Improving Volumetric Sweep Efficiency in Enhanced Oil ...
Transcript of Improving Volumetric Sweep Efficiency in Enhanced Oil ...
Application of Fracturing Technology in Improving Volumetric Sweep Efficiency in Enhanced Oil Recovery Techniques
by
Elias Pirayesh, B.Sc.
A Thesis
In
PETROLEUM ENGINEERING
Submitted to the Graduate Faculty Of Texas Tech University in
Partial Fulfillment of the Requirements for
the Degree of
MASTER OF SCIENCE
Approved
Mohamed Soliman Chair of Committee
Habib Menouar
Shameem Siddiqui
Peggy Gordon Miller
Dean of the Graduate School
May, 2012
IN
PETROLEUM ENGINEERING
Texas Tech University, Elias Pirayesh, May 2012
ii
ACKNOWLEDGMENTS
This research would not have been accomplished without the help and support of
many people. I wish to express my sincere appreciation to my supervisor, Dr. Mohamed
Soliman who was profusely supportive and provided me with his insightful help and
guidance throughout my studies. Genuine gratitude is also to the members of the
supervisory committee, Dr. Shameem Siddiqui and Dr. Habib Menouar without whose
assistance, this work would not have been as fine as it is.
I would like to direct thanks to Halliburton Services for providing me with their
simulator Quiklook ©.
I would like to express my love and gratefulness to my beloved family; for their
understanding and endless love, through the duration of my studies.
Texas Tech University, Elias Pirayesh, May 2012
iii
TABLE OF CONTENTS
ACKNOWLEDGMENTS ............................................................................................ II
ABSTRACT ................................................................................................................. V
LIST OF TABLES ...................................................................................................... VI
TABLE OF FIGURES ............................................................................................... VII
I. INTRODUCTION ..................................................................................................... 1
1.1. Statement of the Problem ............................................................................................. 6
1.2. Objective of the Project ............................................................................................... 7
II. METHODS............................................................................................................... 9
2.1. First case: Edge Water Drive Reservoir ..................................................................... 10
2.2. Second Case: Line Drive Water Flooding Pattern ..................................................... 12
2.3. Third Case: Five Spot Water Flooding Pattern .......................................................... 14
2.4. Optimization .............................................................................................................. 14
2.4.1. Barrier-fracture Length ................................................................... 14 2.4.2. Barrier-fracture Location ................................................................ 16 2.4.3. Number of Barrier-fracture ............................................................. 17 2.4.4. Mobility Ratio ................................................................................. 19 2.4.5. Schedule of Barrier-Fracturing ....................................................... 19
2.5. Relative Permeability Modifier Filled Barriers ......................................................... 19
III. RESULTS ............................................................................................................. 22
3.1. First Case: Edge-water Drive ..................................................................................... 22
3.2. Second Case – Line Drive Water Flooding Pattern ................................................... 24
3.3. Third Case – Five Spot Water Flooding Pattern ........................................................ 27
3.4. Optimization Results .................................................................................................. 30
3.4.1. Barrier-Fracture Length .................................................................. 30 3.4.2. Barrier-Fracture Location ............................................................... 32 3.4.3. Number of Barrier-fractures ........................................................... 35 3.4.4. Effect of Mobility Ratio .................................................................. 39 3.4.5. Effect of Barrier-Fracturing Time ................................................... 43
3.5. Relative Permeability Modifier Barrier ..................................................................... 47
IV. CONCLUSIONS AND RECOMMENDATIONS ............................................... 49
4.1. Conclusions ................................................................................................................ 49
4.2. Recommendations ...................................................................................................... 50
Texas Tech University, Elias Pirayesh, May 2012
iv
REFERENCES ........................................................................................................... 51
A. SENSITIVITY ANALYSIS: EFFECT OF GRIDDING ON SIMULATION
RESULTS ............................................................................................................. 53
Texas Tech University, Elias Pirayesh, May 2012
v
ABSTRACT
The industry has developed methods to improve sweep efficiency during
Enhanced Oil Recovery processes. These methods include the use of certain
injection/production patterns, drilling horizontal and deviated wells, use of special
chemicals as well as inflow control devices (ICDs). The purpose of the first two methods
is to create an even movement of injection fluid across the reservoir. Special chemicals
have been used to divert the injected fluid to eliminate channeling and to improve sweep
efficiency. Inflow control devices have been used to delay water or gas breakthrough,
making possible a more efficient drainage of the reservoir while maximizing production
and recovery.
The technique presented in this work creates a mechanical barrier to flow by
introducing a fracture to the formation at a strategic location. This fracture is then filled
with a conformance fluid which eventually becomes impermeable to fluid flow. The
effects of various design parameters on the performance of barrier-fractures have been
investigated and the results are presented. These design parameters include barrier-
fracture length & location, number of barrier-fractures, mobility ratio and barrier creation
time. It is illustrated that the breakthrough time and potential productivity of producing
wells increase as a result of enhancing the volumetric sweep efficiency of hydrocarbons.
A second technique introduced in this work is creating a chemical barrier to flow
by injecting relative permeability modifying agents into created cracks in reservoir rock.
Injection of relative permeability modifying agents (RPM) into rock reduces the rock’s
water relative permeability to a fraction of its original value. An investigation of the fluid
flow aspects of RPM barriers revealed that in terms of improving recovery the
performance of these chemical barriers is weak and have a strong tendency to rely on
RPM properties. Therefore, they may not be suitable candidates for in-depth flow profile
modification.
