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Performance Analysis of Compositional and Modified Black-Oil Models for a Rich GasCondensate ReservoirB. Izgec and M.A. Barrufet, Texas A&M U.
Copyright 2005, Society of Petroleum Engineers Inc.
This paper was prepared for presentation at the 2005 SPE Western Regional Meeting held inIrvine, CA, U.S.A., 30 March 1 April 2005.
This paper was selected for presentation by an SPE Program Committee following review ofinformation contained in a proposal submitted by the author(s). Contents of the paper, aspresented, have not been reviewed by the Society of Petroleum Engineers and are subject tocorrection by the author(s). The material, as presented, does not necessarily reflect anyposition of the Society of Petroleum Engineers, its officers, or members. Papers presented atSPE meetings are subject to publication review by Editorial Committees of the Society ofPetroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paperfor commercial purposes without the written consent of the Society of Petroleum Engineers isprohibited. Permission to reproduce in print is restricted to a proposal of not more than 300words; illustrations may not be copied. The proposal must contain conspicuousacknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O.Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.
Abst ractThe modified black-oil model (MBO) was tested against the
fully compositional model and performances of both models
were compared using various production and injectionscenarios for a rich gas condensate reservoir.
We evaluated the performance of MBO model by
investigating: the effects of black-oil PVT table generation
methods from a tuned equation-of-state, oil-gas ratio (OGR)
and saturation pressure versus depth as initialization methods,
uniform composition versus compositional gradient withdepth, location of the completions, production and injection
rates, kv/khratios, and vertical wells versus horizontal wells.Contrary to the common belief that OGR versus depth
initialization gives better representation of original fluids in
place, initializations with saturation pressure versus depth
gave closer original fluids in place considering the true initialfluids in place are given by the fully compositional model
initialized with compositional gradient.
Unrealistic vaporization in the MBO model was
encountered in both, production by natural depletion and gas
cycling. The changes in oil-gas ratio of the recyled gas showedthat, it is not possible to accurately represent the changing
PVT properties of the recycled gas with a single PVT table.Unrealistic vaporization also led to different arrival times forthe displacement fronts and different saturation profiles for the
near wellbore area and for the entire reservoir for the two
models even though the production performance of the models
was in good agreement.The MBO model representation of compositional
phenomena for a gas condensate reservoir proved to be
adequate for full pressure maintenance, reduced vertical
communication, vertical well with upper completions, and forhorizontal well producers.
IntroductionBlack-oil simulators represent a high percentage of al
simulation applications and they can model immiscible flowunder conditions such that fluid properties can be treated as
functions of pressure only.
However, gas condensate reservoirs exhibit a complexthermodynamic behavior that cannot be described by simple
pressure dependent functional relations. Compositions changecontinuously during production by natural depletion, or by
cycling above and below dew point pressures.
In another black-oil modeling approach reservoir fluidconsists of a gas component and vaporized oil which allows
the use of a simple and less expensive model.
According to this modified black-oil approach liquid
condenses from a condensate gas by retrograde condensationwhen the pressure is reduced isothermally from the dew point
and retrograde liquid is vaporized by dry gas.Coats1 presented radial well simulations of a gas
condensate that showed a modified black-oil PVT formulation
giving the same results as a fully compositional EOS PVT
formulation for natural depletion above and below dew point
Under certain conditions, he found that the modified black-oimodel could reproduce the results of compositional simulation
for cycling above the dew point. For cycling below the dew
point, the two-component simulation gave results that were
quite inaccurate.According to Fevang and Whitson2, results from Coats
example should be used with caution as EOS characterization
uses seven components with one C7+ fraction. With a moredetailed C7+ split, oil viscosity differences between black-oi
and compositional formulations often yield noticeable
differences in well deliverability.
Fevang et al.3 obtained results which mostly support the
conclusions by Coats.1However, they found differences in oi
recoveries predicted by compositional and MBO models whenthe reservoir is a very rich gas condensate and has increasing
permeability downwards. According to their final conclusionsa black oil simulator may be adequate where the effect of
gravity is negligible, and for gas injection studies black oil
model can only be used for lean to medium-rich gascondensate reservoirs undergoing cycling above dew point.
El-Banbi and McCain4, 5suggested that the MBO approach
could be used regardless of the complexity of the fluid. Their
paper presented the results of a full field simulation study for a
rich gas condensate reservoir. The MBO models performance
was compared with the performance of a compositional mode
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in the presence of water influx and also a field wide history
match study was conducted for above and below the dew
point. Their paper presents an accurate match of averagereservoir pressure and water production rates. However gas-oil
ratio and condensate saturation plots were not provided and
initial condensate production rates do not represent a clear
match for 500 days.
For the present study a representative gas condensate fluidwas selected and a fluid model was built by calibrating the
EOS to the available experimental data, which consisted ofconstant composition expansion (CCE) with relative volume,
liquid saturations and gas density values.
