Polymerflood Simulation in a Heterogeneous Idealized Reservoir with and without Crossflow by Oppong Kwame Submitted in partial fulfillment of the requirements for the Degree of Master of Science in Petroleum Engineering New Mexico Institute of Mining and Technology Department of Mineral Engineering Socorro New Mexico December 2009
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Polymerflood Simulation in a Heterogeneous Idealized
Reservoir with and without Crossflow
by
Oppong Kwame
Submitted in partial fulfillment of the requirements for the Degree of Master of Science in Petroleum Engineering
New Mexico Institute of Mining and Technology Department of Mineral Engineering
Socorro New Mexico December 2009
ABSTRACT A reservoir simulation model predicting polymerflood performance and the potential of
using horizontal well injector in flood operation in stratified (two layers) systems is
presented considering the effect of crossflow and no-crossflow on oil production at varied
mobility ratios. The level of communication (free crossflow) between reservoir layers,
which is characterized by the closeness of the system to vertical equilibrium (VE)
condition, can significantly affect sweep efficiency in heterogeneous reservoirs. In gel
placement as a remedy to early water breakthrough, the details of the gel placement are
strongly affected by the degree of communication between reservoir layers.
The importance of fluid crossflow relative to purely longitudinal convective transport in a
two-dimensional setting depends on several factors. Rock properties such as porosity,
permeability, the ratio of vertical to horizontal permeability and length to thickness ratio
cannot be over looked. Fluid properties such as phase densities, viscosities and interfacial
tension also play important role. Coupled rock-fluid properties, for examples, wettability,
relative permeabilities and capillary pressure are also factors. In this report only the
effects of viscous force on polymerflood performance in a stratified reservoirs is
considered. A fully implicit, black oil reservoir simulation model was used to predict the
displacement efficiency in two-dimensional, fine–grid (x-z) cross-section. At present the
development is limited to two phases and two components injector (water/polymer)
producer (oil) system. These investigations were inspired because planning for efficient
production strategies and targeting unrecoverable oil should be a priority in the petroleum
industry. The conclusion from the simulation model results are comparable to analytical
model results and are directly applicable to similarly scaled viscous-dominated systems at
a reservoir scale.
ii
ACKNOWLEDGEMENTS I would like to express my gratitude and respect to Dr. Randy Seright at PRRC, New
Mexico Institute of Mining and Technology for his constant support and guidance during
my graduate studies at New Mexico Institute of Mining and Technology Dr. Seright, your
knowledge and experience have been great in our development as engineers; your high
standards and dedication not only make us better professionals but also better individuals.
Thank you always.
I would also like to recognize Dr. Lawrence Teufel and Dr. Thomas Engler for their
contributions, and willingness to serve as part of my thesis committee. Not forgetting
PRRC personnel, the author would like to express his appreciation for the financial
support from the PRRC during the period of this research. Thanks to some of my
classmates and friends with whom I had the opportunity to learn, share and enjoy. It has
been a pleasure. Last but not least, special and infinite thanks to the most important
people in my life, my parents, Mr. Adu and Madam Anna Kyremaah, my daughter
Richlove Oppong, and my best friend and love of my live, Twumwaa Elizabeth; all of
your love, respect, encouragement and support have made me the man I am today. I owe
it to you, thank you.
iii
TABLE OF CONTENT
1.1 Description of the Problem ................................................................................. 3 1.2 Geological Considerations .................................................................................. 4 1.3 Research Objectives ............................................................................................ 5
CHAPTER2. ....................................................................................................................... 7 GENERAL CONSIDERATIONS AND BACKGROUND ............................................... 7
2.1 Theoretical Foundation ....................................................................................... 7 2.2 Literature Review............................................................................................. 13 2.3 Horizontal versus Vertical Wells ...................................................................... 17
CHAPTER 3 ..................................................................................................................... 24 THEORY AND RESERVOIR MODELS DESCRIPTION ............................................. 24
3.1 Reservoir Simulation ........................................................................................ 24 3.2 Mathematical Model ......................................................................................... 24
3.3 Numerical Model .............................................................................................. 28 3.3.1 Discretization of the Flux Term ............................................................... 30 3.3.2 Discretization of the Accumulation Term ................................................. 32
3.4 The Polymer Flood Simulation Model ............................................................. 34 3.4.1 Treatment of Fluid Viscosities .................................................................. 35 3.4.2. Treatment of Permeability Reduction. ...................................................... 36 3.4.3. Treatment of the Shear Thinning Effects .................................................. 36
3.5 Solution Technique ........................................................................................... 38 3.6 Well Models ...................................................................................................... 38
3.6.1 Wells Representation in this Study ........................................................... 39 3 .7 Description of Simulation Models .................................................................... 42
3.7.1 Gridblocks Sensitivity Analysis. ............................................................... 44 3.7.2 Communicating Layers System (crossflow model). ................................. 44 3.7.3 Noncommunicating Layers System (No crossflow model). ..................... 44 3.7.4 Polymer Flood ........................................................................................... 45
CHAPTER 4 ..................................................................................................................... 49 PRESENTATION AND ANALYSIS OF SIMULATION RESULTS ............................ 49
4.1 Validation of the Reservoir Simulator .............................................................. 49 4.1.1 Analytical Solution ................................................................................... 50 4.1.2 Volumetric Material Balance .................................................................... 54 4.2.1 Gravitational Effect (Communicating Layers) ......................................... 55 4.2.2 Rock Compressibility................................................................................ 57 4.2.3 Vertical Permeability Ratio (kv/kh). ......................................................... 57 4.2.5 Permeability Contrast................................................................................ 62 4.2.6 Oil Viscosity ............................................................................................. 63 4.2.7 Polymer Solution Viscosity ...................................................................... 67 4.2.8 Summary of Sensitivity Analysis.............................................................. 70
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4.3 Potential of Horizontal Injector in Waterflooding. ........................................... 70 4.3.1 Results Based on Oil Recovery ................................................................. 70 4.3.2 Results Based on Water Cut ..................................................................... 75
NOMENCLATURE ......................................................................................................... 87 REFERENCES ................................................................................................................. 89 APPENDIX A ................................................................................................................... 97 The algorithms for the simulation models in this study is presented brief below: ........... 97 APPENDIX B ................................................................................................................. 100 The results from two simulators: Eclipse 100 and POLYGEL-Petro China .................. 100 APPENDIX C…………………………………………………………………………. 103 The calculation of NPV and NET CASH FLOW at oil prices, $ 20 and $ 50 per barrel for Displacing 1000 cp oil with polymer: (crossflow and no-crossflow)…..........103