Texas Tech University, Elias Pirayesh, May 2012
vi
LIST OF TABLES
2. 1 Edge water synthetic case data ................................................................... 11
2. 2 Line drive reservoir boundaries .................................................................. 13
2. 3 Line drive synthetic case data ..................................................................... 13
Texas Tech University, Elias Pirayesh, May 2012
vii
TABLE OF FIGURES
2.1 Edge water drive reservoir grid ............................................................... 10
2. 2 Edge water drive reservoir map ............................................................... 10
2. 3 Edge water drive reservoir map with a barrier-fracture ........................... 11
2. 4 Line drive reservoir map .......................................................................... 12
2. 5 Line drive reservoir layers ....................................................................... 13
2. 6 Five spot reservoir map............................................................................ 14
2. 7 Barrier-fracture length equal to 25% of reservoir length ......................... 15
2. 8 Barrier-fracture length equal to 50% of reservoir length ......................... 15
2. 9 Barrier-fracture length equal to 75% of reservoir length ......................... 16
2. 10 Barrier-fracture placed at the first quarter of the reservoir ...................... 16
2. 11 Barrier-fracture placed at the center of the reservoir ............................... 17
2. 12 Barrier-fracture placed at the third quarter of the reservoir ..................... 17
2. 13 A reservoir with two barrier-fractures ..................................................... 18
2. 14 A reservoir with three barrier-fractures ................................................... 18
2. 15 A reservoir with four barrier-fractures ..................................................... 18
2.16 Reservoir rock relative permeability curves. (a) Before RPM treatment (b)
After RPM treatment................................................................................................. 20
2.17 Barrier created by injection of RPM agents into a fracture ...................... 21
3. 1 Water breakthrough into the horizontal well with no barrier-fracture ....... 22
3. 2 Water breakthrough into the horizontal well in the presence of a barrier-
fracture ...................................................................................................................... 23
3. 3 Oil production in the presence and absence of a barrier-fracture .............. 23
3. 4 Water production in the presence and absence of a barrier-fracture ......... 24
3. 5 Water saturation distribution in the absence of a barrier-fracture ............. 25
3. 6 Water saturation distribution in the presence of a barrier-fracture ............ 25
3. 7 Cross sectional water saturation distribution in the presence of a barrier-
fracture ...................................................................................................................... 26
3. 8 Oil production in the presence and absence of a barrier-fracture .............. 26
Texas Tech University, Elias Pirayesh, May 2012
viii
3. 9 Water production in the presence and absence of a barrier-fracture ........ 27
3. 10 Water saturation distribution in the presence of a barrier-fracture .......... 28
3. 11 Water saturation distribution in the absence of a barrier-fracture ........... 28
3. 12 Oil production in the presence and absence of a barrier-fracture ............ 29
3. 13 Water production in the presence and absence of a barrier-fracture ....... 29
3. 14 Cumulative oil production ....................................................................... 30
3. 15 Cumulative water production ................................................................... 31
3. 16 Breakthrough time vs. barrier-fracture length ......................................... 31
3. 17 Cumulative oil production vs. barrier-fracture length ............................. 32
3. 18 Cumulative oil production ....................................................................... 33
3. 19 Cumulative water production ................................................................... 33
3. 20 Breakthrough time vs. barrier-fracture location ...................................... 34
3. 21 Cumulative oil production vs. barrier-fracture location .......................... 34
3. 22 Oil saturation distribution map at 2,500 days (a) one barrier-fracture (b)
two barrier-fractures (c) three barrier-fractures (d) four barrier-fractures ................ 37
3. 23 Cumulative oil production ....................................................................... 37
3. 24 Cumulative water production ................................................................... 38
3. 25 Breakthrough time vs. number of barrier-fractures ................................. 38
3. 26 Cumulative oil production vs. number of barrier-fractures ..................... 39
3. 27 Oil production rate ................................................................................... 40
3. 28 Water production rate .............................................................................. 41
3. 29 Cumulative oil production ....................................................................... 41
3. 30 Cumulative water production rate ............................................................ 42
3. 31 Breakthrough time vs. mobility ratio ....................................................... 42
3. 32 Cumulative oil production rate vs. mobility ratio .................................... 43
3. 33 Oil flow rate vs. time ............................................................................... 44
3. 34 Water flow rate vs. time ........................................................................... 44
3. 35 Cumulative oil production vs. Time ........................................................ 45
3. 36 Cumulative water production vs. time ..................................................... 45
Texas Tech University, Elias Pirayesh, May 2012
ix
3. 37 Breakthrough time vs. barrier-fracturing time ......................................... 46
3. 38 Cumulative oil production vs. Barrier-fracturing time ............................ 46
3. 39 Cumulative oil production vs. RPM properties ....................................... 47
3.40 Water saturation distribution maps at 1500 days (a) RPM barrier (b)
Barrier-fracture ......................................................................................................... 48
A. 1 Cumulative oil production at 6,000 days vs. number of grid blocks ........ 53
Texas Tech University, Elias Pirayesh, May 2012
1
CHAPTER I
INTRODUCTION
Excessive water production has been a problem in oil industry for many years.
The two main problems excessive water production causes are wastage of energy for
producing an unwanted fluid and also wastage of oil production potential. To solve this
problem, many research projects have been concentrated on developing conformance
control systems (Dalrymple, Creel et al. 1998). In oil producing wells, unwanted fluid
production conversely impacts the productive life of the well. Produced water treatment
costs have become a major concern for many producers. The control of unwanted fluid
production will allow extraction of more hydrocarbons and consequently increase
profitability (Azari and Soliman 1996).
Conformance control refers to any solution designed for enhancing
injection/production profile of a well. While satisfying environmental regulations,
conformance treatments improve recovery as wells as wellbore integrity. Conformance
treatments involve mechanical or chemical approaches to control the unwanted water or
gas production. These treatments are performed on the producing well, the injection well
or both of them. The treatments may involve minimizing or eliminating the unwanted
fluid production (Azari and Soliman 1996). The first approach, mechanical control, may
involve use of packers or inflow control devices. The second approach, chemical control,
can be divided into several broad groups. The first one involves the injection of a sealant
that is injected into the reservoir to fully stop unwanted fluid flow. The other chemical
approach involves injection of Relative Permeability Modifying (RPM) polymers to
significantly reduce the permeability to water while keeping the relative permeability to
oil fairly intact. Different chemical conformance control methodologies are designed to
reach different effects in the reservoir. An important goal, in most chemical treatments, is
to reduce water relative permeability in the reservoir.
Conformance treatments involve approaches to control the unwanted gas
production as well as unwanted water production. An example of this type is a work done
Texas Tech University, Elias Pirayesh, May 2012
2
in Prudhoe Bay Field of Alaska. Sanders et al. (1994) showed that cross-linked gels can
be used to shut-off unwanted gas production in a more economical manner compared to
cement squeezes. They also found that gel treatments can successfully block fluid
production from channels behind casing and from several zones with different
permeabilities.
Conformance treatments designed for heterogeneous reservoirs include a wide
variety of methodologies. Among all the existing methodologies, crosslinked-polymers
have gained wide acceptance by the operators; however, there are several critical
problems and limitations related to this technology which include being environmentally
hazardous, limited penetration depth, precipitation and degradation under harsh reservoir
conditions, loss of injectivity, loss of viscosity caused by shear degradation and difficulty
in controlling in-situ gelation rates (Llave 1994). In heterogeneous reservoirs, volumetric
sweep efficiency is highly affected by variations in permeability. The overall efficiency
of an enhanced oil recovery (EOR) process is a function of volumetric sweep efficiency
and microscopic sweep efficiency. An improvement in either one of these two factors can
translate into substantial improvement of economics of an EOR project (Llave 1994).