By using the calibrated EOS black-oil PVT tables were
generated for MBO model using Whitson and Torp6 and
Coats1methods.
The compositional model was run either with
compositional gradient or with uniform composition. The
compositional gradient in MBO model was given by depth
variation of OGR (Rv) and GOR (Rs) or saturation pressureversus depth tables.
Initially there was a discrepancy in saturation pressureswith depth in the MBO model which resulted in earlier
condensation and lower oil production rates whether it was
initialized with GOR / OGR or saturation pressure versus
depth tables.
For natural depletion cases as the reservoir gas becomes
leaner during production, the initial differences between themodels, due to saturation pressure changes with depth
disappear and a better match was obtained, especially for the
poor vertical communication.For the gas cycling cases the models were in good
agreement as long as the reservoir was produced with rates
high enough to minimize condensation. If the MBO model isinitialized with compositional gradient, lower production and
injection rates and bottom completions created differencesbetween the performances of the models.
Almost all the cases showed differences in condensate
saturation distribution around the wellbore area and the entirereservoir. The minimum difference between the models is 5 %
in terms of average field oil saturation and this was obtained
for a high rate gas injection case combined with reducedvertical communication.
However, the saturation differences between models
depend on the case and the time interval studied. As an
example, for gas injection with bottom completions, at 1000days, the condensate saturation difference between the two
models was as high as 60 % although they converged to a
close value at the end of the simulation.In MBO model, the runs with horizontal wells exhibited
closer performances with compositional model compared tothe runs with vertical wells.
The changes in oil-gas ratio of the cycling gas showed that,
it is not possible to accurately represent the changing PVTproperties of recycled gas with a single PVT table in the MBO
model since every time the produced gas passes through the
separators and is injected back into the reservoir its oil-gasratio and accordingly vaporization characteristics changes.
Fluid CharacterizationThe fluid selected for the study is a rich gas condensate taken
from Cusiana Field in Colombia.A compositional analysis with hydrocarbon components
that includes a heavy fraction of C30+, a set of experimenta
data obtained from a constant composition expansion and a
separator test were used to characterize the fluid. Table 1
presents the extended compositional description of the fluid.Following the procedure proposed by Whitson6, where the
groups are separated by molecular weight we used sixpseudocomponents and one non-hydrocarbon, CO2. The
pseudocomponents were defined as two pseudo-gases, GRP1
and GRP2, one gasoline group, GRP3 and three heavy
pseudocomponents, GRP4, GRP5 and GRP6. For the purpose
of CO2injection, this component was kept as a separate groupThe corresponding components for each pseudo componen
and the final molar compositions are given in Table 2.
Once the pseudocomponents were defined we proceeded
with the EOS tuning process. The variables used as regressionparameters were binary interaction coefficients, and shif
factors for selected groups. The final values for these variablesare presented in Table 3-4. Binary interaction coefficients
values after tuning are presented in Table 5.
Four parameter Peng-Robinson EOS was selected and
tuned to the data obtained from the constant composition
expansion at 254F, which includes the liquid saturation, gas
density and the relative volume. Figs. 1 through3illustrate the
match between the experimental and the simulated data.
Black-Oil PVT Table GenerationBlack-oil PVT properties in this study have been generatedwith an EOS model using the Whitson and Torp7procedure
Coats1 developed another black-oil PVT table generation
method. Instead of flashing the equilibrium liquid and vapor
compositions separately to obtain Bo, Rs, Bg, Rv directly asindicated by Whitson and Torp, Coats determines only one ofthese properties Rv, from flash separation and determines the
remaining three using equations that force the PVT properties
to satisfy mass conservation equations and yield correct
reservoir liquid density. In determining Rv from the surfaceseparation at each CVD pressure step Coats uses the surface
oil and gas molecular weights and densities obtained from the
separation of the original fluid mixture.McVay8 found better agreement between compositiona
and MBO simulations models if the surface oil, gas molecular
weights and densities are obtained from the separation of the
mixture at each CVD pressure step to calculate Rv at each
pressure. Also by using Coats method it is not possible toobtain the PVT properties of the liquid phase at the saturation
pressure. Coats defined the first CVD pressure step to be 0.1
or 1 psi below the saturation pressure and used the values
calculated at this pressure as the PVT properties at thesaturation pressure. Standard extrapolation of sub-dew poin
properties to dew point can lead to situations where the oil hasnon-physical negative compressibility.
Figs. 4 through 9 give the saturated oil, and gas PVT
properties obtained by Whitson and Torp and Coats methods
Notice that gas formation volume factors at lower pressure
values are quite different for the two methods.
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Coats method was not preferred for this study since it
created convergence problems in MBO model and the run was
automatically terminated due to number of errors encountered.
