Fracture Modeling
Fracture Modeling
Fracture Modeling
by
Adlet S. Jambayev
A thesis submitted to the Faculty and the Board of Trustees of the Colorado School of
Mines in partial fulfillment of the requirements for the degree of Master of Science (Petroleum
Engineering).
Golden, Colorado
Date _______________
Signed: _________________________
Adlet S. Jambayev
Signed: _________________________
Dr. Todd B. Hoffman
Thesis Advisor
Golden, Colorado
Date _______________
Signed:_________________________
Dr. William Fleckenstein
Professor and Head
Petroleum Department
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ABSTRACT
located in North Caspian basin in western Kazakhstan. Predicting the movement of hydrocarbons
in such reservoir is challenging because of the many uncertainties due to the complicated fracture
network and the heterogeneity of carbonate rock. Due to uncertainties involved in modeling fluid
flow, discrete fracture network (DFN) models are constructed for a free well section of “Field
X”. Building realistic and representative models of fracture networks can improve reservoir
characterization and make more accurate flow prediction. Fracture parameters such as intensity,
size, shape, and orientation are assigned to each fracture based on measured data or relevant
Well test results using constructed DFN models and results of actual test are compared.
The main matching involves skin effect and transmissibility. The DFN model is then upscaled
that obtains fracture properties including porosity, permeability, and sigma factor suitable for a
flow simulation model. This ensures that the upscaled DFN model preserves the properties of
actual fractures in the studied sector. Predictions of well’s long term productivity and pressure
response are valuable inputs to main business decision and reservoir management strategies.
Well-C was suspended due to high water cut (up to 60%) shortly after putting it on
production. One concern of this trend is that the water seen at Well-C might end up at nearby
wells. The objective of dynamic analysis was to predict potential water flow from the aquifer
through the fractures to the producing wells. Many different scenarios are simulated with
different water influx rate and different DFN models, which show the wide range of water
breakthrough time (from 16 to 161 months) and cumulative water (from 7907 to 978718 bbl) in
ABSTRACT……………………………………………………………...………………........…iii
LIST OF FIGURES……………………………………………………...……………...….........vii
LIST OF TABLES……………………………………………………..……………...……........xii
LIST OF SYMBOLS………………………………………………...……………...…..…........xiii
ACKNOWLEDGEMENTS……………………………………………………………………...xv
CHAPTER 1 INTRODUCTION………………………………………………………………….1
SIMULATION…………………………………………………………………………………...41
v
6.2 Fracture Upscaling……………………………………………...……………………60
7.1 Summary……………………………………………………………………………..81
7.2 Conclusions…………………………………………………………………………..83
REFERENCES……………………………………………………..……………………………86
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LIST OF FIGURES
Figure 2.1 Orthogonal (a) and Baecher (b) models (Dershowitz and Einstein,1988)……….11
Figure 3.1 Example of fracture in Well-B on FMI log. Original FMI image on the left and
interpreted on the right…………………………………………………………...16
Figure 3.2 Example of open, effective fractures in Well-B on FMI image log (c) and
responses of other tools in the same interval: photoelectric and Stoneley logs (a),
caliper log (b), and production log (d)…………………………………………...18
Figure 3.3 Example of open, effective fractures in Well-A on Caliper (a), Temperature (b)
and Production logs (c) in the same depth interval………………………………19
Figure 3.4 Snapshot from the wellbook of Well-A………………………………………….20
Figure 4.2 Tadpole plot of Well-A (a) and Well-B (b) (snapshot from image log
interpretation). Different colors correspond to the various types of natural
fractures…….…………………………………………………………………….24
Figure 4.3 Dip of cavern walls in similar direction (a) and opposite direction (b) (snapshot
from image log interpretation). Example of cavern walls with simillar dip
direction (c) and opposite dip direction (d) in Well-A built in FracMan………...25
Figure 4.4 Stereoplot of cavern walls defined in Well-A (a) and their 3-D visualization (b).26
Figure 4.5 Example of cavern in Well-A on FMI log with walls in dip opposite direction...27
Figure 4.7 All natural fractures in Well-A on rose diagram (a), lower hemisphere projection
(b), and contoured stereoplot (c)…………………………………………………29
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Figure 4.8 Effective fractures, excluding orientation of cavern walls, in Well-A on rose
diagram (a), lower hemisphere projection (b), and contoured stereoplot (c)…….29
Figure 4.9 Cumulative Fracture Intensity plot of effective fractures in Well-A…………….30
Figure 4.10 Fracture Set 1 in Well-A on rose diagram (a), lower hemisphere projection (b),
and contoured stereoplot (c)……………………………………………………...31
Figure 4.11 All natural fractures in Well-B on rose diagram (a), lower hemisphere projection
(b), and contoured stereoplot (c)………………………………………………....31
Figure 4.12 Effective fractures, excluding orientation of cavern walls, in Well-B on rose
diagram (a), lower hemisphere projection (b), and contoured stereoplot (c)…….32
Figure 4.13 Statistical summary of ISIS analysis for all fracture sets………………………..33
Figure 4.15 Stereoplots of fracture orientations from different models: Model 1-orientation of
Fracture Set 1 (a), Model 2 - orientation of two Fracture Sets 1 and 2 (b), and
Model 3-orientation of Fracture Set 3in Well-B (c)……………………………..34
Figure 4.16 Lognormal distribution for fracture aperture…………………………………….35
Figure 4.19 Histogram of equivalent radius with Normal of Log distribution trend line, Model
1…………………………………………………………………………………..40
Figure 4.20 Histogram of fracture size with Normal of Log distribution trend line, Model 1.40
Figure 5.1 Histogram of fracture aperture with Normal of Log distribution trend line, Model
1…………………………………………………………………………………..42
Figure 5.2 Snapshot of flow rate from PLT report for Well-A (a) and reproduced production
log based on the most prolific fractures (b)……………………………………...44
Figure 5.3 Snapshot of flow rate from PLT report for Well-B (a) and reproduced production
log based on the most prolific fractures (b)……………………………………...45
Figure 5.4 Aperture-Permeability correlation based on PLT analysis, Well-A……………..46
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Figure 5.5 Aperture-Permeability correlation based on PLT analysis, Well-B……..………46
Figure 5.7 Box Regions centered on the wells (a) and created mesh (b)……………………49
Figure 5.9 Log-log plot of pressure and pressure derivative in Well-B as a function of
time……………………………………………………………………………....50
Figure 5.10 History match comparison of simulated (green and purple colors) and measured
results (red and blue), Well-A Model 1 with maximum fracture length 500 m…53
Figure 5.11 History match comparison of simulated (green and purple colors) and measured
results (red and blue), Well A Model 1 with maximum fracture length 1000 m...53
Figure 5.12 Pressure visualization during the well test (time-10 hours), Well-A…………….54
Figure 5.13 History match comparison of simulated (green and purple colors) and measured
results (red and blue), Model 1…………………………………………………..54
Figure 5.14 History match comparison of simulated (green and purple colors) and measured
results (red and blue), Model 2…………………………………………………..55
Figure 5.15 History match comparison of simulated (green and purple colors) and measured
results (red and blue), Model 3…………………………………………………..55
Figure 5.16 History match comparison of simulated (green and purple colors) and measured
results (red and blue), initial permeability Model1………………………………56
Figure 5.17 History match comparison of simulated (green and purple colors) and measured
results (red and blue), permeability decreased Model 1…………………………56
Figure 5.18 History match comparison of simulated (green and purple colors) and measured
results (red and blue), permeability decreased Model 2………………………....57
Figure 5.19 History match comparison of simulated (green and purple colors) and measured
results (red and blue), permeability decreased Model 3…………………………57
Figure 6.1 PLT results in Well-C from three different times. Water crossflow at the rate of
290 m3/d, September 2009 (a), water from the leaky plug at the rate of 120 m3/d,
April 2011 (b), reduced water crossflow at the rate of 49 m3/d, May 2011 (c)….59
Figure 6.2 Grid between surfaces……………………………………………………………61
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Figure 6.3 Exported grid coordinates into ECLIPSE, 3-D view of reservoir in Petrel…..….61
Figure 6.4 Exported fracture permeability in x direction from FracMan Model 1, 3-D view in
Petrel …………………………………………………………………………..65
Figure 6.5 Exported fracture porosity from FracMan Model 1, 3-D view in Petrel………...65
Figure 6.6 Exported fracture porosity from FracMan Model 1, 3-D view in Petrel………...66
Figure 6.7 Reduced permeability in y direction around Well-C Model 1, 3-D view in
Petrel……………………………………………………………………………..67
Figure 6.8 Constant oil rates at different water influx rates, Model 1………………………69
Figure 6.9 Constant oil rates at different water influx rates, Well-A (a), Well-B (b), Model
1…………………………………………………………………………………..70
Figure 6.10 Water production trends of the models at different water influx rates…………..72
Figure 6.11 Water production trends of the wells at different water influx rates, Model 1…..72
Figure 6.12 Water production trends of the wells at different water influx rates, Model 2…..73
Figure 6.13 Water production trends of the wells at different water influx rates, Model 3…..73
Figure 6.14 Simulated water saturation in December, 2012, snapshot from ECLIPSE, Model 1
(a), Model 2 (b), and Model 3 (c)………………………………………………..74
Figure 6.15 Simulated water saturation in December, 2022, snapshot from ECLIPSE, Model 1
(a), Model 2 (b), and Model 3 (c)………………………………………………..74
Figure 6.16 Simulated water saturation in October, 2032, snapshot from ECLIPSE, Model 1
(a), Model 2 (b), and Model 3 (c)………………………………………………..74
Figure 6.17 Breakthrough time of the total water production trend at various permeability
inputs, Model 1…………………………………………………………………..76
Figure 6.18 Water production trends of individual wells with a different fracture
permeability……………………………………………………………………...76
Figure 6.19 Simulated water saturation in December, 2012, snapshot from ECLIPSE Model
1_3 (a), Model 1_2 (b), and Model 1_1 (c)……………………………………...78
x
Figure 6.20 Simulated water saturation in December, 2022, snapshot from ECLIPSE Model
1_3 (a), Model 1_2 (b), and Model 1_1 (c)…………………...…………………78
Figure 6.21 Simulated water saturation in October, 2032, snapshot from ECLIPSE Model 1_3
(a), Model 1_2 (b), and Model 1_1 (c)…………………………………………..78
Figure 6.22 Breakthrough time of the total water production trend at various length inputs,
Model 1…………………………………………………………………………..80
Figure 6.23 Water production trends of individual wells with a different fracture length……80
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LIST OF TABLES
xii
LIST OF SYMBOLS
Length, m (ft)
Constant, unitless
Permeability, mD
Aperture, m (ft)
Time, hr
Probability, unitless
xiii
Grid cell volume, m3 (ft3)
xiv
ACKNOWLEDGEMENTS
First, I have to thank my parents for their love, support and encouragement throughout
my life.
