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SPE 14129
The Role of Reservoir Simulation in Optimal
Reservoir Management
by G.W. Thomas, Scientific Software-intercomp
SPE Member
Copyright
1X, Sockty of
PetroleumEnginaara
This paperwas proaantd at theSPE 19SSInternationalMeeting
on petroleumEngineeringheld in Beijing,CMa
March
17-20,
19SS.The materialis
subjecttocorrectionbythe author.PermissiontoCOPYsrestrictedto an ab.str~ OfMt morethan300 words,WriteSPE. P.O. SoxS33S3S,Richardson.
Taxas 7SCSMS3S. Telex 730SS9 SPE DAL.
SIMULATIONANDVIRGINRESERVOIR DEVELOPMENT
When a reservoir simulator is employed to assist in
ABSTRACT
ptenning the development of a virgin reservoir, the
reservoir description is typically limited. Consequ@ly,
This paper discusses the role reservoir simulators only a minimal degree
of
optimisat ion is poa%ible.
play in formulating initial development plans, history
Nevertheless, some useful insights can be cbtained with
matching and optimizing future production and in planning
the aid of a simulator that can minimise the number of
and designing enhanced oil recovery projects. The Hibernia
decisions one must make in planning field development.
Field in Canada and the Hassi R’Mel in AIgeria illustrate how
In perticuter, the simulator can end should be used to
simulation can be used to asdst in initial reservoir
a$sesa sensitivity in computed results to uncertainties in
development. The Lookout Butte F.undle (Alberta) and others
the reservoir description and rock-fluid data.
It is
are cited to exemplify Optimhsl,fon of future production
surprising how often variations
input data over
plans with the aid of simutetion. Finally, applications to
reasonable ranges of uncertainty, for some reservoirs,
several reported EOR projects are briefly discussed with
yield modest changes in the computed results. On the
major emptux~is concentrating on the Bati Raman Field in
Turkey.
other hand, it is useful to know, in the early stages of
development, where the greatest effort should be
concentrated to obtain those data that affect calculated
INTRODUCTION
performance the most.
‘he purpose of this paper is to provide an overview
Simulation studies at the development stage
on the role of reservoir simulation in managing hydrocarbon
because of the uncertainties involved, are regarded as
reservoirs. As pointed out by Coatsl , reservoir simulation, in
the broad sense, has been practiced since the 1930%, when
preliminary. Npically, they are periodically updated as
more information becomes available; This means that
some
of
the first calculetionaI procedures were deveIoped to
early development plans arising from the first sim’? ation
predict reservoir performance. Here, however, we take a
studies should be sufficiently flexible to accom mudate
narrower view, and restrict our discussion to applications of
future contingencies as one learns more about the
numerical reservoir simulation. ‘his involves solving targe reservoir. This presents a severe challenge where the
s~ algebraic equations on digitaI computers to
reservoir in question is highIy complex, large in extent or
approximate transient, multiphaee
or
muIticomponent flow in in a hostiIe environment - all of which may require large
heterogeneous media. ‘I?tis technoIgy started in the mid to
investments to put it on production.
late 1950%and, within the last twenty years, has played an
increasingly important-role in the development, planning and
In cases where the reservoir description and roek-
management of gas and oiI reservoirs.
fluid properties are reasonably defined, one can we a
simutetor to plan well locations and densities aswtming
In the folluwing, we first discus~ the role of
voidege replacement by injection to maintain pres..ure.
reservoir simulation as a tool in planning the initia 1 Such strategies can be compared to primary depletion
development of a reservoir. The discussion then turns to through the same number of wells to arrive at the best
their uses as predictive tools when investigating various
development policy for the reservoir.
future operating strategies.
Finally, some attention is
devoted to their utility in planning and executing enhanced Arwlication to the Hibcrnia FieId
oil recovery schemes. Illustrations in the form of case
histories are provided, albeit these are necessarily not
To illustrate, we cite the Hibernia Field off the
detailed because of space limitations.
Neverthele$w,
3fIStePn Ccest of Canada2. me fjeId lies abut 32tI km
sufficient references to recent literature on the subject are
southeast of St. John%, Newfoundland in a water depth of
given for the interested reader.
80 m. Five welts were drilIed to confirm the existence of
substantial hydrocarbon reserves
in at least two
reservoirs, the Avalon and the Hibernia sendstones. The
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SPE 14129
Avalon reservoir appears to be heterogeneous with wide
Applications to Gas Condensate Systems
variations in the porosity and permeability, whereas the
deeper Hibernia is more homogeneous. Correlations of the
In the Hibernia Field, a black-oil reservoir simulator
limited porosity - permeabili ty data were used to extrapolate
was employed to arrive at preliminary development
into areas where data were lacking.
