HTCI coefficient, heat transfer, radiation m/eT J3 b HEC coefficient, thermal cubic expansion liT K M COE coefficient or multiplier various SL PVSL SATL combined total liquid saturation log common logarithm, base 10 npj Npj MOLPJ component j, cumulative moles produced nj Nj MOLl component j, moles of x MFRL component, mole fraction of, in liquid phase z MFRM component, mole fraction of, in mixture y MFRV component, mole fraction of, in vapour phase C ne NMBC components, number of Ee <Pe EMFC component of the SP, electrochemical mL2/t2q Ek <Pk EMFK component of the SP, electrokinetic mL2/eq c k,K CMP compressibility Lt2/m z Z ZED compressibility factor (gas deviation factor,

z=PVlnRD




zp Zp ZEDPAV compressibility factor or deviation factor for gas, at mean pressure

Lt2/m cf kfi Kf CMPF compressibility, formation or rock cg kg, Kg CMPG compressibility, gas Lt2/m Co ka> Ko CMPO compressibility, oil Lt2/m Cpr kpT> Kpr CMPPRD compressibility, pseudo-reduced C w kw. Kw CMPW compressibility, water Lt2/m Ac AMPC compressional wave amplitude various C c,n CNC concentration various Cel CCl CNCCI concentration, methane (concentration of various

other paraffin hydrocarbons would be indicated similarly, Cel> CC3, etc.)

C O2 CO2 CNC02 concentration, oxygen (concentration various of other elements or compounds would be

C m Cm,nm CNCFU indicated similarly, Ceo2, CN2 , etc.)

concentration, unit fuel various (see symbol m)

L3 GL gL NGLTI condensate liquids in place in reservoir, initial

GLp gLp NGLP condensate liquids produced, cumulative L3 C L CVnL CNTL condensate or natural gas liquids content various 0 Y SIG conductivity (other than logging) various C 0 ECN conductivity (electrical logging) tq2/mL3

C a Oa ECNA conductivity, apparent tq2/mL3 C fD CNDFQ conductivity, fracture, dimensionless kh A HCN conductivity, thermal (always with additional mLieT

phase or system subscripts) L 3/m w z ARR constant, Arrhenius reaction

rate velocity constant A C LAM constant, decay (I/ed) lit E DIC constant, dielectric q2elmL3

Y constant, Euler's = 0.5772 Dc DSCC constant-income discount factor h HPC constant, hyperbolic decline

[ al r q = qJ 1 + -j;

R RRR constant, universal gas (per mole) mL2/t2T C WDC constant, water-drive L 4elm C L WDCL constant, water-drive, linear aquifer L 4t2/m m FF FCM consumption, fuel various mE FFE FCMEX consumption of fuel in experimental tube run mlL3 m tg FFEg FCMEXG consumption of fuel in experimental tube run m

(mass of fuel per mole of produced gas) m/L3 mR FFR FCMR consumption of fuel in reservoir

e c r,Yc ANGC contact angle C L CL, nL CNTL content, condensate or natural gas liquids various C wg cwg,nwg CNTWG content, wet-gas various h hh,hT HTCC convective heat transfer coefficient m/eT




gc GRVC conversion factor in Newton's second law of Motion

B C COR correction term or correction factor (either additive or multiplicative)

N n,C NMB count rate (general) lit NN NmCN NEUN count rate, neutron lit NCR Ny,Cc NGR count rate, gamma ray lit Sgc PgoSgc SATGC critical gas saturation Pc Pc PRSC critical pressure m/Lt2

Tc 8c TEMC critical temperature T Swc Pwoswc SATWC critical water saturation A S ARA Cross-section (area) L2

I S XSTMAC cross-section, macroscopic IlL a XSTMIC cross-section, microscopic IlL a S XNL cross-section of a nucleus, microscopic L2 j3 b HEC cubic expansion coefficient, thermal lIT GLp gLp NGLP cumulative condensate liquids produced C GFp gFp GASFP cumulative free gas produced L3 Ge ge GASE cumulative gas influx (encroachment) L3 Gi gi GASI cumulative gas injected C Rp Fgp,Fgop GORP cumulative gas-oil ratio Gp gp GASP cumulative gas produced L3

npj Npj MOLPJ cumulative moles of component j produced Ne ne OILE cumulative oil influx (encroachment) L3

Np np OILP cumulative oil produced L3

Qp FLUP cumulative produced fluids (where Np and Wp are not applicable)

C We We WTRE cumulative water influx (encroachment) Wi Wi WTRI cumulative water injected L3

Fwop FACWOP cumulative water-oil ratio mLlt2

Wp wp WTRP cumulative water produced L3

Gwgp gwgp GASWGP cumulative wet gas produced L3

'\Ix curl I i script i,i CUR current, electric q/t rs Rs RADS damage or stimulation radius of well (skin) L Fs Fd DMRS damage ratio or condition ratio (conditions

relative to formation conditions unaffected by well operations)

Z D,h ZEL datum, elevation referred to L A C LAM decay constant (lhd) lit 'td td TIMD decay time (mean life) (111..) t tdN TIMDN decay time, neutron (neutron mean life) t h HPC decline constant, hyperbolic [from equation

[ a·t r q = q;ll + -j;

d DECE decline factor, effective a DEC decline factor, nominal 8 DCR decrement various F DGF degrees of freedom




\l DEL del (gradient operator) td 'td TIMDY delay time t D DLV deliverability (gas well) L3/t

P D DEN density mlL3

Pa Da DENA density, apparent m/L3

Pb Db DENB density, bulk mlL3

Pf Df DENF density, fluid m/L3

Pxo Dxo DENXO density, flushed zone mlL3

n N NMB density (indicating 'number per unit volume') lIL3

PF DF DENFU density, fuel mlL3

Pg Dg DENG density, gas mlL3

Pma Dma DENMA density, matrix (solids, grain) mlL3

nN NMBN density (number) of neutrons I/L3

PL Ih DENAVL density of produced liquid, weight -weighted avg. m/L3

PsE DsE DENSEX density of solid particles making up m/L3 experimental pack

m/L3 Po Do DENO density, oil y s, Fs SPG density, relative (specific gravity) Pt Dt DENT density, true m/L3

Pw Dw DENW density, water mlL3

DE EDE depletion NR NF FUDR deposition rate of fuel m/L3t Dp EDP depreciation D y,H DPH depth L a rs SKD depth, skin (logging) L Z Z ZED deviation factor (compressibility factor)

for gas (z = p VlnR1) zp Zp ZEDPAV deviation factor (compressibility factor)

for gas, at mean pressure a ANGH deviation, hole (drift angle) Pd Pd PRSD dew-point pressure m/Lt2

d D DIA diameter L dh dH,Dh DIAH diameter, hole L di dbDi DIAl diameter, invaded zone (electrically equivalent) L ap Dp DIAAVP diameter, mean particle L (0 DIC dielectric constant q2t2/mL3 A DEL difference or difference operator,

D /-L,a DFN finite (ax = X2-XI or X-X2)

diffusion coefficient L2/t 'YJ DFS diffusivity, hydraulic (klcpc/-L or A/cpc) L2/t QLtD QLtD script I ENCLTQQ dimensionless fluid influx function, linear aquifer QtD ENCTQQ dimensionless fluid influx function

at dimensionless time tD CfD CNDFQ dimensionless fracture conductivity qgD QgD RTEGQ dimensionless gas production rate N NUMQ dimensionless number, in general

(always with identifying subscripts) (Example: Reynolds number, NRe)

qoD QoD RTEOQ dimensionless oil production rate

VpD VpD VOLPQ dimensionless pore volume PD PD PRSQ dimensionless pressure PtD PtD PRSTQQ dimensionless pressure function

at dimensionless time tD qD QD RTEQ dimensionless production rate XD dimensionless quantity proportional to x rD RD RADQ dimensionless radius tD LD TIMQ dimensionless time tDm tDm TIMMQ dimensionless time at condition m qwD QwD RTEWQ dimensionless water production rate e ad ANGD dip, angle of e a ada ANGDA dip, apparent angle of a f3da DAZA dip, apparent azimuth of f3d DAZ dip, azimuth of Dc DSCC discount factor, constant-income D DSC discount factor, general Dsp DSCSP discount factor, sin~le-payment

[1/(1 + i)k; or e-] ,j = In (1 + i)] Dspc DSCSPC discount factor, single-payment

(constant annual rate) [e-jk ( ei - 1 )/j]

i RTED discount rate Ppv CFLPV discounted cash flow K d DSP dispersion coefficient L2/t

~ DSM dispersion modulus (dispersion factor) s L DIS displacement L EDb l'JDb,eDb EFFDB displacement efficiency from burned portion

of in situ combustion pattern EDu l'JDweDu EFFDU displacement efficiency from unburned portion

of in situ combustion pattern ED l'JD,eD EFFD displacement efficiency: volume of hydrocarbons

(oil or gas) displaced from individual pores or small groups of pores divided by the volume of hydrocarbons in the same pores just prior to displacement

8 Fd DPR displacement ratio 80b Fdob DPROB displacement ratio, oil from burned volume,

volume per unit volume of burned reservoir rock 80u Fdou DPROU displacement ratio, oil from unburned volume,

volume per unit volume of unburned reservoir rock

8wb Fdwb DPRWB displacement ratio, water from burned volume, volume per unit volume of burned reservoir rock

d L d,L2 DUW distance between adjacent rows of injection and L production wells

a LmLJ DLW distance between like wells (injection or L production) in a row

L s,! script I LTH distance, length, or length of path L !l.r !l.R DELRAD distance, radial (increment along radius) L

V divergence rd Rd RADD drainage radius L atwl a'twl DEL TIMWF drawdown time (time after well is opened to t

production) (pressure drawdown) a ANGH drift angle, hole (deviation) ir RORI earning power or rate of return (internal,

true, or discounted cash flow) s S,O SKN effect, skin d DECE effective decline factor rwa Rwa RADWA effective or apparent well bore radius (includes L

effects of well damage or stimulation) L2 kg Kg PRMG effective permeability to gas

ko Ko PRMO effective permeability to oil L2 kw Kw PRMW effective permeability to water L2 <Pe fe,Ee PORE effective porosity E 'Y),e EFF efficiency EA 'Y)A,eA EFFA efficiency, areal (used in describing results of model

studies only): area swept in a model divided by total model reservoir area (see Ep)

E Db 'Y)Db,eDb EFFDB efficiency, displacement, from burned portion of in situ combustion pattern

E Du 'Y)DweDu EFFDU efficiency, displacement, from unburned portion of in situ combustion pattern

ED 'Y)D,eD EFFD efficiency, displacement: volume of hydrocarbons (oil or gas) displaced from individual pores or small groups of pores divided by the volume of hydrocarbon in the same pores just prior to displacement

E[ 'Y)b e[ EFFI efficiency, invasion (vertical): hydrocarbon pore space invaded (affected, contacted) by the injection fluid or heat front divided by the hydrocarbon pore space enclosed in all layers behind the injected-fluid or heat front

ER 'Y)R,eR EFFR efficiency, over-all reservoir recovery: volume of hydrocarbons recovered divided by volume of hydrocarbons in place at start of project (ER = Ep E[ED = Ev ED)

Ep 'Y)p,ep EFFP efficiency, pattern sweep (developed from areal efficiency by proper weighting for variations in net pay thickness, porosity and hydrocarbon saturation): hydrocarbon pore space enclosed behind the injected-fluid or heat front divided by total hydrocarbon pore space of the reservoir or project

EVb 'Y)Vb,eVb EFFVB efficiency, volumetric, for burned portion only, in situ combustion pattern

Ev 'Y)v,ev EFFV efficiency, volumetric: product of pattern sweep and invasion efficiencies

E y ELMY elasticity, modulus of (Young's modulus) m/Lt2

I i script i,i CUR electric current q/t Ze ZE,'Y] MPDE electric impedance mL2/t~2 p R RHO electrical resistivity (other than logging) mL3tq R p,r RES electrical resistivity (electrical logging) mL3tq2

'te TORE electrical tortuosity di dbDi DIAl electrically equivalent diameter of the invaded L

zone Kc MoKec COEC electrochemical coefficient mL2/t2q Ec <Pc EMFC electrochemical component of the SP mL2/t2q Ek <Pk EMFK electrokinetic component of the SP me/t2q E V EMF electromotive force mL2/t2q Z D,h ZEL elevation referred to datum L Ge ge GASE encroachment or influx, gas, cumulative L3 !::.Ge !::.ge DELGASE encroachment or influx, gas during an interval L3 Ne ne OILE encroachment or influx, oil, cumulative L3 !::.Ne !::.ne DELOILE encroachment or influx, oil, during an interval L3 e ENC encroachment or influx rate L3/t eg ig ENCG encroachment or influx rate, gas L3/t eo io ENCO encroachment or influx rate, oil L3/t ew iw ENCW encroachment or influx rate, water L3/t We We WTRE encroachment or influx, water, cumulative C !::.We !::.we DELWTRE encroachment or influx, water, during an interval L3 E U ENG energy mL2/t2 H I HEN enthalpy (always with phase or system subscripts) me/t2 Hs Is HENS enthalpy (net) of steam or enthalpy above mL2/t2

reservoir temperature L2/t2 h HENS enthalpy, specific

s a HERS· entropy, specific L2/t2T S at HER entropy, total mL2/t2T ~ GE equal to or larger than !:S LE equal to or smaller than K k,Feq EQR equilibrium ratio (ylx) di dbDi DIAl equivalent diameter (electrical) of the L

invaded zone tp 'tp TIMP equivalent time well was on production prior t

to shut-in (pseudo-time) Rwe RWE equivalent water resistivity mL3tq2

erf ERF error function erfc ERFC error function, complementary En Euler number y Euler's constant = 0.5772 fJ b HEC expansion coefficient, thermal cubic IIT CPE fE,tE POREX experimental pack porosity n NGW exponent of back-pressure curve, gas well m MXP exponent, porosity (cementation) (in an

empirical relation between F Rand cP ) n SXP exponent, saturation eZ expz EXP exponential function




-Ei (-x) exponential integral 00

I ~ dt, x positive x t

Ei (x) exponential integral, modified

'"" [r.!...- dl + ~ dl Jx positive E~ 0 _00 t E t

Pe Pe PRSE external boundary pressure mlLt2

'e Re RADE external boundary radius L Pext Pext PRSXT extrapolated pressure miLe z Z ZED factor, compressibility

(gas deviation factor z = PVlnRT) D DSC factor, discount d DECE factor, effective decline a DEC factor, nominal decline ge GRVC factor, conversion, in Newton's second law of

Motion FR FACHR factor, formation resistivity, equals RolRw

(a numerical subscript to f indicates the value of Rw)

f FACF factor, friction G fa GMF factor, geometrical (multiplier)

( electrical logging) Gan fGan GMFAN factor, geometrical (multiplier)

annulus (electrical logging) Gi fGi GMFI factor, geometrical (multiplier)

invaded zone (electrical logging) Gp fGp GMFP factor, geometrical (multiplier)

pseudo (electrical logging) Gxo fGxo GMFXO factor, geometrical (multiplier)

flushed zone (electrical logging) Gm fGm GMFM factor, geometrical (multiplier)

mud (electrical logging) Gt fat GMFT factor, geometrical (multiplier)

true (non-invaded zone) (electrical logging) F FAC factor in general, including ratios various

(always with identifying subscripts) F8 FACB factor, turbulence w m MRT flow rate, mass mit Q q,fl> HRT flow rate, heat mL2/t3 u 'tp VELV flow rate or flux, per unit area Lit

(volumetric velocity) L3/t q Q RTE flow rate or production rate

qp Q- RTEPAV flow rate or production rate at mean pressure L3/t -p L3/t q Q RTEAV flow rate or production rate, average

Piw! Piw! PRSIWF flowing bottom-hole pressure, injection well miLe Pw! pw! PRSWF flowing pressure, bottom-hole m/Lt2

Pc! Pc! PRSCF flowing pressure, casing m/Lt2

Ptf pt! PRSTF flowing pressure, tubing miLe

ll.twf ll.'twf DELTIMWFflowing time after well is opened t to production (pressure drawdown)

F f FLU fluid (generalized) various vf Vf,uf VACF fluid interval velocity Lit Z D,h ZEL fluid head or height or elevation referred L

to a datum tfscript t ll.tf TACF fluid interval transit time tiL Pf Df DENF fluid density m/L3 QtD ENCTQQ fluid influx function, dimensionless, at

dimensionless time tD QLtD QltD script I ENCLTQQ fluid influx function, linear aquifer, dimensionless Qp QltD script I FLUP fluids, cumulative produced (where Np and

Wp are not applicable) mlL3 Pxo Dxo DENXO flushed-zone density

Rxo Pxmrxo RESXO flushed-zone resistivity (that part of the mL3tq2

invaded zone closest to the wall of the hole, where flushing has been maximum)

Gw fGxo GMFXO flushed-zone geometrical factor (fraction or multiplier)

u 'tV FLX flux various u 'tV VELV flux or flow rate, per unit area Lit

F Q FCE (volumetric velocity)

force, mechanical mLlt2

E V EMF force, electromotive (voltage) mL2/t2q CPR fER PORR formation or reservoir porosity cf kf,Kf CMPF formation or rock compressibility Lt2/m FR FACHR formation resistivity factor - equals

RoIRw (a numerical subscript to Findicates the value Rw)

KR MR,a,C COER formation resistivity factor coefficient (FRm)

Rt Pt,rt REST formation resistivity, true mL3tq2

Ro po,ro RESZR formation resistivity when 100% saturated mL3tq2

with water of resistivity Rw Tf 8f TEMF formation temperature T Bgb Fgb FVFGB formation volume factor at bubble-point

conditions, gas Bob Fob FVFOB formation volume factor at bubble-point

conditions, oil Bg Fg FVFG formation volume factor, gas Bo Fo FVFO formation volume factor, oil Bt Ft FVFT formation volume factor, total (two-phase) B F FVF formation volume factor

volume at reservoir conditions divided by volume at standard conditions

Bw Fw FVFW formation volume factor, water f F FRC fraction (such as the fraction of a flow stream

consisting of a particular phase) fg Fg FRCG fraction gas

h F L,ft script I FRCL fraction liquid Iv Ivb, Vbf FRCVB fraction of bulk (total) volume Iq,sh <Pigfsh FIGSH fraction of intergranular space ('porosity')

occupied by all shales Iq,w <Pigfw FIGW fraction of intergranular space ('porosity')

occupied by water Iq,shd <Pimfshd FIMSHD fraction of intermatrix space ('porosity')

occupied by nonstructural dispersed shale CfD CNDFQ fracture conductivity, dimensionless Lf xf LTHFH fracture half-length (specify 'in the L

direction of' when using xf) If if,/p,ip FRX fracture index G F GFE free energy (Gibbs function) mL2/t2

IFf iFf FFX free fluid index RF Fgp,Fgop GORF free gas-oil ratio, producing (free-gas

volume/oil volume) L3 Gpp gFp GASFP free gas produced, cumulative

GFi gFi GASFI free-gas volume, initial reservoir (=mNBoi) L3 Rp Fgf,Fgop GORF free producing gas-oil ratio (free-gas volumel

oil volume) I v FQN frequency lit I FACF friction factor Pf Pf PRSF front or interface pressure m/Lt2

Cm cm,nm CNCFU fuel concentration, unit (see symbol m) various m Fp FCM fuel consumption various mE FFE FCMEX fuel consumption in experimental tube run m/L3

mEg FFEg FCMEXG fuel consumption in experimental tube run (mass m of fuel per mole of produced gas)

m/L3 mR FpR FCMR fuel consumption in reservoir Pp DF DENFU fuel density m/L3

NR N p FUDR fuel deposition rate m/L3t

I FUG fugacity miLe NGR Ny,CG NGR gamma ray count rate lit y GRY gamma ray [usually with identifying subscript( s)] various G g GAS gas (any gas, including air) always with various

identifying subscripts Sog Pog,Sog SATOG gas-cap interstitial-oil saturation Swg Pwg,Swg SATWG gas-cap interstitial-water saturation cg kg, Kg CMPG gas compressibility Lt2/m z Z ZED gas compressibility factor

(deviation factor) (z = PVlnRT)

R RRR gas constant, universal (per mole) mL2/t2T pg Dg DENG gas density m/L3 zp Zp ZEDPAV gas deviation factor (compressibility factor)

at mean pressure z Z ZED gas deviation factor (compressibility factor,

z = PVlnRT) (deviation factor) L2 kg Kg PRMG gas, effective permeability to

Bg Fg FVFG gas formation volume factor




Bgb Fgb FVFGB gas formation volume factor at bubble-point conditions

fg Fg FRCG gas fraction G g GASTI gas in place in reservoir, total initial L3 G e ge GASE gas influx (encroachment), cumulative L3 flGe flge DELGASE gas influx (encroachment) during an interval L3 eg ig ENCG gas influx (encroachment) rate L3/t G i gi GASI gas injected, cumulative L3 flGi flg; DELGASI gas injected during an interval L3 ig INJG gas injection rate L3/t CL cL,nL CNTL gas liquids, natural, or condensate content various Ag MOBG gas mobility Ct/m fg Fg FRCG gas, fraction

fg Fg MFRTV gas mole fraction [ __ V_] L+V

kglko KglKo PRMGO gas-oil permeability ratio

Rp Fgp, Fgop GORP gas-oil ratio, cumulative RF FgFlFgoF GORF gas-oil ratio, free producing (free-gas volume/

oil volume) R Fg,Fgo GOR gas-oil ratio, producing Rsb Fgsb GORSB gas-oil ratio, solution at bubble-point conditions Rs Fgs, Fgos GORS gas-oil ratio, solution (gas solubility in oil) Rs; Fgsi GORSI gas-oil ratio, solution, initial G p gp GASP gas produced, cumulative L3 flGp flgp DELGASP gas produced during an interval L3 G pE gpE GASPEX gas produced from experimental tube run C qg Qg RTEG gas production rate L3/t qgD QgD RTEGQ gas production rate, dimensionless bg fg,Fg RVFG gas reciprocal formation volume factor bgb fgb,Fgb RVFGB gas reciprocal formation volume factor at

bubble-point conditions L3 G pa gpa GASPUL gas recovery, ultimate

krg Krg PRMRG gas, relative permeability to Sg pg,Sg SATG gas saturation Sgc PgoSgc SATGC gas saturation, critical Sgr PgnSgr SATGR gas saturation, residual Rs Fgs, Fgos GORS gas solubility in oil (solution gas-oil ratio) Rsw GWRS gas solubility in water Yg sg,Fgs SPGG gas specific gravity /-tg 'YJg VISG gas viscosity miLt /-tga 'YJga VISGA gas viscosity at 1 atm miLt C CGW gas-well back-pressure curve, coefficient of L3--2nt4n/m2n

n NGW gas-well back-pressure curve, exponent of D DLV gas-well deliverability L3/t G wgp gwgp GASWGP gas, wet, produced, cumulative L3 h d,e THK general and individual bed thickness L N NUMQ general dimensionless number (always with

identifying subscripts)