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LIST OF TABLES
Table 2.1 Effect of Polymer Concentration on water cut ultimate Recovery, and EOR24 .................................................................................................................... 17 Table 2.2 Effect of Polymer Molecular Weight on EOR24. .................................. 17 Table 3.1 Pertinent properties of the reservoir models ......................................... 46 Table 4.1 Comparison, Analytical and Simulation (No-crossflow). .................... 51 Table 4.2 Comparison of waterflooding, Analytical and Simulation (Crossflow)................................................................................................................................ 52 Table 4.3 Polymerflooding, Analytical versus Simulation (Crossflow). ............. 53 Table 4.4 Polymerflooding, Analytical versus Simulation (No-crossflow) ........ 53 Table 4.5 Effect Vertical Heterogeneity on Oil Recovery (Free crossflow). ....... 60 Table 4.6 Effect Permeability Contrast on Oil Recovery (crossflow). ................. 63 Table 4.7 Crossflow versus No-crossflow, Waterflooding. .................................. 65 Table 4.8 Polymerflooding, crossflow versus no-crossflow ................................. 66 Table 4.9 HW Compared to VW, Waterflooding (Free crossflow). ..................... 73 Table 4.10 HW Compared to VW, Waterflooding (No- crossflow). .................... 74 Table 5.1 Net cash flow Tabulated at oil price of $100/bbl: Displacing 1000 cp oil with polymer (No-crossflow). ............................................................................... 80 Table 5.2 NPV tabulated at oil price of $100/bbl: Displacing 1000 cp oil with polymer (No-crossflow) ........................................................................................ 81 Table 5.3 Net cash flow tabulated at oil price of $100/bbl oil: Displacing 1000 cp oil with polymer (Crossflow) ................................................................................ 82 Table 5.4 NPV tabulated at oil price of $100/bbl oil: Displacing 1000 cp oil with polymer (Crossflow) ............................................................................................. 83
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LIST OF FIGURES
Figure 2.1 Molecular Structure of Hydrolyzed Polyacrylamide ........................... 12 Figure 2.2 Molecular Structure of Partially Hydrolyzed Polyacrylamide ............ 13 Figure 2.3 Molecular Structure of Polysaccharide (Xanthan Gum) ..................... 13 Figure 2.4 Cross-sections of a Horizontal Injector and a Production wells. ......... 22 Figure 2.5 Examples of a Multilateral Well .......................................................... 23 Figure 3.1 One-dimensional discretization into blocks.Error! Bookmark not defined. Figure 3.2 Mass balance ....................................................................................... 31 Figure 3.3 Relative Permeability Curves .............................................................. 43 Figure 3.4 Block sizes analysis ............................................................................. 46 Figure 3. 5 Communicating Layers ...................................................................... 47 Figure 3.6 Non- Communicating Layers ............................................................. 48 Figure 4.1 Waterflooding: Analytical versus Numerical (No-crossflow). .......... 51 Figure 4.2 Waterflooding: Analytical versus Numerical (Free crossflow). ......... 52 Figure 4.3 Polymerflooding: Analytical verse Numerical (Free crossflow). ....... 53 Figure 4.4 Polymerflooding: Analytical versus Numerical (No-crossflow). ....... 54 Figure 4.5 Gravitational effect on oil recovery. ................................................... 56 Figure 4.6 Compressility effect on oil recovery ................................................... 57 Figure 4.7 Effect of kv/kh on the Oil Recovery (VW). ........................................ 60 Figure 4.8 Effect of kv/kh on the Oil Recovery (HW). ........................................ 61 Figure 4.9 Effect of kv/kh on the quantity of oil crossflowed (VW). ................... 61 Figure 4.10 Effect of kv/kh on the quantity of oil crossflowed (HW). ................. 62 Figure 4.11 Effect of Permeability Contrast on the Oil Recovery. ....................... 63 Figure 4.12 Crossflow versus No-crossflow, Waterflooding. .............................. 65 Figure 4.13 Crossflow versus No-crossflow, Polymerflooding 1000 cp Oil. ....... 66 Figure 4.14 Effect of oil viscosity on water wct, Polymerflooding. ..................... 67 Figure 4.15 Effect of oil viscosity on water wct, waterflooding (No-crossflow). 67 Figure 4.16 Effect of Polymer viscosity on oil recovery, 1000 cp oil No-crossflow. .............................................................................................................. 68 Figure 4.17 Effect of polymer viscosity on oil recovery, 1000 cp oil free crossflow. .............................................................................................................. 69 Figure 4.18 Effect of polymer viscosity on water cut on 1000 cp oil. .................. 69 Figure 4.19 Polymerflooding: HW Injector versus VW Injector (No-crossflow)............................................................................................................................... 72 Figure 4.20 Waterflooding: HW Injector versus VW Injector (Free Crossflow)................................................................................................................................ 72 Figure 4.21 Waterflooding: HW Injector versus VW Injector (No-crossflow). .. 73 Figure 4.22 Polymerflooding: HW Injector versus VW Injector (Free Crossflow)................................................................................................................................ 74 Figure 4.23 Polymerflooding: Impact of horizontal injector on Water cut. ......... 76 Figure 4.24 Waterflooding: Impact of horizontal injector on Water cut. ............. 76 Figure 5.1 NPV computed at oil price of ($100/bbl oil): Displacing 1000 cp oil with polymer (No-crossflow) ................................................................................ 79
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Figure 5.2 Net cash flow computed at oil price of ($100/bbl oil): Displacing 1000 cp oil with polymer (No-crossflow). ..................................................................... 80 Table 5.2 NPV tabulated at oil price of $100/bbl: Displacing 1000 cp oil with polymer (No-crossflow) ........................................................................................ 81 Figure 5.3 Net cash flow computed at oil price of ($100/bbl oil): Displacing 1000 cp oil with polymer (Crossflow). .......................................................................... 81 Figure 5.4 NPV computed at oil price of $100/bbl: Displacing 1000 cp oil with polymer (Crossflow) ............................................................................................. 82
1
CHAPTER 1
INTRODUCTION
Traditionally oil production strategies have followed primary depletion,
secondary recovery and tertiary recovery processes1. Primary depletion, also referred to
as primary production, uses the natural reservoir energy to accomplish the displacement
of oil from the reservoir to the producing wells2. As a general rule of thumb, it is
expected that about one third of the original oil in place can be recovered by this method,
in certain cases these recoveries are much lower, and other sources expect only around
10% of the original oil in place to be produced3. Secondary recovery methods are
processes in which oil is subject to immiscible displacement with injectants such as water
or gas. Lastly, tertiary oil recovery involves injection of miscible gases, the use of
thermal energy or the injection of chemicals into the reservoir to accomplish the
displacement of oil from the reservoirs. These operations are also referred to as enhanced
oil recovery (EOR) methods2. Through the entire life of a reservoir, only about thirty to
fifty percent of the original oil in place is produced under primary and secondary
recovery methods altogether1. Consequently, the oil left in the reservoir can be
substantial. The U.S. DOE Fossil Energy Program3 estimates about 65% of currently
discovered resources will not be produced with the use of current production strategies
and present technologies. Planning for efficient production strategies and targeting
unrecoverable oil should be a priority in the petroleum industry. This has challenged
researchers to come up with viable strategies for optimizing our reservoirs.