Llave et al. (1994) evaluated the possibility of using surfactant/alcohol technology
as an in-depth profile modification tool. In-depth modification of flow profile has the
potential of improving volumetric sweep in highly permeable reservoir zones. In-field
application of their proposed methodology resulted in improvements in
injection/production conditions. Some of these improvements include increased oil
production, reduced water production, improved injection profile and delay of water-
breakthrough.
A commonly employed mechanism by conformance control methods is flow
profile modification. Flow profile modification helps improve efficiency by delaying
water/gas breakthrough and improving sweep efficiency. Historical data confirms
effectiveness of profile modification in sandstone and limestone reservoirs (Liu 1995).
Texas Tech University, Elias Pirayesh, May 2012
3
Profile modification can be accomplished in a variety of different ways. An example of a
profile modification methodology is as follows.
For chemical profile modification, 1980’s was a transition period from purely
experimental method to a routine procedure. Different chemicals including different
categories of gels were in North American heterogeneous reservoirs for profile
modification. These exercises involved selective injection of the polymer into the water-
thief zones. The polymer, after gelation, diverted injected water flow to the unswept oil-
bearing zones. A number of research projects have focused on the general theories behind
chemical profile modification technology, as well as the features and benefits of different
chemicals. (Avery, Burkholder et al. 1986).
One chemical system may work for an entire field, however chemical profile
modification treatments must be designed for each individual well. In designing such
treatments, all available data is used, as to attain the highest rate of success, the designs
must be as comprehensive as possible (Avery, Gruenenfelder et al. 1987).
A profile modification optimization method should be capable of determining
many parameters, including selection of wells and target layers, chemical agents and
injection parameters. Liu et al (2000) introduced a method to optimize the design of
conformance treatments based on profile modification, in which Fuzzy mathematics and
a table of commonly-used 40 chemical formulas provided the basis for the selection of
candidate wells and chemical agents, respectively. In most cases, production analysis
after treatment showed that the waterflood efficiency is improved, and that the model
predictions match well with the actual production data.
Profile modification based conformance control treatments are fairly flexible in
terms of application schedule and treatment combination. For example, over more than
five decades, China oil fields have experienced a series of three stages which include: 1)
mechanical water plugging 2) chemical water plugging and 3) comprehensive treatment
for profile modification in injector and water control in producer of blocks in oil fields.
According to Liu (1995), “Application of water control and profile modification in more
Texas Tech University, Elias Pirayesh, May 2012
4
than 20,000 well treatments in oil fields from 1979 to 1993 shows that significant
economic and technical benefits as wells as good production results, such as, the increase
of recoverable reserves and oil production and decrease of water production and so on
have been achieved.”
RPMs were first introduced in the late 1970s and were primarily used for water
conformance. Applications were for water fingering, water coning, early water
breakthrough, and communications with water via high perm streaks. A major benefit of
using RPMs was that they are a non-plugging agent, which reduced the permeability to
water and had little or no effect on the permeability to hydrocarbons. They also were
unaffected by multivalent cations, oxygen, or acids (Weaver 1978). However, the nature
of the polymer used to make the initial RPM fluid allowed only a limited application. The
permeability range in which the RPM fluid would work was 10 md to 750 md, the
polymer itself was shear sensitive, and the upper temperature limit was 250°F.
The chemistry of the initial RPMs has been modified by using different polymers
several times since their introduction to the industry. This has allowed several changes
regarding the application and use of RPMs. In the mid-1990s, RPMs were introduced as a
pre-pad fluid in hydraulic stimulation treatments in areas where breaking into nearby
water zones commonly occurred. The results of this application significantly reduced
post-water production after hydraulic stimulation treatment, and allowed operators to
treat and produce previously bypassed formations (Brocco, Dalrymple et al. 2000; Fry,
Everett et al. 2006; Ortega, Peano et al. 2006).
The current RPMs in use, which were introduced to the industry in 2002, are a
fourth-generation polymer and have a broader permeability range. They are not affected
by shear, have an upper temperature range of 325°F. They have greatly extended the
applications where RPM fluids can be used. Fluids that contain the RPM material have
unique properties that allow them to help minimize water production (Nieves, Fernandez
et al. 2002).
Texas Tech University, Elias Pirayesh, May 2012
5
Once the RPM material is injected into the formation, it rapidly adheres to the
rock surface, hence limiting the ability of water to flow through the formation. While
leaving little or no impact on oil flow, the RPM material restricts the flow area for water-
based fluids substantially. Because this material begins to work immediately, it not only
helps reduce the flow of water being produced, it also helps reduce the amount of a
water-based fluid entering the formation. Therefore, the RPM fluid not only is a self-
diverting fluid, but it also works as a fluid-loss additive that could result in longer
fracture lengths (Garcia, Soriano et al. 2008).
The problem of excessive water production from oil and gas reservoirs can
sometimes be addressed from the injector or producer. It can also be addressed by re-
completing the well or by delaying with cement or polymer gel treatments. However, for
these methods to become feasible the watered-out layer has to be identified and isolated,
which is not always possible. Examples of this include micro-layered formations and
gravel-packed completed wells. The use of RPM agents is an attractive option in these
cases.
Conformance fracturing, a combination of hydraulic fracturing and water control,
has proven as an effective conformance control technique. Hydraulic fracturing has
become the technology of choice for increasing well productivity. Hydraulic fracturing
owes its wide acceptance to the development of the new class of lightweight proppants.
Because of the reduced settling tendency of the proppants, it has become possible to
create more uniform fractures that provide a far better contact with the formation
compared to the past. The chemistry of relative permeability modifiers has also
undergone a lot of change; the most notable result of which is elongated life of water
control treatments using RPMs(Melo and Aboud 2008).
Melo et al (2008) conducted over 100 conformance fracturing operations in Brazil
to date, using conventional as well as lightweight proppants, and relative permeability
modifiers, to meet the different targets they were deployed for. They made a summary of
Texas Tech University, Elias Pirayesh, May 2012
6
these treatments (design, logistics, materials, equipment), with obtained results (oil and
water production over time), showing the improvements made over time.