G fa GMF geometrical factor (multiplier) ( electrical logging)

Gan fGan GMFAN geometrical factor (multiplier), annulus (electrical logging)

Gxo fGxo GMFXO geometrical factor (multiplier), flushed zone (electrical logging)

Gi fai GMFI geometrical factor (multiplier), invaded zoned (electrical logging)

Gm fGm GMFM geometrical factor (multiplier), mud (electrical logging)

Gt fat GMFf geometrical factor, (multiplier), true (non-invaded zone) (electrical logging)

Gp fap GMFP geometrical factor (multiplier), pseudo ( electrical logging)

Gt fGt GMFf geometrical factor (multiplier), true ( electrical logging)

g Y GRD gradient various gG gg GRDGT gradient, geothermal T \1 gradient operator gT gh GRDT gradient, temperature T Pma Dma DENMA grain (matrix, solids) density m/L3

g GRV gravity, acceleration of Llt2

Y s,Fs SPG gravity, specific, relative density Yg sg,Fgs SPGG gravity, specific, gas Yo smFos SPGO gravity, specific, oil Yw sw,Fws SPGW gravity, specific, water ht dt,et THKT gross (total) pay thickness L Vu Ru GRRU gross revenue ('value') per unit produced M/e V R, Vt,Rt GRRT gross revenue ('value'), total M t1l2 TIMH half life t Q q,cfJ HRT heat flow rate mL2/e Lv Av HLTV heat of vaporization, latent L2/t2 a a, 'YJh HTD heat or thermal diffusivity L2/t C c HSP heat, specific (always with phase or system L2/t2T

subscripts) m/t3T h hh,hT HTCC heat transfer coefficient, convective

U UT,Ua HTCU heat transfer coefficient, over-all mleT I In/a HTCI heat transfer coefficient, radiation mleT Z D,h ZEL height, or fluid head or elevation L

referred to a datum h d,e ZHT height (other than elevation) L A SH HWF Helmholtz function (work function) mL2/t2 y f HOL hold-up (fraction of the pipe volume filled by

a given fluid: Yo is oil hold-up, Yw is water hold-up ~of all hold-ups at a given level is one)

8 ANGH hole deviation, drift angle dh dH,Dh DIAH hole diameter L 'YJ DFS hydraulic diffusivity (kl<j>c {t or A<j>C) L2/t

rH RH RADHL hydraulic radius L TH TORHL hydraulic tortuosity <Ph fh,Eh PORH hydrocarbon-filled porosity, fraction

or percent of rock bulk volume occupied by hydrocarbons

IR iR RSXH hydrocarbon resistivity index R/Ro Shr Ph"Shr SATHR hydrocarbon saturation, residual IH iH HYX hydrogen index h HPC hyperbolic decline constant (from equation)

[ a·t r q = q) 1 + -j; g (z) script I imaginary part of complex number z Z MPD impedance various Za MPDA impedance, acoustic m/L2t Ze ZE,lj MPDE impedance, electric mL2/tq2 I I --X index (use subscripts as needed) If if,/F,iF FRX index, fracture IFf iFf FFX index, free fluid IH iH HYX index, hydrogen I IJX index, injectivity L4t/m n JL RFX index of refraction Icp icp PRX index, porosity ICPI iCPI PRXPR index, primary porosity I j PDX index, productivity L4t/m IR iR RXSH index, (hydrocarbon) resistivity

R/Ro Icp2 iCP2 PRXSE index, secondary porosity IshGR ishGR SHXGR index, shaliness gamma-ray

(Ylog - Yen)/(Ysh - Yen) Ct/m Is is IJXS index, specific injectivity

Is js PDXS index, specific productivity L3t/m h d,e THK individual bed thickness L Ge ge GASE influx (encroachment), cumulative, gas L3

Ne ne OILE influx (encroachment), cumulative, oil L3 We We WTRE influx (encroachment), cumulative, water L3 AGe Age DELGASE influx (encroachment) during an interval, gas L3 ANe Ane DELOILE influx (encroachment) during an interval, oil L3 AWe AWe DELWTRE influx (encroachment) during an interval, water L3

QLtD Q'tD script I ENCLTQQ influx function, fluid, linear aquifer, dimensionless

QtD Q'tD script I ENCTQQ influx function, fluid, dimensionless (at dimensionless time tD)

L3/t e ENC influx (encroachment) rate eg ig ENCG influx (encroachment) rate, gas L3/t eo io ENCO influx (encroachment) rate, oil L3/t ew iw ENCW influx (encroachment) rate, water L3/t GL gL NGLTI initial condensate liquids in place in reservoir L3 Ci INVI initial capital investment M

N n OILTI initial oil in place in reservoir L3

Pi Pi PRSI initial pressure m/Lt2

GFi gFi GASFI initial reservoir free-gas volume L3 (=mNBoJ (=GBgJ

Llt2 Rsi Fgsi GORSI initial solution gas-oil ratio W W WTRTI initial water in place in reservoir L3

Swi Pwi,swi SATWI initial water saturation Gi gi GASI injected gas, cumulative L3 AGi Agi DELGASI injected gas during an interval L3

Wi Wi WTRI injected water, cumulative L3 AWi AWi DELWTRI injected water during an interval L3

INJ injection rate L3/t ia INJA injection rate, air L3/t ig INJG injection rate, gas L3/t iw INJW injection rate, water L3/t Piwj Piwj PRSIWF injection well bottom-hole pressure, flowing m/Lt2

Piws Piws PRSIWS injection well bottom-hole pressure, static m/Lt2

I i IJX injectivity index L4t/m Is is IJXS injectivity index, specific L3t/m GL gL NGLTI in-place condensate liquids in reservoir, initial L3 G g GASTI in-place gas in reservoir, total initial L3 N n OILTI in-place oil in reservoir, initial L3 W W WTRTI in-place water in reservoir, initial L3

Fwo FACWO instantaneous producing water-oil ratio b y ICP intercept various

IRCE interest rate, effective compound (usually annual) iM IRPE interest rate, effective, per period j r IRA interest rate, nominal annual Pj Pj PRSF interface or front pressure M/Lt2 0 Y,Y SFT interfacial, surface tension m/t2

<Pig hg'Cig PORIG intergranular 'porosity' (space) (Vb- Vgr)/Vb

-Ei(-x) integral, exponential 00

J ~ dt, x positive x t

Ei (x) integral, exponential, modified

[~ · 1 lim t t

c~ 0 J ~ dt + ~ dt ,x positive _00 t E t

/q,sh <Pigfsh FIGSH intergranular space (porosity), fraction occupied by all shales

/q,w <Pigfw FIGW intergranular space (porosity), fraction occupied by water

/q,shd <Pimjshd FIMSHD intermatrix space (porosity), fraction occupied by non-structural dispersed shale

<Pim !im,Eim PO RIM intermatrix 'porosity' (space) (Vb - V ma)IVb

mele U Ei INE internal energy Sog POWSog SATOG interstitial-oil saturation in gas cap




Swg Pwg,Swg SATWG interstitial-water saturation in gas cap Swo Swb SATWO interstitial-water saturation in oil band tscript t at TAC interval transit time tIL tascript t ata TACA interval transit time, apparent tIL M maD SAD interval transit time-density slope (absolute tL2/m

value) tfscript t atf TACF interval transit time, fluid tIL tmascript t atma TACMA interval transit time, matrix tIL tsh script t atsh TACSH interval transit time, shale tIL di dbDi DIAl invaded zone diameter, electrically equivalent L Gi lGi GMFI invaded zone geometrical factor (multiplier)

( electrical logging) mL3tq2 Ri Pbri RESI invaded zone resistivity

E[ l'Jb e[ EFFI invasion (vertical) efficiency: hydrocarbon pore space invaded (affected, contacted) by the injected-fluid or heat front divided by the hydrocarbon pore space enclosed in all layers behind the injected-fluid or heat front

Siw Piw,Siw SATIW irreducible water saturation v N VSK kinematic viscosity L2/t Ek ENGK kinetic energy mL2/t2 :z (y) script L Laplace transform of y

00 J y (t) e-stdt 0

s Laplace transform variable \l Laplacian operator > GT larger than Lv A.v HLTV latent heat of vaporization L2/t2 L s,fscript I LTH length, path length, or distance L T t TIMAV lifetime, average (mean life) t lim LM limit CL WDCL linear aquifer water-drive constant L4t2/m h h,f script I FRCL liquid fraction h F Ltf script I MFRTL liquid mole fraction L/(L + V) x MFRL liquid phase, mole fraction of component in L nL MOLL liquid phase, moles of SL PL,SL SATL liquid saturation, combined total GL gL NGLTI liquids, condensate, in place in reservoir, initial GLp gLp NGLP liquids, condensate, produced cumulative L3

loga logarithm, base a log logarithm, common, base to Ln logarithm, natural, base e I S XSTMAC macroscopic cross section tiL a s XNL macroscopic cross section of a nucleus L2

JL m PRMM magnetic permeability mLlq2 k I( SUSM magnetic susceptibility mLlq2 M I MAG magnetization mlqt Mf MAGF magnetization, fraction




m MAS mass m w m MRT mass flow rate mit tmascript !l.tma TACMA matrix interval transit time tiL Pma Dma DENMA matrix (solids, grain) density rnIL3 Vma Vma VOLMA matrix (framework) volume (volume L3

of all formation solids except dispersed clay or shale)

1:' t TIMAV mean life (average lifetime) t 1:' t TIMD mean life (decay time) (Ill') t - P PRSAV rnILt2 p mean or average pressure

AV mean or average (overbar) IL MEN mean value of a random variable a Dp DIAAVP mean particle diameter L -x MENES mean value of a random variable, x, estimated F Q FCE mechanical force mLlt2

CCI cej CNCCI methane concentration (concentration of various

other paraffin hydrocarbons would be indicated similarly Cc , Cc , etc.)

XSTMIC • • • 2 3 e a mIcroscoPIc cross sectIOn

z MFRM mixture, mole fraction of component A MOB mobility (kilL) L3t/m Ag MOBG mobility, gas L3t/m Ao MOBO mobility, oil L3t/m M FA MBR mobility ratio, general (Adisplacin/AdisPlaced) Ms MDd,Msu MBRSAV mobility ratio, diffuse-front approximation

[(AD + Ad)SWJ/(AdLnswept]; D signifies displacing; signifies displaced; mobilities are evaluated at average saturation conditions behind and ahead of front

M FA MBR mobility ratio, sharp-front approximation (AD/Ad)

Mt FAt MBRT mobility ratio, total, [(At)swep/(At)unswept]; 'swept' and 'un swept' refer to invaded and uninvaded regions behind and ahead of leading edge of displacement front

L3t/m At A MOBT mobility, total, of all fluids in a particular region of the reservoir, e.g., (Ao + Ag + Aw)

et/m Aw MOBW mobility, water K Kb BKM modulus, bulk rnILt2

'IjJ DSM modulus, dispersion, (dispersion factor) G Es ELMS modulus, shear m/Lt2

E y ELMY modulus of elasticity (Young's modulus) m/Lt2

VM Vm VOLM molal volume (volume per mole) e ~ Fg MFRTV mole fraction gas V/(L + V)

F L,J; script I MFRTL mole fraction liquid LI(L + V) x MFRL mole fraction of a component in liquid phase z MFRM mole fraction of a component in mixture


Letter feserve Computer Quantity Dimensions symbol 'PE letter


y MFRV mole fraction of a component in vapor phase R N MRF molecular refraction L3 M MWT molecular weight (mass, relative) m ML MWTAVL molecular weight of produced liquids, m

mole-weighted average n N NMBM moles, number of nj Nj MOLJ moles of component j npj Npj MOLPJ moles of component j produced, cumulative L nL MOLL moles of liquid phase V nv MOLV moles of vapor phase nt Nt NMBMT moles, number of, total ML MWTAVL mole-weighted average molecular weight m

of produced liquids mL3tq2 Rmc Pmormc RESMC mud-cake resistivity

hmc dmoemc THKMC mud-cake thickness L Rmf Pmf,rmf RESMF mud-filtrate resistivity mL3tq2

Gm fGm GMFM mud geometrical factor (multiplier) ( electrical logging)

mL3tq2 Rm pm,rm RESM mud resistivity G fo GMF multiplier (factor), geometrical

( electrical logging) Gan fGan GMFAN multiplier (factor), geometrical,

annulus (electrical logging) Gxo fGxo GMFXO multiplier (factor), geometrical,

flushed zone (electrical logging) G i foi GMFI multiplier (factor), geometrical,

invaded zone (electrical logging) Gm fGm GMFM multiplier (factor), geometrical,

mud (electrical logging) Gp fGp GMFP multiplier (factor), geometrical,

pseudo (electrical logging) Gt fot GMFT multiplier (factor, geometrical,

true (electrical logging) K M COE multiplier or coefficient various CL cL,nL CNTL natural gas liquids or condensate content various In natural logarithm, base e hn dmen THKN net pay thickness L NN NmCN NEUN neutron count rate lit nN NMBN neutrons, density (number) of tN tN,tn NFL neutron lifetime lit N mcj>ND SND neutron porosity-density slope (absolute value) elm N NEU neutron [usually with identifying subscript(s)] various gc GRVC Newton's Second Law of Motion, conversion

factor in a DEC nominal decline factor (J s XNL nucleus cross section, microscopic L2 Z ANM number, atomic N NUMQ number, dimensionless, in general (always

with identifying subscripts)



Letter symbol symbol

n N NMB number (of variables, or components, or steps, or increments, etc.)

n N NMB number (quantity) M m NMBCP number of compounding periods (usually per year) Cn C NMBC number of components nt Nt NMBM number of moles, total N Re REYQ number, Reynolds (dimensionless number) N n OIL oil (always with identifying subscripts) various Swo Swb SATWO oil band interstitial-water saturation Co kmKO CMPO oil compressibility Lf/m

Po Do DENO oil density m/L3 80b Fdob DPROB oil displaced from burned volume, volume per

unit volume of burned reservoir rock 80u Fdou DPROU oil displaced from unburned volume, volume per

unit volume of unburned reservoir rock ko Ko PRMO oil, effective permeability to L2 Bo Fa FVFO oil formation volume factor Bob Fob FVFOB oil formation volume factor at bubble point

conditions Rs Fgs, Fgos GORS oil, gas solubility in

(solution gas-oil ratio) L3 N n OILTI oil in place in reservoir, initial

Ne OILE oil influx (encroachment) cumulative L3 D.Ne D.ne DELOILE oil influx (encroachment) during an interval L3 eo io ENCO oil influx (encroachment) rate L3/t Ao MOBO oil mobility et/m Np np OILP oil produced, cumulative L3 D.Np D.np DELOILP oil produced during an interval L3 qo Qo RTEO oil production rate L3/t qoD QoD RTEOQ oil production rate, dimensionless bo fmFo RVFO oil reciprocal formation volume factor

(shrinkage factor) Npa npa OILPUL oil recovery, ultimate L3 kro K ro PRMRO oil, relative permeability to So Pmso SATO oil saturation Sag Pog,Sog SATOG oil saturation in gas cap, interstitial Sor PonSor SATOR oil saturation, residual Yo smFos SPGO oil specific gravity iJ-o vA VISO oil viscosity miLt f INC operating cash income M fa INCA operating cash income, after taxes M f INCB operating cash income, before taxes M 0 XPO operating expense various Ou XPOU operating expense per unit produced MlL3 \12 operator, Laplacian U UT,Ue HTCU over-all heat transfer coefficient mlt3T ER lJR,eR EFFR over-all reservoir recovery efficiency: volume

of hydrocarbons recovered divided by volume of hydrocarbons in place at start of project (ER = EpEs Eo = Ev ED)

CO2 CO2 CNC02 oxygen concentration (concentration of other various elements or compounds would be indicated as, CC02,CN , etc.)

e02 Eo UTL02 oxygen utilization _ 2

dp Dp DIAAVP particle diameter, mean L L s,fscript I LTH path length, length, or distance L Ep 'Y/,ep EFFP pattern sweep efficiency (developed from areal

efficiency by proper weighting for variations in net pay thickness, porosity and hydrocarbon saturation: hydrocarbon pore space enclosed behind the injected-fluid or heat front divided by total hydrocarbon pore space of the reservoir or project

ht dt,et THKT pay thickness, gross (total) L hn dmen THKN pay thickness, net L T e PER period t k K PRM permeability, absolute (fluid flow) L2 kg Kg PRMG permeability, effective, to gas L2 ka Ka PRMO permeability, effective, to oil L2 kw Kw PRMW permeability, effective, to water L2

I-L m PRMM permeability, magnetic mLlq2 kika KiKa PRMGO permeability ratio, gas-oil k.Jka KwlKa PRMWO permeability ratio, water-oil krg Krg PRMRG permeability, relative, to gas kra Kra PRMRO permeability, relative, to oil krw Krw PRMRW permeability, relative, to water P NMBP phases, number of I-L v,a PSN Poisson's ratio Vp vp VOLP pore volume Vb - Vs L3 VpD VpD VOLPQ pore volume, dimensionless Qi qi FLUIQ pore volumes of injected fluid, cumulative,

dimensionless <P f,E POR porosity (Vb - Vs)lVb <Pa fa,Ea PORA porosity, apparent <Pe fe,Ee PORE porosity, effective (VpelVb) m MXP porosity exponent (cementation)

(in an empirical relation between F Rand <P) <Ph fh,Eh PORH porosity, hydrocarbon-filled, fraction or percent

of rock bulk volume occupied by hydrocarbons Icj> icj> PRX porosity index Icj>l icj>l PRXPR porosity index, primary Icj>2 icj>2 PRXSE porosity index, secondary <Pne fne,cne PORNE porosity, non-effective (VpnelVb) <Pig /;g, Eig PORIG 'porosity' (space), intergranular (Vb- Vgr)lVb) <Pim fim,Eim PORIM 'porosity' (space), intermatrix (Vb - V malVb) <PE fE,EE POREX porosity of experimental pack <PR frlER PORR porosity of reservoir or formation <Pt /r,Et PORT porosity, total

f POT potential or potential function various V U VLT potential difference (electric) mL2/~Jt Ep ENGP potential energy mL2/t

Pbh Pbh PRSBH pressure, bottomhole m/Lt2

P P PRS pressure mlLt2 pa Pa PRSA pressure, atmospheric m/Lt2

P P PRSAV pressure, average or mean m/Lt2

P Pd PRSAVR pressure, average, reservoir m/Lt2

Pws Pws PRSWS pressure, bottomhole, at any time after shut-in m/Lt2

Pwt Pwt PRSWF pressure, bottom hole flowing m/Lt2

Piwt Piwt PRSIWF pressure, bottom hole flowing, injection well m/Lt2

Pw Pw PRSW pressure, bottom hole general m/Lt~ Pws Pws PRSWS pressure, bottomhole static miLt Pww Pww PRSWW pressure, bottomhole (well), in water phase miLe Piws Piws PRSIWS pressure, bottomhole static, injection well m/Lt2

Pb Ps,Ps,Pb PRSB pressure, bubble-point (saturation) m/Lt2 Pe PoPe PRSCP pressure, capillary m/Lt2

Pet Pet PRSCF pressure, casing flowing m/Lt2

Pes Pes PRSCS pressure, casing static miLe Pe Pe PRSC pressure, critical miLe Pd Pd PRSD pressure, dew-point m/Lt2

PD PD PRSQ pressure, dimensionless Pe Pe PRSE pressure, external boundary m/Lt2

Pexe Pext PRSXT pressure, extrapolated m/Lt2

Pwt Pwt PRSWF pressure, flowing bottomhole mlLt2

Pet Pet PRSCF pressure, flowing casing m/Lt2

Pet Ptt PRSTF pressure, flowing tubing m/Lt2

Pt Pt PRSF pressure, front or interface miLe PeD PtD PRSTQQ pressure function, dimensionless, at

dimensionless time tD Pi Pi PRSI pressure, initial m/Lt2

Ppe Ppe PRSPC pressure, pseudo-critical m/Lt2

Ppr Ppr PRSPRD pressure, pseudo-reduced miLe f!..r Pr PRSRD pressure, reduced PR P PRSAVR pressure, reservoir average m/Lt2

Psp Psp PRSSP pressure, separator m/Lt2

Pse Pse PRSSC pressure, standard conditions miLe Pws Pws PRSWS pressure, static bottom-hole m/Lt2

Pes Pes PRSCS pressure, static casing m/Lt2

Pes Pes PRSTS pressure, static tubing miLe Pt! Pet PRSTF pressure, tubing flowing m/Lt2

Pts Pes PRSTS pressure, tubing static m/Lt2

1<1>1 i<l>l PRXPR primary porosity index GLp gLp NGLP produced condensate liquids, cumulative L3 Qp FLUP produced fluids, cumulative (where Np L3

and Wp are not applicable) L3 GFp gFp GASFP produced free gas, cumulative

Gp gp GASP produced gas, cumulative L3 AGp Agp DELGASP produced gas during an interval L3

GpE gpE GASPEX produced gas from experimental tube run L3 Gwgp 8Jygp GASWGP produced gas, wet, cumulative e 'ih D DENAVL produced-liquid density, weight-weighted mlL3

average

npj Npj MOLPJ produced moles of component j, cumulative Np np OILP produced oil, cumulative L3 D.Np tmp DELOILP produced oil during an interval e Wp wp WTRP produced water, cumulative L3 Awp Awp DELWTRP produced water during an interval L3 Gwgp gwgp GASWGP produced wet gas, cumulative L3 R Fg,Fgo GOR producing gas-oil ratio RF FgHFgoF GORF producing gas-oil ratio, free

(free-gas volume/oil volume) Fwo FACWO producing water-oil ratio, instantaneous qi Qi RTEI production rate at beginning of period L3/t qa Qa RTEA production rate at economic abandonment L3/t qD QD RTEQ production rate, dimensionless qg Qg RTEG production rate, gas L3/t qgD QgD RTEGQ production rate, gas, dimensionless qo Qo RTEO production rate, oil L3/t qoD QoD RTEOQ production rate, oil, dimensionless q Q RTE production rate or flow rate L3/t qjJ Qp RTEPAV production rate or flow rate at mean pressure L3/t q Q RTEAV production rate or flow rate, average L3/t qw Qw RTEW production rate, water L3/t qwD QwD RTEWQ production rate, water, dimensionless AtwJ A. DELTIMWFproduction time after well is opened to

production (presure drawdown) tp .p TIMP production time of well, equivalent, prior to

shut-in (pseudo-time) L4t/m J j PDX productivity index

Pk PRAK profit, annual net, over year k M fpk PRAPK profit, annual, over year k, fraction of

unamortized investment P PI PRFT profit, total M ex: proportional to Js js PDXS productivity index, specific L3t/m Tpe 8pe TEMPC pseudo-critical temperature T Ppe Ppe PRSPC pseudo-critical pressure m/U2 Gp fop GMFP pseudo-geometrical factor (multiplier)

