Subido por Michael Andrés Castaño Escobar


Reservoir Simulation
Calvin C. Mattax, * SPE, and Robert L. Dalton SPE
Exxon Production Research Co.
u •• • the
precision with
which variations In
reservoir properties
can be modeled Is
determined by the
number of blocks In
the model."
In the past 30 years, reservoir simulation has
evolved from a research area into one of the
most flexible and widely used tools in reservoir engineering. Use of reservoir simulation has grown because of its ability to
predict the future performance of oil and gas
reservoirs over a wide range of operating
conditions. Reservoir simulators use numerical methods and high-speed computers to
model multidimensional fluid flow in reservoir rock. Reliable simulators and adequate
computing capacity are available to most
reservoir engineers, so simulation is usually
practical for all reservoir sizes and all types
of reservoir performance studies. Although
the use of simulation frequently is optional, it may be the only reliable way to predict
the performance of a large, complex reservoir, especially if such external considerations as government regulations influence
the production schedule. Even for small
reservoirs where simple calculations or extrapolations may be adequate, simulation is
often faster, cheaper, and more reliable than
alternative methods for predicting performance.
Modeling Concepts
A reservoir simulator models a reservoir as
if it were divided into a number of individual
blocks (gridblocks). Each block corresponds
to a designated location in the reservoir and
is assigned properties-porosity, permeability, relative permeability, etc.-believed to
be representative of the reservoir at that
location. In the simulator, fluids can flow
between neighboring blocks at a rate determined by pressure differences between
blocks and flow properties assigned to the
interfaces between blocks. In essence, the
mathematical problem is reduced to a calculation of flow between adjacent blocks.
For every block-to-block interface, a set of
equations must be solved to calculate the
flow of all mobile phases. The equations
generally incorporate Darcy's law and the
concept of material balance and contain
terms describing the permeability "between" blocks, fluid mobilities (relative per'Now retired.
Copyright 1990 Society of Petroleum Engineers
meability and viscosity), and rock and fluid
Fig. 1 illustrates the most common types
of models used in simulation. Models range
in complexity from a single block, useful
only for classical material-balance calculations, to fully 3D models capable of modeling all major factors that influence reservoir
Each gridblock in a model has only one
set of properties; there is no variation in any
property within a block. For example, phase
saturations in a model block will be volumetric averages of the saturations in that part
of the reservoir represented by the block.
In this respect, a model block can be visualized as a well-stirred tank (Le., its contents
are homogeneous) connected to adjacent
tanks with pipes whose flow capacities are
determined by reservoir flow properties.
This visualization, although simplistic, demonstrates that the precision with which variations in reservoir properties can be
modeled is determined by the number of
blocks in the model.
A simulator also divides the life of a reservoir into discrete increments. Changes in a
reservoir (pressure, saturation, etc.) are
computed over each of many time increments, or timesteps. Conditions are defined
only at the beginning and end of each
timestep; nothing is defined at any intermediate time within a time interval. The accuracy with which reservoir behavior can
be calculated generally will be influenced
by the length of the timesteps as well as the
number of gridblocks.
The preceding discussion implies that for
any size gridblock and any length of
timestep, there will always be abrupt
changes in reservoir conditions from one
block to the next and from one timestep to
the next. Fig, 2 illustrates this point. At the
top of Fig. 2 are plan views of a hypothetical
two-well reservoir being waterflooded and a
four-gridblock simulator model of the reservoir. The two plots show water-saturation
distribution at a given time in both the reservoir and the model. In the reservoir, water
saturation is a smooth function of distance
but in the model, an abrupt drop in wate;
saturation occurs between Blocks 1 and 2
and again between Blocks 2 and 3. A plot
June 1990 • JPT
"The most useful way
to determine whether a
model adequately
describes a reservoir Is
to simulate past
performance and to
compare the simulation
with the reservoir's
actual performance
Fig. 1-Types of models used In reservoir simulation: (a) tank (material balance), (b) 1D
linear, (c) 1D radial, (d) 2D cross-sectional, (e) 2D areal, (f) radial cross-sectional, (g) 3D.
of saturation vs. time in any block in the
model would also be a "stair-step" curve,
whereas a time/saturation plot for the corresponding location in the reservoir would
be a continuous, smooth curve. The stairstep approximation approaches actual reservoir saturation distribution as the sizes of
gridblocks and timesteps decrease.