2
Polymer flooding is a chemically augmented waterflood in which chemicals, (polymer)
such as polyacrylamide or polysaccharides, are added to injected water to increase the
effectiveness of the water in displacing oil.
Formation heterogeneity affects the performance of most flooding operations.
Unfortunately, most oil formations usually exhibit random variations in their
petrophysical properties. In such reservoirs, statistical as well as geological criteria 4
usually are used to divide the pay zone between adjacent wells into a number of
horizontal layers each with its own properties and homogeneous in itself. Such reservoirs
are usually referred to as ‘stratified ’, ‘layered’ or ‘heterogeneous’ reservoirs.
Heterogeneity plays a dominant role in predicting waterflooding performance in stratified
reservoirs. Typically, heterogeneity in reservoir may be present both in the vertical and
the horizontal directions. Throughout the development of this thesis, we assumed
heterogeneities only in the vertical direction of the reservoir. Under this assumption, the
reservoir fluid tends to flow from one layer to the other if there is sufficient
communication between the layers. This is referred to as fluid crossflow between layers
or vertical communications between layers. In some cases, the depositional sequence may
be such that during successive depositions, an impermeable shale layer is sandwiched
between successive reservoir layers to isolate the layers completely form each other, such
that there is very little or no vertical communication between the layers. This is referred
to as no vertical crossflow. Fluid crossflow may be the result of any or all of the four
driving forces: viscous forces, capillary forces, gravity forces and dispersion. These
driving forces interact with each other in the displacement. Our objective will be to
investigate crossflow caused by gravity forces and viscous forces on the sweep efficiency
3
polymer flood process in a stratified reservoir. This is accomplish by simulating cases
with crossflow (no vertical communication) and then crossflow using a black oil model in
Eclipse, a general purpose reservoir simulator.
The concept of vertical equilibrium has been used extensively in the petroleum literature,
mainly as a way of collapsing simulations to the lower dimension5. Vertical equilibrium
(VE) is simply; an assumption that the sum of the driving forces in the vertical direction
is zero for all fluids components at all positions so that pressure will be the same on any
vertical line in each layer. Assuming (VE) implies perfect vertical communication, which
is equivalent to assuming infinite vertical permeability. VE will be good assumption for
reservoirs with aspect ratio (RL) of 10 more5. RL is expressed as:
h
VL K
K
H
LR (1.1)
Where, kV and kh represent vertical and horizontal permeabilities, H and L represents
total thickness and the length of the reservoir respectively.
This thesis evaluates polymer flood potential for an idealized two-layered reservoir by
simulation of waterflood and polymer floods under varying conditions and comparing the
results.
1.1 Description of the Problem
Reservoir heterogeneity plays a major role in oil recovered by
waterflooding/polymer flooding through its influences on fluid crossflow. Simulation
runs were conducted to assess the extent to which the vertical heterogeneity (degree of
fluid crossflow) affects the displacement efficiency. Surprisingly, simulation results using
4
Eclipse100 black oil simulators, agrees well with the results from two other simulators,
VIP and POLYGEL (Petro China), and suggests that fluid crossflow is not a factor to be
consider in waterflooding/polymer flooding operations. Accepted reservoir engineering
(Craig, Lake, Coats) claimed that as the mobility ratio becomes increasingly unfavorable
(high), recovery efficiency worsens more rapidly for the crossflow cases than the non-
crossflow cases. This discrepancy requires further investigations. The Eclipse simulation
results are presented in appendix B figures (B-1 and B-2) and results for POLYGEL
(Petro China) is shown in the same appendix figures (B-3 and B-4).
Furthermore, earlier screening criteria developed for polymer flooding6,7 indicated
that the conventional polymer flooding should be limited to reservoirs with oil viscosity
not exceeding 150 cp for economical recovery. However, a significant number of
reservoirs have been identified with crude oil viscosities above 1000 cp.
1.2 Geological Considerations
Among the factors that influence the success of EOR operations is the
heterogeneity of the oil formation. Reservoir heterogeneities occur both in vertical and
horizontal directions. For heterogeneity in vertical direction, the degree of vertical
communication between the layers is of prime concern of this work. Vertical
heterogeneity depends on the depositional environment of the formation and geologic
time in which it occurs8. Vertical trends are formed and can be monitored with
characteristics of the formation, such as porosity, grain size distribution, and
permeability. Stratigraphy of a reservoir may be identified with logging techniques or
direct measurements on cores. Natural radioactivity measurements can be used to identity
5
depositional environment, and the type and age of the formation9. Gamma ray log
responses are widely used to estimate stratigraphy trend of formation. The identified
vertical trends in most oil-bearing formation are fining upwards and downwards. Fining
upward describes formations that consist of increased grain sizes and permeability in the
downward direction of the depositional sequence of the formation. Fining downward
cases are just the reverse.
In some cases, the depositional sequence may be such that during successive
depositions, an impermeable shale layer is sandwich between successive reservoir layers
to isolate the layers completely form each other, such that there is very little or no vertical
communication between the layers, the layers only communicate through the wellbore
this create a condition of no vertical crossflow between the layers. On the other hand,
vertical crossflow refers to the case where there is direct communication between the
layers. The objectives of this thesis are further outlined in the next section.