( electrical logging) cpr Kpr>Kpr CMPPRD pseudo-reduced compressibility Ppr Ppr PRSPRD pseudo-reduced pressure Epsp <l>sp EMFP pseudo-SP mL2/qt2

Tpr 8pr TEMPRD pseudo-reduced temperature T tp .p TIMP pseudo-time (equivalent time well was on t

production prior to shut-in) fs Q,x QLTS quality (usually of steam)




t:.r t:.R DELRAD radial distance (increment along radius) L I ly,Ie HCTI radiation heat transfer coefficient mleT r R RAD radius L rwa Rwa RADWA radius, apparent or effective, of well bore L

(includes effects of well damage or stimulation) rD RD RADQ radius, dimensionless re Re RADE radius, external boundary L rH RH RADHL radius, hydraulic L rd Rd RADD radius of drainage L rwa Rwa RADWA radius of wellbore, apparent or effective L

(includes effects of well damage or stimulation) rs Rs RADS radius of well damage or stimulation (skin) L rw Rw RADW radius, well L ia INJA rate, air injection Cit 1 k; RTE rate: discount, effective profit, of return,

reinvestment, etc; use symbol i with suitable subscripts

L3/t q Q RTE rate, flow or production NGR Ny,CG NGR rate, gamma ray count lit eg ig ENCG rate, gas influx (encroachment) L3/t ig INJG rate, gas injection L3/t qg Qg RTEG rate, gas production L3/t qgD QgD RTEGQ rate, gas production, dimensionless e i ENC rate, influx (encroachment) L3/t x MENES random variable, mean value of x, estimated

INJ rate, injection L3/t IRCE rate, interest, effective compound

(usually annual) iM IRPE rate, interest, effective, per period j r IRA rate, interest, nominal annual w m MRT rate, mass flow mit u 'lj! VELV rate of flow or flux, per unit area Lit

(volumetric velocity) Q q,CI> HRT rate of heat flow mL2/t3 ir RORI rate of return (internal, true, or discounted

cash flow) or earning power eo io ENCO rate, oil influx (encroachment) L3/t qo Qo RTEO rate, oil production L3/t u 'lj! VELV rate per unit area, flow (volumetric velocity) Lit qoD QoD RTEOQ rate, oil production, dimensionless q Q RTE rate, production or flow L3/t qjJ Qp RTEPAV rate, production, at mean pressure L3/t q Q RTEAV rate, production, average Cit qD QD RTEQ rate, production, dimensionless qs Qs RTES rate, segregation (in gravity drainage) L3/t y e SRT rate, shear lit Vb Vb,Ub VELB rate (velocity) of burning-zone advance Lit ew iw ENCW rate, water influx (encroachment) L3/t iw INJW rate, water injection L3/t




qw Qw RTEW rate, water production L3/t qwD QwD RTEWQ rate, water production, dimensionless FaF FACAFU ratio, air-fuel various Fs Fd DMRS ratio, damage ('skin' conditions relative to

formation conditions unaffected by well operations)

S Fd DPR ratio, displacement Sob Fdob DPROB ratio, displacement, oil from burned volume,

volume per unit volume of burned reservoir rock

Sou Fdou DPROU ratio, displacement, oil from unburned volume, volume per unit volume of unburned reservoir rock

Swb Fdwb DPRWB ratio, displacement, water from burned volume, volume per unit volume of burned reservoir rock

K k,Feq EQR ratio, equilibrium (y/x) RF FgHFgoF GORF ratio, free producing gas-oil (free-gas

volume/oil volume) Rp Fgp, Fgop GORP ratio, gas-oil, cumulative Rsi Fgsi GORSI ratio, gas-oil, initial solution kglKo Kglko PRMGO ratio, gas-oil permeability R FWFgo GOR ratio, gas-oil producing Rsb Fgsb GORSB ratio, gas-oil, solution, at bubble-point conditions Rs Fgs,Fos GORS ratio, gas-oil, solution (gas solubility in oil) M FA MBR ratio, mobility, general

(AdisplacingfAdisplaced) Ms MDd,Msu MBRSAV ratio, mobility, diffuse-front approximation

[(AD + Ad)swep/(Ad)unswept]; D signifies dIsplacing; d signifies displaced; mobilities are evaluated at average saturation conditions behind and ahead of front

M FA MBR ratio, mobility, sharp-front approximation (AD/Ad)

Mt FAt MBRT ratio, mobility, total [(At)swep/(AtLnswept]; 'swept' and 'unswept' refer to invaded and uninvaded regions behind and ahead of leading edge of a displacement front

m Fpl,Fgo MGO ratio of initial reservoir free-gas volume to initial reservoir oil volume

F FAC ratio or factor in general (always with identifying various subscripts)

kglko KglKo PRMGO ratio, permeability, gas-oil R Fg,Fgo GOR ratio, producing gas-oil kw/ko Kw/Ko PRMWO ratio, permeability, water-oil Rsb Fgsb GORSB ratio, solution gas-oil, at bubble-point conditions Rs Fgs, Fgos GORS ratio, solution gas-oil (gas solubility in oil) Rsi Fgsi GORSI ratio, solution gas-oil, initial FwF FACWFU ratio, water-fuel Fwop FACWOP ratio, water-oil, cumulative

kw/ko Kw/Ko PRMWO ratio, water-oil permeability Fwo FACWO ratio, water-oil, producing, instantaneous X XEL reactance ML2/tq2 k r,j RRC reaction rate constant LIt !Yl (z) script R real part of complex number z b f,F RVF reciprocal formation volume factor, volume at

standard conditions divided by volume at reservoir conditions (shrinkage factor)

bg lFg RVFG reciprocal gas formation volume factor bgb gb,Fgb RVFGB reciprocal gas formation volume factor at

bubble-point conditions l/L2 j w reciprocal permeability

bo fmFo RVFO reciprocal oil formation volume fator (shrinkage factor)

ER 'l']R,eR EFFR recovery efficiency, reservoir over-all; volume of hydrocarbons recovered divided by volume of hydrocarbons in place at start of project. (ER = EpE/ED = EvED)

Gpa gpa GASPUL recovery, ultimate gas Pr Pr PRSRD reduced pressure Tr ar TEMRD reduced temperature a RED reduction ratio or reduction term asp REDSP reduction, SP (general) due to shaliness R N MRF refraction, molecular n JL RFX refraction index aSPsh REDSH reduction ratio, SP, due to shaliness Ar AMPR relative amplitude A AWT relative atomic mass (atomic weight) M MWT relative molecular weight (molecular weight) f3 y BRGR relative bearing y s,Fs SPG relative density (specific gravity) krg Krg PRMRG relative permeability to gas kro Kro PRMRO relative permeability to oil krw Krw PRMRW relative permeability to water t2 V2 TIMAV relaxation time, free-precession decay t tt '1:t TIMRP relaxation time, proton thermal t a Fa AIR requirement, air aE FaE AI REX requirement, unit air, in laboratory experimental L3/m

run, volumes or air per unit mass of pack aR FaR AIRR requirement, unit air, in reservoir, volumes

of air per unit bulk volume of reservoir rock L3 GFi gFi GASFI reservoir initial free-gas volume (=mNBoi)

<PR fR,ER PORR reservoir or formation porosity p PR PRSAVR reservoir pressure, average m1Lt2 ER 'l']R,eR EFFR reservoir recovery efficiency, over-all;

volume of hydrocarbons recovered divided by volume of hydrocarbons in place at start of project (ER = [sx] = Ev ED)

L3 VRb VRb VOLRB reservoir rock burned, volume of




VRu VRu VOLRU reservoir rock unburned, volume of L3 TR 9R TEMR reservoir temperature T Sgr PgnSgr SATGR residual gas saturation Shr Phnshr SATHR residual hydrocarbon saturation Sor PonSor SATOR residual oil saturation Swr PwnSwr SATWR residual water saturation r R RST resistance ML2/t~2 R p,r RES resistivity (electrical) mL3tq Ran Pam ran RESAN resistivity, annulus mL3tq2 Ra Pmra RESA resistivity, apparent mL3tq2 Rz pz,rz RESZ resistivity, apparent, of the conductive mL3tq2

fluids in an invaded zone (due to fingering)

mL3tq2 KR MR,a,C COER resistivity factor coefficient, formation (FRcj>m)

FR FACHR resistivity factor, formation, equals RoIRw a numerical subscript to F indicates the Rw

mL3tq2 Rxo Pxmrxo RESXO resistivity flushed zone (that part of the invaded zone closest to the wall of the borehole, where flushing has been the

Ro po,ro RESZR maximum)

resistivity, formation 100% saturated mL3tq2 with water of resistivity Rw

mL3tq2 Rt Pt,rt REST resistivity, formation, true IR iR RSXH resistivity index (hydrocarbon) equals R/Ro Ri pi,ri RESI resistivity, invaded zone mL3tq2 Rm Pm,rm RESM resistivity, mud mL3tq2

Rmc Pmormc RESMC resistivity, mud-cake mL3tq2 Rmf Pmf,rmf RESMF resistivity, mud-filtrate mL3tq2 Rsh psh,rsh RESSH resistivity, shale mL3tq2 Rs ps,rs RESS resistivity, surrounding formation mL3tq2 Rw pw,rw RESW resistivity, water mL3tq2 Vu Ru GRRU revenue, gross ('value'), per unit produced MlL3 V R, V I1 Rt GRRT revenue, gross ('value'), total M NRe REYQ Reynolds number (dimensionless number) cf kfiKf CMPF rock or formation compressibility Lt2/m C c,n CNC salinity various S p,s SAT saturation n SXP saturation exponent Sg Pg,Sg SATG saturation, gas Sgc PgoSgc SATGC saturation, gas, critical Sgr PgnSgr SATGR saturation, gas, residual Sog PogtSog SATOG saturation, interstitial-oil, in gas cap Swg Pwg,Swg SATWG saturation, interstitial-water, in gas cap Sh Ph,Sh SATH saturation, hydrocarbon Shr Phnshr SATHR saturation, residual hydrocarbon So PmSo SATO saturation, oil Sor PonSor SATOR saturation, oil, residual

Pb Ps,Ps,Pb PRSB saturation or bubble-point pressure mlLt2

SL PL,SL SATL saturation, total (combined) liquid Sw pw>sw SATW saturation, water Swc Pwoswc SATWC saturation, water, critical Swi Pwbswi SATWI saturation, water, initial Siw Piw,Siw SATIW saturation, water irreducible Swr Pw"swr SATWR saturation, water, residual I<j>2 i<j>2 PRXSE secondary porosity index qs Qs RTES segregation rate (in gravity drainage) L3/t Psp Psp PRSSP separator pressure mlLt2

Ish script t Atsh TACSH shale interval transit time tiL Rsh psh,rsh RESSH shale resistivity mL3tq2

IShGR ishGR SHXGR shaliness gamma-ray index (Ylog - Ycn)/(Ysh - Yen)

miLe G Es ELMS shear modulus y e SRT shear rate lit As AMPS shear wave amplitude various bo fmFo RVFO shrinkage factor (reciprocal oil formation

volume factor) mlLt2 Pws Pws PRSWS shut-in bottomhole pressure, at any time

Atws A'tws DELTIMWS shut-in time (time after well is shut in) t (pressure buildup)

Dsp DSCSP single payment discount factor Dspc DSCSPC single payment discount factor

(constant annual rate) 8 rs SKD skin depth (logging) L S S,a SKN skin effect various rs Rs RADS skin radius (radius of well damage or stimulation) L m A SLP slope various M meD SAD slope, interval transit time vs density (absolute tL2/m

N meND SND value)

slope, neutron porosity vs density (absolute L3/m value)

< LT smaller than PsE DsE DENSEX solid particles density of experimental rock m/L3 Vs VS VOLS solid(s) volume (volume of all formation solids) L3

Pma Dma DENMA solids (matrix, grain) density m/L3 Rs Fgs, Fgos GORS solubility, gas in oil (solution gas-oil ratio) Rsw GWRS solubility, gas in water Rsb Fgsb GORSB solution gas-oil ratio at bubble-point conditions Rs Fgs, Fgos GORS solution gas-oil ratio (gas solubility in oil) Rsi Fgsi GORSI solution gas-oil ratio, initial Ec <Pc EMFC SP, electrochemical component of mL2/t2q Ek <Pk EMFK SP, electrokinetic component of mL2/t2q Esp <Psp EMFSP SP (measured SP) (Self Potential) mL2/t2q Epsp <Ppsp EMFPSP SP, pseudo mL2/t2q Essp <Pssp EMFSSP SP, static (SSP) mL2/t2q Ls ss,/s script I LENS spacing (electrical logging) L S a HERS specific entropy L2/t2T Y s,Fs SPG specific gravity (relative density) Yg sg,Fgs SPGG specific gravity, gas

Yo sOJFos SPGO specific gravity, oil Yw sw,Fws SPGW specific gravity, water C c HSP specific heat capacity (always with phase or L2/eT

system subscripts) Y k HSPR specific heat capacity ratio Is is IJXS specific injectivity index L3t/m Is js PDXS specific productivity index Ct/m v VS SPY specific volume L3/m Fwv Y WGTS specific weight mL2/t2

Essp <Pssp EMFSSP SSP (static SP) mL2/eq ts 1:s TIMS stabilization time of a well t (J SDV standard deviation of a random variable s SDVES standard deviation of a random variable, estimated Piws Piws PRSIWS static bottom-hole pressure, injection well m/Lt2

Pws Pws PRSWS static pressure, bottom-hole, mlLt2 at any time after shut-in

m/Lt2 Pes Pes PRSCS static pressure, casing Pts Pts PRSTS static pressure, tubing miLe rs Rs RADS stimulation or damage radius of well (skin) L £ e'£n STN strain, normal and general Y lOs STNS strain, shear 8 8v STNV strain, volume 'P STR stream function various (J s STS stress, normal and general m/Lt2 1: SS STSS stress, shear m/Lt2 k SUM summation (operator) u 1jJ VELV superficial phase velocity (flux rate of a Lit

particular fluid phase flowing in pipe; use appropriate phase subscripts)

L3/t qse qmQse RTESC surface production rate (J Y,Y SFT surface tension, interfacial m/t2

Rs ps,rs RESS surrounding formation resistivity mL3t~2 k K SUSM susceptibility, magnetic mLlq T 8 TEM temperature T Tbh 8BH TEMBH temperature, bottomhole T Te 8e TEMC temperature, critical T Tf 8f TEMF temperature, formation T gT gh GRDT temperature gradient TIL Tpe 8pe TEMPC temperature, pseudo-critical T Tpr 8pr TEMPRD temperature, pseudo-reduced T Tr 8r TEMRD temperature, reduced T TR 8R TEMR temperature, reservoir T Tse 8se TEMSC temperature, standard conditions T (J Y,Y SFT tension, surface (interfacial) m/e X tensorofx kh A HCN thermal conductivity (always with additional mLlt3T

phase or system subscripts) f3 b HEC thermal cubic expansion coefficient liT a a,'Yjh HTD thermal or heat diffusivity L2/t h d,e THK thickness (general and individual bed) L ht doet THKT thickness, gross pay (total) L




hmc dmoemc THKMC thickness, mud-cake L hI dt,et THKT thickness, pay, gross (total) L hn dmen THKN thickness, net pay L t 't TIM time t Atwf i>'twf DELTIMWFtime after well is opened to production t

(pressure drawdown) Atws A'tws DEL TIMWS time after well is shut in (pressure build-up) t 't 'tc TIMC time constant t 'td td TIMD time, decay (mean life) (111..) t td 'td TIMD time, delay t At A't DELTIM time difference t

(time period or interval, fixed length) tD 'tD TIMQ time, dimensionless tDm 'tDm TIMMQ time, dimensionless at condition m ts 'ts TIMS time for stabilization of a well t rscript t At TAC time, interval transit tiL ta script t Ata TACA time, interval transit, apparent tiL ryscript t Atf TACF time, interval transit, fluid tIL tina script t Atma TACMA time, interval transit, matrix tIL Tsh script t Atsh TACSH time, interval transit, shale tIL tdN TIMDN time, neutron decay (neutron mean life) t

!t 'tp,tpo TIMPO time, pay-out (pay-off, pay-back) t A't DELTIM time period or interval, fixed length t

tp 'tp TIMP time well was on production prior to shut-in, t equivalent (pseudo-time)

't TOR tortuosity 'te TORE tortuosity, electric 'tH TORHL tortuosity, hydraulic SL PL,SL SATL total (combined) liquid saturation S HER total entropy L2/t2T At A MOBT total mobility of all fluids in a particular region L3t/m

Mt Ft..t MBRT ofthe reservoir, e.g., (1"0 + I..g + I..w)

total mobility ratio [(I..t)swep/(I..t)unsweptl; 'swept' and 'unswept' refer to invaded and uninvaded regions behind and ahead of leading edge of a displacement front

ht dt,et THKT total (gross) pay thickness L V R, Vt,Rt GRRT total gross revenue ('value') M G g GASTI total initial gas in place in reservoir L3 n nt, Nt NMBM total moles CPt ft,Et PORT total porosity Bt Ft FVFT total (two-phase) formation volume factor h hh,hT HTCC transfer coefficient, convective heat rnIeT U UT,Ue HTCU transfer coefficient, heat, over-all rnIt3T I Ir,ls HTCI transfer coefficient, heat, radiation rnIt3T tscript t At TAC transit time, interval tIL ta script t Ata TACA transit time, apparent, interval tIL ryscript t Atf TACF transit time, fluid interval tIL tina script t Atma TACMA transit time, matrix interval tIL Tsh script t Atsh TACSH transit time, shale interval tIL

00

::z (y) script L transform, Laplace of y J y (t)e-stdt

0




s transform, Laplace, variable T T TRM transmissivity, transmissibility various Pt Dt DENT true density mlL3 Rt Pt,rt REST true formation resistivity mL3tq2

Gt fat GMFf true geometrical factor (multiplier) (non-invaded zone) (electrical logging)

mlLt2 Ptt Ptt PRSTF tubing pressure, flowing Pts Pts PRSTS tubing pressure, static mlLt2

FB FACB turbulence factor Bt Ft FVFf two-phase or total formation volume factor Gpa gpa GASPUL ultimate gas recovery L3 Cuk INVUK unamortized investment over year k P un discounted cash flow M VRu VRu VOLRU unburned reservoir rock, volume of L3 aE FaE AIREX unit air requirement in laboratory experimental L3/m

run, volumes of air per unit mass of pack aR FaR AIRR unit air requirement in reservoir, volumes of air

per bulk volume of reservoir rock Cm cm,nm CNCFU unit fuel concentration (see symbol m) various R RRR universal gas constant (per mole) mL2/t2T e02 E02 UTL02 utilization, oxygen z VAL valence y MFRV vapour phase, mole fraction of component V MOLV vapour phase, moles of L{ Av HLTV vaporization, latent heat of L2/t2 0 VAR variance of a random variable S2 VARES variance of a random variable, estimated x vectorofx v V,u VEL velocity Lit v V,u VAC velocity, acoustic Lit Va VmUa VACA velocity, acoustic apparent (measured) Lit Vt Vt,Ut VACF velocity, acoustic fluid Lit Vma Vma,uma VACMA velocity, matrix acoustic Lit Vsh Vsh,Ush VACSH velocity, shale acoustic Lit Vb Vb,Ub VELB velocity (rate) of burning-zone advance Lit El 'YJbel EFFI vertical (invasion) efficiency: hydrocarbon pore

space invaded (affected, contacted) by the injected-fluid or heat front divided by the hydrocarbon pore space enclosed in all layers behind the injected-fluid or heat front

/La 'YJa VISA viscosity, air miLt /LjJ 'YJjJ VISPAV viscosity at mean pressure miLt /L 'YJ VIS viscosity, dynamic miLt /Lg 'YJg VISG viscosity, gas miLt /Lga 'YJga VISGA viscosity, gas, at 1 atm miLt v N VSK viscosity, kinematic L2/t

/La 'YJa VISO viscosity, oil miLt /Lw 'YJw VISW viscosity, water miLt V v VOL volume L3 Vbp Vbp VOLBP volume at bubble-point pressure L3

Vb Vb VOLB volume, bulk L3

VbE VbE VOLBEX volume, bulk, of pack burned in L3 experimental run

L3 Ve Vpe, Ve VOLG volume, effective pore V iv,Fv VLF volume fraction or ratio (as needed, use same various

subscripted symbols as for 'volumes'; note that bulk volume fraction is unity and pore volume fractions are <1>])

L3 GFi gFi GASFI volume, free-gas, initial reservoir (=mNho)

L3 Vgr Vgr VOLGR volume, grain (volume of all formation solids except shales)

L3 Vig Vig VOLIG volume, intergranular (volume between grains; consists of fluids and all shales)

Vim Vim VOLIM (Vb- Vgr)

volume, intermatrix (consists of fluids and L3 dispersed shale) (Vb - V rna)

Vma Vma VOLMA volume, matrix (framework) (volume of all formation solids except dispersed shale)

L3 Vne Vpne' Vne VOLNE volume, noneffective pore (Vp - Ve) VRb VOLRB volume of reservoir rock burned L3 VRu VOLRU volume of reservoir rock unburned C VM VOLM volume per mole (molal volume) L3 Vp vp VOLP volume, pore (Vb - Vs) L3 VpD VpD VOLPQ volume, pore, dimensionless Vshd Vshd VOLSHD volume, shale, dispersed L3 Vshl'script I V shi script I VSHLAM volume, shale, laminated L3

Vshs Vshs VOLSHS volume, shale, structural L3

Vsh Vsh VOLSH volume, shale(s) (volume of all shales: C structural and dispersed)

L3 Vs VS VOLS volume, solid(s) (volume of all formation solids)

Clm v VS SPY volume, specific EVb 'YJVb,eVb EFFVB volumetric efficiency for burned portion only,

in situ combustion pattern Ev 'YJv,ev EFFV volumetric efficiency: product of pattern sweep

and invasion efficiencies q Q RTE volumetric flow rate Cit qdh qw/,qDH,Qdh RTEDH volumetric flow rate downhole L3/t qsc qmQsc RTESC volumetric flow rate, surface conditions Cit M HSPV volumetric heat capacity mlLeT u 'P VELV volumetric velocity (flow rate or flux, Lit

per unit area) W w WTR water (always with identifying subscripts) various Cw kw,Kw CMPW water compressibility Lt2/m Pw Dw DENW water density mlL3

Owb FWb DPRWB water displaced from burned volume, volume per unit volume of burned reservoir rock