Dalrymple et al (1998) discuss field results from conformance fracturing
treatment. The purpose of their treatment was to inject the relative permeability
modifying agent into the fracture while stimulating the reservoir. The RPMs leaked off
into the fracture helped alleviate water production problem. The after-treatment
production data shows a more than 60% increase in oil production, about 60% reduction
in water production and about 120% increase in gas production. It is noteworthy that
previous fracturing treatments had failed in the same field, due to damaging scale and a
subsequent decline in total fluid production.
1.1. Statement of the Problem
A commonly applied enhanced oil recovery solution for recovery improvement is
water-flooding. This mechanism has proven effective in maintaining bottomhole pressure
of many reservoirs around the world. Globally, it has become a common practice to have
injection wells when developing new fields.
The major problem associated with water-flooding projects is the early water-
breakthrough, the main causes of which are high-permeability layers and unfavorable
mobility ratios. Water breakthrough is the main determinant of the productive life of the
reservoir, meaning that after breakthrough, there is a low chance for extracting
hydrocarbons from unswept portions of the reservoir. Also the operational costs will
increase dramatically due to high producing water-oil ratio caused by early breakthrough.
Water-breakthrough solutions usually involve two steps. First, diagnosing the mechanism
to determine the cause and second, applying remediation techniques. The diagnosis can
be performed by production logging, drilling monitor wells, cement evaluation.
Remediation techniques include an extensive number of methodologies, e.g. injecting
sealants, cement and relative permeability modifiers, side-tracking and finally
abandonment. Water-breakthrough treatments sometimes involve changing the flow
Texas Tech University, Elias Pirayesh, May 2012
7
profile chemically or mechanically. Using cement, different polymers and inflow control
devices are examples of chemical of flow profile modification methodologies.
Water breakthrough treatments can be costly in some cases. Since they are
commonly applied to the near wellbore area of the producer, they are effective only for
reducing water encroachment temporarily. Also, depending on the distance between the
injection and producing wells and productivity of the reservoir, it might take a very long
time to evaluate the performance of these techniques.
1.2. Objective of the Project
The purpose of this project is to investigate the application of barrier-fracturing
using simulation. Barrier-fracturing is a novel idea to modify flow profile and divert the
displacing fluid by placing a fracture with essentially zero permeability deep into the
reservoir. There are many ways to create a zero permeability fracture, examples of which
include injection of cement or a conformance fluid into the fracture. A conformance fluid
can be initially injected as a low viscosity fluid, maybe as low as 0.5 cp., and after
gelation, can reach up 500,000 cp., which eventually become impermeable to any kind of
fluid flow.
Three basic simulation models were created. These include an edge water drive
reservoir, and two other reservoirs which have two different flooding patterns, a line
drive and a five spot pattern. The effects of different design parameters on the
performance of a barrier-fracture were analyzed. These design parameters are listed
below:
1. Barrier-fracture length
2. Barrier-fracture location
3. The number of barrier-fractures
4. Mobility ratio
5. Barrier-fracturing time
Texas Tech University, Elias Pirayesh, May 2012
8
To achieve our objectives, this report has been divided into four chapters.
Following chapter I, which is an introduction to the problem, the proposed solution
method and the details of the created simulation models will be discussed in Chapter
II. Simulation results and the interpretation of them are provided in Chapter III.
Finally, the conclusions and recommendations for future work are stated in chapter
IV.
Texas Tech University, Elias Pirayesh, May 2012
9
CHAPTER II
METHODS
As explained in the chapter I, simulation was used as a tool to investigate the
feasibility of achieving recovery improvements by applying the proposed idea. For
optimization purposes, again simulation was used for analyzing the effect of different
design parameters on the performance of a barrier-fracture. All of the simulation runs in
this work were performed by Halliburton commercial simulation software Quiklook ©
version 4.5.232.817.
Three synthetic cases were created. The idea is that the methodology proposed in
this work, could result in some substantial improvements in recovery of the synthetic
cases. The three simulated cases include the following:
1. An edge water drive reservoir
2. A line drive water flooding pattern
3. A five spot water flooding pattern
The reason for selecting these cases is because they represent the most common
problems and the most popular injection/production patterns in use, in oil industry.
The first case simulates the common problem of excessive water production from an
aquifer, caused by water-coning. The next two cases represent reservoirs with two
common injection/production water-flooding patterns in conjunction with a bottom drive
aquifer.
As simulation was used as the analysis tool in this work, there was a need for a
sensitivity analysis on the effect of number of grid blocks. The analysis is presented in
Appendix A.
Texas Tech University, Elias Pirayesh, May 2012
10
2.1. First case: Edge Water Drive Reservoir
One of the major problems in reservoirs with strong edge water drive is water
coning. Water coning can cause can cause an early water breakthrough, which ends the
productive life of a reservoir. In order to illustrate this problem, a synthetic case of a
reservoir with an edge water drive was created (Figures 2.1 and 2.2). Simulation runs
were performed, and then a fracture was introduced into the model, as is shown in Figure
2.3. Table 2.1 provides data that has been used to create the model.
Figure 2.1. Edge water drive reservoir grid
Figure 2. 2. Edge water drive reservoir map
Texas Tech University, Elias Pirayesh, May 2012
11
Figure 2. 3. Edge water drive reservoir map with a barrier-fracture
Boundary Status North No-flow South No-flow East No-flow West Aquifer Top No-flow Bottom No-flow
Reservoir fluid type Black Oil Depth to the top of the formation
4002 ft. Rock compressibility 3.00E-06
1/psi Rock reference pressure 6345 psi Depth of water-oil contact 4800 ft. Bubble point pressure 4275 psi Gas specific gravity 0.60 Oil specific gravity 0.89 Water specific gravity 1.00 Irreducible water saturation 0.37 Residual Oil Saturation 0.10 Critical gas saturation 0.05
Table 2. 1. Edge water synthetic case data
Texas Tech University, Elias Pirayesh, May 2012
12
2.2. Second Case: Line Drive Water Flooding Pattern
In the second case, a reservoir with a line drive flooding pattern with two wells,
an injector and a producer, was simulated. A third well was drilled and a fracture was
placed in the middle of the reservoir. The fracture was then filled up with a conformance
fluid which is capable of forming a gel impermeable to flow of both oil and water. A map
of the reservoir with a fracture in the middle and a vertical profile of the reservoir are
provided in Figures 2.3 and 2.4, respectively.