I would like to sincerely thank my advisor, Dr. Todd Hoffman, for his guidance and
comments throughout this study. I am extremely grateful to Dr. Ramona Graves and Dr. John
Humphrey for serving as committee members and providing me with great feedbacks and
support during my research. Special thanks to Thomas Zalan for advises regarding research
topic.
I would also like to thank Golder Associates for providing the license for FracMan7:
Reservoir Edition software. Many thanks to everyone (they know who they are) from operating
Finally, I would like to express my appreciation to my wife, Aliya Ozibayeva, for her
Without all those people this work would not have been accomplished.
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CHAPTER 1
INTRODUCTION
geological formation that contains a network of fractures, where fractures act as highly
conductive pathways enhancing fluid flow to a wellbore. These reservoirs are found throughout
the world and some of these fields contain billions of barrels of hydrocarbons.
This research will focus on naturally fractured reservoirs’ specific feature: fractures.
According to Aguilera (1995), all reservoirs are naturally fractured to a certain degree. Narr et al.
(2006) defines naturally fractured reservoirs as “…a reservoir in which fractures enhance the
permeability field, thereby significantly affecting well productivity and recovery efficiency”.
Natural fracture detection, evaluation and processing are important goals in reservoir
characterization for geologists, geophysicists and petroleum engineers for proper exploration and
Many hydrocarbon deposits occur in sandstone and carbonate, where natural fractures are
more common in carbonates than in sandstone. Moreover, approximately 60% of the world’s oil
is found in carbonate reservoirs (Akbar et al., 2000). Carbonates are biochemical in nature and
formed in a unique environment. They are usually formed in warm, shallow and clean marine
water with low water energy. Distinctive and unique processes including compaction,
lithification and diagenesis of carbonates play an important role in the broad variation of
cementation, recrystallization, dolomitization and replacement by other minerals create both high
1
permeability zones and permeability barriers in carbonates. Therefore, an accurate estimation of
complexity and heterogeneity. One of these fields that will be examined in this research is a giant
“Field X” is a carbonate reservoir divided into several regions that are characterized by
different geological features and a similar pressure decline. The sector for this study is chosen in
the highly fractured region where the matrix permeability is very low and the main oil
production comes through the fractures. Uncertainties involved in modeling fluid flow usually
lead to building a fracture network. Building realistic and representative models of discrete
fracture network (DFN) can help to improve reservoir characterization and make more accurate
flow prediction.
Reservoir behavior controlled by fluid flow through natural fractures is often complex;
therefore, every fractured reservoir must be studied in detail. The sector for this study is chosen
in the highly fractured region with approximately 10.5 million square meters in surface area and
The purpose of this study is to create a three-dimensional (3-D) geological model from
the collected field data that can predict the reservoir behavior. In this study FracMan7: Reservoir
Edition software will be used to generate 3-D discrete fracture network models of the selected
sector to provide a more realistic description of the fracture patterns. A 3-D DFN modeling has
not been done on this section of “Field X” before. A neighboring section has been modeled
recently so the results obtained in this study could be compared to the neighboring model. With a
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discrete fracture network modeling, many aspects of this “Field X” section are expected to be
evaluated:
well-to-well connectedness
Natural fractures create complex pathways for fluid flow, which impacts reservoir
characterization, production performance, and total recovery. Understanding and making full use
of the fracture properties in the reservoir is an important factor for improving reservoir
performance. Better understanding of the fracture distribution helps to evaluate the potential
location of new wells in order to optimize drilling procedure and direction, among other things.
Borehole connected fracture analysis determines all fractures in the chosen area that are
connected to the well, whether directly or by interconnected fractures, and it shows how the
wells in the sector are interconnected through the fractures. This analysis is very useful in
Dynamic analysis uses time, pressure, and flow to better characterize fractures.
Predictions of well’s long term productivity and pressure response are valuable inputs to main
business decision and reservoir management strategies. Another objective of dynamic analysis
was to predict potential water flow from the aquifer through the fractures to the producing wells.
The scope of the research can be divided into three main steps: (1) data analysis, (2)
building a DFN model, and (3) DFN model analysis. Step one implies analyzing the information
from different sources of data to obtain parameters necessary to build discrete fracture network
3
models. These parameters include fracture locations, size, shape, orientation, flow properties,
and the number of distinct fracture sets. Step two involves generating discrete fracture network
models based on the results of the data analysis. Finally, in the last step these networks can be
analyzed to derive engineering information. This includes simple geometric analysis as well as
complex multi-well flow simulations. The history match of well test results using derived DFN
Just finding fractures or mapping fractures is not good enough for developing fractured
reservoirs because not all fractures contribute to flow. Therefore, dynamic behavior of the
fracture network is very important in determining reservoir performance. The derived DFN
model was upscaled to grid properties suitable to export to the flow simulator, ECLIPSE.
conditions of reservoir development. The geological environment plays an essential role in the
generation of reservoir fractures. Understanding the geological features of the field of study is
located in North Caspian basin in western Kazakhstan. The North Caspian basin is a petroleum-
rich basin located in Kazakhstan and Russia, which occupies the northern part of the Caspian
Sea, and a large plain to the north of the Sea (Figure 1.1) (Ulmishek, 2001). Geologists disagree
on the exact timing of origination of the basin, but they agree that the basin originated as a rift
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system. According to seismic and drilling data, the North Caspian basin can be divided into two
main depositional packages, pre-salt and post-salt, separated by Kungurian salt layer.
are many hundreds of meters high, which provide giant carbonate platform reservoirs. These
5
reservoirs are similar to one another in their depositional history, facies architecture and overall
geometry. The North Caspian basin is one of the deepest basins in the world, with thickness
more than 20 km (Ulmishek, 2001). The depth range of the reservoirs located in the pre-salt
package is between 3500 and 4000 meters, which results in significant overpressure conditions.
The main hydrocarbon source rocks are thick intervals of deep-water, organic-rich Carboniferous
During the early Permian, the North Caspian basin became isolated from the open sea
and subsequently evaporated, leading to significant salt deposition (Barde et al. 2002). The salt
layer filled the basin and formed the regional seal for underlying reservoirs (Ulmishek 2001).
The post-salt package is late Permian-Tertiary in age, and consists of a thick sedimentary
sequence. Sediments of this age were deposited above the thick Kungurian salt layer that
initiated salt movement. As a result, complex networks of salt domes and salt walls were formed.
The North Caspian basin is considered to be one of the most important sedimentary
basins in the world due to its size and petroleum potential. Oil and gas fields have been
discovered over the entire North Caspian basin. Most of these hydrocarbons are in pre-salt
carbonate platforms that have created pure stratigraphic traps in isolated carbonate platforms.
One of these carbonate build-ups is our studied “Field X”, with horizontally bedded grainstones
“Field X” is naturally depleted by solution-gas drive with good matrix properties. The
central platform has good intergranular porosity (up to 18%), while matrix permeability remains
very low (less than 10 mD). The oil is volatile with stock tank gravity about 47o API and highly
undersaturated, with initial pressure of 8000 psi more than bubble point pressure. Moreover,
6
production operations of “Field X” are complicated by extremely sour oil with about 18%
performance and recovery efficiency. A significant portion of oil production comes from the
regions around the buildup margin and slope, where the best well productivities go up to 20,000
barrels of oil per day (BOPD) because of fractures and dissolution-enhanced permeability. The
majority of the fractures in the rim and flank areas tends to be parallel to the depositional margin
and formed due to gravitational collapse of the prograding carbonate platform. Flank and rim
The relationship between the trend of the depositional margin and fracture orientation is
confirmation that the fractures developed relatively early in the evolution of the reservoir. Such
fractures form simultaneously with development of the platform and tend to be parallel to the
depositional margin, while tectonic fractures usually show consistency of fracture orientation
steep slopes consisting of different platform, reef and slope facies, and each of these facies is
affected differently during the compaction process (Goldhammer, 1997). Rapid progradation in
conjunction with differential compaction of underlying sediments is suggested to be the cause for
formation of fractures. Both open and healed fractures are present. Most of the opened fractures
show dissolution enhancement with wide and variable apertures and irregular walls, suggesting
corrosion within the fractures. Some of the fractures have experienced extensive corrosion and
7
formed caverns resulting in significant solution-enhanced fracture porosity. Carbonate is soluble
in a weak acid. When acidic water passes through the fractures, it dissolves the formation
resulting in enlargement of fracture network. If the water table is stable, fractures might grow
of the reservoir, especially in the outer platform and flank regions. Therefore, understanding
complex fracture network is important for proper flow behavior prediction in “Field X”, and
building a representative DFN model of the field becomes an important part of this study.