L4elm C WDC water-drive constant CL WDCL water-drive constant, linear aquifer L4elm kw Kw PRMW water, effective permeability to L2

Bw Fw FVFW water formation volume factor FwF FACWFU water-fuel ratio various Rsw GWRS water, gas solubility in W W WTRTI water in place in reservoir, initial L3 We We WTRE water influx (encroachment), cumulative L3 J1We J1we DELWTRE water influx (encroachment) during an interval L3 ew iw ENCW water influx (encroachment) rate L3/t Wi Wi WTRI water injected, cumulative L3 J1Wi <1 Wi DELWTRI water injected during an interval L3

iw INJW water injection rate L3/t Aw MOBW water mobility L3t/m kwlko KwlKo PRMWO water-oil permeability ratio Fwop FACWOP water-oil ratio, cumulative Fwo FACWO water-oil ratio, producing, instantaneous Wp wp WTRP water produced, cumulative L3 J1Wp J1wp DELWTRP water produced during an interval L3

qw Qw RTEW water production rate L3/t qwD QwD RTEWQ water production rate, dimensionless krw Krw PRMRW water, relative permeability to Rw pw,rw RESW water resistivity mL3tq2

Sw Pw,sw SATW water saturation Swc Pwoswc SATWC water saturation, critical Swi Pwi,Swi SATWI water saturation, initial Swo Swb SATWO water saturation (interstitial) in oil band Swg Pwg,Swg SATWG water saturation in gas cap, interstitial Siw Piw,Siw SATIW water saturation, irreducible Swr PwnSwr SATWR water saturation, residual Yw Sw.Fws SPGW water specific gravity ILw 1']w VISW water viscosity mILt A WVL wave length (I/o) L 0 v WVN wave number (III...) I/L W w,G WGT weight (gravitational) m/Lt2

fh 15L DENAVL weight-weighted average density mlL3 of produced liquid

A AWT weight, atomic m M MWT weight, molecular m rw Rw RADW well radius L rs Rs RADS well radius of damage or stimulation (skin) L Is 1: TIMS well stabilization time t rwa Rwa RADWA wellbore radius, effective or apparent (includes L

effects of well damage or stimulation Cwg cwg,nwg CNTWG wet-gas content various Gwgp gwgp GASWGP wet gas produced, cumulative L3

b W WTH width, breadth, or (primarily in fracturing) L thickness

W W WRK work mL2/t2

E y ELMY Young's modulus (modulus of elasticity) mlLt2

di dbDi DIAl zone diameter, invaded, electrically equivalent L Ri Pbri RESI zone resistivity, invaded mL3tq2


B. Subscripts alphabetized by physical quantity

Subscript de£mition Letter ReserveSPE Computer subscript subscript letter

subscript

abandonment a A A acoustic a A, «alpha A activation log, neutron NA na NA active, activity, or acting a A after taxes a A air a A A air-fuel aF AFU altered a A amplitude log A a A angle, angular, or angular coordinate () theta THE anhydrite anh AH anisotropic ani ANI annulus apparent (from log readings; an AN AN

use tool description subscripts) apparent (general) a ap A apparent wellbore (usually with wellbore radius) wa WA areal A A atmosphere, atmospheric a A A average or mean pressure 2- PAY average or mean saturation S s,p rho SAY band or oil band b B B bank or bank region b B base b r, f3 beta B before taxes b B B bond log, cement CB cb CB borehole televiewer log TV tv TV bottom hole bh w,BH BH bottom-hole, flowing (usually with pressure or time) wi WF bottom-hole, static (usually with pressure or time) ws WS boundary conditions, external e 0 E breakthrough BT bt BT bubble b B bubble-point conditions, oil at (usually with ob OB

formation volume factor, Bob) bubble-point conditions, solution at (usually sb SB

with gas-oil ratio, Rsb) bubble point (saturation) b s,bp B bubble-point or saturation (usually with bp B

volume, Vbp) bulk (usually with volume Vb) b B,t B burned in experimental tube run (usually bE BEX

with volume, VbE) burned or burning b B B burned portion of in situ combustion pattern, displacement Db DB

from (usually with efficiency, E Db) burned portion of in situ combustion pattern, volumetric Vb VB

of (usually with efficiency, Evb) burned reservoir rock Rb RB


Subscript definition Letter ReserveSPE Computer subscript subscript letter

subscript

burned volume, oil from (usually ob OB with displacement ratio, Oob)

burned volume water from (usually wb WB with displacement ratio, Owb)

calculated C calc CA caliper log C c C capillary (usually with capillary pressure, Pc) c C CP capture cap C carbon dioxide CO2 CO2 carbon monoxide CO CO casing or casinghead c cg CS casing, tlowing (usually with pressure) cf CF casing, static (usually with pressure) cs CS cement bond log CB cb CB chemical c C chlorine log CL cl CL clay cl cla CL clean en cln CN coil C c C compaction cp CP compensated density log CD cd CD compensated neutron log CN en CN component(s) C C componentj j J component j produced pj PJ

(usually with moles, npj) compressional wave c C C conditions for infinite dimensions 00 INF INF conductive liquids in invaded zone z Z constant c C C contact c C C

(usually with contact angle, 8c) contact log, microlog, minilog ML mlscript I ML convective C conversion (usually with conversion factor in c C

Newton's law of motion, gc) core c C C corrected cor COR critical c cr CR cumulative intlux (encroachment) e i E cumulative injected i I cumulative produced p P cumulative produced free value

(usually with gas, GFp ) Fp FP

cumulative produced liquid Lp (usually with condensate, GLp)

damage or damaged (includes 'skin' conditions) s d S decay d D deep induction log ID id ID deep laterolog LLD Il'd script II LLD delay d o delta D


Subscriptdeflnition Letter ReserveSPE Computer subscript . subscript letter

subscript

density prho RHO density log, compensated CD cd CD density log D d D depleted region, depletion d 6 delta D dew-point d D differential separation d D differential temperature log DT dt DT diffusivity 'YJ eta ETA dimensionless pore value pD PQ

(usually with volume VpD)

dimensionless quantity D Q dimensionless quantity at condition m Dm QM dimensionless time tD TQ dimensionless water wD WQ dip (usually with angle, ad) d D diplog, dipmeter DM dm DM directional survey DR dr DR dirty (clayey, shaly) dy dty DY discounted value, present worth, or present value PV pv PV dispersed d D D dispersion K d K displaced d s,D DD displacement from burned portion of in situ Db DB

combustion pattern (usually with efficiency, EDb )

displacement from unburned portion of in situ Du DU combustion pattern (usually with efficiency, EDu)

displacing or displacement (efficiency) D s, (J sigma DN dolomite dol DL down-hole dh DH DH drainage (usually with drainage radius, rd) d D dual induction log DI di DI duallaterolog DLL dll'script II DLL earth e E E effective (or equivalent) e E electric, electrical e E E electrochemical c ec C electrode E e E electrokinetic k ek K electrolog, electrical log, electrical EL el, ES EL

survey electromagnetic pipe inspection log EP ep EP electron el e/script el E empirical E EM EM encroachment (influx), cumulative e i E entry e E E epithermal neutron log NE ne NE eqivalent eq BV EV estimated E est ES ethane C2 C2 experimental E EX EX



subscript

experimental value per mole of produced gas Eg EXG (usually with fuel consumption, mEg)

external, outer boundary conditions e 0 E extrapolated ext XT fast neutron log NF nf NF fill-up F f F finger or fingering f F F flash separation f F F flowing bottom-hole (usually with pressure or time) wf WF flowing casing (usually with pressure) cf CF flowing conditions, injection well (usually with iwf IWF

pressure, Piwf) flowing conditions, well (usually with time) wf f WF flowing tubing (usually with pressure) if TF fluid f fl F fluids in an invaded zone, conductive z Z flushed zone xo XO formation 100% saturated with o zero 7ZR

water (used in Ro only) formation (rock) f fm F formation, surrounding s S fraction or fractional f r F fracture, fractured or fracturing f F FR free (usually with gas or gas-oil ratio quantities) F f F free fluid Ff f FF free value, cumulative produced, Fp FP

(usually with gas, GFp ) free value, initial (usually with gas, G n) Fi FI front, front region, or interface f F F fuel, mass of (usually with fuel concentration, em) m FU fuel (usually with fuel properties, such as PF) F FU gamma-gamma ray log GG gg GG gamma ray log GR gr GR gas g G G gas at atmospheric conditions ga GA gas at bubble-point conditions gb GB gas cap, oil in (usually with saturation, Sag) og OG gas cap, water in (usually with saturation, Swg) wg WG gas, dimensionless gD GQ gas-oil, solution (usually with gas-oil ratios) s S gas-water, solution sw

(usually with gas solubility in water, Rsw) geometrical G G geothermal G T GT grain gr GR grain (matrix, solids) ma MA gravity meter log GM gm GM gross (total) t T T guard log G g G gypsum gyp GY half 112 H


Subscriptdeflnition

heat or thermal heavy phase hole horizontal hydraulic hydrocarbon hydrogen nuclei or atoms hydrocarbon, residual hydrogen sulphide imbibition induction log, deep investigation induction log induction log, dual induction log, medium investigation infinite dimensions, conditions for influx (encroachment), cumulative initial conditions or value initial free value (usually with gas, GFi)

initial solution (usually with gas-oil ratio, Rsi) initial value or conditions injected, cumulative injection, injected or injecting injection well, flowing conditions (usually with pressure,

Piw/) injection well, static conditions (usually with pressure,

Piws) inner or interior interface, front region, or front interference intergranular intermatrix internal intrinsic invaded invaded zone invaded zone, conductive liquids in an invasion (usually with invasion efficiency, E /) irreducible jth component jth component, produced junction laminar laminated, lamination lateral (resistivity) log laterolog (add further tool configuration

subscripts as needed) laterolog, dual lifetime log, neutron, TDT light phase limestone limiting value

Letter subscript

h HP h H H h H hr H2S I 1D I D1 1M 00

e i Fi si

i iwf

iws

i f I ig 1m i int

i z I

j pj j ('script 1 ('script L L LL

DLL PNL LP Is lim

ReserveSPE Computer subscript letter

subscript

T, e theta HT hp HP H H h H

HL H H

HY HR H2S

i script i I id ID i I di DI im 1M

INF E I PI SI I

I I inj I

IWF

IWS

l iota, t script i I F F i, t script i I

IG 1M

l iota, { script i I I

I I I I

Z I

ir, l iota, t script i IR J PJ J

L LAM L LAM ('script 1 L If script II LL

d Il"script II DLL n i'script 1 PNL i'p script 1 LP 1st LS

LM


SubscriptderlOition Letter ReserveSPE Computer subscript su!'script Htter

subscript

linear, lineal L tscript I L liquid or liquid phase L tscript I L liquids, conductive, invaded zone Z Z liquid produced, cumulative (usually with Lp

condensate G Lp) location subscripts, usage is secondary to that for 1,2,3, etc.

representing times or time periods log LOG log L lower tscript I L L magnetism log, nuclear NM nm NM mass of fuel (usually with fuel concentration, m FU

Cm) matrix (solids, grain) ma MA matrix [solids, except (nonstructural) ma MA

clay or shale] maximum max MX mean or average pressure ~ PAY mean or average saturation S, prho SAY medium investigation induction log 1M im 1M methane C1 Cl microlaterolog MLL md'script II MLL microlog, minilog, contact log ML mtscriptl ML micro-seismogram log, signature log, variable VD vd VD

density log minimum min MN mixture M z,m M mobility A lambda M LAM molal (usually with volume, V M) M M Mth period or interval M m M mud m M mud cake me MC mud filtrate mf MF net n N neutron N n N neutron activation log NA na NA neutron lifetime log, TDT PNL ntscript I PNL neutron log, compensated CN en CN neutron log N n N neutron log, epithermal NE ne NE neutron log, fast NF nf NF neutron log, sidewall SN sn SN neutron log, thermal NT nt NT nitrogen N2 N2 noneffective ne NE nonwetting nw NW NW normal n N normal (resistivity) log N n N

(add numerical spacing to subscript to N; e.g., N16) normalized (fractional or relative) n r,R N nth year, period, income, payment, or unit n N N nuclear magnetism log NM nm NM

subscript

numerical subscripts (intended primarily 1,2,3, etc. to represent times or time periods; available secondarily as location subscripts or for other purposes)

observed DB OB oil at bubble-point conditions (usually with formation ob OB

volume factor, Bob) oil, dimensionless oD 00 oil 0 N,n 0 oil from burned volume (usually with displacement ob OB

ratio, Sob) oil from unburned volume (usually with displacement ou OU

ratio, Sou) oil in gas cap (usually with saturation, Sog) og OG outer (external) e 0 E oxygen O2 02 particle (usually with diameter, dp) p P particular period, element, or interval k K K pattern (usually with pattern efficiency, Ep) P P pay-out, pay-off, or pay-back p po PO permeability k K K phase or phases P P pipe inspection log, electromagnetic EP ep EP pore (usually with volume, Vp) p P P pore value, dimensionless (usually with volume, pD PO

VpD) porosity phi f, E epsilon PHI porosity data phi j, E epsilon P pressure, mean or average p PAY primary 10ne p,pri PR produced p P P produced component j (usually with moles, npj) pj Pl produced, cumulative p P produced free value, cumulative

(usually with gas, GFp ) Fp FP

produced in experiment pE PEX produced liquid, cumulative Lp

(usually with condensate, G Lp) produced water-oil (cumulative) wop WOP

(usually with cumulative water-oil ratio, Fwop) production period (usually with time, tp) p P P profit - unamortized investment Pk PK proximity log P p P pseudo p P pseudo-critical pc PC pseudo-dimensionless pD PO pseudo-reduced pr PRD pseudo-SP pSP PSP radial r R R radius, radial, or radial distance r R R rate of return r R R


Subscriptdeflnition Letter ReserveSPE Computer subscript subscript letter

subscript

recovery (usually with recovery efficiency, R R ER )

reduced r RD reference r b, prho R relative r R R reservoir R r R reservoir rock, burned Rb RB reservoir rock, unburned Ru RU residual r R R residual hydrocarbon hr HR resistivity R R resistivity log R r, p rho R Reynolds (used with Reynolds number Re

only, NRe)

rock (formation) f fm F sand sd sa SD sandstone ss sst SS saturation, mean or average S 5, prho SAY saturation or bubble point b s B saturation or bubble point (usually with bp BP

volume, Vbp ) scattered, scattering sc SC secondary 2 two s,sec SE segregation (usually with segregation s S, a sigma S

rate, qs) separator conditions sp SP shale sh sha SH shallow laterolog LLS It s script II LLS shear s 1: tau shear wave s 1: tau S sidewall S SW SW sidewall neutron log SN sn SN signature log, micro-seismogram log, VD vd VD

variable density log silt sl sit SL single payment sp SP skin (stimulation or damage) s S S slip or slippage s a sigma S slurry (,mixture') M z,m M solid( s) (all formation solids) s a sigma S solids in experiment sE SEX solids (matrix, grain) ma MA solution at bubble-point conditions (usually with sb SB

gas-oil ratio, Rsb) solution in water (usually with gas solubility sw

in water, Rsw) solution, initial (usually with gas-oil si SI

ratio, Rsi) solution (usually with gas-oil ratios) s S sonde, tool T t T sonic velocity log SV sv SV


Subscriptdeflnition Letter ReserveSPE Computer subscript subscript letter

subscript

SP SP sp SP spacing s L specific (usually with J and l) s S SSP SSP SSP stabilization (usually with time) s S S standard conditions sc (J sigma SC static bottom-hole (usually with pressure or time) ws WS static casing (usually with pressure) cs CS static conditions, injection well (usually with pressure) iws IWS static or shut -in conditions (usually with time) ws s WS static tubing (usually with pressure) ts TS static well conditions (usually with time) ws s WS steam or steam zone s S S stimulation (includes 'skin' conditions) s S S stock-tank conditions st ST storage or storage capacity S s, (J sigma S strain £ epsilon e EPS structural st s ST surface s (J sigma S surrounding formation s S swept or swept region s S, (J sigma S system s (J sigma S TDT log, neutron lifetime log PNL pnfscript I PNL televiewer log, borehole TV tv TV temperature T h, 8 theta T temperature log T t,h T temperature log, differential DT dt DT thermal (heat) h T, 8 theta HT thermal decay time (TDT) log PNL pnfscript I PNL thermal neutron log NT nt NT time, dimensionless tD TQ times or time periods 1,2,3, etc. tool-description subscripts: see individual entries

such as 'amplitude log', 'neutron log,' , etc. tool, sonde T t T total initial in place in reservoir ti TI total (gross) t T T total, total system t T T transmissibility T t T treatment or treating 1: tau T true (opposed to apparent) t tr T tubing flowing (usually with pressure) if TF tubing or tubinghead t tg T tubing, static (usually with pressure) ts TS turbulence (used with Fonly, FB ) B B ultimate a ul UL unamortized u U U unburned u U unburned portion of in situ combustion pattern Du DU

displacement from (usually with efficiency, E Du) unburned reservoir rock Ru RU


Subscript deDnition Letter ReserveSPE Computer subscript sub~cript letter

subscript

unburned volume, oil from (usually with ou OU displacement ratio, 60u)

unit u U U unswept or unswept region u U U upper u U U vaporization, vapour, or vapour phase v V V variable density log, micro-seismogram log, VD vd VD

signature log velocity v V V velocity, sonic or acoustic log SV sv SV vertical V v V volumetric of burned portion of in situ combustion Vb VB

pattern (usually with efficiency, Evb)

volume or volumetric V v V water w W W water, dimensionless wD WQ water from burned volume (usually with displacement wb WB

ratio,6wb)

water-fuel wF WFU water in gas cap (usually with saturation, Swg) wg WG water-oil (usually with instantaneous producing wo WO

water-oil ratio, Fwo) water-oil produced (cumulative) wop WOP

(usually with cumulative water-oil ratio, Fwop) water, solution in (usually with gas solubility sw SW

in water, Rsw) water-saturated formation, 100% o zero zr ZR weight W w W well conditions w W well, flowing conditions (usually with time) wI I WF well, static conditions (usually with time) ws s WS well, injection, flowing conditions iwl IWF

(usually with pressure Piw/) well, injection, static conditions iws IWS

(usually with pressure Piws) well, static conditions (usually with time) ws WS wellbore, apparent (usually with wellbore wa WA

radius, rwa) wellhead wh th WH wet gas (usually with composition or content, wg WG

Cwg) wet gas produced wgp WGP wetting w W W Young's modulus, refers to Y Y zero hydrocarbon saturation o zero zr ZR zone, conductive fluids in an invaded z Z zone, flushed xo XO zone, invaded I I

Appendix 2

Solutions to Examples

Chapter 2

Solution 2.1

Although this problem should place probabilistic ranges on the given data and assumptions, it will be calculated deterministically.

We will assume that the combination of oil expelled from source rocks and trapped in potential structures represents some 8% of the converted source rocks, i.e.:

Oil converted for source rock = 5 x 4500 x 12 x 106 m3

Trapped oil ( = OIP) = 0.085 x 4500 x 12 x 106 m3

= 2.16 x 1010 m3

Assuming an average formation volume factor of 1.4 rm3/sm3 this yields a stock tank oil in place of 1.54 x 1010 sm3 .

For an assumed overall technical recovery factor of 0.35 this yields a recoverable reserve of

1.54 x 1010 x 0.35 = 5.4 x 109 sm3

(This is equivalent to 34 x 109 STB.)

(N.B. The UK Government's 1983 'Brown Book' indicates a probable range of technically recoverable reserves between 11 and 23 x 109 STB, assuming an oil formation volume factor of 1.4 rm3/sm3 .)

(a) The buoyancy factor (BF) is given by SGsteel- SGfluid

BF=-----SGsteel

For the external system: 7.84 - 1.92

BF = = 0.755 7.84

and for the internal fluid system: 7.84 - 1.15

BF = 7.84 = 0.853

Chapter 3

Solution 3.1 Casing Design Example

SOLUTIONS TO EXAMPLES

The neutral point (NP) is thus the depth at which the string above is in tension and below in compression.

NP = 13000 x BF = 13000 x 0.755 = 9820 ft

This is rounded off to 9800 ft.

(b) For the design weight of casing (CWT) we have

CWT = weight in air x BR

where the buoyancy ratio BR is given by BF for outside mud system 0.755

BR = = -- = 0 885 BF for internal fluid system 0.853 .

(c) In the lower section we can check criteria:

(i) Collapse The external mud gradient is SG x 0.433 psi/ft

= 1.92 x 0.433 = 0.831 psi/ft

The collapse limit of the P-110 casing of the various weights is given from Table A3.1 as

9570 0.831 = 11520 ft for 20 ppf casing, and

11630 0.831 = 14000 ft for 23 ppf casing

:. Use 23 ppf casing from bottom to 11520 ft, that is (13000 - 11520) = 1480 ft (NB no tension problem since neutral point is at 9800 ft.)

(ii) Burst check

311

Since a more dense mud is used outside the casing then the greatest internal:external pressure difference is at the top of each section.

At 11 520 ft, internal differential is:

(max surface pressure) + (internal fluid head) - (external fluid head)

Internal pressure gradient = (SG x 0.433) = 1.15 x 0.433 = 0.498 psi/ft

:.8000 + 11520 [0.498 - 0.831] = 4164 psi

As burst pressure of 23 ppf casing is given as 11780 psi no problem arises.

(iii) Joint strength calculation check Since the entire section is below the neutral point, tension is not a problem so an API joint with long threads is sufficient.

(iv) Design weight for the section (CWT)

CWT = Design length x wt per foot x BR = 1480 x 23 x 0.885 = 301251bs.

(d) For the next section N-80, 23 ppf has the next highest collapse pressure to P-110, 20 ppf and can be set below the neutral point (see Table A3.1).

8370 (i) Collapse limit = 0.831 = 10072 ft

Rounding off, we can propose a section length of 11 520 - 10 070 = 1450 ft

(ii) Burst check

8000 + 10 070 [0.498 - 0.831] = 4647 psi no problem arises.


(iii) As we are below the neutral point no joint strength problem.

(iv) Design weight for this section

1450 x 20 x 0.855 =24 795lb

Total weight calculated so far = (30 125 + 24 795) = 54 920 lb.

(e) In the next section we might consider the use of P-ll 017 ppf but only a relatively short section could be used. It is considered more economical to design for N-80, 20 ppf.

6930 (i) Collapse limit = 0.831 = 8339 ft, round to 8340 ft

This is above the neutral point and therefore subject to the weight of casing above.