Figure 2. 4. Line drive reservoir map
Texas Tech University, Elias Pirayesh, May 2012
13
Figure 2. 5. Line drive reservoir layers
Table 2. 2. Line drive reservoir boundaries
Boundary Status North No-flow South No-flow East No-flow West Aquifer Top No-flow Bottom No-flow
Table 2. 3. Line drive Synthetic case data
Reservoir fluid type Black oil Gas specific gravity 0.60 Depth to the top of the formation
4002 ft. Oil specific gravity 0.89 Rock compressibility 3.00e-06 1/psi Water specific gravity 1.00 Rock reference pressure 6345 psi Irreducible water saturation 0.37 Depth of water-oil contact 4800 ft. Residual oil saturation 0.10 Bubble point pressure 4275 psi Critical gas saturation 0.05
Texas Tech University, Elias Pirayesh, May 2012
14
2.3. Third Case: Five Spot Water Flooding Pattern
The third case is a reservoir with a quarter of a five spot injection/production
pattern. Like the previous case, there are three wells in the reservoir which include an
injection, a production and a barrier-fractured well. For symmetry purposes, the fracture
was placed in the center of the reservoir. The reservoir map is shown in Figure 5. This
model is the same as the introduced in section 2.2, except for the well locations.
Figure 2. 6. Five spot reservoir map
2.4. Optimization
Later in the results section, it will be shown that the creation of a barrier-fracture
can increase recovery by as much as 10% or even more. In addition to the basic cases, in
order to optimize barrier-fracture design, a number of models with different barrier-
fracture designs were created and simulated. These runs are concentrated on several basic
design factors, which could have the greatest impact on the performance of a barrier-
fracture. These design parameters include barrier-fracture length & location, the number
of barrier-fractures, mobility ratio and schedule of barrier-fracturing.
2.4.1. Barrier-fracture Length
To investigate the effect of barrier-fracture length on the performance of flooding,
several cases with different lengths were created. The reservoir model properties used are
the same as the five spot pattern reservoir in case 3, except for the barrier-fracture length.
Texas Tech University, Elias Pirayesh, May 2012
15
Different barrier-fracture lengths ranging from 5% to 95% of the reservoir length were
created and introduced into the model. Figures 2.7 to 2.9 show some of these designs.
Figure 2. 7. Barrier-fracture length equal to 25% of reservoir length
Figure 2. 8. Barrier-fracture length equal to 50% of reservoir length
Texas Tech University, Elias Pirayesh, May 2012
16
Figure 2. 9. Barrier-fracture length equal to 75% of reservoir length
2.4.2. Barrier-fracture Location
To investigate the effect of barrier-fracture location, several reservoir models with a same
barrier-fracture, placed at different locations were created. To thoroughly investigate the
effect of barrier-fracture location, fractures were placed at 1/4, 1/3, 1/2, 2/3 and 3/4 of the
reservoir length away from the producer and illustrated in figures.
Figure 2. 10. Barrier-fracture placed at the first quarter of the reservoir
Texas Tech University, Elias Pirayesh, May 2012
17
Figure 2. 11. Barrier-fracture placed at the center of the reservoir
Figure 2. 12. Barrier-fracture placed at the third quarter of the reservoir
2.4.3. Number of Barrier-fracture
To investigate the effect of number of barrier-fractures on the performance of a flooding
project, models with different number of barrier-fractures were created. Barrier-fractures
placement was done in a symmetrical manner, for example, the barrier-fractures of a
model with two barrier-fractures are placed at 1/3 and 2/3 of reservoir length. Figures
2.13 to 2.15 show the reservoirs with two, to four barriers.
Texas Tech University, Elias Pirayesh, May 2012
18
Figure 2. 13. A reservoir with two barrier-fractures
Figure 2. 14. A reservoir with three barrier-fractures
Figure 2. 15. A reservoir with four barrier-fractures
Texas Tech University, Elias Pirayesh, May 2012
19
2.4.4. Mobility Ratio
In any water-flooding project, mobility ratio is a key determinant of the resulting
recovery of the project. This is because breakthrough time strongly depends on mobility
ratio. In order to analyze the effect of mobility ratio on the performance of a barrier-
fracture, several five-spot pattern reservoirs with different fluid systems were analyzed.
The mobility ratios of these cases range from 0.5 to 10, with 0.5 being a highly favorable
mobility ratio and 10 being a highly unfavorable one.
2.4.5. Schedule of Barrier-Fracturing
The time during the life of a flooding project when the barrier-fracture is created can
affect the performance of a barrier-fracturing project. A barrier-fracture can be created at
any time during a flooding project e.g. before or after water breakthrough. To investigate
the effect that timing has on performance, several models with different barrier-fracturing
times ranging from 0 to 6,000 days were created and simulated. This analysis is important
because in practice, operators have little tendency to start conformance treatments before
breakthrough happens. However the best results are likely to be obtained when the
proposed treatment is applied at the beginning of a flooding project.
2.5. Relative Permeability Modifier Filled Barriers
A selective barrier to flow can be created by injecting a relative permeability
modifying agent (RPM) into a crack created in the reservoir rock. This crack can be a
conventional hydraulic fracture that has not been filled with proppant. Injection of
relative permeability modifying agents into the crack will reduce water relative
permeability to a fraction of its original value while leaving the oil relative permeability
intact. Different relative permeability modifying agents tend to have different effects on
rocks. The range of water relative permeability reduction by injection of relative
permeability modifiers is wide. While leaving oil relative permeability fairly intact, some
RPM agents can cause a 90% reduction in water relative permeability of rocks. This
reduction of water relative permeability will reduce water flow through the treated zone.
Texas Tech University, Elias Pirayesh, May 2012
20
The effect of relative permeability modifying agents on the relative permeability curves
of a typical rock and a diagram of a barrier created using RPM agents are shown in
Figures 2.16 and 2.17, respectively.
(a)
(b)
Figure 2.16. Reservoir rock relative permeability curves. (a) Before RPM treatment (b) After RPM treatment
Texas Tech University, Elias Pirayesh, May 2012
21
Figure 2.17. Barrier created by injection of RPM agents into a fracture
Effectiveness of RPM barriers in improving recovery from oil reservoirs was investigated by creating several simulation models. These models are only different in the amount of rock water relative permeability reduction caused as a result of injecting of RPM agents into cracks. The three cases created included RPM barriers with water relative permeabilities ranging from 10% to 75% of the original water relative permeability of reservoir rock.