An important step in simulation clearly is
the selection of the number of blocks in a
model and the timestep size to use in calcuJPT • June 1990
lations. Increasing the number of blocks and
timesteps will increase the time required to
prepare input data and to interpret results
and the cost of calculations.
Other important model design steps are
selecting model dimensions (10, 2D, or 3D)
and determining whether conventional
black-oil, compositional, miscible, chemical, or thermal treatment is needed. Designing the simplest model that will simulate the
displacement process adequately is usually
best. Although study results may be more
credible to decision makers if the model is
more complex than needed to solve the problem, added intricacy almost always increases
the cost of a study.
Usually, models are 2D or 3D and contain from 100 (for a simple 2D model) to
100,000 gridblocks (for a very complex 3D
model) . Small models can be run on a personal computer or a standard mainframe
computer, while the most complex ones re693
"For conventional
primary and secondary
recovery processes,
the ability of reservoir
simulators to predict
performance Is
determined largely by
the quality of the
reservoir and aquifer
description and the
model design."
S i mulator Model
Block Number
Fig. 2-A four-gridblock waterflood model: (a) hypothetical reservoir and Its watersaturation distribution at a given time In the waterflood and (b) four-grldblock model
and simulated water-saturation distribution.
quire a supercomputer. Computer time and
costs for one simulation of reservoir performance can vary from a few minutes, costing less than $100, to many hours, costing
thousands of dollars.
major weaknesses in reservoir description
or operating problems, such as casing leaks.
Experience has shown that simulation can
be a powerful reservoir-description tool.
Testing Model Validity
Reservoir simulators are most frequently
used to predict future production from an
entire reservoir or a major segment of a
reservoir. Such full-field simulators normally predict oil, gas, and water production
rates as a function of time from individual
wells and from the total area modeled. In
addition, the simulator may integrate wellbore constraints into predicted future performance by automatically implementing a
logical sequence of well workovers, recompletions, replacements, and additions (infill
drilling) to optimize economics. Several predictions will frequently be made to reflect
different possible operating conditions or
two or more equally probable reservoir
descriptions . SPE Monograph Vol. 13,
Reservoir Simulation, 1 discusses examples
of this type of simulation.
Simulation can be especially useful when
uncertainty exists about the relative signifi-
Simulation Applications
The most useful way to determine whether
a model adequately describes a reservoir is
to simulate 'past performance and to compare the simulation with the reservoir's actual performance history. If the comparison
is favorable, the model can be used with
some confidence to predict the future. The
simulation should match typical well histories as well as regional and overall reservoir
performance. Pressure, saturation, GOR,
and WOR should all match to within the precision needed to attain the objectives of the
reservoir study.
Usually, not enough is known about a
reservoir to construct a model and to use it
without some modification of permeability ,
porosity, continuity, and stratification. An
unexpected benefit of simulation sometimes
comes from discrepancies between actual
and simulated performance that identify
cance of major factors that influence performance. For example, results of a 3D,
full-field reservoir simulation study of the
Lower Brent reservoir of the Dunlin field
in the U.K. North Sea by Exxon Production Research Co. demonstrated that faults
dominate areal sweep and that vertical permeability distribution controls vertical
sweep. As Fig. 3 shows, injected water has
a tendency to "tongue" through the highquality Etive sands located approximately
midreservoir. The study identified major targets for additional recovery (the Rannoch
sands in the lower half of the section and
the Lower Ness sands at the top of the section). On the basis of a similar 3D simulation
and development study, 2 the field operator
has already undertaken a program of dedicated Rannoch completions to improve
recovery from this unit.
A second interesting application of a fullfield simulator is the modeling 3 of the Troll
field offshore Norway. Numerical simulation is the only practical way to study a
large, complex field such as Troll. Note the
major faulting illustrated in the cross section
of the field (Fig. 4). The simulator used
Fig. 3-Water-saturatlon distribution In
the Dunlin, Lower Brent model
after 9 years of water injection.