Initialization MethodsTo obtain the correct and consistent initial fluids in place for
black-oil and compositional models it is important to initialize
the models properly. The initial reservoir fluid composition iseither constant with depth or shows a vertical compositional
gradient where the effect of gravity is not negligible.Depending on the type of the reservoir fluid, the model should
be initialized either with solution GOR/ OGR versus depth or
saturation pressure versus depth to minimize the errors for
initial fluids in place.
Although initialization with saturation pressure versusdepth gives more accurate representation of fluids in place, at
the bottom of the reservoir where the amount of heavy fraction
increases, this initialization method provided higher
condensate saturations, especially for the gas cycling cases,compared to the MBO model initialized with GOR/OGR
versus depth and the compositional model.
Constant Composition with Depth. For the constant
composition case modified black-oil model was initialized
with either solution oil-gas ratio versus depth or saturation
pressure versus depth tables, which correspond to the
composition at a reference depth of 12,800 ft.The constant composition case was only run for the natural
depletion to show that initialization methods do not affect the
performance of the MBO model if compositional gradient isnot used and identical pressure, oil-gas ratio, recovery factor
and saturation plots can be obtained.
Also if the effect of gravity is negligible, both initializationmethods give the same initial fluids in place. The error in
initial fluids in place is calculated as 4 % for both initializationmethods. Table 6 shows the oil in places values for
compositional and MBO models initialized with two different
methods for the unifom composition case.
Compositional Gradient. Variation of the composition of C1-
N2 and C7+ with depth is presented in Figs. 10 and 11.
Corespondingly MBO model was initialized with solution gas-
oil and oil-gas ratio versus depth tables and saturation pressure
versus depth tables to investigate the effects of different
initialization methods. Table 7shows that when the black-oilmodel was initialized with saturation pressure versus depth, a
better representation of initial fluids in place could be
obtained. The error in initial fluids in place can be as low as 2% with saturation pressure initialization. With the use of
compositional gradient, different initialization methodsexhibited different initial fluids in place values.
Numerical SimulationA quarter of a 5-spot model with the description of a real gas
condensate fluid system was scaled to represent the entire
field. The top of the model is at 12,540 ft with an initialpressure of 5,868 psia at a reference depth of 12,800 ft. The
gas water contact is at 12,950 ft. The 359 ft total thickness is
represented by 18 layers having different porosity and
permeability values. Table 8 gives the thickness, porosity and
permeability values for each layer.
The injector and producer wells are located on the oppositecorners of the model. The producer operates under the
constraint of a fixed gas production rate of 3,000 Mscf/D unti
the minimum bottomhole pressure is reached. For the gas
cycling cases the optimum injection rate was chosen to be
2,500 Mscf/D and a three separators having 500, 30, 15 psiapressure and correspondingly 180, 150, 80 oF temperature
increments, were used on the surface.
Natural DepletionInitially a discrepancy in saturation pressures versus depth was
observed in MBO model for both uniform composition and
compositional grading with depth cases. The differences insaturation pressures versus depth for uniform and
compositional gradient initialization methods are given in Fig
12 and Fig. 13. The second figure shows that error in
saturation pressures increases with depth when thecompositional gradient is used.
The differences in saturation pressures resulted in earliercondensation and lower oil production rates in MBO mode
initialized with oil-gas ratio versus depth. On the other hand
saturation pressure versus depth table initialization made the
model more sensitive to pressure drop in the reservoir and the
model exhibited more condensate drop-out and higher oil
production rates at early times. However, it was observed thatthe error in saturation pressure versus depth had a little impac
on the production performance and recoveries and it
diminished as the reservoir was depleted.Oil production rate and the average field pressure for both
models are given by Fig. 14 andFig. 15.MBO model exhibits
slightly higher-pressures initially since early condensate dropout and accumulation around the wellbore reduces relative
permeability to gas and slows down the gas production and aswell as the pressure drop in the reservoir.
According to Fig. 16 andFig. 17 the effect of initialization
method on the performance of the MBO model is lesspronounced if the composition is not changing with depth.
Fig. 18 shows the comparison of two different
initialization methods for average saturation in each model. Byobserving the oil saturation values below critical saturation
that is 0.24, it can be concluded that a reduction in oi
saturation above this value is due to mobilization of liquid
phase and a reduction in oil saturation below this value is dueto revaporization. The liquid holding tendency of the gas in
modified black-oil model is dependent on the pressure. The
oil-gas ratio plot generated by the EOS determines therevaporization process in MBO model and this allows gas to
pick-up oil until it reaches to the value determined by the PVTtable. The tabulated values of oil-gas ratios at lower pressures
are very small. Accordingly the presence of more gas would
have caused excess amount of revaporization in MBO modeas will be seen gas cycling case.