Correlations of decisions.
This 1s frequently done even though the
verticaI/horizontal permeability ratios were used in a similar
reservoir may contain fluids that undergo substantial
manner. A porosity cutoff of 13% was used to define the net
compositional changes during production. The motivation
pay in the Avalon while 10% was employed in the Hibernia.
for doing so is most often due to lack of data precisely
Average connate and residual oil saturations in the Avalon
defining the compositional behaviour of the fluids in the
were estimated at 25%.
For the Hibernia, connate water
early development stages. Moreover, black-il simulators
varied from 11 to 15% while 30% average residual oil
can still provide usefuI information in such systems at
saturation was assumed.
substantially lea.. cost than a compositional simuIator5.
EventuaNy, however, resources must be devoted early on
AH evidence indicates that the two reservoirs are
to the correct characterisation of the fluids and definition
non-cornmunicating.
The Avalon ccntains an apparent
of their phase behaviour.
undersaturated crude oil with a relative density of 0.873. PVT
properties for the hydrocarbon were obtained from a drill stem
As exampIes, we cite two large gas condensate
test fluid sample.
The Hibernia reservoir has more
reservoirs.
The first, the Has..i R’Mel is located in
complicated fluid propties in two separate fault blocks. In
Algeria6. The field was discovered in 1953 and contained
one, a saturated crude, probably a volatile oil, of relative
about 1.7 x 1012 mS
of
retrograde condensate gas at
density, 0.825, is apparently overlain by what appears to be a
32x10S kPa.
The reservoir has a surface area of 4800
gas condensate with a liquid gas content of 0.001 m /m*. For
km’.
Because of its vast reserves and closeness to ports,
this block the fluid properties
were generated using an ambitious development plan was executed in the earIy
correlations assuming an initial seturat ion pressure of 40x10
1970%baaed on a bleck-oit simulation study. At the time,
end a sclut ion gasail ratio of 356 m ‘/m’. In the other fault
only 20 wells had been drilIed and the geological
block, the oil appears to be undersaturated having a relative description was limited. Consequently, full continuity of
density of 0.850, there again, a drill stem test fluid was
the reservoir was assumed. The objective was to produce
analysed to determine the PVTproperties.
a fixed daily rate of rich gas, extract the condensate,
market scma of the- dry gas end reinject the rest to
The first simulation runs involved 2-dimensional
recover any condensate dropout that might occur.
For
cross-sect ions to generate pseudo functions3~4 for subsequent
this purpose, a line drive gas injection scheme was
use in 3+3imensional model% For the Avalon and Hibernia, 21-
implemented.
and 5-layer models, respectively, were used to generate
pseudo relative permeabiIities.
These subsequently were
Haaei R’Mel now has about 200 welLs and giant
employed in a 28 x 23 x 2 AvaIon model and a 24 x 20 x 2
plants for ga? treatment and gas injection. production to-
Hibernia model. h each case, square grid blocks 569 m on a
date is 5 to 6% of the initial gas reserves. During the
side were employed. Well locations were originally selected to development drilling, en oil ring of 0.82 relative density
give reasonable pettern coverage over thoseregions where the and 15.2 m thickness was discovered - hence Haasi RIMel
oil accumulations were considered to be greatest . Completion
can be regarded as a volatile oil reservoir with a huge rich
intervals for producers and injectors were selected such that
gas cap. A fault system was also discovered that was
oil production would be favoured while production of gas and subsequently better defined by seismic investigation.
water, where pert inent, was minimised.
Some revisions were made in the geological description of
the field when 100 weUa were in place. The subsequent
Four production/injection
scenarios were
need is to @rform a major update using information from
investigated in the Avalon while four and five were considered
all welt., the production history, the seismic surveys and
for each of the fault blocks in the Hibernia reservoir. Some of
state-of-the-art simulation tooLs.
In particular, the
the results of the study are shown in Figs. 1-3. In the~
effects of the faults and retrograde condensation and
figures W.I. and G.I. refer to flank water and crestal gas
revapourisation need to be examined in detail. The
injection, respectively.