WATER - --
June 1990 • JPT
W ••----,t--+> E
;:: 1800
~ 2000
Fig. 4-Westleast cross section, Troll field.
several special techniques to model all significant aspects of reservoir fluid dynamics,
including flow through the faults and water
and gas coning. Fig. 5 shows potential production profiles for two of several possible
development plans. Engineers indicated that
the model proved to be an efficient tool for
comparing alternative development scenarios and for general reservoir management.
Single-well models can be used to study
flow at the sandface and in the region near
a well. These models are usually radial, and
gridblocks adjacent to the wellbore may be
as small as 1 or 2 in. in radius. A radial
cross-sectional model similar to that shown
in Fig. I was used by Addington 4 to predict gas-coning behavior of Prudhoe Bay
wells for a range of reservoir properties and
perforation thicknesses and locations in the
producing interval. With the model results,
gas-coning correlations were developed for
use in a 3D Prudhoe Bay field model to
predict critical coning rates and GOR's of
wells after cone arrival.
Major heterogeneities usually must be
represented in a reservoir model. Detailed
representation of small-sized (a few inches to
a few feet) reservoir heterogeneities seen in
logs, cores, and outcrops, however, usually
is not practical in simulation models because
an excessive number of gridblocks would be
needed. The influence of such small-sized
heterogeneities should be included in a
model through combined geologic and reservoir engineering studies that define the effective reservoir properties needed when a
practical number of blocks is used. For example, Richardson et al. 5 derived effective
vertical permeabilities .that would allow
small, discontinuous shales to be modeled
accurately in simulations of oil drainage with
gridblocks larger than the shales.
For conventional primary and secondary
recovery processes, the ability of reservoir
simulators to predict performance is determined largely by the quality of the reservoir
and aquifer description and the model design. Our understanding of EOR processes
is less advanced. These processes pose
modeling difficulties, and industry has less
experience in modeling them, as discussed
in more detail in Reservoir Simulat{on. 1
1. Reservoir simulation is an effective
technique that is now widely available for
use in reservoir engineering.
2. Careful design of a simulation model
is required to meet the objectives of a reser-
- - 01.. START-UP TROll EAST
voir study and to control personnel and computer costs.
3. History matching, which is a vital part
of a simulation study, can be a powerful
reservoir-description tool.
1. Mattax, C.C. and Dalton, R.L.: Reservoir
Simulation, Monograph Series, SPE, Richardson, TX (1990) 13.
2. Braithwaite, C.I.M. et a!.: "Improving Recovery From the Dunlin Field, U.K. Northern
North Sea, " paper SPE 19878 presented at the
1989 SPE Annual Technical Conference and
Exhibition, San Antonio, Oct. 8-11.
3. Kydland, T. et a!.: "Application of Unconventional Techniques in Constructing an Integrated Reservoir Simulation of the Troll
Field," SPERE (Aug. 1988) 967-76.
4. Addington, D.V.: "An Approach to Gas-Coning Correlations for a Large Grid Cell Reservoir Simulator," JPT (Nov. 1981) 2267-74.
5. Richardson, G.J. eta!.: "The Effect of Small,
Discontinuous Shales on Oil Recovery," JPT
(Nov. 1978) 1531-37.
51 Metric Conversion Factors
Calvin C. MaUax, retired division
manager from Exxon Production Research, is a consultant in Houston. He
holds a BS degree from the U. of Tulsa
and a PhD degree from Louisiana State
U., both In chemistry. Mattax is editor
and coauthor of the newest SPE Monograph, Reservoir Simulation, and is a
member of a Technical Program Committee for the 1990 Annual Meeting.
Robert L. Dalton, division manager at
Exxon Production Research Co. in
Houston, is editor and coauthor of
Reservoir Simulation. He holds a BS
degree in chemical engineering from
Rice U. Dalton served on Technical Program committees for the 1974 and 1976
Annual Meetings and was a 1984-85
Distinguished Lecturer. He has been a
member of the Editorial Review Committee since 1987 and is a 1989-90 Continuing Education Committee member.
;f """-------------------------------I
bbl x 1.589 873
ft x. 3.048"
in. x 2.54"
E-Ol = m'
E-Ol = m
E+OO = em
• Conversion factor is exact.
TIME (years>
This paper is SPE 20399. Technology Today Series arti·
cles provide useful summary information on both classic and
emerging concepts in pelroleum engineering. Purpose: To
provide the general reader with a basic understanding of
a significant concept, technique, or developmenl within a
specific area of technology.