We calculate the ratio (R) for unit tensile stress to minimum yield strength using the ellipse of biaxial yield stress curve (Fig. A3.1) to obtain the percent offull collapse pressure that is appropriate. From Table A3.1 the plain end area (A) of 20 ppfN-80 is 5.828 in2 • For the minimum yield strength (Ym ) of 80000 psi we have:

weight in air of casing above neutral point R= Y .A

m

Assume casing above neutral point is 20 ppf 20 (9800 - D)

R = 80000 (5.828)

We have to choose D such that the reduction factor (FR ) correlated with R to obtain the effective collapse depth is consistent:

. 6930 J 20 (9800 - D)} I.e. 0.831 X FR = f(R) = f \80000 (5.828)

This is solved by trial and we might choose D to be 7900 ft 20 (9800 - 7900)

R = 80 000 (5.828) = 0.0815

From Fig. A3.1 the value of FR corresponding to 0.0815 is 0.956% 6930

Collapse limit is 0.956 x 0.831 = 7972 ft

We could converge a little better but might accept 7900 ft as a suitable depth, giving 2170 feet of casing required between 7900 and 10 070 ft.

(ii) Burst check for internal differential at 7900 ft

= 8000 + 7900 [0.498 - 0.831] = 5369 psi

This is within the tolerance of both 20 and 23 ppf N-80

(iii) Joint strength check Section design weight = (2170 x 20 x 885) = 38 409lb Total design weight = 38 409 + 54 920

= 93 329lb

We can see that the joint strengths of 20 and 23 ppfN-80 casing are both greater than the design weights (Table A3.1):

23 ppf : 251 000 lb 20 ppf: 214000 lb

(f) In abnormal pressure wells, a depth can be reached where either collapse or burst may control. A design trial for the next section is made using 17 ppf N -80.

5240 (i) Collapse check 0.831 = 6305 ft


g ~

go ~ -0 0; .;;'

E ~ ·c ·E

05

0.1

~ 0.05 o o ~ ;;

'" ·w i .'§ 0,02 'l; o c a:

0.85 0.90

Of full collapse pressure

We can converge on a reduced setting depth of 5430 feet. 20(9800 - 7900) + 17(7900 - 5430) ..

R = 4.962 (80 000) = 0.202, gIvmg FR = 0.884

and a collapse limit of 5573 ft which is in tolerance.

The possible length of this section is thus (7900 - 5430) = 2470 ft

(ii) Burst check

Internal differential at 5430 ft

= 8000 + (5430 [0.498 - 0.831]) = 6192 psi

The burst strength of 17 ppf N-80 is quoted in Table A3.1 as 6180 psi.

1.00

We must check the depth at which burst governs, i.e. the depth equivalent to a burst strength of 6180 psi. 8000 - 6180

Depth = 0.831 _ 0.498 = 5466 ft

313

The depth that 17 ppf N-80 will withstand the internal pressure differential is below its allowable collapse depth and this grade cannot be used in this part of the design. We must therefore consider using 20 ppf N-80 as we know that this is collapse designed down to 7900 ft. The burst strength for this is 7400 psi.

8000 -7400 Depth = 0.831 _ 0.498 = 1802 ft, round up to 1820 ft

This means that we could design a section of length (7900 - 1800) = 6080 ft

(iii) Joint strength check Design weight for section is (6080 x 20 x 0.885) = 107 616lb

Total weight is 107 616 + 93329 = 200 945lb

The joint strength for 20 ppf N-80 is given in Table A3.1 as 214000 lb. We have so far designed 11180 ft of the total well depth of 13000 ft. The remaining 1820 ft are considered using P-110, 17 ppf grade casing.


(g) (i) Collapse check 20(9800 - 1820) + 17(1820)

R = 11 000 (4.962) = 0.35

FR = 0.78 7000 (0.78)

Setting depth = 0.831 = 6570 ft

a proposed setting at 1820 ft is acceptable.

(ii) Burst check

Internal difference at top of string is 8000 psi (max) and Table A3.1 gives burst rating as 8500 psi, therefore design is acceptable.

(iii) Joint strength check Design weight of section added = 1820 x 17 x 0.885 = 27382lb

----------------------------------------Total string weight = 27 382 + 200 945 Joint strength of P-ll0 L = 247 OOOlb design is acceptable.

(h) We can summarize the design as follows:

Section

Surface -1820 1820-10 070

10 070 - 11 520 11 520 - 13 000

Length (ft)

1820 8250 1450 1480

Casing Grade

17 ppfP-ll0L 20 ppfN-80L 23 ppfN-80L 23 ppf P-11O L

It should be emphasized that this design is one of many combinations which may be acceptable and optimization in terms of economics is possible.

Solution 3.2 The average gradients give a pore pressure at 13 000 ft of

13 000 x 0.455 = 5915 psi

and a fracture pressure at 13 000 ft of

13 000 x 0.80 = 10 400 psi

The minimum setting depth is given by equating, above 13 000 feet, the gas and fracture gradients to a common pressure. If the distance above 13 000 ft is D' then

Pg = 5915 - (0.1 x D') Plr = 10 400 - (0.8 X D')

Setting Pg = Plr we have

10400 - 5915 D' = = 6407ft

0.8 - 0.1

Minimum setting depth is 13 000 - 6407 = 6593 ft.

TABLE A3.1 Casing data for example (Grade NSO-L/PllO-L 5.5 in. OD.)

Weight Wall thickness Collapse incl. Burst strength Joint strength Section (lblft) (in) safety factor into wk. press (incl. S.F.) lOOOlb area

(psi) (incl. S.F.) psi (in2)

17.0 PlIO 0.304 7000 8500 247 4.962 17.0 N80 0.304 5240 6180 174 4.962 20.0 PlIO 0.361 9570 10 180 274 5.828 20.0N80 0.361 6930 7400 214 5.828 23.0 PlIO 0.415 11 630 11 780 322 6.630 23.0N80 0.415 8370 8570 251 6.630

Minimum yield strength (Y m) = 80 000 psi for N-80 = 110 000 psifor P-ll0


141.5 API = SG - 131.5

SG API SG API

0.70 70.6 0.80 45.4 0.72 65.0 0.82 41.0 0.74 59.7 0.84 36.9 0.76 54.7 0.86 33.0 0.78 49.9 0.88 29.2

0.90 25.72

NB API gravity is non-linear, inverse scale. Water SG = 1.0; API = 10.

Yj MW YjMW

C1 0.90 16 14.4 ~ 0.05 30 1.5 C3 0.03 44 1.32 C4 0.02 58 1.16

(a) L = 18.38

MW 18.38 (b) Specific gravity = 28.97 =28.97 =0.634

Chapter 4

Solution 4.1

Solution 4.2

Pc YjPci

673 605.7 708 35.4 617 18.5 551 11.0

(c) L = 670.6

. _ m _ MP _ 18.38 x 14.7 _ -2 3

Gas denSIty - V - RT - 10.732 x 520 - 4.8 x 10 Ibft

(d) At 2000 psia and 595°R 595

Tpr = 371.5 = 1.60

2000 P pr = 670.6 = 2.98

(e)Fromgraphsz=0.825 (fig 4.7) . _ MP _ 18.38 x 2000 _ 3

(t) DenSIty - zRT - 0.825 x 10.732 x 595 - 6.9771bft

6.977

(~sBg ~a( ;,r( ~r~ ~ro~:: ~;'5~:it®6 ~ 6.9 x I~' vowvoL = 6.9 x 10-3 5.615 = 1.235 BBLIMSCF

(h) From graphs, Itl = 0.0116 (Fig. 4.8) and

Ratio ~ = 1.3 (Fig. 4.9) 1-11

Therefore 1-1 = 0.015 cp

315

Tc YjTcj

343 308.7 550 27.5 666 19.9 765 15.3

(c) L = 371.5


1 1 dz (i) Compressibility cg = PI - (~ ~P 1 dz )

= Ppc Ppr - -; dPpr

1 (Ppc 1 dz ) = Ppc p--; dPpr

from graph (Fig. 4.7) of z vs. reduced pro1erties, by graphical differentiation

1 (670.6 1 cg = 670.6 2000 - 0.825 X ( - 0.01)

= 5.2 X 10-4 psi-!

0) At 4100 ft SS aquifer pressure would be 0.44 x 4100 = 1804 psi

Since gas has a smaller density than water, it will lie above water. At gas-water contact, pressures are equal. From the given data clearly this gas-water contact will be below 4100 ft. Let this extra distance be x ft. Assume too that density of gas is a constant over the distances concerned, and that the reservoir temperature is 135°F, thus the density takes the value calculated in (f), 6.9771b ft3 (or gradient 0.0485 psi ft-!).

Pressure balance at gas-water contact:

(4100 + x) 0.44 = 2000 + 0.0485 x

:. x = 196/0.3915 = 500 ft

Therefore gas-water contact depth = 4600 ft SS

(k) From 0), gas-water contact is at 4600 ft SS, and pressure is 4600 x 0.44 = 2024 psi

Assuming the gas density remains constant for 1000 ft, pressure due to gas = 0.0485 x 1000 = 48.5 psi

Therefore pressure at crest of structure = 2024 - 48.5 = 1975.5 psi

Therefore pressure of mud at this point will be = 1975.5 + 500 = 2475.5 psi

Assuming the mud to be incompressible, let density of mud = p Ibslcu ft

Pressure exerted by mud at 3600 ft = 1~ x 3600 = 2475.5 psi

Therefore p = 99.0 Ibslcu ft

i.e. specific gravity of mud = 1.58

Cg = IIp = 1/1923 = 520 x 10-6 psi-!

(a) Total compressibility

= 10-6 [5 + 0.45(10) + 0.24(3) + 0.31(520)]

= 171.5 X 10-6 pS(1

Solution 4.3

(b) Effective hydrocarbon compressibility CT 171.5 x 10-6

Coe = = 225 X 10-6 psi-! 1 - Swi 0.76


Solution 4.4

(a) From graphs (Fig. 4.21, 4.22) or correlation equations for

API = 38°; GOR = 750; T = 175°F; and Yg = 0.7:

bubble point pressure = 2800 psia

formation volume factor = 1.4 RB/STB 141.5

specific gravity oftank oil = 131.5 + 38 = 0.834

(weight of oil and gas in SOlution}

(b) Density of reservoir oil = . volume of oIl reservoir conditions

317

"'" " 13"'+,'-+_f--+7--f:";C",~--t==j .. '''+--+-~''=f-=-b-!''''f'''=+--l

""'¥7""b-=t---t-I---1--t--l

,OOO"----'-----'----'-_L-.-'-----'----' Pp,:{ps;.) &00

I~ 1-"':::: ~ ~ ..."

'" "-~ 12 ::::::--300 -.::::: ::-:::: f::: 100 120 140 1SO t80 200 220 240

MOlECULAA WEIGHT

Fig. A4.1 Pseudo critical properties of hydrocarbon liquids

Weight of one barrel of water = 5.615 x 62.4 = 350.4 pounds (density of fresh water is 62.4lb/fe and 5.615 cu ft = 1 barrel).

From specific gravity of tank oil, weight of one barrel of oil is 350.4 x 0.834 = 292.2 lb.

Avogadro's law states that lIb-mole of any ideal gas occupies 379.4 cu ft at 60°F and 14.7 psia.

:. weight of gas which will dissolve in 1 STB of tank oil is given by the number of moles of gas times its molecular weight. The molecular weight of gas is the gas gravity x molecular weight of air :. weight of gas/STB = (R,I379.4) x 0.7 x 28.971bs = 0.05345 Rslbs.

Volume of 1 STB oil at reservoir conditions = Bo BBL [292.2] + [750 x 0.053445]

:. Density of reservoir condition oil = 1.400 lbs/BBL

density at reservoir conditions :. SG = 350.4 = 0.677

The reservoir oil gradient is therefore 0.677 x 0.433 psi/ft where 0.433 is the fresh water gradient :. oil gradient = 0.293 psi/ft.

For an oil-water contact of 7000 ft SS the hydrostatic pressure is 7000 x 0.465 = 3255 psi.

The bubble point pressure is the pressure of oil saturated with gas in equilibrium at the gas-oil contact :. pressure at top of oil column = 2800 psi.

8255 - 2800 For constant oil gradient, height of oil zone = 0.293 = 1550 ft

:. GOe = 7000 - 1550 = 5450 ft SS

For a molecular weight of 180 and 38° API oil the liquid critical temperature is 12200R and the liquid critical pressure is 310 psia

(460 + 175) 4000 Tpr = 1220 = 0.52 and P pr = 310 = 12.9

The reduced compressibility from charts (Fig. A4.1) is given at this Tpn P pr condition as CR = 0.002. 0.002

Since CR = Co· Pc then Co = 310 = 6 x 10-6 psia-I

From a constant oil compressibility between 2800 and 4000 psia

Bo = Bob (1 - Co!).P)

= 1.40 ( 1.0 - 6 X 10-6 (4000 - 2800))

= 1.389 RB/STB

From graphs, viscosity of dead oil at reservoir conditions = 1.4 cP

:. viscosity ofreservoir crude = 0.6 cPo

Solution 4.5

From graph of system pressure vs. system volume the bubble point is estimated by inflexion at 2500 psi.

Liquid volume at standard conditions = 29l;~)

At 3000 psi a liquid compressibility Co = - V \dP T

(404-410) _1_ -6 '-1

Co = (4000 _ 2500) . 408 = 9.8 X 10 pSI

408 B03000 psi a = 295 = 1.383 RB/STB

410 Bo2500 psia = 295 = 1.390 RB/STB

26.275 Rs = 295 (10-3) = 89.06 v/v = 89.06 (5.615) = 500 SCF/STB

At 2000 psia 388 430

Bo = 295 = 1.315 RB/STB ; Bt = 295 = 1.457 RB/STB 21

Rs = 295 X 10-3 X 5.615 = 400 SCF/STB

:. Bt = Bo + (Rsi - Rs) Bg . Bt - Bo (1.457 - 1.315)(295) -3

.. Bg = (Rsi _ Rs) = (26.275 _ 21.0)103 = 7.94 x 10 v/v

(Pl) (T2) (Vl) _ (2000) (520) -3_ Z = Tl . P2 . V2 . - 660 . 14.7 ·7.94 x 10 - 0.85

F: <p:

30 0.092

19.3 0.120

12.5 0.165

ChapterS

Solution 5.1

8.4 0.205

Plot either on log: log scales, or log F: log <p on coordinate scales.

6.0 0.268

4000

3500 ~ ::l

til 3000 ~ 0.

~ 2500 If)

'"' (f)

2000

1500!-:::-;;---'------::*o::-------'-~---"" 400

System volume

t LL

100

80

60

40

30

20

10

8

6

4

3

2

1

0.8

0.6

\

\,\ , , \\

o , ._, , , 0.

Slope' length Faxis -17.95

m = length </> axis = ~

Intercept at '" = 1

a = 0.774

= -1.53

, , , '0

\ , , 0,\

'0

'\ , , , , \ , , , , , ,

\

\ \ , , ,

--a

0.5 '-------'--'---'--L.L--'-l0=-'. OO:-:1-----'----'---'---'----'---L--L..11,J. 0

From plot m = - 1.53 a = 0.774

Fig.A5.1 Fvs. </>

Substitute back into laboratory data to calculate check values of F.

Check Calculate

</> F

0.092 29.8

0.120 19.8

0.165 12.2

If the true resistivity is 1.29 Qm and water resistivity is 0.056 Qm then Ro 1.29

F = Rw = 0.056 = 23.04

</>= 0.109 1

If I = ~ where exp n = 2 w

R/ = 11.84 Qm Ro = 1.29 Qm 11.84

then I = 1.29 = 9.18

[ 1]0.5 Sw = I = 0.330

If exp = 1.8 Sw = 0.292

Ifexp = 2.2 Sw = 0.365

0.205 8.7

0.268 5.80

319

320

(a)

Log values GR

Shale 102 Zone A 52

B 72 C 20

2.0

PETROLEUM ENGINEERING: PRINCIPLES AND PRACTICE

Solution 5.2

Data values

FDC SNP

2.52 29.0 2.22 22.5 2.37 20.5 2.20 21.0

Bul k density grams/cc

C1LD

1100 150 350

4650

Correction r-------T------

-0.5 0 +0.5

2.5 3.0

R1Ld

0.91 6.67 2.86 0.215

Fig.A5.2.1

Calculated values

V SHGB VSHDas: CPDIN

1.00 1.00 0.39 0.00 0.26 0.63 0.31 0.14 0.00 0.00 0.25

Porosity %

Sidewall

Gamma ray 20 API units 120 Depth

Resistivity Ohms mlm

Conductivity Millimhos 1m

10 divisions

Radiation intensity increases ~

Oil bose mud Temp =226

A

B

C

lS"normol o o

Induction conductivity 40" spacing

4000 o o Induction resistivity 8000

0 ____ 1C;i:.s.E!!.~'!L __ 19 4000

0 _____________ 1<2.0

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

"

Fig. AS.2.2 '--__ ---"'"--'

, , , . . I

Fig. AS.2.3 Density/SNP crossplot.

2.0

2.2

2.8

Matrix point

Pr=1.0g/cc

Shale

~~

~"i ~.,.~.,

() '" 3q';;10=---L--;0~~L-~:;----L----;:!;=----1.-~:-----'--~_...J

Sidewall neutron apparent limestone porosity (%)

321

(b) For zone C, point plots close to clean sandstone line with cJ> = 0.25. Assuming C to be water bearing Ro = FRw = 1/cJ>2 . {Rw} Rw = cJ>2Ro = 0.262 X 0.215 = 0.0145 (taking R1Ld as Ro)

(c) Shale values are listed above.

(d) GRclean = 20, GRshale = 102 GR - GRclean

VshGR = --------GRshale - GRclean

GR-20

82

VshGR values calculated are tabulated above.

(e) See Fig. A5.2.3 for shale point. Only level B shows a significant displacement from clean line. Graphically Vsh for zone B = XB/XS = 1.25/4 = 0.31.

(f) Taking the minimum shale indication (from DIN) gives only B as shaly. Presumably there are radioactive minerals in the sands (such as feldspar) so the GR overestimates shale content.

As above graphically for level B, Vsh = 0.31. The porosity is given by point Yon the clean sandstone line where BY is parallel to the matrix shale line, i.e. cJ> = 0.14. The graphical construction is complicated by the curve on the sandstone line. More rigorously convert density and neutron values to sandstone matrix cJ>D = 16.5, cJ>N = 24.2. cJ>NSH = 32, cJ>DSH = 7.5, cJ> = cJ>N - VSH cJ>NSH, cJ> = cJ>D - VSH cJ>DSH

Solving the equations for unknown VSH cJ>N - cJ>D 24.2 - 16.5

VSH = = = 0.31 cJ>NSH - cJ>DSH 32 - 7.5

cJ> = cJ>N - VSHcJ>NSH = 24.2 - 0.31 x 7.5 = 0.14

(g) Saturation calculations

LevIe! Ala~ eq)uatiO:S reduce t~ I(r~~: ()VSH ~ ~) / Rw 1 '\ /0.0145

:·Rr = FRw ·Sw :.Sw= V R; =~VR;= 0.26 V 6.67 =0.18

Level B with n = 2, Rw = 0.0145, Rt = 2.86, RSH = 0.91, VSH = 0.31, </> = 0.14.

Archie

~, ~ (F~w) . Sw' :. 0.35 ~ 1.352 S.' :. Sw = 0.51

r~"O:~)· S.' + (~::) :. 035 ~ I.352S.' + 0341

:. Sw = 0.082

~o~ifi(e~ Si)mandzoux(VSH ) . _ z R - FR . Sw + R . Sw .. 0.35 - 1.352 Sw + 0. 341Sw

t w SH . . Solvmg quadratIc + ve root only

:. Sw = 0.376


Poupon and Leveaux (Indonesia) 1 1 VSH(1-VsH/2)

'I!Rr = YFRw Sw + VRsH . Sw

:. 0.592 = 1.163 Sw + 390 Sw

:. Sw =0.38

where 1 1 1 -=- =0.350;~=0.592 Rt 2.86 VRt V (1-VsHI2)

V SH = 0.341 ; VSH(l - VSH/2) = 0.372; s~ = 0.390 RSH SH

1 ~2 1 FRw = Rw = 1.352 ; YFRw= 1.163

Thus the modified Simandoux and Indonesia equations give similar Sw's which are less than the Archie Sw. The shale conductance in the basic Simandoux is already near to the measured conductance so the solution gives an unlikely optimistic value for a shaly sand.

Solution 5.3

Waxman and Thomas equation with a = 1, m = 2, n = 2

~ =~ 2+BQv Sw R FR Sw F

t w

= - - Sw + BQvSw 1 { 1 2 ) F Rw

BQv = 0.046 x 0.3 mho.cm2.meq-!.meq/cc

= 0.0138 mho cm-! or ohm-! cm-!

= 100 x 0.0138 = 1.38 ohm-) m- l

1 1 :. R

t = F (10 Sw2 + 1.38 Sw)

F = 1I~2 = 1/0.262 = 14.79 Rt = 5

:. 0.2 = 0.0676 (10 S} + 1.38 Sw)

= 0.676 S} + 0.0933 Sw

:.0.676 Sw2 + 0.0933 Sw - 0.2 = 0

Solving the quadratic _ (-0.0933 ± \1[0.09332 - 4.676 . ( -0.2) 1) = 0.4

Sw - 2(0.676)

'\ 1FRw (see Archie solution, Sw = V Ii; = 0.544)

Modified Simandoux model

~_~ 2 VSH

Rt FRw Sw + RSH . Sw

Comparing with the Waxman Thomas equation

323

324

BQv VSH BQv p= RSH :. VSH=RsHp

1.5 X 1.38 VSH = 14.79 = 0.140


i.e. it would take 14% shale with resistivity 1.5 ohm-m to get the same result as the Waxman Thomas equation

.. ! _~ 2 VSH.. _ 0.0676 2 0.14 BaslcSlmandoux Rt - FRw Sw + RSH , .. 0.2 - 0.1 Sw + 1.5

0.2 = 0.676 Sw2 + 0.0933

1 1[0.2 - 0.0933] Sw = V 0.676 = 0.397

(a) Prove

From Darcy's law: -kA JP

q=---!.t Jx

Assuming Boyle's law:

QscPo = qP and Po = 1 atm.

Hence: -kA JP

Q =-P-sc !.t Jx

kA p/- P12

orQsc =-; 2L

Qsc!.t2 L (b) k = A(P12 - p/)

6.2 x 2 x 0.018 x 2.54

XX 127' «(~:r -1)

=0.2D

Solution 5.4

3000ff

1000 ft:-I ______ ----'

1501~

~-5750

Solution 5.5 The problem requires correction of pressure so that the linear Darcy law can be used. In field units:

kAAP q = 1.127 X lO-3 -; L BBLId

Assuming average water gradient of 0.45 psi/ft (0.433 x 1.038) and referring to a HWC datum of 5250 ft SS, static pressure at the outcrop is:

PS2so = 0.45 x 5250 = 2362.5 psi

But pressure = 1450 psi at 5250 3 750 x 3000 x 65 (2362.5 - 1450)

Hence, q = 1.127 x lO- x 1 x 52 800

q = 2848.5 BBLId

--\ _------- j Poutcrop

--------------------P HWC .::::/// -/ f P outcrop at HWC datum

..... "";------10 miles ----"


Solution 5.6 Using the equation:

Qsc 2 ilL k = A(PI2 - pl)

(6.4/60) x 2 x 0.018 x 2.54

2 (861)2 2 3t 1.27 (760 - 1 )

Sc for rate 1 = 0.0068 D = 6.8 mD

Scfor rate 2 = 6.02mD

Scforrate 3 =5.0mD

This is because of the Klinkenberg effect.