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CHAPTER 2
This chapter presents three methods to describe fluid flow in the naturally fractured
discrete fracture network models. In addition, the following subsection provides literature review
According to Gilman (2003), there are three approaches usually used to describe fluid
flow in naturally fractured petroleum reservoirs. The first approach is represented by a dual‐
porosity/single-permeability model, in which matrix blocks are connected only through the
fracture network. In such model most of the fluid storage is provided by the porous matrix,
whose porosity is much larger than the porosity of the fractures, and the fluid flow occurs only in
permeability model, in which in comparison to the previous model, the matrix blocks also
communicate with each other allowing fluid flow in the matrix in addition to matrix‐to‐fracture
flow.
The third approach, the discrete fracture network flow modeling, is the most recent
bounded by fracture planes, is a matrix block. The main advantage of a DFN model over the
other two models is that fractures are represented as discrete features rather than being presented
9
as a set of regularly spaced fracture network inside the matrix cubes. The purpose of this study is
to build discrete fracture network model for the naturally fractured reservoir, “Field X”.
These kinds of DFN models were developed in the late 1980s, because of the need to
investigate flow in a proposed nuclear waste repository, which led to the emergence of the
stochastic fracture models. These models also found application in mining engineering. A
discrete fracture network model represents the natural fracture system consisting of a group of
planes. Early models of fracture network were deterministic as a group of previously defined
fractures. This fracture network model was simple in which fractures were fixed, splitting the
space in equal cubes (Figure 2.1a). When examining outcrop example, fractures did not appear in
The first stochastic models were simple models in which fractures were considered planar
and finite. Since there was no indication of their actual shape, fractures were considered as disks.
The methodology for the modeling of a fracture network has been developed by many authors.
One of such models is Baecher model in which finite-size fractures are disks with random
diameters and orientations (Figure 2.1b). The simplest stochastic assumption distributed disks of
different shape, size and direction at different locations of formation; as a result, fractures
intersect each other. Later this methodology has been reviewed and extended by other
and depends on the geological conditions of reservoir development. This geological environment
plays an essential role in the generation of reservoir fractures. Fractures of the same category that
are probably generated at the same time are grouped into a fracture set. Each fracture network
10
containing fractures is created of at least one fracture set but is not necessarily limited to it. The
situation for sedimentary rocks is very different, so more complex models were developed to
Figure 2.1 Orthogonal (a) and Baecher (b) models (Dershowitz and Einstein,1988).
Conrad and Jacquin were probably the first who presented a two stage model which
includes the relationship between subsequently generated fracture sets (Einstein et al., 2000). In
the 1990s, the rock mechanics group of the Massachusetts Institute of Technology (MIT)
developed a model in which the fractures are created in a hierarchical pattern. This model
produces more realistic two-dimensional fracture representation. At the same time, similar
models were developed by other researchers. These models were typically two-dimensional and
have a loose relationship to the geological genesis of the fractures. Later it was improved at MIT
by Ivanova (1998) and Meyer (1999) by creating a three-dimensional model which is relatively
powerful and flexible. Figure 2.2 shows two different fractures sets combined in one model. It
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represents the essential geologic genesis of the fractures. This model is both stochastic and
networks and has been used increasingly in naturally fractured reservoir characterization for
hydrocarbons. Generation of the fracture network is predicted by statistical information from the
field measurement data. In this study, FracMan7: Reservoir Edition software, developed by
Golder Associates, will be used to build and analyze DFN that supports an integrated assessment
of fractured reservoirs from data analysis, through fracture generation, to flow simulation. In
12
DFN models, a series of individual fractures are generated based on stochastic descriptions of
fracture properties including intensity, orientation and size. FracMan7 generates 3-D fracture
network models to provide a more realistic description of the pattern of fractures. The statistical
properties of the generated fracture network reflect the properties of actual fracture distribution
in the studied area. This software uses a hierarchical object model for all required objects to
Beside the static analysis, dynamic fracture analysis can be performed in built DFN
model. Dynamic analysis uses time, pressure, and flow to better characterize fractures. The
primary objective of DFN models is to serve as the basis for flow simulation of the carbonate
reservoir. A generated fracture network is usually an input for a flow simulation model.
Therefore, the flow simulation of an accurately built DFN model can help in choosing an
Three wells are selected in a highly fractured region of “Field X”. These wells
demonstrate high production potential. It is believed that these wells are interconnected through
the fracture network since they show similar pressure decline regardless when an individual well
came online or well cumulative production. Connection to the fracture network explains wide
range in production behavior. However, these three wells appear to be somewhat disconnected
from the rest of the field, because pressure response is not observed in further offset wells. The
boundary between regions is drawn where individual well pressure decline trends appear to
separate from the rest of the group. The geological concept for this region is that the fracture
network is somewhat disconnected from other fracture networks, while at the same time, intra-
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CHAPTER 3
Field data analysis implies analyzing the information from different sources of data to
obtain parameters necessary to build discrete fracture network models. The main objective of this
chapter is to show the raw data that is used for constructing the DFN models, and to discuss how
There are basically three major sources of data acquisition on natural fractures: outcrop
data, seismic data and well data. For the region of “Field X”, high resolution seismic data are not
helpful because these fractures fall below the seismic resolution. For this research, mainly well
log data was used along with some outcrop analog data. Only “effective” fractures are used for
computation of fracture properties. According to Narr (2010): “An effective fracture is one that
is both open and thought to have a significant extent, either individually or via connection with
other fractures and significantly affect fluid flow to the wellbore.” Borehole data are used to
define various important inputs to build representative fracture models. These properties are
Conventional logging methods, drilling information, and production logs provide the
critical information for judging whether the fractures are “effective” or not. All effective
fractures were interpreted by a company geologist and are supplied including depth and fracture
orientation. While these fractures were examined in the current work, our assumption is that the
14
fractures were accurately interpreted by the geologist, and these fractures will form the
Many well logs respond in a certain way to the fractures. Below is the brief description of
each log used for fracture interpretation with respect to its fracture response. Moreover,
analyzing a single log is not enough, but reviewing all logs together results in the best and most
coherent conclusion. Some data was modified in order not to reveal the nature of the field;
however, not in a manner that would influent the results of the work.
Formation Micro Imager (FMI) logs are the main source for fracture characterization.
FMI logs provide an electrical borehole image generated from microresistivity measurements.
The logs were interpreted by company geologist to calculate important information including
orientation, depth, and aperture of the fractures and bedding plane. Every fracture detected from
FMI logs is analyzed as to whether it is open or healed and how it corresponds to the dynamic
responses at the wellbore. Open fractures generally are filled with resistive oil-based drilling
mud or formation oil and as a result, show high resistivity and appear white on the images. FMI
logs provide images of a 360 degree view of the borehole wall in 2D such that fractures
correspond to sine waves on these images. Figure 3.1 shows the FMI log for Wll-B.
The photoelectric log measures the photoelectric absorption of gamma rays by electrons.
Barite, one of the components of drilling mud, has a very large photoelectric absorption index
(Pe). When drilling mud penetrates into open fractures, it results in sharp peaks of the Pe-curve.
15
Noisy responses on the PEF log (filled with yellow color) show that these fractures are open
(Figure 3.2a).
Figure 3.1 Example of fracture in Well-B on FMI log. Original FMI image on the left and
interpreted on the right.
Stoneley waves are usually generated during borehole sonic logging. They propagate
along the walls of a fluid-filled borehole. Fractures have significant effects on Stoneley waves,
especially in the low frequency range. Waves traveling past permeable fractures cause
attenuation of wave amplitude. This log response is shown as filled with purple color (Figure
3.2a).
The Caliper tool measures the size of the borehole along its depth. Any deviation in the
borehole diameter from the drilled diameter might indicate the presence of fractures. However,
16
washouts also an indicate increase in the borehole diameter, which is why fracture interpretation
should be made in conjunction with different methods based on different sources. In this case
(Figure 3.2b) the Caliper log does not show any enlargement in borehole diameter, although
other tools show the presence of fractures. In the next example in Well-A, the Caliper log shows
clear response to the fractures which were also confirmed by temperature and production logs
(Figure 3.3a).
The Production logging tool (PLT) analyzes dynamic well performance and the
productivity of different zones. It also can be used to evaluate proportional contribution or total
flow of specific wellbore intervals. In the fractured reservoir, the PLT is run in the well under
flowing conditions to evaluate fluid contribution from the fractures. The zones with a sharp
increase in flow rate on the PLT log of cumulative oil production are potential zones with
The temperature of the drilling mud in the well is usually cooler than the formation
temperature. Hot formation fluid influx should increase the temperature and acts as a good
indicator of potential fracture location. Generally the temperature log is plotted as a second
derivative of temperature against depth. The second derivative measures how the rate of change
is itself changing. The Temperature log below indicates two possible inflow points into the
wellbore which are perfectly correlated to the responses of other tools (Figure 3.3b).
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Figure 3.2 Example of open, effective fractures in Well-B on FMI image log (c) and
responses of other tools in the same interval: photoelectric and Stoneley logs (a), caliper log (b),
and production log (d).
Besides conventional logs, some drilling information can be used in order to identify
potential fractures. The initial indicator when drilling through the fractures are inconsistent
torque, sudden increase in rate of penetration and where caverns exist, drill bit drop.
Encountering those conditions leads to severe lost circulation and, as a result, well controls
issues. Generally lost circulation information is useful in detection of the presence of conductive
fractures. Figure 3.4 provides some drilling information of the same fractures which were
defined in Figure 3.3 by temperature and production logs. There are two main high density
intervals of fractures which correspond to lost circulation and drill bit drop zones, represented by
last two columns in purple and black colors, respectively. Lost circulation zones can give a
18
qualitative estimation of fractures conductivity based on the lost volume. For example, the upper
fractured interval experienced lost circulation about 200-220 bbl/hr and drill bit drop up to 5
meters, while the lower zone only lost 50 bbl/hr. Thus the upper zone should be more conductive
Figure 3.3 Example of open, effective fractures in Well-A on Caliper (a), Temperature (b)
and Production logs (c) in the same depth interval.