Fig. 5-Productlon profiles, southern oil province, Troll field.
JPT • June 1990
Discussion of Reservoir Simulation
Leendert Schenk, SPE, independent
I read with interest the Technology Today
Series article "Reservoir Simulation" by
Mattax (retired) and Dalton of Exxon Production Research Co ., published in the June
1990 JPT (Pages 692-95). I have the following comments to make.
1. Am I really to accept the statement at
the end of the Introduction: "Even for small
reservoirs where simple calculations or extrapolations may be adequate, simulation is
often faster, cheaper, and more reliable [my
underlining] . .. "? Too bad that the article
does not offer any proof.
2. In red at the top of Page 694 is the
statement, "For conventional primary and
secondary recovery processes, the ability of
reservoir simulation to predict the performance is determined largely by the quality of
the reservoir and aquifer description. .. ."
The last sentence of Testing Model Validity says: "Experience has shown that simulation can be a powerful reservoir-description tool. " What a beautiful vicious circle:
the simulator itself can "predict" what it
needs to make predictions!
3. The examples given in the Simulation
Applications section do not look very convincing for the needs of reservoir simulators . The third column on Page 694 says:
JPT • November 1990
"For example, results of a 3D, full-field
reservoir study of the Lower Brent reservoir of the Dunlin field in the U .K . North
Sea by Exxon Production Research Co .
demonstrates that faults dominate areal
sweep and that vertical permeability distribution controls vertical sweep. As Fig. 3
shows, injected water has the tendency to
tongue through the high-quality Etive
sands. . . ." Does one really need simulators to draw the underlined conclusions? Or
is it sometimes a relief to find that simulators can predict the obvious? Regarding the
Troll field offshore Norway, the paper says:
"Engineers indicated that the model proved
to be an efficient tool for comparing alternative development scenarios and for general reservoir management." This sounds
more like an article of faith* than a technical argument.
4. I was flabbergasted by a statement in
the Modeling Concepts section at the bottom of Page 693: "Although study results
may be more credible to decision ma"kefsif
the model is more complex than needed to
solve the problem, added intricacy almost
always increases the cost of the study."
What a concept this is! It gives rise to many
questions .
a. For example, how does it jibe with
Point 2 of the Summary: "Careful
design of a simulation mod~
quired to meet the objectives of a
re'servoir study and to control personnel and computer costs."
b . Does the statement hold only for the
Exxon corporate culture or should it
also extend to outside-Exxon decision makers-e.g., those in companies involved with joint ventures or
in government agencies?
c. Considering that " . .. added intricacy almost always increases the
cost. . . ," what increase is considered advisable or permissible? Maybe 25 or 50% ?
5. Finally, I found it a great relief to read
in the Introduction that" . .. the use of simulation frequently is optional . . . ." In conclusion, I am sad to have to say that I was
disappointed to encounter the article in a
journal of the caliber of the JPT, particularly in the Technology Today Series.
(SPE 21606)
• The Devi/'s Dictionary by Ambrose Bierce gives this defi·
nition: " Faith-belief without evidence .
Authors' Reply to Discussion of
Reservoir Simulation
Calvin C. Mattax,* SPE, and'Robert L. Dalton, SPE,
Exxon Production Research Co.
We wish to emphasize that simulation is a
reservoir-management tool and only a tool;
it should not be used as a substitute for engineering knowledge and skill. The quality
of the results of any simulation and the ease
with which those results can be obtained depend entirely on the skill and judgment of
the engineer using the simulator. ** It is with
this philosophy in mind that we offer the following comments in response to Schenk's
five specific questions and remarks.
1. Whether simulation has an advantage
over simple calculations or extrapolations
depends on the engineer' s experience with
simulation and with alternative methods. It
also depends heavily on the reservoirmanagement issue being considered. Most
alternative methods do not allow the reservoir engineer to consider directly the physics
of the reservoir-depletion mechanism . We
are aware of many situations where, in
retrospect, starting with a simple , cheap,
easy-to-run simulation model would have
saved time and money because critical factors affecting reservoir performance were
not well understood.