1.3 Research Objectives
The main objective of this research focuses on use of water-soluble polymers to
provide greater sweep efficiencies in multi-layered unconventional reservoirs with and
without crossflow. Specifically, this study consists of polymer injection simulation
studies for this work consists of polymer injection simulation studies for chemical EOR
processes, immiscible displacement operations. Also we will spread our wings to
examine the potentials of the use of horizontal well injectors to improve sweep efficiency
of heterogeneous viscous oil reservoirs at varied mobility ratio. This is accomplish by
simulation for the cases model in Eclipse, a general purpose reservoir by:
6
1. Developing reservoir simulation models for waterflood and polymer flood at
varied mobility ratio,
2. Comparing the performance of horizontal well injectors with vertical well
injectors in improving sweep efficiency during polymer flood,
3. Examine the impacts of the degree of fluid crossflow (gravity and viscous),
Layering, permeability contrast, and mobility contrast between the displacing
fluid and the injectant on the levels of the sweep improvement and compare the
results to analytical results
4. Investigate the impact of the variation in polymer viscosity on the polymer
performance,
5. Economic analysis.
7
CHAPTER 2.
GENERAL CONSIDERATIONS AND BACKGROUND
This section focuses on important theoretical aspects waterflooding and immiscible
displacement operations, which are the basis of these simulation studies. Also a literature
review is presented on past work, to examine how polymers provide mobility control and
also compare the success of using horizontal wells versus vertical wells to enhance
displacement efficiency of waterflooding and polymer flooding operations.
2.1 Theoretical Foundation
Many factors influence the success of waterflooding operations and immiscible
displacement processes. These factors can be separated into two categories, one that refer
to characteristics of the reservoir fluids and one that referred to the formation8, 10.
Reservoir characteristics that influence the efficiency of waterfloods may include depth,
porosity, fluid saturation distribution, rock structure and type, and the degree of
formation heterogeneity. This last reservoir characteristic, the degree of formation
heterogeneity, is a primary focus of this study10. The heterogeneity effect on immiscible
displacement and waterflooding processes depends on horizontal and vertical non-
uniformities that allow fluids to move preferentially through the high permeability porous
medium. This flow allows for part of the oil in place to be bypassed in lower permeability
areas10 Many prediction methods have been created for this type of process, where fluid
flow, well patterns, and vertical heterogeneity are considered. Most of these methods
8
assume formations with homogeneous areal rock properties and include heterogeneities
only in the vertical direction8, 10, 11. These techniques originate from Buckley and
Leverett’s work10, and consist of prediction methods for waterfloods in stratified
formations. The earliest group of prediction methods in which heterogeneity of the
formation was considered includes works by Dykstra and Parsons12, Stiles4, and Yuster-
Suder-Calhoun13. These methods have been modified and have become the basis of other
methods, such as, Higgins and Leighto14, Craig-Geffen-Morse15, and Prats-Matthews-
Jewett-Baker16. These methods are among the most accepted although the use of
reservoir simulation has diminished the use of these prediction techniques17.
Some results published on stratified reservoirs show that the variation of reservoir rocks
is mainly controlled by specific factors such as depositional environment, grain size
distribution, and formation mineralogy. Consequently, fractures, re-deposition, and
compaction could also be factors to consider in the origin and variation of the reservoir
arrangement18. All of these parameters and formation characteristics influence oil
recovery efficiency (ER), which measures the fraction of oil in place at the start of a
secondary or tertiary displacement process that can be recovered during displacement
operations10, 19 ER can be expressed as:
DVR EEE (2.1)
In this equation, (ED) represents the microscopic displacement efficiency, which can be
defined as the fraction of the total oil present in the reservoir that has been displaced by
the injecting fluids. ED is control by the wettability of the formation rock, as well as, the
pore size distribution of the reservoir volume contacted by the displacing fluid. In
equation (2.1), the volumetric sweep efficiency (EV) represents the portion of the
9
reservoir that is contacted or swept by the injected fluids with respect to the total volume
of the reservoir. This parameter is affected mainly by the degrees of formation
heterogeneity and the mobility ratio between the displacing and the displaced fluids
during the displacement process19. The three-dimensional volume sweep efficiency can
be separated into two-dimensional areal sweep efficiency term and a vertical sweep
efficiency term8, 11, 19. The volumetric sweep efficiency can be express in terms of the
areal sweep efficiency (EAS) and the vertical sweep efficiency (EVS) as:
VSASV EEE (2.2)
Thus the overall oil displacement efficiency is express as:
DVSASR EEEE (2.3)
The areal sweep efficiency (EAS) depends on the mobility ratio, inter- walls spacing, and
the well arrangement36. In the literature, most prediction methods designed to examine
the behavior of waterflooding operations, combined the effect of the microscopic
displacement efficiency and the areal sweep efficiency. The vertical sweep efficiency
component describes the volumetric sweep efficiency dependency on the vertical
stratigraphy or heterogeneity of the formation and mobility ratio. Mobility ratio
measures the relative velocity of the phases in the reservoir. During the displacement
process, the fluid with higher velocity break through first in the production wells. This
further suggests that viscosity of the phases in the reservoir is the primary fluid
characteristic that affects waterflooding performance, as viscosities of the displaced and
displacing phases affect the mobility ratio in immiscible displacement operations1, 2, 8.
Many techniques have been developed to improve the recovery of oil when
mobility ratio and formation heterogeneity cause adverse effects on the waterflooding
10
operations. One such method is the mobility control technique. This method uses
chemical agent such as polymers to enhance the volumetric sweep efficiency11 by altering
the relative fluid flow in favor of the displaced fluids. According Muskat20 mobility ratio
(M) is the ratio of the mobility of the displacing fluids to that of the displacing fluids in
the regions of the reservoir contacted by the injected fluid2, 11, 12. Equations (2.4) and (2.5)
present the mobility and mobility ratio respectively.
i
iri
kk
(2.4)
In this equation, λi is the mobility of the phase i, where i is the displacing or the displaced
fluid, (k) is the absolute permeability, and (kri) is the relative permeability to the ith phase
and, (µi) is the viscosity of the ith phase. The mobility ratio is presented next.
d
DM
(2.5)
Equation (2.5) presents an expression for the mobility ratio as a function of the mobility,
relative permeability and viscosities of fluid phases. The displacing phase is represented
with the D subscript and the displaced phase distinguished with the d subscript. For
situations in which the displaced fluid (oil) has a higher viscosity (viscous oil), the
mobility ratio is unfavorably (M>1). For such cases, the displacing fluid finger through
the porous medium, leaving oil behind in the unswept regions of the reservoir10. Because
of the understanding of this important concept, EOR processes have incorporated the use
of higher viscosity injection fluids, most commonly accomplish with large
macromolecules called polymers1, 19.