The oil saturation distribution at the end of the simulation
time is given by Fig. 19 andFig. 20. In compositional modean additional condensate bank away from the producer is
observed. The same bank cannot be observed in the MBO
model. The wells are completed in the first nine layers and the
drainage of the fluids is faster from these layers in relation to
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completions and their higher permeability values. At the top of
the reservoir even though the gas is not as rich as in the
bottom layers because of compositional grading, condensationis still more effective due to faster drainage. At some distance
away from the producer, closer to the top of the reservoir
where no flow boundary conditions dominate, quick drainage,
pressure drop and lack of pressure support from the
neighboring layers in the region may form this kind ofbanking. If the injector well is completed inside this
additional bank or outside the bank but in the lower layers, itwill only be effective around the near wellbore region and
production from top layers will be negatively affected. The
size of the bank in the case of uniform composition is much
larger as can be seen in Fig. 21 since the percentage of heavy
components in the upper layers increases when the uniformcomposition is assumed.
For the natural depletion case two types of runs were
conducted to investigate the effect of completions. The first
one with the well completed in the first two layers and thesecond with the well completed in the last two layers. For the
two runs conducted average field pressure, oil production rate,saturation and gas-oil ratio comparison plots exhibited exactly
the same patterns as the previous examples. The differences in
recovery factors between compositional and MBO models for
upper and lower completions are given as 4 % and 7 % at the
end of the simulation time. The effect of the location of the
completions on the production performance is morepronounced for gas cycling cases and will be further
investigated in this section.
Gas CyclingTo investigate the effect of different parameters on
revaporization process, the producer is completed in the topnine layers and the injector is completed in the bottom nine
layers for all the cases except, the cases including theinvestigation of the effects of completion locations. By doing
so the bottom layers with high permeability and higher heavy
fractions are open to flow and also consequent channelingwith revaporization is expected to be maximized. Production
and injection rates are 3,000 and 2,500 Mscf/day.
Compositional model has the produced gas as injection gas,which gets leaner with time by passing through the three-stage
separator system and MBO model has the regular gas phase
option as an injection gas. The injected gas behavior in MBO
follows the gas PVT table characteristics obtained by Whitsonand Torp6method.
In compositional model the revaporization process begins
with the lighter ends of the oil and proceeds slowly with timesince the stripping of the liquid components is in inverse
proportion to their molecular weight. In MBO model the oiluptake of the injected gas is only a function of pressure which,
results in excess amount of revaporization. According to Fig.
22 andFig. 23 higher pressure dependent vaporization leavesless oil in the reservoir giving slightly higher oil production
rates for MBO model towards the end of the simulation.
The extent of vaporization occurring in both models can bequantified from Fig. 24through Fig. 28. According to the first
three plots, the third gridblock from the producer for layer
nine (23, 23, 9), gives zero condensate saturation at 5000 days,
which is not the case with compositional model and MBO
model initialized with saturation pressure versus depth table
The last two plots are the examples of unrealistic vaporization
in oil-gas ratio versus depth initialized MBO model forgridblocks at the producer in layer four and five. Higher oil
saturation is obtained from MBO model but as soon as the
displacement front arrives all the oil is vaporized. This type o
formulation allows dry gas to pick up oil until the gas becomes
saturated. Since miscibility cannot be represented in MBO, thearrival time of displacement front differs for both
compositional and MBO models and as well as for differentinitialization methods among the MBO models.
The liquid content of the initial gas composition and
different gas compositions obtained by flashing the origina
gas to different pressures is given in Fig. 29. The figure was
generated by flashing the original gas to 5,000, 4,000 and3,000 psia and generating black oil tables for each pressure
In fact, this process represents the changes in oil-gas ratio of
the injected gas during the cycling. According to the figure
especially at high pressures, it is not possible to accuratelyrepresent the continuously changing PVT properties of the
recycled gas with single PVT table in MBO model since everytime the produced gas passes through the separators and is
injected back into the reservoir its oil-gas ratio and
accordingly vaporization characteristics changes.
In the swept zone, the reservoir pressure is either above or
below its original dew point when the injection gas fron
arrives. If it is above the dew point a gas-gas miscibledisplacement will yield 100 % recovery of the curren
condensate in place, which is the case with higher production
and injection rates. If reservoir pressure is below the dew poinwhen the displacement front arrives, ultimate recovery of
condensate depends on both gas-gas miscible displacement o
the reservoir gas, and partial vaporization of the retrogradecondensate. The latter case is encountered with lower
production and injection rates and the amount of condensatedrop-out before gas-gas miscible displacement takes place is
determined by the fluid type. Fig. 30 shows the average oi
saturation obtained from both models for low production andinjection rates. The condensation times indicate the increasing
differences between the models with lower production and
injection rates.The richest part of the gas is located at the bottom of the
reservoir due to gravitational forces and the compositiona
effects, such as development of miscibility changes with
depth. Since miscibility cannot be represented with black-oimodels, more discrepancies are expected in the regions where
highly miscible processes take place i.e. around the bottom
completions. When the producer and injector were completedat the bottom part of the reservoir (layer 10 to 18), it has been
observed that saturation pressure versus depth initializationmethod resulted in extreme amounts of condensate
accumulation initially in MBO model. An unrealistic
vaporization of all the condensed oil follows in the swept zoneuntil the saturation becomes to the level given by the
compositional model. Fig. 31 andFig. 32 show the average oi
saturation and gas-oil ratio plots for the bottom completionscenario.