It is seen that in the AvaIon,
appropriatenes~ of the line drive is aLscin question.
differences in the water and gas injection cases were
insignificant with the present geological description of the In such an update, one first determines to what
reservoir. In the Hibernia, it was found that an ultimate
extent, if any, he can use previous seismic, geological and
recovery level of 50% of the original oil-in-place may be
petrophysical interpretations.
With regard to a
achieved through an optimised production/injection strategy.
retrograde condensate, the effect of liquid dropout on
The uncertainties in these reauIts are linked to the geological well deliverability is also an important issue. Moreover,
model. As”the latter is improved in the early development
where cycling is performed, one would like to know what
planning process, optimum recovery schemes can be desigiwd the .~timum is to maximise Iiquid revapouriaation.
to account for the reservoir complexities.
Again, in reservoirs with thin oil zones overlain by
massive gas reserves - and possibly underlying water - the
probebitity of coning can be high should producing weila
be completed in the oil zone. The question arises, can the
oil be recovered through displacement or vapouriaat ion by
selective completion of dry gas injection welLs, as an
alternative to producing directly from the oil zone?
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SPE 14129
G.w. Thomas
Finally, given a certain well pattern - like the line drive in
development. Here we’ve just conveyed the flavour for
the Has$i R’Mel -
is it the optimum in view of possible
some particular cases. The approach one takes is of
geological discontinu{ties such as faults, pinchouts etc?
course problem+ependent and may be unique for a given
These and similar issues constitute the natural province for
reservoir. (2) The devebpment plan, even though aided by
reservoir simulators and sometimes definitive answers can
sophisticated tools, should be regarded as tentative.
emerge from carefully constructed models.
Effort should be made, during the early stages, to endow
it with maximum flexibility and continually upd&te it with
The issues of lSquid dropout, revapourisation, etc.
additional simulation studies as new data are obtained.
may at some point require application of a compositional
wimulator. Such simulators internaUy generate the PVT SIMULATORS AS PREDICTIVE TOOLS IN DEVELOPED
characteristics of the hydrocarbon fluids using a “tuned”
RESERVOIRS.
phase behaviour package. me ‘tuning” as performed prior to
the simulations by adjusting certain coefficients and/or
In a sense, development of a reservoir is an on-going
parameters in the phase behaviour package such that it
process that continues over its productive life. However,
reproduces, within acceptable limits? the results of a
one can divide reservoirs into two categories - those with
particular laboratory experiment on the hydrocarbon fluid.
little or no productive history, end those that have
The coefficient adjustment is accomplished using regression
produced for some period of time. ‘Ihe distinction is
analysis5 or trial-and+rror computer runs. It is important in
particularly clear with regard to reservoir simulation. In
such applications that data errors (from sampling, laboratory
the former case, the simulator is applied in a qualitative
analysis, etc) be kept to en absolute minimum. Furthermore,
sense, i.e., it is not a priori calibrated to a particular
fluid samples from different wells wiU, hopeful~y, have
reservoir% characteristics, since these are largely
similar or neer+imilar characteristics such that a
unknown. In the latter, the response of the reservoir to
representative or several regional representatives can be
some predecided development plan is presumably known,
used to typify the whole. Unfortunately, this is not always
and effort is first devoted to the task of calibrating the
the case.
simulator such that it reproduces the response i.e. the
past production history. This history matching involves
For
example, h Fig. 4’we djspley plots of retrograde
trial-end-error runs with the simulator in which input data
liquid dropout (as percentage of hydrocarbon pore volume) as
adjustments are made within reasonable bounds until a
functions of pressure for several fluid samples taken from a
satisfactory match is achieved. *
large (2000 km*) lean gas retrograde condensate reservoir
(the name and location are witheld for proprietary reasons).
TypicaUy, one seeks to reproduce the field-wide pressure,
Such data are derived from constant volume depletion
water-oil ratio and ges+il tatio performance and also
experiments under controUed laboratory conditions on what
match individual weU behaviour for the asme vnriables.
presumably are representative fluid semples7. Obviously,
Unfortunately, the procedure frequently involves iu-
from Fig. 4 one cannot easily decide which well sample is conditioned systems, and unique results are not
representative.
The proper choke becomes even more
guaranteed.
As a consequence, it can be time
cIouded given the poasibititiea for eempting errora
consuming, coatty, and, at times, frustrating. However, a
(contamination, fluid 10ss, long dMsnce transport, etc.).
reaourcefuI engineer with in-depth understanding of
However, in development planning, one frequently empIoye a
reservoir behaviour can achieve meaningful matches.
simulator in worst caee/beet case scenarios.