19
Figure 3.4 Snapshot from the wellbook of Well-A.
The sector for this study was chosen in the highly fractured region with approximately
10.5 million square meters of surface area. The interest region is surrounded by a boundary
separating it from other fracture networks on 3 sides, and has no boundary on one side. The 4th
side is connected to a larger fracture network, but it is large distance between producing wells,
and is represented by a no flow boundary in the flow models. The top and bottom layers of
20
reservoir can be determined from the logs, which can be used to construct the top and bottom
Field data for the three wells are available in the selected sector. Based on the log data for
these wells, a measured thickness range of reservoir is defined from 500 meters to 700 meters.
For this model two surfaces of reservoir layers will define the fracture generation region, where
the south-west corner is thicker than the north-east corner (Figure 3.5).
21
CHAPTER 4
This chapter explains how inputs for FracMan software are derived from the data for
“Field X” and analyzed to build a DFN model. These parameters include fracture locations,
intensity, size, shape, orientation, and the number of distinct fracture sets.
FracMan allows using three different fracture generation models: Enhanced Baecher,
Nearest Neighbor, and Levy Lee. The Enhanced Baecher is the most common model for
fractured reservoirs, and was used in this study. The Enhanced Baecher model extends the
The fracture generation region was defined as a volume between the top and bottom
layers of reservoir. There are two options to terminate fractures within generation region:
generation by “surface points” and “centers”. Both methods generate fractures at a random
location in the generation region. In this research, generation of fractures was chosen by the
“centers”, where generation location is the center of the fracture, while for “surface points”, the
location is a random point on the fracture, which may generate a large portion of the fracture out
of the generation region. In the Enhanced Baecher model, FracMan inspects every fracture. If it
intersects a pre-existing fracture, the portion of the fracture is terminated at that intersection.
22
4.2 Fracture Intensity
(1984), fracture intensity can be measured in one, two, and three dimensions. However, field
measurements of fracture intensity in the formation are usually in one dimension, along a
sampling borehole. One dimension fracture intensity measurements generally represent the
(Eq. 4.1)
where,
- length, m (ft)
23
According to the company geologist’s interpretation, no effective fractures are defined in
Well-C. Since only effective fractures are used for computation of fracture properties, field data
for Well-A and Well-B are analyzed. Figure 4.2a shows interpreted natural fracture (full dots)
and bedding (hollow dots) data as a tadpole plot from Well-A, where fractures are plotted as dots
on a depth-dip graph and tails show azimuth direction of the fractures. Different colors
correspond to the various types of natural fractures. In this study, there is no difference between
colors; they all correspond to natural fractures. Totally, 101 natural fractures were analyzed from
the image log, from which only 31 fractures were interpreted as effective fractures.
Figure 4.2 Tadpole plot of Well-A (a) and Well-B (b) (snapshot from image log
interpretation). Different colors correspond to the various types of natural fractures.
24
According to the drilling information, 8 caverns were defined. Cavern is a solution
enlarged fracture and is shown on the Tadpole plot by the two fractures, which represents paired
cavern walls. Those two fractures do not show true orientation of the cavern because dip
direction of the cavern walls depend on the location where the cavern was drilled through and the
Stereoplots are used to visualize 3-D orientation of fracture poles in 2-D space. The
values around the circle represent azimuth direction and values toward the center represent a dip
angle. All cavern walls are plotted on stereoplot and also in FracMan for better visualization of
dip direction (Figure 4.4). As apparent, the dip directions of most of the cavern walls are in
Figure 4.3 Dip of cavern walls in similar direction (a) and opposite direction (b) (snapshot
from image log interpretation). Example of cavern walls with simillar dip direction (c) and
opposite dip direction (d) in Well-A built in FracMan.
25
Figure 4.4 Stereoplot of cavern walls defined in Well-A (a) and their 3-D visualization (b).
opposite directions. Below is the example of dip orientation in opposite directions of the biggest
interpreted cavern (around 4 meters in depth) in Well-A on the FMI log with fracture responses
on other logs (Figure 4.5). This particular cavern was also reproduced in FracMan for
Analysis at the defined caverns was performed in order not to double count the number of
fractures, since cavern represents one solution enlarged fracture represented by the two fractures
which are paired cavern walls. Representing the cavern by a single fracture decreases the number
of effective fractures from 31 to 23 fractures. Fracture intensity over the studied interval (627
meters (2057 ft)) was calculated by equation 1and equal to 0.0366 1/m (0.011 1/ft).
The same analysis was perfermed on Well-B, where a total number of 21 effective
fractures and 1 cavern were interpreted (Figure 4.2b). Fracture intensity over the logged interval
26
(376 meters (1234 ft)) was calculated and equal to 0.0532 1/m (0.016 1/ft). Unfortunately, image
data does not cover the part of reservoir which is about 324 meters (1063 ft), where fracture
intensity could be same or 0. To be unbiased the fracture intensity for the unknown depth was
assumed same to the logged interval with 50% probability which is 0.0266 1/m (0.008 1/ft) or 8
effective fractures. Fracture intensity value in Well-B over the total depth in reservoir is equal to
0.04 fractures/m (0.012 1/ft) or 28 effective fractures. By avareging outputs from two wells, the
fracture intensity value for reservior was calculated as an input for FracMan model and equal to
Figure 4.5 Example of cavern in Well-A on FMI log with walls in dip opposite direction.
27
4.3 Fracture Orientation
fluid flow by controlling directional permeability. Planar polygons are used to model fractures in
FracMan. Orientation of the fractures surface in FracMan is defined by dip and pole (Figure
4.6). Dip is the inclination of the fracture plan from horizontal, and pole is a vector normal to the
fracture plane. There are many data sources that provide information on fracture orientation. In
this study wellbore images were used by the company geologist to interpret dip and azimuth of
fractures intersecting the wellbore. For orientation analysis only effective fractures were
analyzed excluding dip direction of the cavern walls because dip direction of cavern walls
depend on the location where the cavern was drilled through and the shape of the cavern (Figure
There are several different ways to display fracture orientation including a tadpole plot,
and a stereoplot, which were introduced in subsection 4.2, a rose diagram and a countered
stereoplot. A Rose diagram represents a histogram of the strike of natural fractures, and a
28
countered stereoplot shows pole density contours on the stereoplot. Orientations of all natural
fractures were analyzed for the Well-A (Figure 4.7). Overall, the trend of all natural fractures is
parallel to the platform margin, which agrees with the syn-sedimentary theory of the fractures
origin. The trend of the effective fractures is more scattered, while the overall trend is also
Figure 4.7 All natural fractures in Well-A on rose diagram (a), lower hemisphere projection
(b), and contoured stereoplot (c).
Figure 4.8 Effective fractures, excluding orientation of cavern walls, in Well-A on rose
diagram (a), lower hemisphere projection (b), and contoured stereoplot (c).
29
Fractures of the same category, which are probably generated at the same time, are
grouped into a fracture set. The assumption in grouping fractures into sets is that they probably
One thing that can help us to identify fracture sets is a Cumulative Fracture Intensity
(CFI) plot. A CFI plot displays the percentage of fractures as a function of measured depth along
the well. Two constant slopes (grey and brown) in the CFI plot indicate zones of constant
fracture intensity, which usually correspond to distinct stratigraphic zones in the reservoir
(Figure 4.9). Fracture Set 1groups fractures of depth range 1000-1100 meters, while Fracture Set
2 groups fractures of depth range 1100-1400 meters. Fracture Set 1 is more representative,
Applying the same approach for estimating fracture orientation, field data of
Well-B was analyzed. Overall, the trend of all natural fracture orientations is SE-NW, which is
consistent with the fracture orientation of effective fractures (Figure 4.11-4.12). Effective
fractures are plotted mainly far away from the center on the stereoplot (Figure 4.11b), which
implies that the fracture dip angle is steep and fractures are almost subparallel to the wellbore.
Figure 4.11 All natural fractures in Well-B on rose diagram (a), lower hemisphere projection
(b), and contoured stereoplot (c).
31
Figure 4.12 Effective fractures, excluding orientation of cavern walls, in Well-B on rose
diagram (a), lower hemisphere projection (b), and contoured stereoplot (c).
FracMan has a statistical optimization tool called the Interactive Set Identification System (ISIS).
ISIS analyzes field data of fracture sets with similar properties and estimates distribution
parameters. ISIS analyses was run on the identified fracture sets in Well-A and fractures in Well-
B. Statistical analysis defined how well the data fit different distributions, and showed that all
fracture orientations are best described with a Fisher distribution (Figure 4.13). It describes the
data by mean pole orientation and the dispersion parameter ( ), which is similar to the standard
deviation. Dispersion parameter, (kappa), can vary from 0, when data is essentially randomly
dispersed on the sphere, to ∞, when all orientations are exactly the same (Figure 4.14) (Golder,
2012).
Based on field data analyses from Well-A and Well-B, different trends of fracture
orientations were defined over reservoir. Three different DFN models (Figure 4.15) are built
based on distinctive trends observed in studied wells: orientation of Fracture Set 1 (Model 1),
orientation of two fracture sets (Model 2), and orientation of fractures in Well-B (Model 3). By
running the ISIS analysis, Fisher distribution parameters are collected in Table 4.1.
32
Figure 4.13 Statistical summary of ISIS analysis for all fracture sets.
33
Figure 4.14 Examples of dispersion parameter in Fisher distribution (Golder, 2012).