When kv/kh ratio is reduced to an extreme value of 10-4
which almost restricts the mass transfer between layers, it is
clearly observed that compositional and MBO models showed
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closer performances both for natural depletion and gas cycling
cases.
The reduced communication between layers prevented themixing of the leaner reservoir gas (relative to initial
conditions) with the oil formed after condensation. In the case
of good vertical communication; the leaner gas after the first
drop-out, tends to go up and at the same time vaporizes the oil
on its path during the continuing depletion process. Also theaccumulated condensate tends to go down under gravity
forces. Both scenarios are not possible with the restrictedvertical communication. Every layer is left with its own ability
to vaporize the condensate accumulated. In the case of
reduced vertical communication, condensate accumulation and
vaporization process for each layer is proportional to the
layers content of heavy and light component fractions.Compositional effects gain importance at the bottom part of
the model because of the isolated richer gas phase. Fig. 33 and
Fig. 34 show the oil production rate and gas-oil ratio plots for
reduced vertical communication.The lower drawdown pressure for horizontal well,
compared to the vertical well, for the same flow rate,considerably reduces retrograde condensation.9 Therefore
there is less condensate deposited near the horizontal wellbore.
This means lesser liquid drop-out and smaller amounts of
vaporization for MBO model, which in turn makes the models
give similar performances. Dehane and Tiab9 compared the
productivity of the horizontal and vertical wells for a gascondensate reservoir. According to their results the
productivity of the horizontal well outperforms the
productivity of the vertical well and drain hole length is themost important criteria for the productivity of a horizontal
well. Longer drain hole causes a lower drawdown and less
condensation around the wellbore, which is an importantfactor in duplicating the fully compositional model
performance with MBO model. In comparison with the runsthat had horizontal well completed in upper and bottom layers,
it can be concluded that MBO model performance with
horizontal well approaches to the compositional modelperformance if the well is placed closer to the area where fluid
sample is coming from, even if the sample is coming from the
bottom part of the reservoir. If the well is placed in the upperlayers also a good match can be obtained since the gas
becomes heavier with increasing depth. Also with the
horizontal well, error in dew point pressure versus depth is
almost eliminated for the gas cycling case and a betteragreement between the models has been obtained compared to
the vertical wells. Fig. 35 through Fig. 37 gives the oil
production rate, gas-oil ratio and recovery factors for gascycling with horizontal well set as a producer.
Conclusions1. The performance of the MBO model is not affected
by the initialization method if composition is constantwith depth. Also OOIP is the same for all
initialization methods if no compositional gradient is
used.2. Unrealistic vaporization in MBO model is not just
limited to gas cycling, it can also be encountered in
natural depletion to some degree depending on the
depletion scenario.
3. In natural depletion the gas present in MBO has alower capacity to hold liquid and more oil is left in
the reservoir.4. In gas cycling case, the injected gas in MBO can pick
up oil as a function of pressure and the oil left in the
reservoir is always lower than in the compositional
model.
5. Lower kv/khratios provide a better match between themodels.
6. The arrival time of displacement front differs for bothcompositional and MBO models and as well as for
different initialization methods among the MBO
models.
7. Due to reduced retrograde condensation and partialelimination of the error in dew point pressure versusdepth, MBO model with the horizontal wells exhibits
better agreement with compositional model.
8. Oil saturation distributions around the well andthroughout the reservoir may be quite different in twomodels regardless of a match with the production
performance.
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presented at the 1980 SPE Fall Technical Conference and
Exhibition, Dallas, Texas, 21-24 September.24. Hirschberg, A.: Role of Asphaltenes in CompositionalGrading of a Reservoirs Fluid Column, JPT (January1988), 5, 89.
25. Kenyon, D. E. and Behie, G.A.: Third SPE ComparativeSolution Project: Gas Cycling of Retrograde CondensateReservoirs, paper SPE 12278 presented at the 1983Reservoir Simulation Symposium, San Francisco, 15-18
November.26. Izgec, B.: Performance Analysis of Compositional and
Modified Black-Oil Models for Rich Gas CondensateReservoirs with Vertical and Horizontal Wells, MS
Thesis, Texas A&M University, College Station, Texas(2003).