An example of this is the reservoir study
of the "Tom O'Connor 5,lOO-Ft Sand in
South Texas." (A paper describing this
study is planned for submittal to SPE for
presentation at a general meeting.) This
waterdrive gas reservoir began repressuring
in the mid-1980's as a result of reduced purchaser takes . A reservoir study was needed
to confirm and quantify reserve losses from
continued water encroachment to secure
Texas Railroad Commission approval for
blowdown by special allowable .
Initial attempts with simple, tank-type,
material-balance calculations were unsuccessful in reproducing the repressuring observed in the 5,100-ft sand. It was concluded
that conventional, material-balance methods
could not properly account for the compression of the gas that was trapped with rep ressuring and, hence, could not be used to
evaluate the influence of repressuring on
'Now retired .
, 'Many excellent simulators are available for modeling conventional oil/gas/water displacements. For a large frac·
tion of reservoir studies. the simulators can safely be
assumed to solve the match correctly. The SPE Mono·
graph Reservoir Simulation discusses exceptions to this
general statement.
water influx. The engineer found, however,
that she could use a very simple, 1D model
to simulate performance and to match the
5, 100-ft -sand pressure history.
The model was used to estimate an optimal depletion rate and to demonstrate that
reserves would be lost at lower rates. As a
consequence, a special allowable was granted and the blowdown project was implemented immediately. Blowdown was
completed late last year with a recovery very
near that predicted by simulation.
2 and 3. There may be some misunderstanding about the use of history matching
to improve reservoir description. In history matching, the engineer first attempts to
model history by use of his best current
description of the reservoir. If historical performance cannot be matched with current
description, then either the description is
wrong or the physics of the reservoir depletion mechanism is being modeled incorrectly. In either case, a better understanding of
the reservoir is necessary if future performance is to be predicted reliably . Using a
simulator is a practical way to consider the
influence of acceptable changes in reservoir
description on past performance.
The Dunlin reservoir discussed in the
Technology Today Series paper is an excellent example of the benefits of history
matching. The prime question answered in that
study was which faults were sealing and
which were not. We know of no way to answer that question without developing a
reservoir flow model and matching history
with the model. Perhaps we were too superficial in our comments on the benefits of the
Dunlin study . Certainly, with the reservoir
description we now have, it is obvious that
"faults dominate areal sweep ... ," etc.
More specifically , however, what are the
quantitative effects of faulting and vertical
permeability and how much injected water
will flow through the Etive? Only with a
simulator can a reservoir engineer hope to
study enough probable reservoir descriptions
to develop rational answers to these
questions .
We point out here that in most reservoir
simulations , results are qualitatively similar
to prior expectations. There are seldom
major "surprises," especially if geologists
and engineers have attempted to develop an
understanding of the reservoir. What a simulator provides is quantitative results that
forecast timing of future events and produced and injected fluid volumes. These
types of forecasts can provide invaluable information for planning depletion and developing operating strategies.
Our experience and that of others (see the
Reservoir Simulation monograph for references) suggest, however, that in many reservoirs with complex geology and where heterogeneity and multi phase fluid flow must
be considered, prior expectations based on
intuitive judgment are likely to be in error.
4. The degree of complexity needed for
a reservoir-simulation model must be based
first on what model design will provide an
answer to the reservoir-management question being considered. Often, an important
design factor concerns what simplifying assumptions will be accepted by the decision
maker for whom the study is intended.
When planning a simulation study , it is important to determine whether the cost of adding model complexity to lend credibility to
study results can be justified. Frequently ,
in dealing with others who may not have an
in-depth reservoir engineering background,
it is cost-effective to construct a complex
model rather than to do the work necessary
to develop convincing evidence that simpler
models are adequate. Of course, there is no
answer to Schenk's question about how
much intricacy is advisable. It depends on
the objectives of the study .
5. In Reservoir Simulation, we repeatedly made the point that the reservoir engineer
should use the fastest and cheapest engineering methods that will give adequate answers
to the reservoir-management questions under consideration. If simulation is not needed, and if it is more costly than an alternative
method, then by all means, don't use it. Our
contention, however, is that in today's environment, computing power is often cheaper
and faster than manpower and that simulation is a superb tool that every reservoir engineer should at least know how to evaluate.
SI Metric Conversion Factor
ft x 3.048*
E-Ol :
'Conversion factor is exact.
(SPE 21620)
November 1990 • JPT