Polymer flooding has been referred to as an improved waterflood in which water-
soluble polymers are added to the injection water to improve the efficiency of the
11
displacement process19. Polymer flooding improves oil recovery by increasing the
viscosity of the displacing fluid. A polymer flood would improve recoveries where
mobility ratios between the displaced and the displacing fluids are unfavorable (greater
than one) and in formations where the heterogeneity is moderate.
There are two principal types of polymer being used in field applications to accomplish
displacement processes: hydrolyzed polyacrylamides (HPAM) and polysaccharide
biopolymer or xanthan gum. Polyacrylamides are produced synthetically through
polymerization of the acrylamide monomer19. The hydrolyzed Polyacrylamides are
usually hydrolyzed to reduce the adsorption property of the original polymer when
injected into the formation. Through hydrolysis, some of the reactive acrylamide are
converted carboxylate groups with negative charges1. The degree of hydrolysis of the
polymer is usually within the ranges of 20% to 40%. In saline water, the electrolyte in
solution causes the molecule to coil. This reduces the viscosity. The hydrolyzed
polyacrylamide solutions are salt sensitive. Other susceptibilities of HPAM solutions are
caused by the presence of oxygen and divalent ions, which are the sources of instability
and chemical degradation by temperature and mechanical degradation. The HPAM
molecules’ long chain may be broken, especially at high velocity and temperature
conditions when the injected solution passes through the well’s perforation interval and
flow through the porous spaces of the formation near the wellbore. Being less expensive
and providing higher residual resistance to drive water injection, polyacrylamide is more
widely used in the field than the polysaccharide as a mobility control agent. Biocide such
as formaldehydes, need to be used to prevent the viscosity loss cause by microbes. On the
12
other hand, polysaccharide biopolymer is obtained from sugar in a fermentation process
caused by the bacterium, Xanthomonas campestris.
The polysaccharide molecular structure gives the molecules a greater stiffness13,
their behavior being like a semi-rigid-rod molecule13. In contrast to polyacrylamide, the
viscosity of a xanthan gum is not affected by salinity, and shearing can be tolerated.
Despite, the advantages, the polysaccharide biopolymer is expensive, and its stability
decreases with temperatures of about 160οF. Biodegradation of polysaccharide by
enzymes is very common. Biocides are always added to the Xanthan biopolymer before
injection to the formation to protect the integrity of the polymer from bacterial attack and
aerobic degradation19. Xanthan biopolymers have low retention on reservoir rock surface.
Figure 2.3 shows the molecular structure of xanthan gum and Figures 2.1 and 2.2 both
forms of polyacrylamides.
Figure 2.1 Molecular Structure of Hydrolyzed Polyacrylamide
13
Figure 2.2 Molecular Structure of Partially Hydrolyzed Polyacrylamide
Figure 2.3 Molecular Structure of Polysaccharide (Xanthan Gum)
2.2 Literature Review
As mentioned in Chapter 1, the objectives of this research are to examine the
effectiveness of using water-soluble polymers and horizontal well to provide a more
sweep efficiencies of multi-layered unconventional reservoirs with and without
crossflow. This was done with the help of a reservoir simulator, developed for this study.
An extensive review of the literature was performed to understand the procedure in
14
building a simulator with proper representation of the horizontal well in a reservoir
simulator. The following is an overview of the literature.
Waterflooding is the most common secondary recovery operations in the
petroleum industry8. The method has gained lot of acceptability in the industry since the
mid 1890s. However, the method has a limited applicability when the displacement is
characterized by a remarkably unfavorable mobility ratio. Kumar et al22 examined
waterflood performance using unfavorable mobility ratios. They concluded that viscous
fingers dominate high mobility ratio floods, that mobile water can significantly reduce oil
recovery and that thief zones accentuate poor displacement performance. They strongly
suggested that any improvement in mobility ratio (e.g., polymer flooding) could improve
recovery and sweep efficiency.
Polymer floods have been applied during several occasions13, 17, 20, 23. These
include polymer floods applied at the Daqing oil field24, 25, the world’s largest polymer
flood field, Marmul26, Oerrel7, and Courtenay 27. Field tests have proved that the method
has potential to provide superior oil recovery. In formations where long fractures
dominate the formation, and cause severe channeling, gel treatments or other types of
“profile modification” methods before polymer flooding can greatly enhance reservoir
sweep24. Polymer flooding has been widely used as an improved waterflooding operation;
its mechanism of oil displacement and the chemistry of the polymers are not being
questioned in this work. Polymer injection studies conducted in this thesis will focus on
how the degree of crossflow (vertical heterogeneities), permeability contrast, polymer
slug size, adsorption, and concentration affects polymer flooding recoveries. Some of
these components will be examine at varied mobility ratio to establish a limit of mobility
15
ratios within which polymer flooding will be more advantageous over the conventional
waterflooding operations. Several authors7, 28, 29, 31, 32 have examined polymer flooding
operations and have published about the degree of crossflow, molecular weight of
polymer, polymer concentration, viscosity, degradation, brine salinity and cost
effectiveness. These researchers affirmed that that the aforementioned properties are
critical during polymer flood operations.
Zhang and Seright33 examined the degree of crossflow in polymer flooding.
They concluded that if crossflow can occur between adjacent strata, sweep in the less-
permeable zones can be almost as great as that in the high-permeable zones if the product
of mobility ratio and the permeability differential is less than unity. However, if no
crossflow occurs, sweep in the less- permeable zones will not be better than the square
root of the reciprocal of the permeability differential. Wu et al34 devised a separate-layer
injection technique to improve the sweep efficiency when crossflow does not occurs. The
technique was found to improve flow profile, reservoir sweep efficiency and also
minimize water cut in the production wells. Numerical simulation studies conducted by
Wu et al34 revealed that efficiency of polymer flood depends on permeability contrast
between the adjacent layers and at the time at which separate –layer injection occurs.
Recent work published24 on polymer systems, where properties such as molecular
weight viscosity have been modified to create a system that could effectively improve the
mobility ratio between the displacing and the displaced fluids and improve sweep
efficiency in returns. The effectiveness of the system was found to increase with
increased polymer viscosity Table 2.1 shows these results. At a giving set of conditions,
polymer viscosity increases with increasing polymer molecular weight. Wu et al35
16
performed laboratory tests with affixed volume of polymer solution injected but varied
the molecular weight of the polymer. They confirmed that oil recovery increases with
increasing polymer molecular weight.