Table 1 Extended mix ture composition
Com ponent Sym bol Mol %
Carbon Dioxide CO2
4.57
Nitrogen N2 0.52
Methane C1
68.97
Ethane C2
8.89
Propane C3
4.18
Isobutane iC4
0.99
N- Butane nC4 1.4
Isopentane iC5
0.71
N-Pentane nC5 0.6
Hexanes C6
0.99
Heptanes C7
1.02
Octanes C8
1.28
Nonanes C9
0.97
Decanes C10 0.73
Undecanes C11
0.53
Dodecanes C12 0.44
Tridecanes C13 0.48
Tetradecanes C14
0.41
Pentadecanes C15
0.36
Hexadecanes C16
0.28
Heptadecane C17
0.26
Octadecanes C18
0.24
Nonadecanes C19
0.19
Eicosanes C20
0.16
C21 's C21
0.13
C22 's C22 0.11
C23 's C23 0.1
C24 's C24
0.08
C25 's C25
0.07
C26 's C26
0.06
C27 's C27
0.06
C28 's C28 0.05
C29 's C29
0.04
C30+ C30+ 0.13
Table 2 Pseudocomponent grouping andcomposition
Ps eudocom ponent Com ponents Mol %
CO2
4.57
GRP1 N2-C
1 69.49
GRP2 C2-C
3 13.07
GRP3 C4-C
6 4.69
GRP4 C7-C
10 4
GRP5 C11
-C16
2.5
GRP6 C17-C34 1.68
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Table 3 Pseudocomponent properties
Com ponent Molecular Weight Pc (ps ig) Tc (0F)
CO2 44.01 1056.6 88.79
GRP1 16.132 651.77 -117.46
GRP2 34.556 664.04 127.15
GRP3 67.964 490.47 350.279
GRP4 112.52 384.19 591.912
GRP5 178.79 269.52 781.912
GRP6 303.64 180.2 1001.13
Table 4 Pseudocomponent properties
Component ZC VC(ft3/lb-mo l) s-Shifts
CO2
0.27407 1.50573 -0.045792
GRP1 0.28471 1.56885 -0.144168
GRP2 0.28422 2.63712 -0.095027
GRP3 0.27197 4.67964 -0.041006
GRP4 0.25668 7.26188 0.003672
GRP5 0.23667 11.09534 0.00893404
GRP6 0.21972 17.67366 0.0115616
Table 5 Variation in parameters selected forregression
Parameter Ini tial Value Final Value % Change
BICGRP6-GRP1 0.0544 0.1231 -126.28BIC
GRP6-GRP2 0.01 0.0226 -126
BICGRP5-GRP1
0.0464 0.1052 -126.72
BICGRP5-GRP2
0.01 0.0226 -126
BICGRP4-GRP1
0.0377 0.0248 34.21
BICGRP4-GRP2
0.01 0.0066 34
BICCO2-GRP1 0.1 0.0657 34.3
BICCO2-GRP2 0.1 0.0657 34.3
BICCO2-GRP3
0.1 0.0657 34.3
BICCO2-GRP4
0.1 0.0657 34.3
BICCO2-GRP5
0.1 0.0657 34.3
BICCO2-GRP6
0.1 0.0657 34.3
SFCO2 0.0066 -0.0458 793.93SF
GRP4 0.0525 0.0037 92.95
SFGRP5
0.0714 0.0089 87.53
SFGRP6 0.095 0.0116 87.78
Table 6 Fluid in place and CPU time for uniformcomposition with depth
OOIP, s tb CPU, s ec. Er ror in OOIP, %
Compositional 999916.20 785.91 -
Rv vs Dept h 958733.40 64.47 4.11
Pd vs Depth 958733.40 65.00 4.11
Table 7 Fluid in place and CPU time withcompositional gradient
OOIP, s tb CPU, s ec. Er ror in OOIP, %
Compositional 941669.40 745.56 -
Rv vs Dept h 888033.20 72.22 5.69
Pd vs Depth 922730.10 64.28 2.01
Table 8 Reservoi r Propert ies
Layer Thickness Poros ity Perm eability (m d)
1 20 0.087 0.1
2 15 0.097 0.2
3 26 0.111 0.3
4 15 0.16 0.2
5 16 0.13 7
6 14 0.17 0.1
7 8 0.17 14
8 8 0.08 2
9 18 0.14 12
10 12 0.13 3
11 19 0.12 10
12 18 0.105 9
13 20 0.12 0.1
14 50 0.116 0.3
15 20 0.157 0.2
16 20 0.157 0.2
17 30 0.157 0.2
18 30 0.157 0.2
Table 9 CPU time in seconds for vertical wells
Com pos itional MBO MBO
Rvvs Depth Pdvs DepthNatural Depletio n
Constant Composition 785.91 64.47 65
Compositional Gradient 745.56 72.22 64.28
Bottom Completion 539.12 82.58 81.32
Top Completion 820.37 80.35 79.01
Reduced kv
985.45 106.35 103.2
Gas Cycling
Compositional Gradient 3021.78 597.77 582.49
Bottom Completion 3068.71 458.86 479.42
Top Completion 3296.56 531 603.04
Reduced kv
4743.82 363 453.81
Low Rates 1957.74 401.39 626.68
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0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 1000 2000 3000 4000 5000 6000 7000Pressure (psia)
RelativeVolu
me
Simulated
Experimental
Fig. 1 Simulated and experimental relative volume data from CCEat 254 F
0
0.05
0.1
0.15
0.2
0.25
0 1000 2000 3000 4000 5000 6000 7000