Figure 4.15 Stereoplots of fracture orientations from different models: Model 1-orientation of
Fracture Set 1 (a), Model 2 - orientation of two Fracture Sets 1 (red dots) and 2 (blue dots) (b),
and Model 3-orientation of Fracture Set 3in Well-B (c).
34
4.4 Fracture Aperture
calculated directly from FMI logs. Previous research showed that the fracture aperture
distribution follows lognormal distribution (Keller, 1996; Gale, 1987). The lognormal
distribution is described by the mean and standard deviation. In this study the mean and standard
deviation for a lognormal distribution were specified in log10 space. In FracMan it can be done
by using the Normal of Log distribution. The cumulative distribution function of the lognormal
distribution for aperture was plotted (Figure 4.16). Plot contains data of all interpreted effective
fractures from Well-A and Well-B (total 43) including caverns. Caverns have big contribution to
flow capacity, which is represented by transmissibility, the product of the aperture and
permeability.
Fracture size is probably the least known parameter because it cannot be measured
directly with any downhole tool. Deriving fracture size from image logs is difficult, because a
wellbore intersects only part of the fracture. Another source of size information can come from
examination of outcrop analogs. Dynamic data can provide a general idea of the length of the
Information on fracture shape is also limited since even an outcrop exposure does not
provide complete information on shape. Fractures in FracMan are generated as planar polygons
with a given number of sides. Moreover, FracMan allows specifying an aspect ratio and a
direction in which the fractures are to be stretched. In our study fracture shape is assumed to be a
square shape with equal sides, where fracture length represents the fracture side (Figure 4.17).
36
Fracture size in FracMan is specified in terms of equivalent radius ( ) of the fracture.
Equivalent radius is the radius of a circle that would have the same area as the area of the
fracture ( ).
(Eq. 4.2)
where,
– area of the fracture, m2 (ft)
– constant
– equivalent radius, m (ft)
(Eq. 4.3)
By combining Equations 4.2 and 4.3, fracture size is estimated in term of equivalent radius:
√ (Eq. 4.4)
By rearranging Equation 4.4, the equivalent radius can be defined in term of fracture length:
Several DFN models were built based on different assumptions. The first model assumed
constant size fractures. Fracture size is measured by the company geologist based on
examination of outcrop analogs. This source of length information measured at an outcrop even
in the same formation may differ significantly from the length in the reservoir. Even though this
is an important reason, the outcrop analog can be particularly clarifying with respect to the
reservoir. The company geologists measured exposed lengths of fractures on two scan lines in
mechanically similar analog. The average exposed length was between 20-50 meters (65-164 ft)
37
with maximum length up to 120 meters (394 ft). However, most of the fractures are incompletely
measured due to limitation of the exposure, so their actual length could have been greater than
measured. The first model assumed constant size of a square fracture with 100 m. (328 ft) of
fracture length, since is input in FracMan it was calculated and equals 56 m. (184 ft).
The second model is based on correlation of fracture size to the aperture distribution. It is
a well-known fact that fracture size is correlated to fracture aperture. Although the accurate
functional relationship is not well understood, a linear relationship is probable (Ozkaya, 2003).
Since we have an aperture distribution, fracture size can be estimated using the linear
relationship. Fracture size is assumed to be 1000 times bigger than the fracture aperture but not
more than 1000 meters in length. Some fractures on the FMI log have an aperture up to 3.5
meters (11.5 ft); therefore, the maximum size limit was implemented. Additional model
sensitivity is built with a size assumption 2000 times larger than the fracture aperture.
Based on the assumptions stated in this chapter, the DFN model was built (Figure 4.18,
38
Figure 4.18 Discrete Fracture Network model, Model 1.
39
Figure 4.19 Histogram of equivalent radius with Normal of Log distribution trend line, Model
1.
Figure 4.20 Histogram of fracture size with Normal of Log distribution trend line, Model 1.
40
CHAPTER 5
The objective of this chapter is to describe the well test simulation that was done in this
research using FracMan software and to compare simulated results with actual test results. Well
values with the pressure and derivative data in graphical form were provided in a well test
When the DFN model is built, fracture properties such as aperture, permeability and
compressibility are assigned to the generated fractures. As it was discussed in Chapter 4, the
fracture length was assumed 1000 times bigger than the aperture, so the fracture aperture was
calculated back (Figure5.1). Compressibility is defined by the change in volume of fluid and
rock in a response to a pressure. Storage properties of the fractures come from the
compressibility of the fluids in the fractures and the compressibility of the fractures. In the
fracture generation section of FracMan software, fracture compressibility is used as one of the
many inputs. In the well test inputs of the Fracman software, fluid compressibility is used. The
well test data provided by the operating company contains total compressibility. For the DFN
models fracture compressibility was assigned a negligible value and total compressibility was
used as fluid compressibility in the well test section. This provides an approximate solution and
41
has been used successfully to model well test behavior with FracMan in similar situations
(Golder, 2012).
Figure 5.1 Histogram of fracture aperture with Normal of Log distribution trend line, Model 1.
Fluid flow through fractures is a different process than the flow through homogeneous
pore systems. In the fractured region, the natural fractures play a significant role in controlling
hydrocarbon flow. The fracture permeability is so large that the matrix permeability is not
important. Fracture permeability is calculated based on dynamic data from production logging
tests (PLT) and pressure transient tests (PTT). This method estimates transmissibility ( ), the
product of the permeability and the aperture, that represents flow capacity.
The production log profile represents cumulative oil production along the depth starting
at the deepest producing fracture through the shallowest producing fracture (Figure 5.2a). The
42
impact of each effective conductive fracture creates a jump in the flow rate on the log (bright
green color), where the height of the elevation shows the fracture’s flow rate. The jumps on the
production log match some interpreted effective fractures from the FMI logs. The most prolific
fractures were chosen for permeability computation purposes. Each conductive fracture was
assigned a percent of the flow (Table 5.1). A reproduced production log was build based on the
The total transmissibility values for Well-A and Well-B were estimated by the company
reservoir engineer and were equal to 9280 and 4690 mD*m, respectively. Transmissibility of
each conductive fracture can be calculated by multiplying total transmissibility by its percentage
of the flow rate. Finally, permeability of the fractures can be calculated by dividing fracture
(Eq. 5.1)
The outputs for Well-A are presented in Table 5.1. The same procedure was performed
with data for Well-B in order to calculate fracture permeability (Figure 5.3 and Table 5.2).
Notice that individual fractures can have permeability as high as hundreds of Darcy’s.
The calculated permeability values from both wells were analyzed for the relationship to
its aperture values. Log-log plots for each well demonstrate strong aperture-permeability
correlations (Figure 5.4 and 5.5). Those plots show that aperture and permeability have a power
law relationship with displayed equations of the trend lines. By analyzing the equations, a
universal equation was estimate to calculate permeability for each fracture in the DFN model
(Eq. 5.2)
43
Figure 5.2 Snapshot of flow rate from PLT report for Well-A (a) and reproduced production
log based on the most prolific fractures (b).
44
Figure 5.3 Snapshot of flow rate from PLT report for Well-B (a) and reproduced production
log based on the most prolific fractures (b).
45
Aperture-Permeability correlation
1000000
100000 y = 912.12x-0.675
Permeability, mD
10000
1000
100
10
1
0.001 0.010 0.100 1.000 10.000
Aperture, m
Aperture-Permeability correlation
1000000
100000 y = 1026.5x-0.786
Permeability, mD
10000
1000
100
10
1
0.001 0.010 0.100 1.000
Aperture, m
46
Figure 5.6 Histogram of fracture permeability, Model 1.
The main objective of the well test analysis is to compare well test results using built
DFN models and the results of actual tests. A well test data provided by the operating company
contains reservoir property values with the pressure drop and pressure derivative as data and in
graphical form.
The well test data only available for Well-A and Well-C; therefore, the history matches
of well test results were compared only for those wells. Well test simulation was still done for
Well-B, in FracMan; although there was no measured data to match it to. In addition to the well
47
test data, the PLT data was also available. The oil in the reservoir is highly undersaturated and
not expected to drop below bubble point during well test flowing; as a result, single phase is
specified in the well test simulations. The flow rate for Well-A was estimated at around 1113
m3/d (7000 bbl/d) with a formation volume factor 2.213, and the test was run for 10 hours. Oil
properties are assigned such as density 782 kg/m3 (6.53 ppg), viscosity 0.175 cP, and
compressibility 0.000324 1/bar (22.34*10-6 1/psi). As was discussed in the previous subsection,
the fracture compressibility was assigned a negligible value and total compressibility was used as
the fluid compressibility in well test simulations. The initial pressure was 623.6 bar (9044 psi).
To decrease the model size and increase simulation speed the Box Region was installed
with each well in the middle. A 1000 meter (3281 ft) square Box Region was defined. The size
was selected by a trial and error method; with successively lager sizes until the larger box did not
change the well test outputs, 1000 meter (3281 ft) fit these criteria (Figure 5.7). The well effects
such as skin factor, well bore storage, diameter are also included in the simulation, while the
matrix effects are not because in this research, the matrix has little influence. The well effects
take account well storage of 0.07 m3/bar (0.17 ft3/psi), diameter of 0.1524 m (0.5 ft), and skin
effect of -0.356. In the same way, inputs for the well test simulation for Well-C were assigned in
FracMan, while the inputs for Well-B were approximate (Table 5.1).
The well test simulation run with FracMAn produces the pressure-time plot and the log-
log plot of pressure and pressure derivative (Figure 5.8 and 5.9) as a function of time.
48
Figure 5.7 Box Regions centered on the wells (a) and created mesh (b).
49
Figure 5.8 Pressure responses in Well-B as a function of time.