Table 2.1 shows the results of this study24. For a giving polymer, chemical retention
increases and the rate of polymer propagation decreases, as the rock permeability is
decreases. High-molecular weight polymers usually experience high retention and low
propagation rate for lower rock permeablities6, 36.
Properties of hydrolyzed polyacrylamide solutions are salt sensitive, the solution
viscosity decrease drastically with slight increase in salinity21. Thus, for high-salinity
formations, HPAM solution is fairly ineffective during a polymer flood. Maitin7 studied
polymer flooding of high- salinity reservoirs using HPAM. He injected fresh water of low
salinity before injection of HPAM solutions. Maitin7 suggested that pre-conditioning a
high-salinity formation with fresh water of low salinity can effectively reduce the
formation salinity and improve the performance of the polymer flood.
Jennings et al38 presented numerical variables defined as the “resistance factor
(Fr)” and “Residual resistance factor (Frr)” to account for the mobility reduction of the
injected polymer solution and measure of reduction in rock’s permeability to water after
polymer injection. The resistance factor (Fr) express the ratio of mobility of the water in
place compared to the polymer injected, and the Frr, the change of the mobility of the
water in place before and after the polymer injection has taken place38.
Residual resistance factor (Frr) and resistance factor (Fr) are express mathematically as:
p
wrF
(2.4)
17
)after(
)before(F
w
wrr
(2.5)
In equations (2.4) and (2.5), λW and λP denotes mobility of water and polymer
respectively.
Table 2.1 Effect of Polymer Concentration on water cut ultimate Recovery, and EOR24
Polymer Concentration
(mg/L)
Minimum
water cut, %
Ultimate
Recovery, %
EOR
%
600 87.1 50.58 7.69
800 85.0 52.52 9.64
1000 83.1 52.83 9.95
1200 82.4 52.89 10.01
1500 81.0 53.03 10.15
Table 2.2 Effect of Polymer Molecular Weight on EOR24. Molecular Wight Waterflood Polymer Ultimate
Figure 4.14 Effect of oil viscosity on water wct, Polymerflooding.
Figure 4.15 Effect of oil viscosity on water wct, waterflooding (No-crossflow).
4.2.7 Polymer Solution Viscosity
Similar studies analogous to the oil viscosity were analyzed for the polymer
solution viscosity used in the polymerflooding under the assumption that polymer
68
solution is a Newtonian, and no polymer retention. The polymer used in this analysis has
viscosities of 10, 100 and 1000 cp displacing oil of 1000 cp. Figure 4.17 and 4.16 show
the oil recovery responses for the free crossflow and no-crossflow cases. It can be seen
that, at higher polymer viscosity, oil recovery is higher, and decrease as the polymer
viscosity decreases. The reason is that, high polymer viscosity reduces the mobility
contrast between injectant and the displacing fluid (oil) thus, increases oil recovery. Also,
high polymer solution viscosities delay the breakthrough of the injected fluid. It also
slows the velocity of the water by increasing its viscosity. Figure 4.18 show the plot of
water cut as the function of pore volume injected. It is clear from the plot that the
breakthrough time is longer at high polymer viscosity and decrease as the viscosity
decreases.
Figure 4.16 Effect of Polymer viscosity on oil recovery, 1000 cp oil No-crossflow.
69
Figure 4.17 Effect of polymer viscosity on oil recovery, 1000 cp oil free crossflow.
Figure 4.18 Effect of polymer viscosity on water cut on 1000 cp oil.
70
4.2.8 Summary of Sensitivity Analysis
It is evident from Figure 4.5 through Figure 4.11(discussed earlier) that gravity
and rock compressibility have virtually no appreciable impact on the oil displacement
performance. Apart from these, all the other parameters study under sensitivity analysis
has slight influence on the oil recovery performance. The HW-configuration immerged to
have shown a slight sensitivity or advantage for the range of the parameter studied than
the VW-configuration. Now that the sensitivity analyses have been discussed, further
results generated by the simulator to see the potential of horizontal well injector in
polymer injection and waterflooding can be presented.
4.3 Potential of Horizontal Injector in Waterflooding.
This section is presented to determine the advantage that the horizontal well
injector pair has over vertical well injector pair in the polymer and in waterflooding. This
is done by comparing the performance of horizontal well injector pair with the
performance of the vertical well injector pair in both the polymer and waterflooding. This
comparison will help determine the conditions under which it is beneficial to use
horizontal well injector pair in the flooding operations. The performance of the horizontal
well injector pair based on oil recovery and water cut as a function of pore volume
injected will be discussed next.
4.3.1 Results Based on Oil Recovery
The oil recovery as a function of the pore volume injected for a range of oil
viscosities 1, 10, 102, 103, 104 and 105 cp for water flooding cases and 102, 103, 104 and
71
105 cp for polymerflooding cases under the assumptions of infinite vertical permeability
(vertical communication between layers) and non-communicating layers systems is
plotted in Figure 4.19 through Figure 4.22. These figures show the comparison of the
performance of the HW-configuration and VW -configuration for different oil viscosity
under assumptions stated above. Figure 4.20 and Figure 4.21 shows the oil recovery as a
function of the pore volume injected for the HW- configuration compared with the VW-
configuration for waterflooding case; crossflow and no-crossflow cases. Figure 4.22 and
Figure 4.19 show the communicating layers case and no communicating layer case of the
polymerflooding. It can be seen in Figure 4.19 through Figure 4.22 that the oil recovery
from HW-configuration is slightly higher than that of VW-configuration for the
waterflooding and mobility control cases for the range viscosities study. This advantage
is attributed to the increased contact area of the HW- configuration with the reservoir
formation as against the VW- configuration. These comparisons are further simplified
quantitatively in Table 4.23 though 4.26. It is openly from these tables that the horizontal
well injector has a slight advantage of the vertical well injector. For example, in table
4.26 (free crossflow , waterflooding), at 1 pv of injection, HW – configuration recovers
75.66 % of the mobile oil(10 cp) but, the VW- configuration recovers only 68.40 %. This
trend is seeing in all the tables. It must be noted that the length of the horizontal wells
used in this studies remains unchanged for all the simulation cases studied.