Plotting k against 11 P mean gives k L as 11 P mean ~ 0 as 3 mD.

Assume cross-sectional area A. dh

Solution 5.7

q = -A dt where q is flow rate and h is current height measured from bottom of core plug.

Flow across core is: -kA I1P

q=--Il L

But I1P = datum correction pressure difference, so: -kA pgh dh

q=--=-A-Il L dt

JL dh kPg'Jt so- -=- dt

h ilL ho 0

ho kpg' or log., It = L t ho ho

Il (lOg - - log -J so k = IlL ~[log (holh)] = ilL e h2 e hI

pg' ~t pg' I1 t

Note: pg' has to be in units such that pg' h = atm. 1 x 2 X 106 loge84 -loge 15.5

Hence k = 1.02 x 981 x 4500

=0.8D

Note: a plot of log.,h against t would be best.

50 Poil = 50 lb/fe = .144 psi/ft = 0.3472 psi/ft

Solution 5.8

(a) Correct well pressures to 5750 ft = 1750 + 0.3472 x 750

= 2010.4 psi

(b) Flowing gradient kA I1P

q = -;-L 1.127 X 10-3

I1P = qllL 1000 x 1.135 x 7 x 3000 1.127 X 10-3 x k x A = 1.127 X 10-3 x 150 x 150 x 1000

= 94 psi

325

So, Powc = 2010.4 + 94 = 2104.4 psi

PV res = 3000 X 1000 X 150 X cp

Equating production Vp = VTc· llP, then 3000 X 1000 X 150 x 

PVaquifer = (2104.4 _ 500) 3 X 10-6 = 93.5 X 109 x ft3

Solution 5.9 Q k dP

Darcy's equation A = - -; dx for non-compressible flow

(a) Linear beds - parallel flow

Q = qi + q2 + q3

Assume infinitely thin barriers between layers llP llP

Q

Q=qI+q2+" .=kIAIf..tL +k2A 2 f..tL + ...

llP =k'A-

f..tL

where k' is the apparent permeability and A the total area.

Hencek'A = kiAI + k2A2 + ... n

Lk;A; Therefore k' = ~

LA; I

Lkh· or if beds all same width = f (b) Series flow

P,

q, ---fIto-\

q2--~-\ r------~------~ k, --... Q

Assume equal areas

Al =A2 =. - . P, P2 P2 P3 P3 p.

q, = qi = q2 = q3 - ..

Now PI - P4 = (PI - P2) + (P2 - P3) + (P3 - P4) ..•

Using Darcy's law

L f..t LI f..t L2 f..t qtAk' = qi Aki + q2 A ki + ...

o D B B -\LJ~U-U

L, L2

Since flow rates, cross-sections and viscosities are equal in all beds

(c) Radial flow parallel

From the figure, it is noted that the same terms appear in the radial flow network as in the linear system. 2Jtkh (Pe - P w)

Q= f..tln(re/rwJ

e - external boundary w - internal boundary

SOLUTIONS TO EXAMPLES 327

-1

hi qi k,

-h2 q2 k2 ht

j -h3 q3 k3

The only difference in the two systems is the manner of expressing the length over which the pressure drop occurs. All these terms are the same in each case.

"[k·h· Therefore k' = --' -'

hI

(d) Radial flow series

By same reasoning as in the linear case

k' = _In_(.o...r::....,/r...::w~) -'t In (r/rj_l)

j=1 kj

Bed

1 2 3 4

Depth/ Length of bed

250 250 500

1000

Horizontal permeability; mD

25 50

100 200

For radial systems, wellbore = 6", and radius of effective drainage 2000' and bed 1 is adjacent to wellbore.

Linear flow - parallel, and radial flow - parallel, take data lengths as bed depths and bed lengths and radii to be equal.

Linear flow in parallel

k' = 250 x 25 + 250 x 50 + 500 x 100 + 1000 x 200 = 134.4 mD 2000

Radial flow in parallel "[kh

k'=T 250 x 25 + 250 x 50 + 500 x 100 + 1000 x 200

k' = 2000

268750 k' = 2000 = 134.4 mD


Linear flow in series 2000

k' = 250 250 500 1000 2s +50 +100+ 200

Radial flow in series

2000 -=80mD

25

In (200010.5) k'=--------------~----~-------------

In 25010.5 + In 500/250 + In 10001500 + In 200011000

25 50 100 200

= 30.4mD

i.e. permeability near wellbore most important.

Chapter 6

Solution 6.1

Pc 0 4.4 5.3 5.6 Sw 100 100 90.1 82.4 h 0 33.3 40.2 42.4

(h = Pc )

(Pw - Po)/144

- Crest 200 -

----

150 r---

7.6 60.0 57.5

.e

a; > ~

l-

I-

I-

\\-+-\-----samPle location Sw = 0.31

o ... ~ c ~ CI)

~ CI) > 0

.Q c 1: c>

'CD :I:

I-

100 I-

----

50-~

\0 ~o

"-----0 OWC at 33 ft relative

10.5 43.7 79.6

-0 ~o I J I I I I I I J

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Sw (fraction)---

Fig. A6.1 Saturation distribution.

15.7 35.0 32.2 29.8

119.0 265.3


Note that the oil-water contact is at Sw = 1.0, not at Pc =0. At 100 ft above owe, Sw = 0.31 (135 ft relative)

- ISw dh S =--

w h From area under Sw against h curve:

Sw = 0.37

Solution 6.2

Sw 100 100 90.1 82.4 (Pc)O-w 0 4.4 5.3 5.6 (PdH 0 65.1 78.4 82.9

g

f(J)=PcYf 0 1534.4 1847.9 1954.0

(PC)Hg 0 110.7 133.3 140.9

for25mD and 0 = 0.13

Solution 6.3

329

60.0 43.7 32.2 29.8 7.6 10.5 15.7 35.0

112.5 155.4 232.4 518.0

2651.7 3662.8 5477.7 12209.0

191.2 264.1 395.0 880.4

For the laboratory data YkTcj>c = (150/0.22) 0.5 = 26.11 and using ](Sw) = PC(Sw~ Vi with CJ cos e = 72 dyne/cm the ](sw) vs Sw relationship is calculated. CJ cos cj>

] (Sw) = 0.363 Pc (Sw)Jab

1.0 o

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.2 0.363 1.451 2.176 2.901 3.445 4.862 4.968 5.984 8.341 36.27

At reservoir conditions PC(Sw)", =

for CJ cos e = 26 and v'kTcj> = 44.72

](sw> CJ cos e v'kicj>

Pc (Sw)", = 0.581] (Sw) and the reservoir condition Pc curve is therefore calculated as

1.0 o

1.0 0.9 0.8 0.7 0.6 0.211 0.843 1.264 1.685 2.00

For the reservoir specific gravity of oil and water given

Ap = (1.026-0.785) = 0.241

0.5 0.4 0.3 0.2 0.2 2.823 2.886 3.451 4.846 21.07

The relationship between capillary pressure and height H above FWL is, in the units required, pc(sw) = 0.433 HAp :. H= Pc(sw)

0.104

Using the threshold value of pc(sw) (= P ct) as the observed oil water contact, then

0.211 Howe = -- = 2 ft above the FWL

0.104 4.85

HTIZ = 0-- = 46.5 ft above the FWL .104


Chapter 7

Solution 7.1

From Darcy's law modified for effective permeability in horizontal linear flow

qo!-loL qw!-lw L Ko (s) = A I1P and Kw (s) = A I1P

o w

Assuming zero capillary pressure (Pc = 0 = Po - P w) so I1Po = I1P w = I1P, and using Darcy units of eels for rate and atmospheres for I1P, then:

q!-l [(4) (9) (1000)] Ke (md) = I1P n: (3.2)2 3600

For oil Ko = ~P (9.14) qw

For water Kw = I1P (5.0) Ko Kw

For Kro= ~and Krw = ~ O(cw) o (cw)

90 Ko(cw) = 49.25 (9.14) = 16.7 md

15.0 19.8 25.1 32.1 41.0 54.9 68.1

1.0 0.452 0.30 0.20 0.12 0.05 o

These data are plotted in Fig. A 7.1

t

1.0

0.9

0.8

0.7

0.6

~cpl.x:g 0.5

II OA ~

0.3

0.2

0.1

o 0.017 0.025 0.049 0.075 0.156 0.249

0

0

:::::---'--=,-:--'--::,-~'o I I 0.8 10

sw-

Fig. A7.1 Steady-state relative permeability.

For pressure maintenance, the oil rate in RB/D is

10 000 x 1.2765 = 12765 RB/D

The end points of the relative permeability curve are

K ro' = 0.9 at Swi = 0.28 Krw' = 0.7 at Sor = 0.35

Solution 7.2

The ratio Ilw is then calculated from the given end point mobility ratio of 2.778. flo krw' flo flw krw' 0.7

Since M' = flw • kro' , then flo = M' kro' = 2.778 (0.9) = 0.28

The fractional flow curve can now be calculated for the horizontal reservoir: 1

fw = f k } 1 + 0.28 l k::

0.28

o 0.30

0.082

0.35

0.295

0.45

0.708

0.55

0.931

0.60

0.984

0.65

1.00

331

A line tangential to the fractional flow curve from Sw = 0.28 gives the tangent at Swf = 0.4 (fw = 0.535) and the intercept withfw = 1 at Sw = 0.505. The gradient of this tangent[dfwfdSwlswis 4.44.

From Buckley-Leverett theory the constant rate frontal advance of the 40% saturation front is:

q(t) (5.615) [df ] Xflday = (A)(<I» dSw swf

(12765) (5.615) (4.44) Xflday = (5280) (50) (0.25) = 4.82 ftlday

For a system le~gth of 5280 ft, breakthrough therefore occurs in 1095 days (= 3 years) At year 4 the pore volume injected is

_ _ 4-,-(3_65...:.)-,-(1_2_7_65.:....) ..:.-(5_.6_15..;...)_ =0.3PV

(5280) (50) (5280) (0.25)

and dflds] = _1_ = 3.33 Swe 0.3

The tangent of gradient 3.33 to the fractional flow curve at saturations greater than frontal occurs at Swe = 0.45 dfw

(from a plot of dS vs Sw)· w

At this saturation (Swe),fwe = 0.71, the reservoir condition water cut.

The average saturation remaining in the reservoir is given by the Welge equation as:

- foe Sw = Swe + [dfwfdSwlswe

_ (1-0.71)_ Sw = 0.45 + 3.33 :. Sw = 0.537

The reco~ry factor is thus: S -S .

RF = W WI = 0.36 1- Swi

Solution 7.3 The critical injection rate for gas is given in field units of SCF/D as:

4.9 x 10-4 k k r/ A (Yg - Yo) sin a: q SCFID = Ilg Bg (M - 1)

where Bg is in units of RBISCF and a: is negative for updip injection.

The density difference in terms of specific gravity is: 17 -48

Ay = 62A = -0.4968

0.5 (1.8) M' = 0.028 (0.9) = 35.71

sin (-10°) = -0.1736 4.9 x 10-4 (800) (0.5) (8000) (100) (-0.4968) (-0.1736)

:. qcrit = (0.028) (35.71 - 1) (7.5 x 10-4)

= 18.589 MMSCF/D

The rate of injection proposed (15 MMSCFID) is less than the critical rate and might almost lead to a stable displacement.

The oil rate expected prior to breakthrough is therefore: 15 x 106 x 7.5 X 10-4

Qo = 1.125 = 10 MSTB/D

Solution 7.4 1.0

I

O 8 \ Distribution after 0.5 yrs . :--1:." I

t .. ~ 0.6 \ I

i ./ Calculated frontal iY position

0.4

0.2

Fig. A7.2 Saturation distributions

i i i i j

Initio I I distribution ---.l....-_!.-

From the given data the saturation is plotted as shown in Fig. A 7.2

ql = 9434 rbld Dip = 6° 110 = 1.51 cp h = 100' k = 276 mD Ilw = 0.83 cp w = 8000' = 0.215 Ay = 0.04 A= 800 000 ft2

The fractional ~ow curv(e is calculated as fO~I~:~ [ ]1 fw = 1 + 1.127 X 10-3 qt 110 - 0.4335 Ay sina: Ilw kro

1+-·-krw 110

The results are shown in Fig. A 7.3

1.0 / ..... 0.9

0.8 I 0.7

• t 0.6

/ 0.5 ~ - 0.4

• 0.3 / 0.2

0.1 /. 0 • ...,.. I I I I I

0.2 0.4 0.6 0.8 1.0 Sw

Therefore: Fig. A7.3 Fractional flow curve.

Sw 0.16 0.25 0.35 0.45 0.55 0.65

fw 0 0.036 0.127 0.344 0.64 0.88

Since there is no uniform saturation distribution initially a material balance solution is used:

5.615 q, At [Afw 1 [Llfw 1 (LlX)s"'j = A LlS = 0.308 At LlS for At in days <P w S"'j w S"'j

Sw

2.5

2.0 t 1.5 ;-', ~

-(/)

1.0 -0 ~

0.5

1.0

Fig. A7.4 Slopes of fractional flow curve.

0.75 0.79

0.98 1.0

The slope of the fractional flow curve as a function of saturation is plotted in Fig. A 7.4. Selecting saturations

ForSw = 0.79 ForSw = 0.75 ForSw = 0.7

t(yrs) X t (yrs) X t(yrs) X

o 10ft o 12 ft o 15 ft 0.5 10 + 23.5 = 33.5 0.5 12 + 36.5 = 48.5 0.5 15 + 56.2 = 71.2 1.0 10 + 47 = 57 1.0 12 + 73.0 = 85 1.0 15 + 112.4 = 127.4 2.0 10 + 94 = 104 2.0 12 + 146 = 158 2.0 15 + 225 = 240

333

At 0.5 years the saturation distribution is shown on Fig. A7.2 and is represented in 10' increments.

( 5.615 qt Llt )

Note: <j>A = 56.22

Llx LLlx Swi Sw (0.5 yr) Llx (Sw - SWi) LLlX (Sw - SWi)

10 10 0.79 0.79 0 0 10 20 0.70 0.79 0.9 0.9 10 30 0.56 0.79 2.3 3.2 10 40 0.45 0.78 3.3 6.5 10 50 0.375 0.755 3.8 10.3 10 60 0.33 0.730 4.0 14.3 10 70 0.30 0.710 4.10 18.4 10 80 0.278 0.690 4.12 22.52 10 90 0.254 0.675 4.21 26.72 10 100 0.24 0.650 4.10 30.83 10 110 0.23 0.640 4.10 34.93 10 120 0.215 0.630 4.15 39.08 10 130 0.205 0.620 4.15 43.23 10 140 0.20 0.613 4.13 47.36 10 150 0.195 0.605 4.10 51.46 10 160 0.190 0.600 4.10 55.56 10 170 0.183 0.595 4.12 59.68

Interpolation { 56.22 - 55.56) :. Xf = 160 + 10 59.68 _ 55.56 = 161.6 ft from owe

From Fig. A 7.2, at Xf = 161.6 ft, Swf = 0.60

Solution 7.5

For the particular example the problem reduces to the following tabulation, numbering layers n, from n = 0 to n = N = 5, bottom to top. n 5

- _ 0.7n + 0.15 (5 - n) . - _ 0.5 f. kj . - _ 'hf'j Swn - 5 ,Krwn - ___ , K ron - 0.9_

5 5

~ kj ~ k j

5 where: L kj = 50 + 500 + 1500 + 2000 + 500 = 4550 mD.

1

n N

f. kj Lk· n+l 1

N 5 5

n L kj Lkj krwn kron n L kj Lk· SWn

1 n+l 1 1 1

0 0 4550 0 1.000 0 0.900 0.15 1 50 4550 0.0110 0.989 0.0055 0.8901 0.26 2 550 4000 0.1209 0.879 0.0605 0.7911 0.37 3 2050 2500 0.4505 0.5494 0.2253 0.4940 0.48 4 4050 500 0.8901 0.1099 0.4451 0.0989 0.59 5 4550 0 1.00 0 0.50 0 0.70

The resultant pseudo-relative permeability is plotted as Sw vs j(rw and j(ro n n n

ChapterS

Solution 8.1

Using the relationship h + 139 = 164/sinh x the saturation vs height relation is calculated as follows:

X (frac) sinh x h (ft)

0.33 0.3360

349

0.40 0.4108 260.2

0.50 0.5211

175

0.60 0.6367

118

0.70 0.7586

77

0.80 0.8881

45

0.90 1.0265 20.8

335

1.0 1.1752 0.55

Fig. A 8.1 shows the plot of water saturation and porosity as a function of depth. Fig. A. 8.2 shows the plot of isopach value vs area contained within the contour. In the absence of a phinimeter to measure area use metric graph paper in a simplified approach. Take 50 ft intervals from base to crest. Count squares to determine volume for each interval. Assign appropriate value of 0

.J:l C -.s:: 80 CI

·CP ::I:

40

0

Water saturation (Sw) ~

Fig. AS.1 Sw and vs. depth.


Area within contour (acres)

Interval No. of squares Gross rock volume Saturation (lffacreft) (Sw)

0- 50 46 115.00 0.875 50-100 35 87.50 0.70

100-150 26.7 66.75 0.57 150-200 21.5 53.75 0.49 200-250 17.0 42.50 0.43 250-300 11.3 28.25 0.39 300-350 3.0 7.50 0.36

L =401.250

Hydrocarbon in place = 230326250 BBLs reservoir oil = 170 x 106 BBLs stock tank/oil

Solution 8.2 The oil in place at stock tank conditions is evaluated using the relationship

7758Ahcjl So N=--~--=-

Hoi

where N is in STB A is in acres h is in feet cjlSo is a fraction Hoi is in RBISTB

Porosity Hydrocarbon (~) (volume x UP

HHLs)

0.160 16.73 0.178 36.25 0.197 43.87 0.215 45.72 0.234 43.98 0.252 33.69 0.271 10.09

L =230.326

The recoverable reserve is N.(RF) where RFis the recovery factor (fraction). Deterministically, the minimum, 'most likely', and maximum values are calculated as:

minimum 43 x 106 STB 'most likely' 116 x 106 STB maximum 274 x 106 STB


The distribution functions of the reservoir parameters are shown in Fig. A 8.3. These data are interrogated randomly using a Monte Carlo approach in the recoverable reserve calculation. The resulting cumulative frequency greater than a given value plot is shown in Fig. A 8.4. The values associated with the 90%, 50% and 10% levels are as follows:

at 90% the recoverable reserve is at least 72 x 106 STB at 50% the recoverable reserve is at least 120 x 106 STB at 10% the recoverable reserve is at least 185 x 106 STB

100i hne! .-

t ~ ~ a.

I-'l

0

100 \ • cf>So

t ~

100

•

100

t ~ \ ~

a. 50 0\ 0: 50 I-'l I-'l

• \ 0

100 100

~BO ~ t ~ ~

50 50 a.

o~~ I-'l

• 0 0

, Area

o~ •

~ .,

0\ RF

•

~o

\0 cf>

\ •

Fig. A8.3 Distribution functions.

100 -0 .l!! c 90 0 'ii .E c:

80 c ~ ..... ., C 70 ~ c>

.!!! ., 60 => ~ C 50 ~

E: £i

40 c ..c 0 a. .,

30 c> c C ., e

20 ., a. ., .~ C 10 :; E => u

20 106 STS----

Fig. A8.4 Recoverable reserves distribution.

K t

to = <PJUr

with (a) to = 1481 (b) to = 14815 (c) to = 7.4 X 10-3

p;-p= 4:~h [-+ ~:':) 1 <PJUr

For (a) x = 4Kt

= 4.2 x 10-3

as x is small

- E;(-x) = - 0.5772 -Jogex

= 4.895

Hence AP = 22.72 atmospheres

Chapter 9

Solution 9.1

Solution 9.2

For (b) x = 0.4375 From graph - E; (-x) = 0.62

Hence AP = 2.875 atmospheres

For (c) x = 0.49 From graph - E; (-x) = 0.55

Hence AP = 64 atmospheres

260


From the plot shown in Fig. A 9.1, of P wi vs 10glOt

m = 18 psi/cycle 162.6 (500) (0.5) (1.7535)

ThenKh = 18

= 3960 mD ft 3960

KO=60=66mD

4940

4930

t

4920

Solution 9.3

m = 18 psi /cycle

•

~ ." .~

Fig. A9.1 PwtVS 1091Ot.

Solution 9.4

•

f HAt) From a graph of P vs llog ---;;;:r with the points in the table calculated, the slope is determined as 21. 7 psi/cycle ( = m).

For a reservoir rate q of 500 (1.454) rb/d (= 727 rb/d) 162.6q(..t

Then, kh = = 3800 mD.ft m

For h = 120 ft then Ko = 32 mD.

The value of P{h' corresponding to a Homer time function of 3.16 is 4981 psi 4981 - 4728 32 )

S = 1.151 21. 7 10glO (0.135)(0.7)(17 X 10-6)(0.5)2 + 3.23

= +7

339


!!.Ps = 0.87 m S = 132 psi 4981 - 4728 - 132

Efficiency = 4981 - 4728 = 0.5 (approx.) t+!!.t [t+!!.t]

Data points for Horner plot on semi-log paper, P vs At or a plot of p vs log At on linear scales are as follows:

t = 60 x 24 = 1440 hours

Time (h) t+!!.t logJO P (psi)

!!.t {(t+ !!.t)/ !!.t}

0.25 5761 3.76 4967 0.5 2881 3.46 4974 1.0 1441 3.16 4981 1.5 961 2.98 4984 2.0 721 2.88 4987 3.0 481 2.68 4991 6.0 241 2.38 4998 9.0 161 2.21 5002

18.0 81 1.91 5008 36.0 41 1.61 5014 48.0 31 1.49 5017

Solution 9.5 Examination of the data shows that: !!.P/day = 3 psi

Assuming 1 - Sw = 0.7

We have NBoi = NpBo/(co).!!.P

and (co)e = 15 x 10-6/0.7 = 21.4 x 10-6

and Np = 500 bId. For Bo = Boi then 500 6

N = 21.4 X 10-6 x 3 = 7.8 x 10 BBL

Solution 9.6

Rate

1 2 3 4

Q (MSCFID)

7290 16737 25724 35522

(!!.p2) total

42181 126120 237 162 391616

Assume tflow prior to build up is 4.5 hours:

Time since shut in

1 1.5 2 2.5 3 4 5 6

0.7404 0.6201 0.5119 0.4472 0.3979 0.3274 0.2788 0.2430

P

2509.7 2510.7 2511.3 2511.7 2512.1 2512.5 2513.0 2513.2

Slope = 7 psi/cycle from Homer plot 162.6 (q Bg) IA.