An effort is
then made to determine the most likely case between these
Performing Evaluation of the
extremes (this could be the average
of the
extremes), and
Lookout Eutte RundleA Pool
then plan the development around the latter. In this context.
if one considers depletion without cycling, men the data from Once a satisfactory match is achieved, the
WeUe 1 and 6 clearly define the worat and best cases,
simutator is used in a predictive mode to investigate
respectively, assuming retrograde liquid condensation occurs
various production alternatives. Here again, the objective
in the reservoir prior to fluid entry into the welLs. The phase
is to optimise future operations of the reservoir. As an
behaviour package is then tuned to each situation, i.e. an example of such an appUcation, we cite the Lookout Butte
effort is made to reproduce the curves in Fig. 4 for WeUs 1
Rundle A Pool located in Alberta, Canada~4. The
end 6 to characterise the hydrocarbon properties for the
reservoir is a tight, interbedded limestone having an
worst end best case situations. Should the resuIts from the
average porosity of 6.5% and permeabilities in the range
subsequent simulations for each scenario not differ
0.1 to 0.3 md. fie reservoir dips to the west end north
subetant. ‘Jly, then one need not concern himself about and is delineated by en extensive aquifer on the west, and
defining the most likely case since averages from the
a fault on the east (see Fig 5). It contains a dry gas
eXtrema would be sufficient. Otherwise, one might take
some curve weighted in favour of the pIots that are closest
together in Fig. 4 (shown by the dashed line), fit the phase
beheviour package to this, end w this tuned result in the
*Efforts have been made to deveIop software
simulator for the moat Iikely scenario.
~ams that automate the history matching t-e=.
However, these have not found Iairge scale use on a
In concluding this section we emphasise two things: commerical basis to+ate.
(1) ‘llIere are many different waya in which a reservoir
simulator can play a vital role in optimum reservoir
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SPE 141
condensate underIain by the aquifer. GeoIogicaI and core
northern and southern parts. Moreover, it is aIso regarded
data indicate the reservoir is extensively fractured and that
ashight’isk since it is near to Well 4-32 which was shut i
vertical fractures dominate.
In late 1963 production
because of high water production. The 13-32 location
commenced by depletion coupled with gaa cycling. Dry gas
gives the highest cumulative gas production and increase
was injected into one weU(We114-13 in Fig. 5)untiIlate 1967
field deliverability 3.4 x 106 m:/D over the productivity
at which time it was converted to a producer and blowdown
in 1972 (the year the study was performed). This well
started.
Prior
to this, only minor amounts of water, were
in communication with some other wetls in the field an
produced. However,
thereafter four producing welL~
was considered as a future drilling location. There wa
experienced water production that increased steadily until
however, some concern because of its proximity to th
the water-gas ratio averaged 1 x 10-5 m‘/m 1 by June, 1972. fault on the east.
The objectives of the study were to determine the
The utility of a reservoir simulator should b
mechanisms causing the water production, develop an
recognised in this brief case history.
It provide
optimum depIetion plan for the reservoir, and evaIuate the
engineering answers to certain questions that one migh
surface facilities required to carry out the depletion plan. To
pose regarding future exploitation of a reservoir. I
determine if water production was caused by water coning or
however, cannot make the decision as to which possibilit
fingering, two types of modeI studies were executed:
is the optimum. This remains within the realm of huma
Individual well coning studies using a radial gas-water
judgment (thankfully). The judgment, in this case, wa
simulator, and crossaectional studies to evaluate fingering.
that Well 5-21, because of Iow risk, should be drilled
t
Both invoked history matching the performance data. In
recover gas from the southern portion of the reservoir
addition, the adequacy of the reservoir description required
Moreover, Well 14-13 shouId be drilled even though
to match the history was evaluated. Finally, calibration of
constitutes a high risk because of substantial water influx
the simulator was accomplished by matching the pressure
However, without it, gas in the North may be trapped
history of the entire
field and the individual well
otherwise by the incoming water.
FinalIy, one shouI
performances. The results of the history match were used to
abandon Well 15-29 as a poasibilit y and re+vaIuate
determine the distribution of gas-in-place and the water
drilling of Well 13-32 after more history become
influx in the prediction and optimisation phases of the study.
available.