Figure 5.9 Log-log plot of pressure and pressure derivative in Well-B as a function of time.
50
5.3 Well Test Matching
Curve matching approach is based on comparison of the actual pressure response of the
well with the simulated model that accounts for the main characteristics of the reservoir. By the
achieving a match, reservoir parameters can be estimated. The main matching involves skin
effect and transmissibility. The skin effect controls the “hump” shape curve, while the
transmissibility moves the derivative up and down by changing permeability or aperture. Since
The results (for example, Figure 5.13) were compared to the measured results on the
same plot. The pressure drop is simply the pressure difference between the initial pressure and
pressure at each step. The pressure derivative is calculated by the following equation:
(Eq. 5.3)
where,
– time, hr
FracMan allows visualizing the pressure drop during the well test simulation (Figure
5.12). Initial assumption was to limit fracture length at 500 m (1640 ft) which resulted in higher
derivative curve (Figure 5.10). The bigger the fracture is, the higher its permeability is. The
maximum fracture length of 1000 meters (3281 ft) was implemented to improve the permeability
(Figure 5.11). An upward trend at the end of the derivative curve indicates boundary effect, so
the high permeability values will bring that upward in earlier. Simulated derivative curve as a
51
measured data is not flat and has some waves, which is sign of fractured reservoir with variable
The model with improved fracture length produced good simulation (Figure 5.11) results.
The pressure and derivative plots show good match except the “hump” shape at the beginning of
derivative, which is controlled by the skin factor. This probably shows that properties of the
generated fractures that intersect the wellbore are not same to the actually observed, while the
remote fracture permeability shows a good match. In order to match “hump” curve, the skin
The history matching of well test results were compared for Well-A and Well-C, because
the data for Well-B is not available. Three different cases were examined based on various
fracture orientation models which were defined in Chapter 4 (Table 4.1). Well-A showed good
history matching results throughout all models (Figure 5.13, 5.14, and 5.15) after improving the
There were no effective fractures observed in Well-C; therefore, simulated well test
results did not match with actual tests (Figure 5.16). In order to match the results, the
permeability values for simulated fractures are decreased. New values are defined by the trial
and error method. The derived permeability input was estimated 50 times less than the original
value. The same three models of fracture orientation were simulated. The history matches do not
show perfect coincidence, even though the pressure drop curves have some similarities (Figure
52
Figure 5.10 History match comparison of simulated (green and purple colors) and measured
results (red and blue), Well-A Model 1 with maximum fracture length 500 m.
Figure 5.11 History match comparison of simulated (green and purple colors) and measured
results (red and blue), Well A Model 1 with maximum fracture length 1000 m.
53
Figure 5.12 Pressure visualization during the well test (time-10 hours), Well-A.
Figure 5.13 History match comparison of simulated (green and purple colors) and measured
results (red and blue), Model 1.
54
Figure 5.14 History match comparison of simulated (green and purple colors) and measured
results (red and blue), Model 2.
Figure 5.15 History match comparison of simulated (green and purple colors) and measured
results (red and blue), Model 3.
55
Figure 5.16 History match comparison of simulated (green and purple colors) and measured
results (red and blue), initial permeability Model1.
Figure 5.17 History match comparison of simulated (green and purple colors) and measured
results (red and blue), permeability decreased Model 1.
56
Figure 5.18 History match comparison of simulated (green and purple colors) and measured
results (red and blue), permeability decreased Model 2.
Figure 5.19 History match comparison of simulated (green and purple colors) and measured
results (red and blue), permeability decreased Model 3.
57
CHAPTER 6
Well-C was suspended due to high water cut (up to 60%) shortly after putting it on
production. One concern of this trend is that the water seen at Well-C might end up at nearby
wells. The objective of this chapter was to simulate water flow through the natural fractures and
determine potential water breakthrough in the producing wells (Well-A and Well-B). The built
DFN models were upscaled to grid properties suitable to export to the flow simulator, ECLIPSE,
where the water flow can be modeled. In the current work, many different scenarios were
simulated with different water influx rate and different DFN models to examine the range of
Natural fractures enhance the reservoir permeability and act as conduits within the
reservoir for fluid flow, including oil and water. Generally water production in “Field X” wells is
Well-C was drilled in 2002 using the Closed Hole Circulation Drilling (CHCD) method
to drill through the fractured zone. In March 2004, PLT surveys conducted after acidizing
showed water crossflow, which was interpreted to be CHCD sacrificial water so no action was
taken. Well-C was put on production in March 2008 but it was suspended soon due to high water
cut, which was up to 60% in May 2008. According to a September 2009 PLT survey, the water
influx was estimated around 290 m3/d (1824 bbl/d) (Figure 6.1A). A water shut-off workover
was conducted in February 2011 to isolate water influx from the underlying reservoir. An April
58
2011 PLT survey showed that the set plug leaked (Figure 6.1B). The workover operation was
continued by setting another plug and dumping cement on the plug in May 2011. A May 2011
PLT survey showed that the water crossflow rate had reduced to 49 m3/d (314 bbl/d) (Figure
6.1C). This water rate was still considered too high to put the well online, so the well has
Figure 6.1 PLT results in Well-C from three different times. Water crossflow at the rate of
290 m /d (1824), September 2009 (a), water from the leaky plug at the rate of 120 m3/d (755
3
bbl/d), April 2011 (b), reduced water crossflow at the rate of 49 m3/d (314 bbl/d), May 2011 (c).
59
6.2 Fracture Upscaling
Fracture and matrix simulation cells are associated with each grid block to model dual
porosity system in ECLIPSE, which is one of the popular commercial software in the petroleum
industry. In this model, fluid flow is assumed to happen not only in the fracture, but also in the
matrix. In dual porosity models, fractures provide conduits for fluid flow, while the matrix
provides the storage for fluid. These matrix blocks feed hydrocarbon to the fracture network
through which fluid flow to the producing well. The dual porosity model in ECLIPSE uses the
conventional transfer function to describe the interaction between the matrix block and fracture
system. This model requires two simulation cells to represent each grid block. ECLIPSE
associates one cell of each grid block with the matrix and the second cell with the fracture. All
cells need to have porosity and permeability values. Matrix cells in the model are assumed
homogeneous with 5% porosity and 0.1 mD permeability. When upscaling of fracture properties,
FracMan preserves heterogeneity and translates the geological description of fracture networks
The FracMan software is used to populate the fracture part of the dual porosity cells with
properties including porosity, permeability and sigma factor. FracMan is also used to generate
the cell coordinates. Before upscaling analyses can be performed, a 46 x 44 x 30 (60720 cells)
grid was created between the surfaces, which corresponds to 4500 x 4200 x 600 meters (14764 x
13780 x 1969 ft) of simulated reservoir section (Figure 6.2). FracMan supplies a corner-point-
gridding coordinate system for the entire grid. When exporting the grid to an ECLIPSE, the
coordinates are converted into the ECLIPSE system (Figure 6.3). An upscale analysis includes
Oda permeability in the x, y and z directions, fracture porosity, and sigma factor analysis.
60
Figure 6.2 Grid between surfaces.
Figure 6.3 Exported grid coordinates into ECLIPSE, 3-D view of reservoir in Petrel.
61
6.2.1 Fracture permeability
fractures, and fracture transmissivities (Golder, 2012). Oda (1985) developed an approach to
approximate solution of the fracture permeability. Oda’s method starts with the orientation of
each fracture in a grid cell expressed as a unit normal vector . Integrating the fractures over all
of the unit normal , Oda obtained a tensor describing the mass moment of inertia of fracture
∫ (Eq. 6.1)
where,
– number of fractures in
An empirical fracture tensor can be calculated by adding the individual fractures for a specific
∑ (Eq. 6.2)
where,
– fracture tensor
– area of fracture
62
– transmissivity of fracture
Finally, the Oda’s permeability tensor is derived from by assuming that expresses fracture
flow as a vector along the fracture’s unit normal. Assuming that fractures are impermeable in a
direction parallel to their unit normal, must be rotated into the planes of permeability:
( ) (Eq. 6.3)
where,
– permeability tensor
– Kroenecker’s delta
Oda’s solution has the advantage that it can be calculated without requiring flow
Generally, fracture porosity is the proportion of the total volume of fractures over the unit
volume. The fracture porosity depends only on fracture geometry and can be calculated as the
product of fracture area per cell volume and the aperture of the fractures (Equation 6.4), where
∑( )
(Eq. 6.4)
where,
63
– total volume of fracture, m3
– total volume, m3
Fracture porosity depends on the fracture intensity, size, and aperture. In FracMan, the fracture
porosity can be calculated for each grid cell, based on the fracturing in this cell (Figure 6.5). If
the fracture extends beyond the grid cell, it is cut off at the cell edge.
Matrix blocks contribute the main portion of the reservoir pore volume, but they have
very low permeability in comparison to the fractures. Sigma factor is one of the important factors
in a dual porosity model which measures the flow term between the matrix block and the fracture
network. The sigma factor (shape factor) introduced by Kazemi (1976) combines the average
distance in three perpendicular directions to describe this flow term in the fractured reservoir.
The Gilman and Kazemi (1983) option was chosen to calculate sigma factor in the FracMan
( ) (Eq. 6.5)
where,
From the equation above it is obvious that sigma factor can be very large if cells are very
small. High sigma value means that fluid would flow very quickly from matrix to the fractures.
Kazemi et al. (1976) derived shape factor based on direct material balalnce on a cubic matrix
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block under assumptions of pseudo steady state. Once the isgma factors are calculated in
FracMan, they can be exported into simulator for flow simulation (Figure 6.6).
Figure 6.4 Exported fracture permeability in x direction from FracMan Model 1, 3-D view in
Petrel.
Figure 6.5 Exported fracture porosity from FracMan Model 1, 3-D view in Petrel.