72
Figure 4.19 Polymerflooding: HW Injector versus VW Injector (No-crossflow)
Figure 4.20 Waterflooding: HW Injector versus VW Injector (Free Crossflow).
73
Table 4.9 HW Compared to VW, Waterflooding (Free crossflow). uo/uw Recovery (%) at 1 PV. Recovery (%) at 5 PV.
VW HW VW HW
1 99.87 99.99 99.16 99.99
10 68.40 75.66 99.64 99.86
102 44.07 47.03 63.89 66.00
103 18.89 20.39 37.55 40.40
104 6.52 8.36 14.32 16.42
105 2.40 3.69 5.17 6.42
Figure 4.21 Waterflooding: HW Injector versus VW Injector (No-crossflow).
74
Table 4.10 HW Compared to VW, Waterflooding (No- crossflow). uo/uw Recovery (%) at 1 PV. Recovery (%) at 5 PV.
VW HW VW HW
1 87.00 88.51 99.35 99.97
10 70.00 67.05 92.28 92.32
102 49.21 53.78 72.89 74.58
103 34.99 38.51 46.99 52.47
104 14.46 23.97 23.82 30.69
105 7.83 7.10 12.03 12.53
Figure 4.22 Polymerflooding: HW Injector versus VW Injector (Free Crossflow).
75
4.3.2 Results Based on Water Cut
Another parameter used to compare the performance of a horizontal well injector
with the performance of a vertical well injector is water cut. Water cut measures the
fraction of water in the total flow stream (oil plus water). Water cut as a function of pore
volume injected is plotted in Figure 4.23 for the polymerflooding and Figure 4.24
waterflooding. It can be seen in these figures 4.23 and 4.24 that water breakthrough times
are slightly higher for the horizontal injector than that with vertical injector. We believed
that because horizontal injector invades the reservoir stronger (Figure 4.34) in the vertical
region, the vertical fluid flow uniforms the front thereby delaying the water breakthrough.
This advantage weakens as the injection progresses. Summarizing the results presented
in this chapter, the horizontal well injector in polymer and in waterflooding operations is
compared to a vertical well injector. The horizontal well injector proved advantageous of
over the vertical well injector. This advantage of a horizontal well deceases as if the
vertical permeability is not very favorable for the horizontal well to invade in the vertical
zone of the reservoir. Furthermore, the advantage of horizontal injector on water cut over
vertical injector is pronounced within the range of the parameter studied. The viscosity
controls the recovery performance in the flooding operations.
76
Figure 4.23 Polymerflooding: Impact of Horizontal Injector on Water Cut.
Figure 4.24 Waterflooding: Impact of Horizontal Injector on Water Cut.
77
CHAPTER 5
ECONOMICS
The objective function used in this project is the net present value of the
polymerflood operation for a given production period. The objective is to design the best
production and injection strategy for the unconventional reservoir. This chapter explains
the concept of net present value and how it can be determined.
5.1 Net Present Value (NPV)
Present value of money compares the value of a certain amount of money today to
the value of that same amount in the future and vice versa, taking into consideration
inflation and returns. Net present value (NPV) is actually the present value of the net cash
flow (the present value of cash inflows less the present value of cash outflows). Given an
investment opportunity, NPV is used by an organization to analyze the profitability of the
project or investment and to make decisions with regards to capital budgeting. It is
sensitive to the future cash inflows that an investment or project will yield. NPV can be
computed b y the relation below54.
NPV =
T
tot
t Cr
C
1 1 (5.1)
Where t = Time of cash flow (time step)
Ct = Net (after tax) cash inflow (cash inflow-outflow) after time t, (PV) $
r = Annual (or periodic) discount rate, fraction
T = Cumulative investment (or production) period or pore volume injected (PV),
78
Co = Initial investment cost, $
A conservative annual discount rate of 10% was used in this study in the estimation of the
present value of money and is based on the current rates at which eligible institutions are
charged to borrow short-term funds directly from a Federal Reserve Bank (approximately
6.5%). Also, most oil companies use this rate for evaluating the viability of proposed
investments.
Cash inflow is calculated from the oil, water production and injection rates obtained from
of the filed or from the cumulative production from the reservoir. The price of oil is
pegged at $20, $50, and $100 per barrel for the entire three-week production period while
the cost of water handling is $0.25 per barrel of water and $2/lb of polymer (specifically
for the polymerflood section in this study). The total cash inflow for the floods operations
for the entire production periods are given by,
Cw = (fopt × $/bbl) − (Fwt × $wat) (5.2)
Cp = (fopt × $/bbl) − Fwt × ($wat+$Fp) (5.3)
Where, C = Net cash inflow, (w, p represent water and polymer respectively), $
$/bbl =Price of Oil per bbl, $
$wat= Cost of water handling per bbl, $
$Fp= Cost of polymer treatment per bbl, $
Fopt = Cumulative oil production, SCC
Fwt = Cumulative water production and injection, SCC
Figures 5.1 and Figure 5.2 show the net cash flow (revenue) for the free crossflow and
no-crossflow cases for oil price of $100 per barrel of oil and used to compute their
corresponding NPV plot in figure 5.3 and figure 5.4. The NPV plots and the net cash
79
flow plots show economically attractive project but this advantage diminishes after about
5 PV of injection. Also, as the oil price dropped, example $ 50, and $ 20 per barrel, and
the viscosity of polymer solution reduces, the project (polymer injection) becomes less
and less economically attractive. Tables 5.1 through 5.4 show the net cash flow and NPV
computed at 5 and 15 PV for the crossflow and no-crossflow to further aid in the
explanations/interpretations of the graphs. The net cash flow and NPV plot corresponding
to the oil prices of $ 20 and $ 50 per barrel are presented in appendix C. It must be noted
that the NPV is computed at Co = 0 (no initial investment cost) and the injection rate was
constant for all the cases study. If the injection is inversely proportional to polymer
viscosity, that could affect the results.
Figure 5.1 NPV computed at oil price of ($100/bbl oil): Displacing 1000 cp oil with polymer (No-crossflow)
80
Table 5.1 Net cash flow Tabulated at oil price of $100/bbl: Displacing 1000 cp oil with polymer (No-crossflow). Viscosity NPV at $100/bbl of oil, (NoX), $ Relative profit, $
5 PV 15 PV 5 PV 15 PV
1 cp water 2.641 7.942 - -
10 cp, pol. 7.270 15.432 4.629 7.490
100 cp, pol. 26.482 38.881 23.831 30.939
1000 cp, pol. 30.501 42.187 27.870 34.245
Figure 5.2 Net cash flow computed at oil price of ($100/bbl oil): Displacing 1000 cp oil with polymer (No-crossflow).