Texas Tech University, Elias Pirayesh, May 2012
22
CHAPTER III
RESULTS
The results of the simulations for barrier-fracturing efficiency fall under three
categories as the following:
First case: Edge-water drive reservoir
Second case: A reservoir with a line-drive water-flooding pattern
Third case: A reservoir with a five-spot water-flooding pattern
3.1. First Case: Edge-water Drive
Figures 3.1 and 3.2 show the water saturation distribution in the presence and
absence of a barrier-fracture at 911 days and 914 days, respectively. The comparison of
the saturation profiles in the presence and absence of a barrier-fracture in Figures 3.1 and
3.2 clearly shows the improvement in sweep efficiency by creating the barrier-fracture.
The increase in oil production and decrease in water production are depicted in Figures
3.3 and 4.3. The numerical simulation indicates that the cumulative oil production will
increase by 213,000 STB (5.35%) and decrease in water production will be about the
same amount, 213,000 bbl (6.41%).
Figure 3. 1. Water breakthrough into the horizontal well with no barrier-fracture
Texas Tech University, Elias Pirayesh, May 2012
23
Figure 3. 2. Water breakthrough into the horizontal well in the presence of a barrier-fracture
Figure 3. 3. Oil production in the presence and absence of a barrier-fracture
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
0 500 1000 1500 2000 2500 3000 3500 4000
Time, days
To
tal
Oil
Pro
du
cti
on
, M
illi
on
ST
B
With a barrier
Without a barrier
Texas Tech University, Elias Pirayesh, May 2012
24
Figure 3. 4. Water production in the presence and absence of a barrier-fracture
3.2. Second Case – Line Drive Water Flooding Pattern
Figures 3.5 and 3.6 show the saturation distribution in the presence and absence
of a barrier-fracture. These two figures demonstrate the improved displacement profile
resulting from the creation of the barrier-fracture. Figure 3.7 shows a vertical water
saturation profile in the reservoir. This figure shows how existence of a barrier-fracture
has completely stopped passage of fluids through the fracture. Figures 3.8 and 3.9
illustrate the increase in oil production and decline in water production. The two figures
also indicate that optimization of the fracture position and dimension may be very
important in the design process.
0.00E+00
5.00E-01
1.00E+00
1.50E+00
2.00E+00
2.50E+00
3.00E+00
3.50E+00
0 500 1000 1500 2000 2500 3000 3500 4000
Time, days
To
tal
Wa
ter
Pro
du
cti
on
, M
illi
on
BB
L
With a barrier
Without a barrier
Texas Tech University, Elias Pirayesh, May 2012
25
Figure 3. 5. Water saturation distribution in the absence of a barrier-fracture
Figure 3. 6. Water saturation distribution in the presence of a barrier-fracture
Texas Tech University, Elias Pirayesh, May 2012
26
Figure 3. 7. Cross sectional water saturation distribution in the presence of a barrier-fracture
Figure 3. 8. Oil production in the presence and absence of a barrier-fracture
Texas Tech University, Elias Pirayesh, May 2012
27
Figure 3. 9. Water production in the presence and absence of a barrier-fracture
3.3. Third Case – Five Spot Water Flooding Pattern
As is illustrated in Figures 3.10 and 3.11, sweep efficiency improves by creating
the barrier-fracture. This is due to the delay in breakthrough caused by the existence of
the barrier-fracture. The increase in oil production and decrease in water production are
shown in Figures 3.12 and 3.13.
Texas Tech University, Elias Pirayesh, May 2012
28
Figure 3. 10. Water saturation distribution in the presence of a barrier-fracture
Figure 3. 11. Water saturation distribution in the absence of a barrier-fracture
Texas Tech University, Elias Pirayesh, May 2012
29
Figure 3. 12. Oil production in the presence and absence of a barrier-fracture
Figure 3. 13. Water production in the presence and absence of a barrier-fracture
Texas Tech University, Elias Pirayesh, May 2012
30
3.4. Optimization Results
3.4.1. Barrier-Fracture Length
Results of using different barrier-fracture sizes are shown in the following figures.
The cumulative oil and water production are shown in Figures 3.14 and 3.15,
respectively. For this case, the longest fracture produces the best results, i.e. more oil and
less water. Figure 3.16 provides a better relationship between barrier-fracture length and
breakthrough time which is the time when producer oil production rate drop below the
determined production constraint. As expected, the longest barrier-fracture results in the
longest breakthrough time. Figure 3.17 provides a similar relation between recoveries at
6,000 days with different barrier-fracture lengths. Most naturally, the longest fracture
gives the highest recovery among all other fracture lengths.
Figure 3. 14. Cumulative oil production
Texas Tech University, Elias Pirayesh, May 2012
31
Figure 3. 15. Cumulative water production
Figure 3. 16. Breakthrough time vs. barrier-fracture length
Texas Tech University, Elias Pirayesh, May 2012
32
Figure 3. 17. Cumulative oil production vs. barrier-fracture length
3.4.2. Barrier-Fracture Location
The results of placing barrier-fractures in different locations in the reservoir are shown in
the following figures. Cumulative oil and water production are shown in Figures 3.18 and
3.19, respectively. These two figures indicate that the barrier-fracture located at the
center of the reservoir would produce the highest amount of oil and the least amount of
water. Figure 3.20 shows how breakthrough time changes as a function of barrier-
fracture location. The barrier-fracture located at 220 ft. away from the producer shows
the longest breakthrough time. Figure 3.21 provides a similar relation between recoveries
at 6,000 days with different barrier-fracture location. Unlike breakthrough time, the
barrier-fracture located at the center of the reservoir gives the highest oil production all
others.
Based on the figures provided, performance of a barrier-fracture is not very sensitive to
barrier-fracture location after all.
Texas Tech University, Elias Pirayesh, May 2012
33
Figure 3. 18. Cumulative oil production
Figure 3. 19. Cumulative water production
Texas Tech University, Elias Pirayesh, May 2012
34
Figure 3. 20. Breakthrough time vs. barrier-fracture location
Figure 3. 21. Cumulative oil production vs. barrier-fracture location
Texas Tech University, Elias Pirayesh, May 2012
35
3.4.3. Number of Barrier-fractures
Oil saturation distribution maps of all cases at 2,500 days 20 days is shown in Figures
3.22 to 3. Cumulative oil and water production are shown in Figures 3.22 and 3.23,
respectively. A reservoir with four barrier-fractures has produced less water and more oil
over the production period. Figure 3.24 shows breakthrough time changes vs. number of
barrier-fractures. A single barrier-fracture yields the longest breakthrough time. Figure
3.25, provides a similar relationship between recovery and the number of barrier-
fractures. As expected, the design that includes four barrier-fractures results in the highest
recovery.