65
Figure 6.6 Exported fracture porosity from FracMan Model 1, 3-D view in Petrel.
solutions of fluid flow in a reservoir by including input data such as rock/fluid properties and
initialization of well condition. The outputs from the simulator, including fluid rates and pressure
forecast, are important for future field development strategy and reservoir management.
The dual porosity model is characterized by highly permeable fractures and a porous
matrix, which provides the most fluid storage (Gilman, 2003). Production from the naturally
fractured reservoirs can be associated with various physical mechanisms including: oil
expansion, imbibition, gravity drainage, and viscous displacement. In the studied reservoir the
production from the porous matrix is associated with oil expansion mechanisms. The matrix
system of the studied section is carbonate rock with low permeability. The properties of rock and
fluids including pressure, volume, and temperature (PVT) measurements and real permeability
66
curves for the reservoir are taken from a previous study of this reservoir (Hoffman et al., 2009).
Well-A and Well-B are vertical producing wells. Well-A was completed as an open hole
allowing the fluid to flow directly from the formation, while Well-B is perforated in several
As was mentioned before, no effective fractures were defined in Well-C, and this was
confirmed by the well test simulation. The permeability values were decreased gradually around
the wellbore in order to match well test curves. The greatest reduction by 50 times was near the
wellbore and as moved away from the well, the permeability reduced less and less, eventually
reaching the original values. Five steps of gradual reduction were implemented around the well
with 50% reduction of initial permeability until reaching target value (Figure 6.7).
Figure 6.7 Reduced permeability in y direction around Well-C Model 1, 3-D view in Petrel.
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6.4 Sensitivity Analysis
Sensitivity analysis was performed to see how various simulation inputs influence the
simulation outputs. The simulation inputs which are analyzed consist of fracture orientation, size,
permeability, and water influx rate. Since the problem of water influx is investigated in this
research, water breakthrough time and cumulative water production rates are utilized from the
simulation outputs. In the following subsections each input is analyzed separately to see its
Various simulations were run based on various fracture orientation of fracture sets which
were defined in Chapter 4 (Table 4.1). Besides the various fracture orientations (Figure 4.15),
different water influx rates were utilized. In total, nine cases were run. Simulated results of oil
production rates did not match with actual rates. In order to match them, the fracture
permeability in simulator was increased by 3.6 times for Model 1, by 5.5 times for Model 2, and
by 3.7 for Model 3. As we can notice, fracture permeability in generated DFN Model 2 with two
fracture sets is lower than in models with single fracture set. Water influx is introduced into
Well-C at different flow rates. Ranges of the rates were defined based on the last PLT survey
(314 bbl/d), initial water influx rate (1824 bbl/d), and proposed worst case scenario (5000 bbl/d),
where the water might crossflow not only through the well but also through other sources. Inputs
and outputs of sensitivity analysis on fracture orientation are presented in Table 6.1.
Oil production rates do not show dependence on fluctuated water influx rates (Figure
6.8a). The main production mechanism in the reservoir is oil expansion. When the pressure drops
in the permeable fractures, oil starts flowing from matrix to fractures to balance the pressures.
68
Initial pressure is so high, that water influx does make any difference in supporting pressure in
reservoir. The difference can be noticed only when a closer look is taken (Figure 6.8b).
Individual oil production responses of each well are also same as the total oil production trend
(Figure 6.9), where different water influx rates have no influence on oil production trends.
Figure 6.8 Constant oil rates at different water influx rates, Model 1.
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Figure 6.9 Constant oil rates at different water influx rates, Well-A (a), Well-B (b), Model 1.
Fracture orientation has no influence on cumulative water production and water cut
percent (Table 6.1). All three models showed almost the same responses to various water influx
rates. The water breakthrough time is faster in Model 2 with two fracture sets, while it is almost
the same for models with single fracture sets (Figure 6.10). Model 2 has more complex fracture
network in comparison to other two models, where Fracture Set 2 has scattered fracture
orientation.
Responses of individual wells are different in terms of water production rates and
breakthrough time, which are highly dependable on fracture orientation and individual
breakthrough time and rates in Well-B are earlier and higher, respectively, than in Well-A, in
spite of the distance from Well-C to Well-A being shorter (Figure 6.11). This can be explained
In Model 2 with two fracture sets, at an earlier period the breakthrough time and
production rates are governed by higher productivity of Well-A. After some time fracture
70
permeability takes over in Well-B (Figure 6.12), since the fracture intensity of Fracture Set 1 is
In Model 3 with NW-SE fracture orientation, the water breakthrough time and rates in
Well-A are earlier and higher, respectively, than in Well-B (Figure 6.13). At an earlier period the
water production trend is governed by both fracture orientation and well productivity. Shortly
after the reaching the total maximum production rate, the trend is governed by fracture
orientation that keeps high water production rate in Well-A. Overall the production trends of
individual wells in each model are the same with different magnitude due to various water influx
rates.
Figures from 6.14 to 6.16 show water saturation propagation through the simulated
reservoir as a function of time at the maximum water influx rate 5000 bbl/d. Some of the influx
water bypassed the producing wells and accumulated in the lower part of the reservoir.
Three cases were run to check how different permeability inputs affect water saturation
propagation at constant influx rates. In order to examine the influence of various permeability
inputs, all simulations were performed using the same model, Model 1. The first case uses
fracture permeability inputs exported from the base FracMan model. In the second case, the base
permeability increased by 3.5 times in order to match simulated oil production rates with actual
history data. Finally, in the third case very high permeability is tested. The results are presented
in Table 6.2.
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6000
5000
5000 bbl/d
Water Production (bbl/day)
4000
Model 2
3000
Model 3
Model 1
2000
1824 bbl/d
1000
314 bbl/d
0
Dec-12 Sep-15 May-18 Feb-21 Nov-23 Aug-26 May-29 Feb-32 Nov-34
Time (months)
Figure 6.10 Water production trends of the models at different water influx rates.
Figure 6.11 Water production trends of the wells at different water influx rates, Model 1.
72
Figure 6.12 Water production trends of the wells at different water influx rates, Model 2.
Figure 6.13 Water production trends of the wells at different water influx rates, Model 3.
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Figure 6.14 Simulated water saturation in December, 2012, snapshot from ECLIPSE, Model 1
(a), Model 2 (b), and Model 3 (c).
Figure 6.15 Simulated water saturation in December, 2022, snapshot from ECLIPSE, Model 1
(a), Model 2 (b), and Model 3 (c).
Figure 6.16 Simulated water saturation in October, 2032, snapshot from ECLIPSE, Model 1
(a), Model 2 (b), and Model 3 (c).
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Table 6.2 Sensitivity analysis on fracture permeability
Cumulative
Breakthrough
Case Model Permeability Water Water Cut (%)
Time (month)
Production (bbl)
As was expected, the breakthrough time and cumulative water production are the highest
in the most permeable model. It is interesting to notice that water cut does not follow the same
trend (Table 6.2). Fractures enhance the reservoir permeability and act as conduits within the
reservoir for fluid flow, including oil and water. With increased permeability, not only water
production increased, but oil production also increased leaving the water cut percent low. When
the fracture permeability is high, the water production rates reach the maximum quickly, while
the model with initial permeability has not reached the maximum water production in the time
Behavior of individual wells also depends on fracture permeability (Figure 6.18). The
production trends of individual wells are different from case to case. For Model 1_3 with the
highest permeability, the production rate in Well-B keeps growing rapidly until it almost reaches
the influx rate, while the production rate in Well-A slightly increases at the beginning and stops
producing after some time. For the second model with moderate permeability, at an earlier period
the water production trend is governed by both fracture orientation and well productivity. Shortly
after the reaching the total maximum production rate, the trend is governed by fracture
orientation that keeps high water production rate in Well-B. Finally, in Model 1_1 both wells
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2000
1800
1600
Water Production (bbl/day)
1400
1200
Base
1000 3.5x
10x
800
600
400
200
0
Dec-12 Sep-15 May-18 Feb-21 Nov-23 Aug-26 May-29 Feb-32 Nov-34
Time (months)
Figure 6.17 Breakthrough time of the total water production trend at various permeability
inputs, Model 1.
Figure 6.18 Water production trends of individual wells with a different fracture permeability.
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have the same water production trend. Fracture orientation and well productivity have same
Figures from 6.19 to 6.21 show water saturation propagation through the simulated
reservoir as a function of time at a constant water influx rate of 1824 bbl/d. Model 1_1 has
spread water saturation footprint; on the other hand, Model 1_3 aim down the reservoir and has
narrow footprint. It can be explained by swept efficiency, which is higher in low permeable
reservoir.
Three cases were run to check how different fracture length inputs affect water saturation
propagation at constant influx rates of 314 bbl/d. To examine the influence of various fracture
length inputs, all simulations were performed using the same model, Model 1. The first case
assumes constant size fractures with 100 m (328 ft). of fracture length. In the second case, the
fracture length inputs exported from the base FracMan Model 1. Finally, in the third case the
highest fracture length was tested, which is twice bigger than the length from base model. The
According to simulation results, the smallest fractures with constant size have the smallest water
cut (9%) and cumulative water production (7907 bbl/d) in 20 years forecast (Table 6.3). The
same Model 1_4 has the latest breakthrough time, 161 months. Only Model 1_6 barely reached
the same water production rate as the influx rate, while the rest models have not reached this rate
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Figure 6.19 Simulated water saturation in December, 2012, snapshot from ECLIPSE Model
1_3 (a), Model 1_2 (b), and Model 1_1 (c).
Figure 6.20 Simulated water saturation in December, 2022, snapshot from ECLIPSE Model
1_3 (a), Model 1_2 (b), and Model 1_1 (c).