81
Table 5.2 NPV tabulated at oil price of $100/bbl: Displacing 1000 cp oil with polymer (No-crossflow) Viscosity Revenue at $100/bbl of oil, (NoX), $ Relative profit, $
5 PV 15 PV 5 PV 15 PV
1 cp water 0.165 0.187 - -
10 cp, pol. 0.270 0.275 0.105 0.088
100 cp, pol. 0.338 0.330 0.173 0.143
1000 cp, pol. 0.348 0.338 0.183 0.151
Figure 5.3 Net cash flow computed at oil price of ($100/bbl oil): Displacing 1000 cp oil with polymer (Crossflow).
82
Table 5.3 Net cash flow tabulated at oil price of $100/bbl oil: Displacing 1000 cp oil with polymer (Crossflow) Viscosity Revenue at $100/bbl of oil, (crossflow), $ Relative profit, $
5 PV 15 PV 5 PV 15 PV
1 cp water 0.118 0.140 - -
10 cp, pol. 0.173 0.182 0.055 0.042
100 cp, pol. 0.232 0.232 0.114 0.092
1000 cp,
pol.
0.364 0.350 0.246 0.210
Figure 5.4 NPV computed at oil price of $100/bbl: Displacing 1000 cp oil with polymer (Crossflow)
83
Table 5.4 NPV tabulated at oil price of $100/bbl oil: Displacing 1000 cp oil with polymer (Crossflow)
Viscosity NPV at $100/bbl of oil, (crossflow), $ Relative profit, $
5 PV 15 PV 5 PV 15 PV
1 cp water 5.034 9.848 - -
10 cp, pol. 7.940 14.440 2.906 4.592
100 cp, pol. 11.847 20.409 6.813 10.561
1000 cp, pol. 27.902 62.019 22.868 52.171
84
CHAPTER 6
CONCLUSIONS AND RECOMMENDATIONS
6.1 Conclusions
The simulation models developed in this study was used to investigate the scheme
of polymer injection in waterflooding. The conclusions are as follows.
1. The important factors that affect the recovery of oil when a horizontal well is used
as injector are vertical to horizontal permeability ratio. The permeability ratio
(kv/kh) was varied from 0.05 to 0.35.
2. The results of this study showed that the use of horizontal well injectors in
waterflooding is advantageous as compared to the vertical well injectors for the
range of kv/kh, considered in this study.
3. The use of horizontal well injector results in more oil recovered at the producer as
compared to a vertical well injector. Specifically, this advantage of horizontal
well injector was more pronounced when the vertical to horizontal permeability
ratio was 0.3 and above.
4. This study showed that the water cut at the producer is less when a horizontal well
injector is used as opposed to when a vertical well injector is used, below the pore
volume injected value of about 0.40. This water cut for horizontal well injector
case becomes more than the water cut for vertical injector case above pore
volume injected value of about 0.5.
85
5. At stable displacement, Crossflow adds advantage to displacement with crossflow
then the corresponding no-crossflow case. As the displacement become
increasingly unstable, the performance of crossflow model is worsen more for the
crossflow case then the no-crossflow case.
6. The economic gain from the polymer injection operations is higher for the
displacement with no–crossflow then the crossflow at any giving oil price and
polymer viscosity, but this advantage reduces for both models beyond about 4 PV
of injection
6.2 Recommendations
The development of this thesis is base on idealized geological models from which
many ideals may be derived for further investigate the advantage of using HW-
configuration and the impact vertical heterogeneities have on polymerflooding and
waterflooding. The recommendations for the future work using the simulation model,
developed in this study, are as follows.
1. The horizontal well length, which was kept constant in this study, can be varied to
see if an increase in horizontal well length always increases horizontal well's
advantage over a vertical well or if there is an optimum horizontal well length
beyond which there is no increase in advantage.
2. A vertical well was used as a producer in this study. Several simulation runs can
be performed to evaluate if the use of a horizontal well producer would
significantly increase the oil recovery.
86
3. The thickness of each reservoir layer was kept constant in this study. An opposite
scenario would be to vary the layer thickness to evaluate the potentials of a
horizontal well injector.
4. Further work can also be carried out on reservoir geology while considering
uncertainties in the reservoir model parameters and also on full field scale
including reservoir heterogeneity.
5. The study should include capillary curves developing at low injection rates to
study the effect capillary force have on the oil recovery.
6. The crossflow model fails to match the results of the analytical model the subject
of discrepancy should be investigated.
87
NOMENCLATURE
Bo = Oil formation volume factor, rcc/SCC
Bw = Water formation volume factor, rcc/SCC
Ct = Net cash flow
Cf = Rock compressibility, atm-1
Co = Oil compressibility, atm-1
Cw = Water compressibility, atm-1
EAS = Areal sweep efficiency, fraction
ED = Microscopic displacement efficiency, fraction
Figure B-4 No-crossflow result from POLGEL Simulator by PetroChina
102
APPENDIX C The calculation of NPV and NET CASH FLOW at oil prices, $ 20 and $ 50 per barrel for Displacing 1000 cp oil with polymer: (crossflow and no- crossflow).
Figure C-1 NPV computed at oil price of $ 20/bbl: Displacing 1000 cp oil with polymer (Crossflow)
103
Figure C-2 NPV computed at oil price of ($ 20/bbl oil): Displacing 1000 cp oil with polymer (Crossflow)
Figure C-3 Net cash flow computed at $ 50/bbl of oil: Displacing 1000 cp oil with polymer (Crossflow)
Figure C-4 NPV computed at $ 50/bbl oil: Displacing 1000 cp oil with polymer (Crossflow)
104
Figure C-5 Net cash flow computed at $ 20/bbl of oil: Displacing 1000 cp oil with polymer (No-crossflow)
Figure C-6 NPV computed at $ 20/bbl of oil: Displacing 1000 cp oil with polymer (No-crossflow)
105
Figure C-7 Net cash flow computed at oil price of $ 50/bbl: Displacing 1000 cp oil with polymer (Crossflow)
Figure C-8 NPV computed at oil price of ($ 50/bbl oil): Displacing 1000 cp oil with polymer (No-crossflow)