Pressure (psia)
LiquidSaturation
Simulated
Experimental
Fig. 2 Simulated and experimental liqu id saturation data from CCEat 254 F
0
5
10
15
20
25
30
0 1000 2000 3000 4000 5000 6000 7000
Pressure (psia)
GasDensity
(lb/ft3)
Simulated
Experim ental
Fig. 3 Simulated and experimental gas density data from CCE at254 F
0
0.5
1
1.5
2
2.5
3
0 1000 2000 3000 4000 5000 6000
Pressure, psia
GOR,M
scf/stb
Whitson and Torp Coats
Fig. 4 Gas-oil ratio comparison from Coats versus Whitson andTorp methods
0
0.5
1
1.5
2
2.5
3
0 1000 2000 3000 4000 5000 6000
Pressure, psia
Bo,rb/stb
Whitson and Torp Coats
Fig. 5 Oil formation volume factor comparison from Coats versusWhitson and Torp methods
0
0.1
0.2
0.3
0.4
0.5
0.6
0 1000 2000 3000 4000 5000 6000
Pressure, psia
Viscosity,cp
Whitson and Torp Coats
Fig. 6 Oil viscosity comparison from Coats versus Whitson andTorp methods
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Fig. 7 Oil-gas ratio comparison from Coats versus Whitson andTorp methods
Fig. 8 Gas formation volume factor comparison from Coatsversus Whitson and Torp methods
Fig. 9 Gas viscosity comparison generated from Coats versusWhitson and Torp methods
12500
12550
12600
12650
12700
12750
12800
12850
12900
12950
13000
0.6 0.62 0.64 0.66 0.68 0.7 0.72 0.74
Molar composit ion fraction
Depth(ft)
GWC
0
0.02
0.040.06
0.08
0.1
0.12
0.14
0.16
0.18
0 1000 2000 3000 4000 5000 6000
Pressure, psia
OG
R,stb/Mscf
Whitson and Torp Coats
Fig. 10 C1-N2compositional gradient
12500
12550
12600
12650
12700
12750
12800
12850
12900
12950
13000
0.04 0.06 0.08 0.1 0.12 0.14 0.16
Molar composit ion fraction
Depth(ft)
GWC
0
1
2
3
4
5
6
7
8
0 1000 2000 3000 4000 5000 6000
Pressure, psia
Bg,rb/Mscf
Whitson and Torp Coats
Fig. 11 C7+compositional gradient
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0 1000 2000 3000 4000 5000 6000
Pressure, psia
Fig. 12 Change in dew-point pressure with depth, uniformcomposition case
Viscosity,cp
Whitson and Torp Coats
4000
4500
5000
5500
6000
12500 12550 12600 12650 12700 12750 12800 12850 12900
Depth, ft
Press
ure,psi
Compositional Model MBO Model
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Fig. 13 Change in dew-point pressure with depth, compositionalgradient case
Fig. 14 Oil production rate for the model initialized withcompositional gradient
Fig. 15 Average field pressure with composi tional gradient
0
100
200
300
400
500
600
0 500 1000 1500 2000
Time, days
ProductionRate,stb/day
MBO initialized w ith fixed RvCompositionalMBO initialized w ith fixed Pd
4000
4500
5000
5500
6000
12500 12550 12600 12650 12700 12750 12800 12850 12900
Depth, ft
Pressure,
psi
Compositional Model MBO Model
1044 psia900 psia
4000
4500
5000
5500
6000
12500 12550 12600 12650 12700 12750 12800 12850 12900
Depth, ft
Pressure,
psi
Compositional Model MBO Model
1044 psia900 psia
Fig. 16 Oil production rate for the natural depletion case, constancomposition
0
20
40
60
80
100
120
0 500 1000 1500 2000
Time, days
GOR,Mscf/stb
MBO initialized w ith fixed RvCompositionalMBO initialized w ith fixed Pd
0
100
200
300
400
500
0 500 1000 1500 2000
Time, days
ProdcutionRate,stb/day
MBO with Rv vs DepthCompositionalMBO with Pd vs Depth
Fig. 17 Gas oil ratio for the natural depletion case, constantcomposition
0
1000
2000
3000
4000
5000
6000
7000
0 500 1000 1500 2000
Time, days
Pres
sure,psia
MBO w ith Rv vs DepthCompositionalMBO w ith Pd vs Depth
0
0.05
0.1
0.15
0.2
0.25
0 500 1000 1500 2000
Time, days
Saturation
MBO w ith Rv vs DepthCompositionalMBO w ith Pd vs Depth
Fig. 18 Oil saturation distribution for the model initialized withcompositional gradient