HenceKh = m

0.00504zT Bg = P BBLlscf = 0.00103·

Kh = 14 500 K= 72mD

2 2_14241A.zTQ { ) NowPe -Pw - Kh InO.606re/rw +Sl

Rate 1 2 3 4

= 0.855 Q {8.93 + Sl}

Pe2 - Pw2

Or Sl = 0.855 Q - 8.93

-2.16 -0.12 +1.85 +3.96

Q 7290

35522

D = AS/AQ = 2.16 x 10.4

S = -3.7

f3 = DhWw = 2.865 x 109 2.22510 15 KYg

48211 f3theoretical = <1>5.5 v'K = 1.80 X 109

This is order of magnitude agreement.

The inertial pressure term Ap2inertial is calculated from B as follows: 3.16 x1O-1ZygTzf3

B= 2 h rw

= 0.000185

Hence (Ap2)inertial is as follows:

Rate

1 2 3 4

Q(MSCFID)

7290 16737 25724 35522

9851 51928

122665 233906

42181 126120 237162 391616

Comparison between the numbers shows that at high rates the inertial drop is over half the total drop, and that in this case only the inertial drop is close to the total drop of the previous rate. The AOF plot is shown in Fig. A 9.2 and when Ap2 is equal to Pe2 (6.32X106psi2) then QAOF = 220 X 106 SCFld

'" o

AOF= 220mm SCF/D C B -----------------e--------------------------------------------.

i I I I I I I I I I I I

n = 0.65 [= distance AB] ! distance Be I

I I I I I I I I I I I I tA

107~--~L--L~~~~~~---L--~-L-L~~~----~~--L-~~LU ~ 1~ ~ ~

Fig. A9.2 AOF determination.

341


Chapter 10

Solution 10.1

Volume ofreservoir = V = 100 x (5280? x 500 cu.ft

Volume ofreservoir available for fluid = (1 - Sw) cj>V = Vr = 0.65 x 0.12 x V

_ 2000 l520 _ 12 Vsc - 14.7 0.825595 - 15.6 x 10 SCF

(1) Assume no water influx,

Pi Vr (PVi) Initial moles in place ni = . RT = RT Z, r SId

Vi - gas in place measured at standard conditions.

Pa Vr (PVa) Abandonment moles left in place na = --n= RT Za r SId

Vr (Pi Pj Ps Gas recovered !1n = - - - - = - !1 V RTr Zi Za RTs

Recoverable gas measured at stan dar conditions

Vr Ts (Pi Pa) =-- ---TrPs Zi Za

500 At 500 psi, reduced pressure Ppr = 671.6 = 0.75

Vr TsPi Z, Pa) Therefore recoverable gas = -T P 1 - - -P

r s Zl Za I

_ X 12( 0.825 500) - 15.6 10 1 - 0.94 ·2000

= 15.6 X 1012 (1 - 0.219)

= 12.2 X 1012 SCF 12.2

Recovery factor = 15.6 = 78%

Z = 0.94

Solution 10.2 2nkoh

Radial flow of oil q 0 = --Bflo 0

2nk h !1Pg Radial flow of gas qg = =..:::£.::B -~'--

flg g re log -

e rw

and if the capillary pressure gradient is negligible, and the pressure drop over the same radii are considered,

~ _ kgfloBo

qo - ko flgBg

To this must be added the gas evolved from solution in the oil. The total measured gas-oil ratio will then be:

kg flo Bo + Rs

ko flg Bg

For the figures given:

(96)(0.8)(1.363)

(1000)(0.018)(0.001162) + 500

= 5005 + 500

= 5505 SCF/STB

We = Np B, + Bg(Rp - Rsi) - N(B, - Bo;)

(i) At cumulative 1.715 x 106 BBL (P = 1600)

Solution 10.3

Wei = (1.715 X 106) [1.437 + 0.0015(878 - 690)] - 14.5 X 106[1.437 - l.363]

= 1.875 X 106

(ii) At cumulative 3.43 X 106 BBL (P = 1300)

We2 = (3.43 X 106) [1.594 + 0.0019(996 -690)] - 14.5 [1.594 - l.363]

= 4.112 x 106

At P = 1000 estimated water influx = 6.375 x 106 (from trend) N(B, - Boi) + We

Np= B, + Bg(Rp - Rsi)

14.5(1. 748 - l.363) x 106 + 6 375 000

1.748 + 0.0025(1100- 690)

= 4.312 X 106 BBL

Total hydrocarbon in place = i:n: ,-2h<j> (1 - Sw)

Solution 10.4

9 750 x 0.17 x 0.76 = :n: 3 (528W 5.615 = 4.54 x 109 BBL

Since bubble-point is 1850 psi, this must be pressure at any gas-oil contact.

Elevation of gas-oil contact above oil-water contact is:

(1919 - 1850) 144 43.4 = 229 ft

This is less than hydrocarbon column so gas-oil contact exists at 4031 ft SS

Height of gas zone = 750 - 229 = 521 ft

r2h2 h3 (520)3 Ratio gas/total = ~h: = h~ = 750 = 0.34

0.66 x 4.54 x 109

Therefore, oil in place = 1.363 = 2.198 x 109 STB

343

344

m = 0.5 (= 113 +- 2/3)

Material balance Np[B/ + BiRp - Rs;)] - We + Wp Bw

N= mBoi

(B/ - Bo;) + B. (Bg - Bgi) gl

At 1600 psi:

B/ + BiRp - Rs;) = 1.437 + 0.00150(1100 - 690)

= 2.0520


m Boi 0.5 (1.363) B/ - Boi + Bgi (Bg - Bg;) = 1.437 - 1.363 + 0.00124 (0.0015 - 0.00124)

= 0.0740 + 0.1429

= 0.2169

We = (2.052 X 3.1 X 108 + 31 X 106) - 2.198 X 109 X 0.2169

= 1.904 X 108 BBL

At 1300 psi:

B/ + Bg(Rp - Rsi) = 1.594 + 0.0019(1350 - 690)

= 2.8480 m Boi 0.5 (1.363)

B/ - Boi + Bgi (Bg - Bgi) = 1.594 - 1.363 + 0.00124 (0.0019 - 0.00124)

= 0.5937

We = 5.5 X 108 X 2.8480 + 55 X 106 - 2.198 X 109 X 0.5937

= 3.164 X 109

This is not simply linear with pressure but extrapolation is reasonably straightforward and water influx at 1000 psi is estimated at 3.75 X 109 BBL

B/ + BiRp - Rs;) = 1.748 + 0.0025(1800 - 690)

= 4.523 m Boi (0.5)1.363

B/ - Boi + Bgi (Bg - Bgi) = 1.748 - 1.363 + 0.00124 (0.00250 - 0.00124)

= 1.0775 (denominator term) N X denom.) + We - Wp Bw

N=------'-----'--P B/ + Bg (Rp - Rsi)

2.198 X 109 X 1.0775 + 3.75 X 108 - 63 X 106

4.5230

= 5.926 X 108

= 590 X 106 STB

Solution 10.5

. . . _ GBgi _ 120.7 X 109 X 6.486 X 10-4 _

Gas cap. OIl zone ratio m - NBoi - 300 X 106 X 1.3050 - 0.2

From PVT data the values of Bo, Rs and Bg at 4300 psi can be estimated by linear interpolation as:

Bo = 1.228 RBISTB; Rs = 338 SCF/STB; Bg = 7.545 X 10-4 RB/SCF

From production data the value of Rp is calculated as GpfNp to give the following table.

Time

1.1.80 1.1.81 1.1.82

pepsi)

5000 4300 4250

o o

25.55

o 21.9 43.8

RpCSCFISTB)

o 550 600

Using the relationship F = N(ET) + We + WinjBwinj the following is calculated where:

ET = mEg + Eo + Efw

Units 1.1.B1

(a) F = Np Bo + (Rp - Rs)Bg 106 RB 30.28

(b) Eo = (Bo - Boi) + (Rsi - Rs) Bg RB/STB 0.0420

(c) E,~ Bo; [~-ll RB/STB 0.2131

(d) [c.$W + cf 1 RB/STB 0.0061 Efw = (1 + m) Boi t!..P 1 - Sw

(e) ET = mEg + Eo + Efw RB/STB 0.0887

(f) We = F - N (ET) - Winj Bwinj 106 BBL 3.67

Solution 10.6 The dimensionless radius ratio is:

r aquifer 81000 re = =--=9

D r oil zone 9000

The dimensionless time tD is related to real time by: 2.309 k t (years) 2.309 (707t)

tD = <l>ql, ~ = (0.18)(7x 10-6) (0.4) (900W = 40t

R.(SCFISTB)

500 338 325

1.1.B2

62.41

0.0435

0.2302

0.0065

0.0960

8.06

345

The instantaneous pressure drops which at the start of each year are equivalent to the continuous pressure declines are:

Pi - PI 5870 - 5020 . t!..Po = --2- = 2 = 425 pSI

Pi - P2 5870 - 4310 t!..P I = ---= = 780 psi

2 2 PI - P3 5020 - 3850

t!..Pz = --2-= 2 585 psi

The aquifer constant is:

U = 1.119 f<l>h c rb U = 1.119 x 1 x 0.18 x 200 x (7 x 10-6) x (900W

U = 22841 BBLIpsi

From tables or charts for dimensionless influx at reo = 9 we have:

40 80

120

21 29 34

346 j=n-I

From We = U L APWD (T D - (Dj) j=O

Wei = 22841 [425 (21)] = 203.9 X 106 BBL


We2 = 22841 [425 (29) + 780 (21)] = 655.7 X 106 BBL

We3 = 22841 [425 (34) + 780 (29) + 585 (21)] = 1127.3 X 106 BBL

1 [0.00708 k kro h 1 PI=-" re ,,"0 In - - 0.75 + S

rw

For re = 1500 ft rw=0.5ft S= +4 Kro = 0.6 h = 100ft k= 1325mD 50

PI=!.to

Chapter 11

Solution 11.1

0.5 5 50 500 5000 .. ------------------------------------------------

PI 100 10 1 0.1 0.01

The injectivity index is given in field units by: 0.00708 k krw h

II=----~[~----~-----!'w In ~ - 0.75+ s]

Assuming all other factors equal then

Solution 11.2

Solution 11.3

Use is made of the plot in Fig. 11.4 which correlates areal sweep efficiency E A as a function of end point mobility ration (M') for different fractional injection volumes, V D.

Kw' !.to 0.4 3.4 M'=-·- =--·-=4

!.tw Ko' 0.4 0.85

The volume of injected fluid, in reservoir barrels, after 10 years is:

10 X 365.25 X 53 000 x 1.005

= 1.945 x 108 RB

The displaceable pore volume (= PV (I-SoT - Swi» is given in reservoir barrels as follows:

(4 x 5280) (1 x 5280) (98) (0.25) 5.615 [1 - 0.3 - 0.3]

= 1.946 x lOS RB 1.945 X 108

VD = 1.946 X 108 - 1

From Fig. 11.4 the value of EA corresponding to M' = 4 and V D = 1 is 0.7

For stable cone formation

~' = g' X (Pw - Po)

Solution 11.4

For ~' (in psi), and cone height X (in feet) and density difference as specific gravities then 62.4

~' = 144 (1.01 - 0.81) 50

= 4.33 psi

(a) In field units 1.25 (4000)

U= 70(1500) 0.0476 BID - ft3

The viscous-gravity force ratio is calculated from 2050 UItaL

Rv_g = ( _ ) kh Po Ps 2050 (0.0476) (0.5) (1500)

= (0.8 - 0.4) (130) (70) = 20

(a)

Oil

Regions I and n

(c)

Solvent

Region N

Chapter 12

Solution 12.1

(b)

Solvent

Oil

Region m

Region I : Single gravity override tongue

Region n : Single tongue but sweepout independent of RV-G for given M

Regionill: Transition region with secondary fingers below main tongue

RegionN: Multiple fingers with sweepout independent of RV- G for given M

Fig. A 12.1 Displacement regimes.

347

For a mobility ratio, M represented by !1ot'1ls (= 25), Figure A 12.2 shows a breakthrough sweep efficiency of about 15% and a flow dominated by gravity tonguing. (Fig A 12.1)

(b) In field units 1.25 (1000) 2

u = 30 (2000) = 0.0208 BID - ft

The viscous gravity force ratio requires an approximation of permeability as:

k=VKv·Kh

:. k = «1) (3»°·5 = 1. 73md

Then 2050 (0.0208) (0.36) (2000)

Rv_g = (0.75 - 0.64) (1.73) (30)

= 5378

For a mobility ratio of M (IlJIls = 0.36/0.055 = 6.55), Figures A 12.1 and A 12.2 show a breakthrough sweepout efficiency of around 50% and a flow dominated by viscous fingering.

100

~ ~ >-u c: Q)

·u ::: Q) 60 -; 0

t-Regionill-i------Region N 0-Q) Q)

~ til M=6.5

.£: CI> :::J

e .£: ~ 0

M = 27 Region N E co I-----Regionll---·I .... • -----Region ill----------<-t-''-i

10 100 1000 10000

. . . .. 2050UJ-L L (B/O-FT2)(CP)(FT) Viscous-gravity force ratiO (RV- G)' field units, _ 0 , '----,3:;--'-'----'--'----'

At kh (G/cm )(md) (FT)

Fig. A12.2 Breakthrough sweep efficiency.

Solution 12.2 The tie lines for the system join the equilibrium compositions of systems A and B in the two phase region. The compositions are plotted in Figure A12.3

(a) The critical point (CP) is estimated where the limiting tie line becomes tangential to the phase envelope and has the composition, wt%, 21 % surfactant, 67% oil; 12% brine.

(b) The point with the composition 4% surfactant and 77% oil is given on Figure A12.3 as point A. From the slope of tie lines in this region the equilibrium phase compositions are AI and A2 with weight percents estimated as:

AI 10% oil; 10% surfactant; 80% brine A2 97% oil; 2% surfactant; 1 % brine

For an original 200 g mixture containing

8g surfactant, 154 g oil, 38 g brine


Wt% Brine

100% Surfactant

\ Wt% Surfactant

-~~~::;Z::::::::::::TW~O=p:~:se:,~eg~io:n:~~~~~~~~~~ 100% 100t Brine 0 30 40 50 60 70 80

The tie line ratios give:

wt of AI phase 3/13 x 200 = 46 g wt of A2 phase 10/13 x 200 = 154 g

:. Composition of AI = 4.6 g oil 4.6 g surfactant 36.8 g brine

:. Composition of A2 = 149.5 g oil 3.0 g surfactant 1.5 g brine

Wt% Oil~

Fig. A12.3 Ternary diagram.

100% Oil

349

(c) On Figure A 12.3 the composition 20% oil and 80% brine is shown at location B. A line from B to the 100% surfactant point leaves the two phase region at location B', having a composition oil 16.5%, surfactant 17.5%, brine 66%. The oil + brine weight is 100 g and would constitute 82.5% of the mixture, so surfactant needed is 0.175 (100/0.825) = 21.2 g.

(d) On Figure A 12.3, location 1 is 10% oil, 40% surfactant and location 2 is 50% oil, 40% surfactant. They are in a single phase region and the resulting mixture contains 30% oil, 40% surfactant and 30% brine, as denoted by position 3.

(e) On Figure A 12.3, location 4 is 12% surfactant, 5% oil and location 5 is 20% surfactant, 77% oil.

The mixture weight is 200 g and contains 41 % oil, 16% surfactant, and 43% brine. It is shown as location 6. The mixture is in the two phase region and equilibriates to compositions C and D on the equilibrium tie line through location 6. The compositions are:

C: 58% brine; 21.5% oil, 20.5% surfactant (146 g total) D: 94% oil; 5% surfactant; 1 % brine (54 g total)


Solution 12.3 For conventional production

208.71AO.S

tJ.o In I - 0.964

700 (0.003541 (1000)(60»

150 ... H2O':': (3») - 0964] = 161 rbld For 9 acre spacing and a 200 psi differential.

For thermal stimulation and steam injection a 5 fold improvement in flow resistance between producers and injectors would lead to rates around 800 bid. To determine the steady state production/injection time at which such rates will lead to 50% of the pattern volume being occupied by steam we can conduct the following analysis:

The cumulative heat injected into the reservoir, Q;, can be calculated from heat injection rate, using the mass rate of injection Wi

Qi [ ] t = Wi Cw ~T+ fsdhLYdh

= qinj (5.615) (62.4) [Cw (380 - 100) + 0.75 (845)]

The average specific heat, Cw, over the temperature range 380 - 100°F is given by:

Cw = hw(Ts) - hw(Tres) 355 - 69

T T 1.02 Btullb m - degF s - res 380 - 100

:. Qi = t· qinj . 322118 Btu

The ratio of latent heat to total energy injected, fhv is calculated from:

_ { Cw ~T )"1 _ { (1.02 (380 - 100) )"1 fhv - 1 + fsdb LVdb - 1 + 0.75 (845)

= 0.689

Figure A 12.4 can now be used to estimate the thermal efficiency of the steam zone, Ehs, at different values of dimenSionle[:sti]~e;sto. The values of to are given from:

to = 4t MR h2

[45]2 [0.75] = 4t 35 (60?

= 0.00138t days or 0.504 t years

The following table may now be constructed usingfhv = 0.689 on Fig A 12.4.

t (yr) t(days) to

1.0 365.25 0.5 1.5 547.9 0.75 2.0 730.5 1.0 2.5 913.1 1.25

The volume of a steam zone, V., is in general given by: QiEhs

Vs = 43560MR AT

0.64 0.59 0.56 0.52

233.8 323.3 409.1 474.8

1.0 .. .c:.

W

oJ c:: 0 N

E c 2 If)

15 0.6

>-() c:: Q)

.<3 0.4 ;;:: -Q)

c E Q) 0.2 .c:: I-

0 0.01 0.1

Dimensionless time, tD

Fig. A 12.4 Thermal efficiency

For the case of 50% steam volume in the pattern of area A acres then

_ (43560 MR AT) Qi - 0.5Ah E

hs

Equating values of Qi we obtain the relationship 0.5 (9) (60) (43560) (35) (280)

322118 qinj . t = E hs

where t is in days 357817.5

That is

fhv (ratio latent heat to total energy injected) =

A 1.O 0.50 0.33 0.23 0.167 0.091

351

100

The injection rates needed to provide 50% pattern volume of steam at the following times are therefore as shown in the following table.

t (yr) qinj (rblD)

1.0 1531 1.5 1107 2.0 875 2.5 753

These data may be further evaluated in terms of steam injection equipment capacity and project economics.

Solution 12.4

The wet condensate gas volume is obtained from the volumetric calculation: Ahn </> (,5)

V = g sc B .

g.

In terms of standard cubic feet this is: 1

Vsc = s. [It(3 x 5280? 300 (0.18) (0.75)] gl


3.1937 X 1010

Vsc = B SCF g;

In order to find Bg; we need the super compressibility factor z which can be obtained from Fig 4.7 using the reservoir condition molecular weight or gas gravity.

The oil molecular weight is given by 44.3 PL

Mo = (1.03 - PL) 141.5

NOWPL= API + 131.5 0.75

:.Mo = 119

The weight associated with a stock tank barrel of liquid is given by:

W = (5.615 x 62.4 = 0.75) 5000 (0.58) (28.97) + 379.4

= 262.78 + 221.44

= 484.22

The number of moles associated with this weight is 5000 (62.4) (0.75) (5.615)

n = 379.4 + 119

n = 13.18 + 2.21

n = 15.39 W 484.22

:. MW(res) = -;;= 15.39 = 31.46

MW(res) 31.46 and Yg(res) = 28.97 = 28.97 = 1.086

i.e. Yg(res) = 1.09

From Fig 4.7, P pc = 620 and Tpc = 465

From reservoir datum conditions 4500 670

P pr = 620 = 726 and Tpr = 465 = 1.44

So, from Fig 4.7 z = 0.925

Then: (0.02829) (0.925) (670)

Bg;= 4500

= 3.8962 x 10-3 RCF/SCF 3.1937 x 1010

Vsc = 3.8962 X 10-3

= 8.197 X 1012 SCF

The dry gas volume

- [ x 12] [5000/379.4] G - 8.197 10 15.39

G = (8.197 x J(p) (0.8563)

G = 7.019 X 1012 SCF

Similarly the oil volume Vsc 8.197 x 1012

NX R = 5000

N = 1.639 X 109 STB


Chapter 13

Solution 13.1

353

Using the relationship that the depth equivalent of the total head is equal to the sum of the depth equivalents of the well head pressure and the well depth, then:

DT = D whp + Dwell

(a) From Fig. A 13.1 at a well head pressure of 400 psi then DwhQ = 3700 ft. Since Dwell = 6000ft then DT = 9700 ft. At the GOR of 200 scf/stb the pressure at a depth equivalent of Y700 ft is read as 2400 psi.

(b) From Fig. A 13.2 at the bottom hole pressure of 1200 psi and GOR of 500 scflstb the depth equivalent Dr. is read as 8900 ft. Since Dwell is 5000 ft then Dwhp is 3900 ft. The well head pressure is read from the graph at 3900 ft as 360 psi.