According to the results of this analysis, a direct relationship between breakthrough time
and the final recovery does not exist with regard to the number of fractures. It is
interesting to see that the improvement in recovery changes only slightly as the number
of barriers is increased from 3 to 4. In a real application, it might not suffice to pay off
the investment made on adding the fourth fracture.
(a)
Texas Tech University, Elias Pirayesh, May 2012
37
(d)
Figure 3. 22. Oil saturation distribution map at 2,500 days (a) one barrier-fracture (b) two barrier-fractures (c) three barrier-fractures (d) four barrier-fractures
Figure 3. 23. Cumulative oil production
Texas Tech University, Elias Pirayesh, May 2012
38
Figure 3. 24. Cumulative water production
Figure 3. 25. Breakthrough time vs. number of barrier-fractures
Texas Tech University, Elias Pirayesh, May 2012
39
Figure 3. 26. Cumulative oil production vs. number of barrier-fractures
3.4.4. Effect of Mobility Ratio
Results of using different mobility ratios are shown in the following figures. Figures 3.26
and 3.27 show changes in oil and water production rate with time, respectively. Like all
other flooding schemes, cases with lower mobility ratios are expected to produce more
favorable results than those with higher ones. As expected, the case with a mobility ratio
of 0.5 shows a much longer sustained oil flow rate compared to others. It has also
maintained a lower water production rate for the entire production time period. Based on
the figures shown here, it can be concluded that the performance of a barrier-fracturing
project is highly dependent on mobility ratio.
Cumulative production figures (Figures 3.28 and 3.29) confirm the previously obtained
results. Figure 3.30 shows how breakthrough time changes as a function of mobility ratio.
The mobility ratio of 0.5 shows the longest breakthrough time. Figure 3.31 provides a
similar relationship between recovery and mobility ratio. In addition to showing the
effect of mobility ratio, Figures 3.30 and 3.31 can also be interpreted as a comparison of
Texas Tech University, Elias Pirayesh, May 2012
40
two different designs with and without a barrier-fracture. An almost constant difference
in recovery exists between the two cases at different mobility ratios.
Figure 3. 27. Oil production rate
Texas Tech University, Elias Pirayesh, May 2012
41
Figure 3. 28. Water production rate
Figure 3. 29. Cumulative oil production
Texas Tech University, Elias Pirayesh, May 2012
42
Figure 3. 30. Cumulative water production rate
Figure 3. 31. Breakthrough time vs. mobility ratio
Texas Tech University, Elias Pirayesh, May 2012
43
Figure 3. 32. Cumulative oil production rate vs. mobility ratio
3.4.5. Effect of Barrier-Fracturing Time
Creating a barrier-fracture at different times during the life of a flooding project results in
different production behaviors. Oil and water flow rate vs. time plots are shown in
Figures 3.32, 3.33, 3.34 and 3.35, respectively. Among all the investigated cases, the case
where a barrier-fracture was created at the beginning of the project maintains a higher oil
flow rate and less water flow rate for most of the flooding project. Figures 3.36 and 3.37.
provide a relationship between barrier-fracturing time with breakthrough time and
cumulative oil production at 6,000 days.
Texas Tech University, Elias Pirayesh, May 2012
44
Figure 3. 33. Oil flow rate vs. time
Figure 3. 34. Water flow rate vs. time
Texas Tech University, Elias Pirayesh, May 2012
45
Figure 3. 35. Cumulative oil production vs. Time
Figure 3. 36. Cumulative water production vs. time
Texas Tech University, Elias Pirayesh, May 2012
46
Figure 3. 37. Breakthrough time vs. barrier-fracturing time
Figure 3. 38. Cumulative oil production vs. Barrier-fracturing time
Texas Tech University, Elias Pirayesh, May 2012
47
3.5. Relative Permeability Modifier Barrier
Based on cumulative oil production results presented in Figure 3.39, RPM barriers have the potential of improving recovery in a water-flooding project; however the amount of improvement in recovery is only marginal. The amount of improvement in recovery also depends on the effectiveness of RPM agents in reducing water relative permeability in rock.
The highest improvement in recovery as a result of creating a RPM barrier is 0.35% where water relative permeability in the barrier was reduced to 10% of its original value. This amount of improvement in recovery is fairly small, especially compared to the improvement achieved by creating a barrier-fracture.
Figure 3. 39. Cumulative oil production vs. RPM properties
The small improvement in recovery achieved by RPM barriers can be explained by analyzing hydrocarbon sweep profiles. In contrast to barrier-fractures, RPM barriers are not effective in changing the sweep patterns in the reservoir. As such RPM barriers cannot change the water paths in the reservoir. Consequently they have very little effect
Texas Tech University, Elias Pirayesh, May 2012
48
on improving recovery. A comparison between the sweep patterns in the presence of a RPM barrier and a barrier-fracture is presented in Figure 3.40.
(a)
(b) Figure 3.40. Water saturation distribution maps at 1500 days (a) RPM barrier (b)
Barrier-fracture
Texas Tech University, Elias Pirayesh, May 2012
49
CHAPTER IV
CONCLUSIONS AND RECOMMENDATIONS
The purpose of this project was to investigate the application of barrier-fracturing
using simulation. Barrier-fracturing is a novel idea to modify flow profile and divert the
displacing fluid by placing a fracture with essentially zero permeability deep into the
reservoir.
This research provides three basic simulation models. These include an edge
water drive reservoir, and two other reservoirs which have two different flooding
patterns: a line drive and a five spot pattern. The effects of different design parameters on
the performance of a barrier-fracture were analyzed.
4.1. Conclusions
Based on the saturation distribution maps of reservoirs with and without a barrier-
fracture, a barrier-fracture has the ability to modify flow profile and divert the
displacing fluid.
Barrier-fractures can help improve recovery by delaying water-breakthrough and
improving the volumetric sweep efficiency of a water-flooding project.
Oil production increased and water production decreased as a result of
introducing a barrier-fracture into a reservoir which was under water-flooding.
Barrier-fracture performance can be improved by optimizing design parameters
such as: fracture length, location, number of barrier-fractures, schedule of barrier-
fracturing, and the mobility ratio.
Models with longer barrier-fractures show better performance than those with
shorter barrier-fractures.