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Fig. 19 Oil saturation distribution from compositional model withcompositional gradient
Fig. 20 Oil saturation distribution from MBO model withcompositional gradient
Fig. 21 Oil saturation distribution from compositional model foruniform composition
0
0.02
0.04
0.06
0.08
0.1
0.12
0 1000 2000 3000 4000 5000 6000
Time, days
Saturation
MBO w ith Rv vs DepthCompositionalMBO with Pd vs Depth
Fig. 22 Average oil saturation for gas cycling case
0
20
40
60
80
100
120
0 1000 2000 3000 4000 5000 6000
Time, days
GOR,Mscf/stb
MBO with Rv vs DepthCompositionalMBO with Pd vs Depth
Fig. 23 Gas-oil ratio for gas cyclin g case
0.05
0.1
0.15
0.2
0.25
0.3
1 2
Gridblock Number
Satura
tion
3
500 day s 1000 day s 1500 day s 2000 day s
2500 days 3000 days 4000 days 5000 days
Fig. 24 Saturation distributi on for compositional model for layer 9
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Fig. 25 Saturation distr ibution for MBO model for layer 9
Fig. 26 Saturation distribution for MBO model (Pd versus depthiniti alization) for layer 9
Fig. 27 Saturation di stribu tion for MBO model gri dblock (25, 25, 4)
0
0.05
0.1
0.15
0.2
0.25
0.3
1 2 3
Gridblock Number
Satura
tion
500 day s 1000 day s 1500 day s 2000 day s
2500 days 3000 days 4000 days 5000 days
0
0.05
0.1
0.15
0.2
0 1000 2000 3000 4000 5000 6000
Time, days
Saturation
CompositionalMBO with Rv vs Depth
Fig. 28 Saturation di stribut ion f or MBO model gri dblock (25, 25, 5)
Fig. 29 Oil-gas ratio versus pressure generated from differencompositions
Fig. 30 Average oil saturation for low production and injectionrates
0.1
0.15
0.2
0.25
0.3
1 2
Gridblock Number
Saturation
3
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0 1000 2000 3000 4000 5000 6000
Pressure, psia
LiquidContentofGas,stb/Mscf Without flashing original gas
Flash to 5000 psiaFlash to 4000 psiaFlash to 3000 psia
500 day s 1000 day s 1500 day s 2000 day s
2500 days 3000 days 4000 days 5000 days
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0 1000 2000 3000 4000 5000 6000
Time, days
Saturation
MBO w ith Rv vs DepthCompositionalMBO Pd vs Depth
0
0.05
0.1
0.15
0.2
0 1000 2000 3000 4000 5000 6000
Time, days
Saturation
Compositional
MBO with Rv vs Depth
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Fig. 31 Average oil saturation with wells completed at the bottomof the model
Fig. 32 Gas-oil ratio with wells completed at the bottom of themodel
Fig. 33 Oil productio n rate for kv/khratio of 0.0001
0
20
40
60
80
100
120
140
160
180
0 1000 2000 3000 4000 5000 6000
Time, days
GOR,Mscf/stb
MBO with Rv vs DepthCompositionalMBO with Pd vs Depth0
0.02
0.04
0.06
0.08
0.1
0 1000 2000 3000 4000 5000 6000
Time, days
Saturation
MBO w ith Rv vs DepthCompositionalMBO w ith Pd vs Depth
Fig. 34 Gas-oil ratio f or k v/khratio of 0.0001
0
50
100
150
200
0 1000 2000 3000 4000 5000 6000
Time, days
GOR,Mscf/stb
MBO w ith Rv vs DepthCompositionalMBO with Pd vs Depth
0
100
200
300
400
500
0 1000 2000 3000 4000 5000 6000
Time, days
Rate,stb/day
MBO Compositional
Fig. 35 Oil production rate for gas cycling with horizontal well
0
50
100
150
200
0 1000 2000 3000 4000 5000 6000
Time, days
GOR,M
scf/stb
MBO Compositional
0
50
100
150
200250
300
350
400
450
0 1000 2000 3000 4000 5000 6000
Time, days
ProductionRate,stb/day
MBO with Rv vs DepthCompositionalMBO with Pd vs Depth
Fig. 36 Gas-oil ratio for gas cycling with horizontal well
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0
0.1
0.2
0.3
0.4
0.5
0 1000 2000 3000 4000 5000 6000
Time, days
Recovery
Factor
MBO Compositional
Fig. 37 Recovery factor for gas cycling w ith hori zontal well