In addition the reservoir simulator, after history matching,
was coupled with a gas gathering system simulator to
Other interesting case histories involving histor
optimise the surface faciUtiea15. The latter exercise
matching and predictions have appeared in the recen
involved examining various possible effective line diameters
literature. One involves the Leroy Gas Storge Facility i
and welI connections to yield a maximum in deliverability. In
Wyoming16. A simulator wqa used to match the pressur
Figs. 6 and 7 we show typical matches of pressure and water- history of the reservoir incIuding the effect of a time-and
gas ratio for one of the wells in the field.
pressure-dependent leak to the surface. The simulato
was a useful tool in the ccmprehensi /e analysis required
It was concluded from the history match runs that
to understand, monitor and control the leakage. The cas
water coning was the cause
of
the water production in the
history is significant in that it documents how reIevan
reservoir. The prediction phase
of
the study involved computer simulations can, with other engineering studies
choosing one or more optimum infill drilling locations from lead to safe and economic gas storage operations. Tw
among the four possible sites indicated by the arrows in Fig.
other recent studies akc are of interest. One describe
5. A base case, with no infiU drilling was also run. The total
application of a black OK simulator to the El Gueri
field deliverability for each case is shown in Fig. 8. For the
reservoir in the Ashstart Field
of offshore Tunisia17. Th
predictions, both the reservoir and surface system were other treats the Sawtelle Field in California 18, The E
simulated simultaneously. The field was produced at the
Gueria is a moderately to highly fractured nummulitic
maximum of the production facilities. Wells were shut in
limestone originaUy containing an undersaturated oil o
when their production declined below 0.15 x 106 m‘/D or
0.88 relative density. The reservoir is produced wit
when the gas-water contact reached the bottom perforations. injection of seawater to maint~in pressure above th
bubblepoint pressure. A three+imensional model wa
Well 14-13 initially increased the field deliverability
constructed to perform the history match and predictions
about 3 x 106 m ‘/D over the other cases and 5.8 x 106 ma/D ‘Ihe model was also augmented by wellbore hydraulic
over the base case. Because the gas-water contact had been
routines to simulate vertical
or
inclined flow to th
depressed by gas-injection in the proximity of this location, surface. fie Sawtell study employed a two+imensional,
the water influx rate was very high as the contact rebounded.
three-phase black oil model and is of interest since
As a result, the well watered out at Lfie end of 1978.
involves a complex and unusually shaped reservoir
Consequently, this is regarded as a high risk well. Well 5-21
Finally, we cite the simulation study of the East Velm
presents a low risk end is necessary to drain gas from the West Block Sims Sand Unit in 0klahoma19. This study
tighter portions of the reservoir in the south. The 15-29 weIl
of intereat since it involves a rather old reservoir fo
is located in that part of the reservoir which is poorly
which
few data exists for the primary production phas
defined.
This region has limited communication with the
(1949-1962). The history match of field pressures, gas
and water+il ratios was largely for the secondary
recovery phase (1962-1972) in which water was injected
Predictions included the possibility of continue
waterflood operations and inject ion of carbon dioxide.
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G.K.
Thomas
APPLICATIONS TO EOR PROJECTS
Sometimes reservoir simulators are used to assess
the relative merits of various enhanced oil recovery (EOR)
schemes. In such cases, the simulator is used in a predictive
mode both with or without prior history matching. In
particular, Aydelotte and Pope20 and George, et a121 report
on the novel use of reservoir simulators to validate and assist
in the development of simplified, reliable inexpensive
predictive- modeLs for steamfloodin
~ and micell
ar~lymer
flooding. Recently, Frazier and Todd 2 employed a simulator
to design and evaluate an application of Iiquified petroleum
gas (LPG) in a reservoir that had previously been
waterflooded. The choice was to either abandon the field or
attempt an EOR process. The simulation study indicated that
an additional 7% of the original oil in-place could be
recovered from a miscible LPG flood.
me predictions
involved use of the best available reservoir description, i.e.
no history match runs were employed to calibrate the
simutator. l%e project was initiated in the field with propane
injection in three wells starting in July, 1980.
As of
December 1981, it appeared as though the process was
working as predicted by the simulation study.
Simulation has been used to design, monitor and
evaluate several steam in”ection projects23-27. The
A
Georgsdorf Field in Germany 7 presents an interesting case
history. Here, production history over 10 years, including six
with
steam injection,
was
satisfactorily
matched.
Considering the usual reservoir complexities and the
difficulties associated with nonisothermaI operations, the
matches are remarkably good. Predictions were then made
to determine steam requirements in certain portions of the
reservoir, to arrive at a plan for future project expansion,
and to ascertain where new injection welLs and infill
producers should be located.