The optimum location to place a barrier-fracture is the middle of the distance
between the producer and the injector. Similarly, when there is more than one
barrier-fracture, a symmetrical design with equal fracture spacing is likely to give
the best results.
Texas Tech University, Elias Pirayesh, May 2012
50
The higher the frequency of barrier-fractures, the higher the performance of
barrier-fracturing. For more than three fractures, the improvement in recovery will
be small, making the economic justification of adding a fracture difficult.
Models with low mobility ratios tend to produce better results than those with
higher mobility ratios, i.e. they show longer breakthrough times, larger
cumulative oil production and less cumulative water production.
Simulation results show that the earlier the barrier-fracture is created, the higher
the recovery will be.
The application of barrier-fracturing is not limited to a specific reservoir type or
completion. It may be applied to a wide variety of conditions such as edge water
drive and various patterns of injection.
RPM-barriers can be created by injecting relative permeability modifying agents
into created cracks in reservoir rock. RPM-barriers are not effective in changing
water flow profile in the reservoir. Consequently, they do not contribute to
recovering more oil from reservoir in a flooding project.
4.2. Recommendations
Streamline simulation provides a convenient tool to investigate enhanced oil
recovery schemes, as it offers a more understandable visualization tool and a
shorter run time. Therefore, it is strongly recommended to use this type of
simulation for comparison of results with those obtained in this work.
Barrier-fracturing needs to be tested with many more types of reservoirs and more
enhanced oil recovery processes such as CO2 injection schemes.
Experimental work can help get more insight into the idea of barrier-fracturing.
For instance, micro-model experiments may provide an easy and reliable tool to
visualize the process.
After experimental investigations, field testing can be the next step in evaluating
the idea of barrier-fracturing.
Texas Tech University, Elias Pirayesh, May 2012
51
REFERENCES
Avery, M. R., L. A. Burkholder, et al. (1986). Use of Crosslinked Xanthan Gels in Actual Profile Modification Field Projects. International Meeting on Petroleum Engineering. Beijing, China, 1986 Copyright 1986, Society of Petroleum Engineers.
Avery, M. R., M. A. Gruenenfelder, et al. (1987). Design Factors and Their Influence on Profile Modification Treatments for Waterfloods. Middle East Oil Show. Bahrain, 1987 Copyright 1987, Society of Petroleum Engineers.
Azari, M. and M. Soliman (1996). Review of Reservoir Engineering Aspects of Conformance Control Technology. Permian Basin Oil and Gas Recovery Conference. Midland, Texas, 1996,. Society of Petroleum Engineers Inc.
Brocco, C., E. D. Dalrymple, et al. (2000). Relative Permeability Modifier Preflush Fracture-Stimulation Technique Results in Successful Completion of Previously Bypassed Intervals. SPE/DOE Improved Oil Recovery Symposium. Tulsa, Oklahoma, Copyright 2000, Society of Petroleum Engineers Inc.
Dalrymple, E. D., P. Creel, et al. (1998). Results of Using a Relative-Permeability Modifier with a Fracture-Stimulation Treatment. SPE Annual Technical Conference and Exhibition. New Orleans, Louisiana, 1998 Copyright 1998, Society of Petroleum Engineers Inc.
Fry, L. E., D. M. Everett, et al. (2006). Successful Application of Relative-Permeability Modifiers To Control Water Production in Rose Run Fracturing. SPE Eastern Regional Meeting. Canton, Ohio, USA, Society of Petroleum Engineers.
Garcia, B., J. E. Soriano, et al. (2008). Novel Acid-Diversion Technique Increases Production in the Cantarell Field, Offshore Mexico. SPE International Symposium and Exhibition on Formation Damage Control. Lafayette, Louisiana, USA, Society of Petroleum Engineers.
Liu, X.-E. (1995). Development and Application of the Water Control and Profile Modification Technology in China Oil Fields. International Meeting on Petroleum Engineering. Beijing, China, 1995 Copyright 1995, Society of Petroleum Engineers, Inc.
Llave, F. M. (1994). Field Application of Surfactant-Alcohol Blends for Conformance Control. SPE Annual Technical Conference and Exhibition. New Orleans, Louisiana, Society of Petroleum Engineers.
Melo, R. C. B. D. and R. S. Aboud (2008). Over 100 Conformance Fracturing Operations in Brazil: Results and Improvements. Europec/EAGE Conference and Exhibition. Rome, Italy, Society of Petroleum Engineers.
Texas Tech University, Elias Pirayesh, May 2012
52
Nieves, G., J. Fernandez, et al. (2002). Field Application of Relative Permeability Modifier in Venezuela. SPE/DOE Improved Oil Recovery Symposium. Tulsa, Oklahoma, Copyright 2002, Society of Petroleum Engineers Inc.
Ortega, A. T., J. R. Peano, et al. (2006). Conformance While Fracturing: Technology Used To Reduce Water Production in North Mexico. First International Oil Conference and Exhibition in Mexico. Cancun, Mexico, Society of Petroleum Engineers.
Weaver, J. D. (1978). A New Water-Oil Ratio Improvement Material. SPE Annual Fall Technical Conference and Exhibition. Houston, Texas, 1978 Copyright 1978, American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc.
Texas Tech University, Elias Pirayesh, May 2012
53
APPENDIX A
SENSITIVITY ANALYSIS: EFFECT OF GRIDDING ON SIMULATION
RESULTS
Using simulation as the analysis tool in this work necessitates a sensitivity analysis to ensure that the reported results are not affected by the number of grid blocks used in simulation models. In this study, the most commonly used simulation model is the case of a reservoir with a five spot flooding pattern. The reservoir grid is a 42 41 13 system. Cumulative oil production at 6,000 days vs. total number of grids is shown in Figure A.1.
Figure A. 1. Cumulative oil production at 6,000 days vs. number of grid blocks
The plot shows that increasing the number of grid blocks from 16,380 (36 35 13) to 123,578 (98 97 13) will cause a difference of 0.6% in cumulative oil production at 6,000 days. This shows that the simulation results are relatively insensitive to the number of grid blocks and any grid system between 36 35 13 and 98 97 13 can be an optimal gridding candidate.
Texas Tech University, Elias Pirayesh, May 2012
54
VITA
Permanent Address:
Bob L. Herd Department of Petroleum Engineering Texas Tech University, Lubbock TX 79409
Email Address:
Education:
M.Sc., Petroleum Engineering
Texas Tech University
Lubbock TX 79409 B.Sc., Petroleum Engineering
Sharif University of Technology
Tehran, Iran