3

Vertical flawing_pressure gradients (all oil)

Tubing Size 4 in.I.D. Producing Rate 2000 Bbls/day Oil API Gravity 35° API Gas Specific Gravity 0.65 Average Flowing Temp. 140° F

Vertical flowing_pressure gradients (all oill

Tubing Size 4 in.I.D. Producing Rate 3000 Bbls/day Oil API Gravity 35° API Gas Specific Gravity 0.65 Average Flowing Temp. 140°F 3

Q; ~ 4 0 0 $2 .!: 5

Q; ~ 4 0 0 $2 .!: 5

.c C. c: 6 Q)

..J

.c C. c:

6 Q)

..J

7 7

8 8

9 9

10 10

Fig. A13.1 Fig.A13.2

Solution 13.2

The maximum production rate qrnax can be evaluated using the Vogel relationship, withp, the static pressure, i.e.

q/qm~~ H.2 [~]- 08 [~]'

~ 1 - 0.2 [~: ]- 08 [= r = 0.619

3315 therefore, qrnax = 0.619 = 5355 bid


Pressure in 100 PSIG

Verlical flowing_pressure gradienls (all oil)

Tubing Size 4in.1.0. Producing Rale 1000 8bls/day Oil API Gravily 35° API Gas Specific Gravily 0.65 Average Flowing Temp. 3 140°F

3

Verlical flowing_p.ressure gradienls (all oil)

Tubing Size 4 in.I.O. Producing Rale 4000 8bls/day Oil API Gravily 35° API Gas Specific Gravily 0.65 Average Flowing Temp. 140°F

Q; ~ 4 0 0 $2 .S; 5 .t:: "6> c

Q; 4 ~ 0 0 $2 5 .S;

Q) 6 ...J .t:: "6> 6 c Q)

...J 7

7

8

8 9

9 10

10

Fig. A13.3

Fig. A13.4

Verlical flowing_pressure gradienls (all oil)

Tubi~g Size 4 in. 1.0. Producing Rale 5000 8bls/day Oil API Gravily 35° API Gas Specific Gravily 0.65 Average Flowing Temp. 140°F

3

Q; ~ 4 0 0 $2

5 .S; .t:: "6> c 6 Q)

...J

7

8

9

10

Fig.A13.5


From Fig. A 13.1 to A 13.5 the different vertical flowing pressure gradient curves at different rates are found for 4 in. tubing and a GOR of 200 SCF/STB. The total head depth is obtained as the sum of the well depth and the depth equivalent to a tubing head pressure of 400 psig. The flowing bottom hole pressure equivalent to the total head depth is recorded as a function of flow rate. It can be seen that the bottom hole pressure is essentially independent of rate at this

condition and is 2200 PSi[. (2200 ) (2200 )2] Hence q = qmax 1 - 0.2 2600 - 0.8 2600

= 1400 bid

Solution 13.3

For a residence time of 3 min. the volume of oil in the separator will be: (1000) (3) 3

Vo = (24) (60) = 2.083 m

At 40°C and 20 bar the volumetric rate of associated gas will be V (1000) (95) (313.15) (1) 3 --II. = (24) (60) (60) (273.15) (20) = 0.06303 m Is

At separator conditions the gas density Pg is given by (273.15)

Pg = 1.272 (0.75) (20) (313.15)

= 16.682 kg/m3

The maximum velocity equation is then used:

[796 - 16.682]0.5

Umax = 0.125 16.682 mls

= 0.8544m/s

Since cross-sectional area = volume ratelvelocity then for an interface half way up the separator we have: n D2 0.06303

(2) (4) 0.8544

:.D = 0.4334 m

Total volume of the separator is thus twice the oil volume for an interface half way up the separator :.

Vsep = 2Vo

= 4.166 m3

Design length for LID = 3 gives (4.166) (4)

3D = L = nD2

. 3_(4.166)(4) .. D - 3n

:. D = 1.209m

and L = 3.627 m

Design length for LID = 4 gives

D3 = (4.166)(4) 4n

:. D = 1.099

and L = 4.396 m

In practice the separator design would be based on a standard size selected to be nearest the size calculated.

Index

Abandonment pressure 159 absolute permeability 102 AFE (authorisation for expenditure) document 23, 24-S Amerada gauge 147, 148 API (American Petroleum Institute) gravity and oil density 14 aquifer characteristics

correlation with model 167 determination of 165-6

aquifers and pressure change 165 areal sweep efficiency 176, 182-3

Back pressure equation 143-4, 221 barrel 14 bedforms, grain size and stream power 242 biocides and injection water 229 biopolymers 197 black oil reservoir modelling, uncertainties in 24&-7 black oil systems 42 blow-out 35 blow-out preventers 34-5 blowdown 210 Boltzmann transformation 134 bond number 191 BOPs see blow-out preventers bottlenecks 219 bottom-hole sampling 52 Boyle's law method and grain volume 73 Brent Sand reservoirs 10, 11 brine disposal 186 bubble-point 41, 51, 53, 54, 55,159,220,221 bubble-point pressure 52, 54-5, 56-7,160,163,221

in volatile oil reservoirs 211 Buckley-Leverett theory 105 Buckley-LeverettlWelge technique 107, 109

Footnote: Numbers in italic indicate figures; Numbers in bold indicate tables

Capillary number 191,193 capillary pressure 93

and residual fluids 111-12 defined 92

capillary pressure data (given rock type, correlation 99 capillary pressure hysteresis 97-8 capillary suction pressure see imbibition wetting phase threshold

pressure carbon dioxide in miscible displacement 195, 196 casing a well, reasons for 2S casing eccentricity 35-6 casing selection 27

main design criteria 28 casings 23, 25, 26, 28 caustic solutions 196 cementation problems 35-6 chemical flood processes 196-200 choke assembly 146 Christmas tree 36 coalescer 227 Coates and Dumanoir equation 86 combination drive material balance equation 166 compaction drive 161 complete voidage replacement 173 completion 28,29 completion for production (permanent, normal) 36 composite cores 111 compressibility 42-3,55 Compton scattering 76 conceptual models 233,245 condensate analysis 208 condensate reservoirs and liquid drop-out 208 condensate systems 42 condensing gas drive 194-5 cone height, critical 182 coning 181-2 core analysis

357

and permeability distribution 83-4 routine 69-71, 81 presentation of results 70,71


core data and palaeogeographical reconstruction 237-8 and recognition of sand body type 238

core-derived data 68 core floods and surfactant testing 200 core for special core analysis 67, 68 core length and imbibition processes 110-11 core log 64,68 core plug experiments, concern over

laboratory-derived data 113-14 core plugs 68

analysis on 65 and effective permeability 109 and fluid saturation 93-4 and oil saturation 193 and permeability 81 and porosity 72 and residual saturation 174

core porosity, compaction corrected 131 core preservation 67-8 core recovery, fluids for 31 Core gamma surface logger 68 cores 62

composite 111 correlation with wireline logs 63,65,75 data obtainable from 63 diversity of information available 64 and geological studies 68-9 and heavy oil reservoirs 202 residual fluid saturation determination 69

coring the case for 65 conventional and oriented 66 of development wells 65--{i of exploration wells 65

coring decisions 64--{i coring mud systems 66-7 corresponding states, law of 44-5,47 Cricondenbar 41 , 42 Cricondentherm 41 critical displacement rate 177 critical displacement ratio 112 critical gas (equilibrium) saturation 159 critical production rate (coning) 182 crude oil

flow of in wellbore 221, 223 metering of 229 processing 226-8

cushion 147 cuttings logs 31 cyclic steam stimulation 205

Darcy (def. )79 Darcy's equation 79 data acquisition during drilling 30-1 datum correction 79-80 deltaic environments, division of 238,240, 241,242 deltaic models, use of 238-43 deltaic system model 242, 244 demulsifiers and heavy oil processing 228 depositional processes and reservoir rocks 7 dew-point 41 dew-point locus 42 diamond coring 33 differential liberation at reservoir temperature 53 displacement calculations, validation of relative permeability data for 113-14

displacement principles 173-5 drawdown testing 138 drill bits 22, 32-3 drill collars 23 drill stem testing 145

testing tools and assemblies 145-7 drilling, turbine versus rotary 33 drilling costs 23, 24, 25 drilling fluid see drilling mud drilling logs 30 drilling mud pressure, excessive 29 drilling muds 22-3

control of 28-9 main constituents 67

drilling muds and cements, rheology of 29-30 drilling optimization 32-3 drilling, special problems in cementation problems 35--{i

pressure control and well kicks 34-5 stuck pipe and fishing 33-4

drillstring 23 drive mechanisms 159 dry gas reservoirs 41-2 dual porosity systems 71,73

and gravity drainage 164-5

Early (transient) time solution 138 economic factors and oil production rates 180 effective permeability 102

and wettability 108 enhanced oii recovery schemes and uncertainty 247 equity, distribution of, petroleum reservoirs 130-1 exploration well drilling 7, 8

Faults, identification of 238 faults (in-reservoir), effect on injection/production well locations 180 field processing 224 filtration, injection water treatment 229 flash liberation at reservoir temperature 52-3 flash separation tests 53-4 flooding efficiency ratio 110 flow equations, linear and radial 80-1 flow string 145 fluid contacts 12-13

multiple 12 fluid flow in porous media 78-9 fluid pairs 93 fluid pressure and overburden load 11-12 fluid pressures, hydrocarbon zone 12-13 fluid saturation, laboratory measurements and relationship with reservoir systems 93--{i fluids, recovery of by depletion 211 Forcheimer equation 143 formation breakdown pressure 30 formation density logs and interpretation of porosity 202-3 formation density tool response 75--{i formation factor see formation resistivity factor

formation interval tester (FIT) 148 formation resistivity factor 74 formation tester (FT) 148 formation volume factor 14, 55

two-phase 55--{i formation volume factors B 49-51 formation waters 14 fractional flow 104--{i

analysis methods 105--{i effect of dip angle and wettability 175, 177 free water level (FWL) 12,95

INDEX

Gas cap expansion drive 163-4 gas compressibilities 48-9 gas condensate, critical properties of 210 gas condensate and volatile oil reservoirs,

uncertainties in 247 gas condensate reservoirs 207-11

production methods for 209-11 gas deviation factor Z 46, 47 gas expansion during production 157 gas flow and gradient 159 gas flow and permeability 81 gas flow rate, measurement of 150, 229 gas formation volume factor 157 gas formation volume factor Bg 49-50 gas properties 45 gas recycling, gas condensate reservoirs 210 gas reinjection 186 gas reservoirs, recovery from 157-9 gas viscosities 47-8 gas-kicks 12 gas-oil ratio 14,51-2,54,159 gas-oil systems and relative permeability 103-4 gas well testing 143-5 gases, behaviour of 43-4 gases, flow of in wellbore 221 geological model, development of 237-8 geothermal gradient and hydrocarbon generation 7, 9 geothermal gradient and reservoir temperature 13 GOR see gas-oil ratio grain density 71 grain volume and Boyle's law method 73 gravity drainage and dual porosity systems 164-5 gravity segregation and recovery efficiencies 164-5 gravity stabilization and reservoir dip 175

Head loss in wellbores 221 heavy crude oil

characteristics of UKCS heavy crude oils 201 general classification 200 Yen classification 200, 201

heavy oil processing 228 heavy oil recovery 200-2 heavy oil reservoirs

examples of 201 permeability increase and production improvement 204 production characteristics of 203-4 properties of 202-3 and thermal energy 204-7 and uncertainty 247

heavy oil systems and thermal energy addition 204 HKW (highest known water) 12,13 homogeneous reservoirs and coning 181-2 Horner analysis 13 hydrates 224 hydrocarbon accumulation and sedimentary basins 7 hydrocarbon accumulations and formation waters 14 hydrocarbon exploitation, types of interactions 16 hydrocarbon field 7 hydrocarbon generation and geothermal gradient 7, 9 hydrocarbon pore thickness (HPT) 126--7 hydrocarbon pore volume maps 126--7 hydrocarbon properties 47 hydrocarbon recovery, improved 191-211 hydrocarbon reservoir fluids 15 hydrocarbon systems

volumetric and phase behaviour 40-1 applications to field systems 41-2

hydrocarbon volume in place calculations 127-8 hydrocarbons, migration of (modelled) 93-4 hydrocarbons (commercial reservoirs),

geological characteristics 62 hydrostatic gradient, regional 10-11

Ideal gas law (and modification) 43 imbibition processes

and core length 110-11 liquid 104

imbibition wetting phase threshold pressure 97 in-place volume 122 inflow performance relationship, 220

dimensionless, for oil wells 220-1 for gas wells 221

injection fluids, compatibility with reservoir fluids 183-4 injection fluids, quality of 183-6 injection water, viscosity of 184 injection water treatment 229 injectivity index 174, insert bits 33 isobaric thermal expansion coefficient 43 isocapacity maps 126 isochores 124 isochronal testing 144 isoliths 124 isopachs 124 isoporosity maps 125 isosaturation lines 99 isosaturation maps 126 isothermal compressibility 43 isothermal retrograde condensation 42

Kay's rule 45 kelly 23 kick 34-5 Kimmeridge Clay 7, 9 Klinkenberg correction 81, 82 Kolmogorov-Smirnoff test 84

Lasater correlation (bubble-point pressure) 55 leak off tests 30 Leverett J-function correlation 99 light oil processing 226

foaming problems 227-8 separator design considerations 227 wax problems 228

line source solution (fluid flowing in a porous medium) 134-5 development of 135-6

liquid drop out 208 liquids systems, generalized correlations 54-8 lithofacies representation 125 LKO (lowest known oil) 12,13 low interfacial tension (Iff) systems 193

359

Material balance, reservoirs with water encroachment or water injection 165-8

material balance calculations generation of data 52 sources of error 168-9

material balance equation 158 combination drive 166 gas cap expansion drive 163-4 solution gas drive 161-3

material balance residual oil saturation 174 mathematical models 233-4

360

mercury injection and porosimetry 73,96,97 meters 229 microemulsion 198 middle (late transient) time solution 139 miscible displacement mechanisms 194-5 miscible displacement processes 193 miscible floods 194

applications 195-6 examples 196

miscible fluids, properties of 195 mobility ratio 104-5, 107, 175,176

and polymers 197 modelling of reservoirs 130-1 models 233--4 mole (def.) 44 Monte Carlo

approach, probabilistic estimation 127 technique and recoverable reserves estimate 130

movable hydrocarbon formula (MHV) 130 mud cake 36 mud circulation system 22, 23 mud composition, general limitations on 67 mud logging 30-1 mud systems, bland (unreactive) and core recovery 31-2,67 multicomponent systems, phase behaviour 41 multimodal porosity 78 multirate data, analysis of 144-5 multiphase flow, equations of 234-5

Natural gas calorific value 226 dehydration 224-5 onshore processing 225-6 sales specification 224 sweetening 225

natural gas processing 224-6 nitrogen in miscible displacement 195, 196 non-wetting phase fluid 94 non-wetting phase saturation 102 North Sea, heavy oil reservoirs 202 North Sea, hydrocarbon fields

Beryl field 196 Brent field 196 Buchan field 37 Dunlin field 131,178 Forties field 249 Fulmar field 249-51 Magnus field 184 Maureen field 187 Montrose reservoir (RFf data) 151 Murchison field 125 Rough gas field 123, 124, 126, 127 Statfjord field 196, 245, 246 Thistle oil reservoir 122, 123, 125

North Sea, oil correlations, recent 56-8 North Sea, reservoirs, fluid choice for miscible displacement

196 North Sea, reservoirs and surfactants 198, 199

ODT (oil down to) 13 offshore production/injection system,

principle components of 184,185,186 offshore system 21 oil bank formation 195 oil density 14 oil flow rate, measurement of 150 oil formation factor Bn 51


oil saturation, local, influences on 191 oil viscosity 56 oil-water contact (OWC) 96, 98-9 oil-water systems and relative permeability 102-3 open-hole tests 145 optimal salinity 198 orifice meters 229 overpressure 11, 12

Packer 146 Peng and Robinson equation 44 permeabilities, averaging of 83 permeability 7, 78-86

and critical displacement ratio 112 anistropy 82-3 distributions 83--4 improvement 193--4 laboratory determination of 81-2 ratios 104-5 variation, effects of 106-8

permeameter 81 petroleum

migration of 9-10 origin and formation of 7 recovery 5

petroleum engineering function of 1 problem solving in 3

phase (def.) 14 phase inversion temperature (PIT) 198 physical models 233 piston displacement, stratified reservoirs 107-8 planimeter 124, 127 polyacrylamides 197 polymer fluids 193 polymer systems and adsorption 197 pool see reservoir pore fluid pressures 11 pore pressure, significance in drilling and well completion 26, 28 pore size distribution 96-7 pore space characteristics and equilibrium saturation distribution 92-3 pore volume compressibility 160

of reservoir rocks 203 poro-perm data, validity of 242 porosity 7, 71-8

and permeability, relationship between 84-6 cut-off 124 distributions 77-8 logs 75-7 main logging tools for 75 measurement of 72-3

potential gradient 174 pressure (abnormal) and d-exponent 25-6 pressure build-up analysis 139-40 pressure build-up (testing) 149 pressure control and well kicks 34-5 pressure decline, rates of 137 pressure depletion 210 pressure drawdown and reservoir limit testing 142-3 pressure equilibrium, static system 12 pressure gauges 137, 147

(downhole), characteristics of 136 pressure gradients and heterogeneity of reservoir pore space 129 pressure maintenance 173 pressure regimes, abnormal 11-12 primary recovery, oil reservoirs 159-64

INDEX

probabilistic estimation 127-8, 129, 130 produced fluids and offshore processing 184-{5 produced water treatment 228 producing rates (well inflow equations/pressure loss calculations) 174-5 production costs, significance of 1, 3 production engineering, and well performance 220-1 production engineering described 218 production operations, influencing factors 218-29 production rate effects 180-2 production rates, technical and economic factors 219 production system 218-19 production testing 150-1 productivity index (PI) 245

and inflow performance 220 pseudo-critical temperatures and pressures 45-7 pseudo-relative permeability in dynamic systems 115 pseudo-relative permeability functions 177,178, 243,245

static 115-16 pseudo-relative permeability

relationships and thicker sands 107 PVT analysis 52-4 PVTrelationships, single and multicomponent systems 40-1

Radial equations in practical units 136 radial flow in a simple system 134-5, 137 recombination sampling 52 recovery efficiency, water reservoirs 168 recovery factors and reserves 128-30 recovery string 34 recovery targets 191 Redlich-Kwong equation 44 relative permeability 102-4,106-7

effect of temperature 204 relative permeability

data, laboratory determination of 109-11 from correlations 112-13 improvement, heavy oil reservoirs 204

relative spreading concept 93 repeat formation tester (RFf) 148-50 reservoir behaviour in production engineering 220-1 reservoir condition

material balance techniques 160 volumetric balance techniques 160-1

reservoir data, sources 14-15, 17 reservoir (def.) 7 reservoir description in modelling 237-45

uncertainty in 245-7 reservoir development, costs of3, 4 reservoir dip angle 175,177 reservoir flow rate, effect of 181 reservoir fluid properties,

measurement and prediction of 43-9 reservoir fluids

and compressibility 42-3 nature of 14 properties of 40-58

reservoir geometry and continuity 180, 238-45 reservoir heterogeneity 177-80 reservoir mapping and cross-section interpretation 245-6, 247 reservoir modelling analysis and data requirements 237 application in field development 248-51

concepts in 233-48 reservoir performance analysis 157-68 reservoir pore volume and change in fluid pressure 42-3 reservoir pressures 10-12

reservoir rocks, characteristics of 62-86 pore volume compressibility 203

reservoir simulation modelling 233-7 reservoir simulation and vertical communication 243, 245 reservoir temperatures 13 reservoirs 7-18

areal extent of 122-4 residual oil 53, 191

influence of recovery mechanism 191, 193 residual oil saturation 192

average 174 and material balance 174 measurement of 191, 192

residual saturations 111-112 resistivity factor see formation resistivity factor resistivity index 74 retrograde condensation 208 reverse circulating sub 146 rotary table 23

Safety joints and jars 147 salinity and water viscosity 56 samplers 147 sand body continuity 180

importance of 238,239-40 sand body type

effect on injected water and oil displacement 178-80 recognition of 238

saturation distributions in reservoir intervals 98-9 saturation gradients 164 saturation pressure see bubble-point pressure scribe shoe 66 sea water as injection water 184

361

seawater floods (continuous) and low surfactant concentration 199-200 secondary recovery and pressure maintenance 173-86 secondary recovery techniques 173 sedimentary basins

and hydrocarbon accumulation 7 origin of7 worldwide 2

segregated displacement 177 sensitivity studies 246-7 shaliness, effect of 13 Shinoda diagrams 198 simulators

applications 235 classification of 235,236

single component systems, phase behaviour 40-1 skin effect 140-2

negative factors 142 skin zone 194 slabbing 68 solution gas drive, analysis by material balance 159-63 solution gas-oil ratio 53, 54, 55 Standing-Katz correlations 46, 47 Standing'S data (bubble-point correlation) 55 STB (stock tank barrel) 14 steady state permeability tests 110 steam flooding 205 steam properties 206, 207 steamdrive analysis, example data requirements 207 Stiles technique 107-8 stock tank oil 54

and retrograde condensation 208 stock tank oil in place and equity

362

determination 130 stock tank units 14 stock tank volume 53 Stratapax bits 33 stratified reservoir analysis 106 stripping 191 structure contour maps 122 stuck pipe and fishing 33-4 summation of fluids and porosity 72-3, 74 superposition technique 140 surfactant concentration (low) and continuous seawater floods 199-200 surfactant flooding 198-200 surfactant phase systems 197-8 surfactant processes 197-200 surfactants 193

synthetic 199 sweetening, natural gas 225

Tester valve 146 thermal energy 204-7 thermal injection processes 204-6 thickness maps 124 threshold capillary pressure (reservoir rocks) 95 threshold pressure 94 traps (structural and stratigraphic) 10 tricone bits 32, 33 trip gas 34 turbine meters 229

Ultimate recovery formula see movable hydrocarbon formula uncertainty in reservoir model description 245-8 unitization 130-1 universal gas constant, values of 43 unsteady state relative permeability tests 109-10 USA, heavy oil resource distribution 202

Van der Laan method (volume in place) 128 vaporizing gas drive 194, 195 vapour phase 42 vertical bed resolution 76 vertical permeability variation and fractional flow curve 177 vertical pressure logging 148-50 Viking Graben area (N North Sea) 10 Vogel dimensionless IPR 220-1 volatile oil reservoirs 211 volatile oil systems 42 volumetric balance techniques 160 vugular carbonates and whole core analysis 69


Walther's law offacies 238 water drive and gas condensate reservoirs 209,210 water drive reservoirs 167

recovery efficiency of 168 water formation factor Bw 50-1 water influx 165, 166 water influx, gas reservoir 158-9 water injection 166, 178 water saturation distribution, homogeneous reservoir 96 water viscosity 56 waterflooding 178, 179,180 Welge analysis 106 Welge's equations 174 well arrangements, dipping reservoirs 181 well classification 20 well description log 31, 32 well drilling operations 20-3 well locations and patterns 182-3 well performance, radial flow analysis of 134-51 well productivity improvement 193-4 well test methods, applications of analytical solutions 136-9 well test procedures 145-50

data analysis 147-8 well testing and pressure analysis 150-1 well/reservoir responses, different reservoir systems 139 wellbore, altered zone 141 wellbore flow 221-3 wellbore inflow equations 174 wellsite controls and core recovery 68 wettability 175

change in 67, 196 degree of 93

wettability control, in situ 112 wettabilityeffects 108 wettability preference 93 wetting phase fluid 93 wetting phase saturation 94 wetting preference 175 wireline logs, correlation with cores 63, 65, 75 wireline testing 148-50 WUT (water up to) 13

Xanthan gums 197

Zonation 99, 131,242,243,245 Forties reservoir 249 and geological core study 68-9 and histogram analysis 84 and permeability distributions 84

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