A very interesting application of the use of
reservoir simulators in the management of reservoirs is
provided by the Bati Raman Field in Turkey 28. The reservoir
contains substantial reserves (2.9 x 108 m‘) of a heavy crude
oil (relative density = 0.986) with a bubble point pressure of
1103 kPa, The amount of gas in solution at the bubble point
pressure is quite low, i.e. 3.2 m ‘/m 1. There is no natural
water intlux into the reservoir.
At discovery in 1961 the
reservoir prewre was 11,032 kPa. Currently, it is 2,758 kPa.
There are 103 wells - all pumping - with a total production
rate of 413 m‘/D. The estimated primary recovery is 1.5%
of the original oil in-place. A pilot waterflood indicated that
an additional 3.5% could be recovered by this means. The
reservoir presents an intriguing and difficult challenge for
two reasons: (1) lt is Turkey??largest single oil reserve; (2) It
has essentially no internal energy to as..ist production, i.e.
recovery must rely almost entirely on external means.
A suite of simulation studies were executed to
screen various EOR processes. Simulation of water flooding
led to a prediction of 5% recovery, confirming the field pilot
tests. ‘fhe reservoir presents other complexities in that it is
fractured and displays dual porosity29 characteristics in .aome
parts. Simulation of steam flooding indicates 32% recovery if
the system behaves like a single poiosity system whereas only
half
this amount is recoverable by steam if it is indeed a dual
system throughout.
Nevertheless, this process and
immiscibIe carbon dioxide injection appear the most
favorable. From an economic viewpoint, the latter
process is the most feasible because of a nearby carbon
dioxide gas reserve and the high initiaI investment
requirements for steam injection. Currently, a large
reservoir simuiat ion study using a fractured reservoir
simuIator capable of handling carbon dioxide diffusion
into the heavy oil is being executed. At the same time a
field pilot project is being planned to assist in optimum
development of the reservoir. Early indications are that
17- 32% recovery can be expected.
CONCLUSIONS
Reservoir simulators play an active and important
role in the optimum management of oil and gas reservoirs.
They prGvide insights which could not otherwise be
obtained, especially in complex systems where simpler
reservoir engineering methods are found wanting. We
have seen how they can be used in the infancy, maturity
and final days of a reservoir% life. Indeed, in some
instances, they have indicated the existence of additional
oil reserves which were later ‘discovered” by subsequent
driIling30. However, we emphasise that there is no
substitute for sound engineering judgment. Ultimately,
the opt imisation must be done on that level. A reservoir
simulator is just another tool in the engineer% arsenal
that, hopefully, enables him to probe deeper, and gain a
larger measure of “understanding.
REFERENCES
1.
Coats, K.H.: “Reservoir Simulation: State~f-the-
Artn, J. Pet. Tech (Aug., 1982) 1633-1642.
2. Handyside, D.D. and Chipman, W.I.: “A Preliminary
Study of the Hibernia Fieldw, Paper No. 82-32-24,
Presented at the 33rd Annual Technical Meeting of
the PetroIeum Sociey of CIM, Calgary, Cmada 6-9
June, 1982.
3.
Costs, K.H., Dempsey, J.R. and Henderson, J. H.:
‘me Use of VerticaI Equilibrium in Two-
Dimensional Simulation of Three-DimensionaI
Reservoir Performance”, Sot. Pet. Eng. J. (March,
1971), 63.
4. Kyte, J.R. and Berry, D.W.: “New Pseudo Functions
To Control Numericai Dispersion”, Sot. Pet. Eng. J.
(August, 1975), 269.
5.
Coats, K.H.:
‘Simulation of Gas Condensate
Reservoir Performance”, Paper SPE 10512, Sixth
SPE Symposium on Reservoir Simulation, 31 Jan, -3
Feb., 1982, New Orleans, La.
R Gondouin, M., Iffly, R, and Husson, J.: “An Attempt
to Predict the Time Dependence of Wet
Deliverability in Gas Condensate Fields,” Sot. Pet.
Eng. J. (June, 1967), 113-124.
. ..
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THE ROLE OF RESERVOIR SIMULATION IN OPTIMAL RESERVOIR MANAGEMENT
SPE 14129
7.
8.
9.
10.
11.
12.
13.
1.4.
15.
16.
17.
18.
19,
Whitson, C.H., and Torp, S.B.: ’’Evacuating Constant
volume DepIetion Data”, J/of Pet, Tech. (March,
1973),610-620.
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