Figure 6.21 Simulated water saturation in October, 2032, snapshot from ECLIPSE Model 1_3
(a), Model 1_2 (b), and Model 1_1 (c).
78
Table 6.3 Sensitivity analysis on fracture length
Cumulative
Rate Water Water Cut Breakthrough
Case Model Size
(bbl/d) Production (%) Time (month)
(bbl)
1 Model 1_4 Constant 7907 9% 161
2 Model 1_5 314 Base 26886 14% 101
3 Model 1_6 2X 40303 22% 71
Behavior of individual wells also depends on fracture length (Figure 6.23). The
production trends of individual wells are almost same for Model 1_5 and Model 1_6 with
different magnitude. Water breakthrough time and rates in Well-B are earlier and higher,
respectively, than in Well-A. This can be explained by the fracture orientation which is in the N-
S direction. Model 1_6 shows completely different trends of individual wells. Well-A is
dominant in production in comparison to Well-B. In Model 1_6 fractures are so big that several
fractures can control water movement from Well-C. Water saturation propagations through the
79
400
350
300
Water Production (bbl/day)
250
200 2X
Base
150
Constant
100
50
0
Dec-12 Sep-15 May-18 Feb-21 Nov-23 Aug-26 May-29 Feb-32 Nov-34
Time (months)
Figure 6.22 Breakthrough time of the total water production trend at various length inputs,
Model 1.
Figure 6.23 Water production trends of individual wells with a different fracture length.
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CHAPTER 7
This chapter briefly summaries the main points of research and contains conclusions
derived from this research and proposed future work. The main objective of this thesis was to
build a DFN model for realistic representation of fracture networks in the carbonate reservoir.
Another objective was to perform dynamic analysis to predict potential water flow from the
7.1 Summary
1. DFN models have been built for a three well section using well data inputs from
conventional logs, drilling information, and production logs. The fracture intensity,
orientation, and aperture are taken directly from the image logs. Fracture length is
2. Three DFN models were generated using various fracture orientation of fractures sets
defined in Chapter 4 (Table 4.1, Figure 4.15). Fracture sets represent distinctive trends
observed in studied wells. Orientations of Fracture Sets 1 and 3 are parallel to platform
margin, which agrees with the syn-sedimentary theory of the fractures origin. Orientation
of Fracture Set 2 is more scattered, while the overall trend is also parallel to the platform
margin. Most of the fractures have steep dip angle which implies that fractures are almost
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3. All DFN models for Well-A show reasonable matches to the well tests. Curve matching
approach is used for comparison of the actual pressure response of the wells with the
simulated models. The main matching involves skin effect and transmissibility. No
by 50 times to match with actual tests. No data available for Well-B. Generated DFN
model for Well-A, with relatively little calibration, reproduce the well test behavior.
4. The upscaled DFN model preserves the properties of actual fractures in the studied sector
including porosity, permeability, and sigma factor. Those properties are exported to
simulator to predict fluid flow through the fractures. Since the problem of water influx is
investigated in this research, water breakthrough time and cumulative water production
rates are utilized from the simulation outputs. Many different scenarios are simulated
with different water influx rate and different DFN models, which show the wide range of
water breakthrough time (from 16 to 161 months) and water rates (from 7907 to 978718
5. Fracture orientation has no influence on cumulative water production and water cut
percent. All three models with various fracture orientation showed almost the same
responses to various water influx rates. The water breakthrough time is faster in Model 2
with two fracture sets, while it is almost the same for models with single fracture sets.
Individual wells show very high dependence on fracture orientation and productivities of
the wells. When the production rate reaches its maximum rate, it is governed mainly by
6. Various fracture permeability inputs have high influence on cumulative water production
and water cut percent. Increased permeability increases breakthrough time and
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cumulative water production, while the water cut percent decreases. With increased
permeability, not only water production increased, but oil production also increased
leaving the water cut percent low. Behavior of individual wells also depends on fracture
cases.
7. Different fracture length inputs have high influence on cumulative water production and
water cut percent. All simulated outputs including water cut percent, breakthrough time,
and cumulative water production are higher and faster in the models with the biggest
fractures. Behavior of individual wells also depends on fracture length. Several big
7.2 Conclusion
Built DFN models show wide range in water breakthrough time from 16 months to 161
months, in water cut percent from 9% to 41%, and in cumulative water production from 7907 bbl
to 978718 bbl in 20 years of simulated time. This large range of possibilities is due (1) the
different amount of water influx around Well-C, and (2) the variability in fracture properties
such as fracture permeability and size. The amount of water influx is not well known. There
could be water going through the fractures and not going only through the well. In the model, the
In worst case scenario, where fracture permeability was increased by 10 times or at high
constant water influx rate of 5000 bbl/d, water might be seen in 15-16 months, which is not since
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In best case scenario, water might be seen in produced wells in 161 months or 13-14 years, if
the water influx determined from the last PLT survey remains constant at 314 bbl/d and fracture
length is considered constant and equal to 100 m. Even if fracture size is increased by correlating
to aperture, the water breakthrough time is still relatively low about 101 months.
Sensitivity analyses show that fracture conductivity has strong influence on studied
parameters; therefore, fracture properties should be studied very carefully to build representative
Even if the crossflow remains low at around 314 bbl/d, it is likely that water will start to be
produced in the wells A and B in 5-10 years. Planning for increased water production should
begin sooner rather than waiting for water to be produced and then try to manage it.
During this study several recommendations are developed for future work:
1. Extend analyses on DFN model by performing cluster analysis and pathway analysis.
fractures, showing how the area is compartmentalized. Pathway analysis calculates the
geometric connection between two wells through the fracture network. It then reports
build more realistic DFN model in order to predict fluid flow. Study the range of influx
rate from the aquifer, since water influx rates show huge influence on water breakthrough
84
3. Study the propagation of water remained in the reservoir, since not all influx water is
produced through the production wells. Understand the source of the water and water
movement mechanism.
4. Study water flooding as a second recovery method, when the pressure drops during
production.
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REFERENCES
Aguilera, R., 1995, Naturally fractured reservoirs. 2nd ed. Tulsa: PennWell Publishing Company,
p. 1.
Akbar, M., Vissapragada, B., Alghamdi, A.H., Allen, D., Herron, M., Carnegie, A., Dutta, D.,
Olesen, J.R., Chourasiya, R.D., Logan D., Stief. D., Netherwood, R., Russel, S.D.,
Saxena, K., 2000, A snapshot of carbonate reservoir evaluation: Oilfield Review, v. 12,
no. 4, p. 20-21.
Barde, J., Gralla, P., Harwijanto, J., Marsky, J., 2002, Exploration at the eastern edge of the
Precaspian basin: Impact of data integration on Upper Permian and Triassic
prospectivity: American Association of Petroleum Geologists Bulletin, v. 86, no. 3, p.
399–415.
Dershowitz, W. S., 1984, Rock joint systems: Massachusetts Institute of Technology,
Cambridge, Massachusetts, Ph.D. Thesis.
Dershowitz, W. S., Einstein, H.H., 1988, Characterizing rock joint geometry with joint system
models: Rock Mechanics and Rock Engineering, v. 21, p. 21-51.
Einstein, H.H., Stephansson O., 2000, Fracture system, fracture propagation and coalescence: An
International conference on Geotechnical and Geological Engineering.
Gale, J. E., 1987, Comparison of coupled fracture deformation and fluid flow models with direct
measurement of fracture pore structure and stress-flow properties: American Rock
Mechanics Association, p. 1213-1222.
Gilman, J. R., 2003, Practical Aspects of Simulation of Fractured Reservoirs: International forum
on reservoir simulation, Baden-Baden, Germany.
Gilman J.R., Kazemi, H., 1983, Improvement in simulation of naturally fractured reservoirs:
Society of Petroleum Engineers , v. 23, no. 4, p. 695-707.
Golder Associates Inc., 2012, FracMan User’s Manual Release 7.4.
Hoffman, B. T., Narr,W., Li, L., 2009, Using PLT data to estimate the size of natural fractures:
Paper SPE 121293 presented at the SPE Western Regional Meeting, 24-26 March.
Ivanova, V. M., 1998, Geologic and stochastic modeling of fracture system in rocks:
Massachusetts Institute of Technology, Cambridge, Massachusetts, PH.D. Thesis.
Kazemi, H., Merrill, L., Porterheld, K., Zeman, P., 1976, Numerical simulation of water-oil flow
in naturally fractured reservoirs: Society of Petroleum Engineers, v. 16, no. 6, p. 317-326.
Keller, A. A., 1996, Single and multiphase flow and transport in fractured porous media:
Stanford University, PH.D. Thesis.
86
Meyer, T., 1999, Geologic, Stochastic modeling of rock fracture system related to coastal faults:
Massachusetts Institute of Technology, Cambridge, Massachusetts, M.Sc. Thesis.
Narr, W., Schechter D. S., Thompson L. B., 2006, Naturally fractured reservoir characterization:
Society of Petroleum Engineers, p. 1.
Narr,W., Tankersley, T., King, G., Camerlo, R., Zhumagulova, A., Skalinski, M., Pan, Y., 2010,
Reservoir modeling to characterize dual porosity, Tengiz field, Republic of Kazakhstan:
Paper SPE 139836 presented at the SPE Caspian Carbonates Technology Conference, 8-
10 November.
Ozkaya, S. I., 2003, Fracture length estimation from borehole image logs: Mathematical
Geology, v. 35, no. 6, p. 737-753.
Oda, M., 1985, Permeability tensor for discontinuous rock masses: Geotechnique, v. 35, p. 483-
485.
Schlumberger, 2012, ECLIPSE Technical Description Manual.
Ulmishek, G., 2001, Petroleum geology and resources of the North Caspian basin, Kazakhstan
and Russia: US Geological Survey Bulletin
87