MSc Petroleum Engineering Individual Project 2015 – 2016 Panagiota Papageorgiou OPTIMISATION OF POLYMER FLOODING USING GENETIC ALGORITHMS Heriot – Watt University School of Energy Geoscience Infrastructure and Society Institute of Petroleum Engineering Supervisor: Dr. Karl D. Stephen
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MSc Petroleum Engineering
Individual Project 2015 – 2016
Panagiota Papageorgiou
OPTIMISATION OF POLYMER FLOODING USING
GENETIC ALGORITHMS
Heriot – Watt University
School of Energy Geoscience Infrastructure and Society
Institute of Petroleum Engineering
Supervisor: Dr. Karl D. Stephen
i
DECLARATION
I, Panagiota Papageorgiou, confirm that this work submitted for assessment is my own and is
expressed in my own words. Any uses made within it of the works of other authors in any form
(e.g. ideas, equations, figures, text, tables, programs) are properly acknowledged at the point
of their use. A list of the references employed is included.
Signed: Panagiota Papageorgiou
Date: 18th of August, 2016
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ACKNOWLEDGEMENTS
I would like to dedicate this dissertation to my family, who provided me with the necessary
guidance and support to pursue a master degree in Petroleum Engineering at Heriot – Watt
University.
Special appreciations to my sponsor company Hellenic Petroleum SA whose financial support
made my willing to study at this prestigious university reality. This sponsorship was a
recognition of my previous educational effort and an encouragement of my current studies.
I would also like to thank my supervisor Dr Karl Stephen for his willingness to provide me
help, guidance and support throughout this individual project.
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SUMMARY
The present project describes the way of optimising polymer flooding design by the use of
genetic algorithms. This optimisation involves the well placement and polymer injection
characteristics like polymer concentration, injection rate control and adsorption. The purpose
of this study is to find the most adequate engineering control parameters in an economical
efficient way.
Polymer flooding is an enhanced oil recovery technique aiming in waterflood sweep efficiency
improvement and viscous fingering reduction by decreasing the mobility of injected water. The
mobility reduction can be contributed to the increased viscosity of polymer compared to water
and polymer adsorption to the rock. Injection rate has also an impact on polymer flooding
efficiency. By simulating these parameters, a proposed polymer design strategy will be
decided.
Genetic algorithms are commonly used for solving optimisation problems based on natural
selection theory and genetics. They are considered a robust algorithm method by generating a
population of models in each iteration with best model approaching the optimal solution and
selection based on random number generators. These algorithms are already applied in oil and
gas industry for production optimisation, well placement and economic analysis.
In this project genetic algorithms were used with success to indicate an optimal well placement
based on one injector and one producer heal and toe coordinates as well as an appropriate slug
design of polymer initiation, duration, initial and final concentration. Sensitivities were
conducted on the most optimal polymer flooding model by varying injection rate and
adsorption by the rock. NPV was also calculated for the same model and demonstrated a high
value.
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TABLE OF CONTENTS
ACKNOWLEDGEMENTS ....................................................................................................... ii
SUMMARY ............................................................................................................................. iii
TABLE OF CONTENTS .......................................................................................................... iv
LIST OF ABBREVIATIONS ................................................................................................... vi
LIST OF FIGURES ................................................................................................................. vii
LIST OF TABLES ................................................................................................................. viii
AIM AND OBJECTIVES.......................................................................................................... 1
Figure 1. HPAM molecular structure ...................................................................................................... 2 Figure 2. Effect of viscosity ratio on fractional flow curves during water and polymer flood ............... 4 Figure 3. Water saturation profile during polymer flooding ................................................................... 5 Figure 4. Polymer slug Design ................................................................................................................ 6 Figure 5. Polymer concentration in injected solution vs polymer injection time ................................... 7 Figure 6. Field-B Permeability Distribution, Erosional surface and Oil Saturation profile .................. 13 Figure 7. Genetic Algorithm Process .................................................................................................... 14 Figure 8. Straight-line-wells program interface .................................................................................... 15 Figure 9. Evolution of Generations vs FOPT for global (Case 1) and modified population (Case 2)
during water flooding ............................................................................................................................ 21 Figure 10. Well Coordinates Convergence for Case 1 .......................................................................... 22 Figure 11. Well Coordinates Convergence for Case 2 .......................................................................... 23 Figure 12. Water flooding model in restricted area (Case 2) ................................................................ 24 Figure 13. Case 6 vs 7: Evolution of Generations vs Oil Recovery ..................................................... 25 Figure 14. Case 6: Optimal Initiation Time .......................................................................................... 26 Figure 15. Case 6: Optimal Duration Time ........................................................................................... 26 Figure 16. Case 6: Optimal Initial Concentration for Tapered Rate ..................................................... 27 Figure 17. Case 6: Optimal Final Concentration for Tapered Rate ...................................................... 27 Figure 18. Case 7: Optimal Initiation Time .......................................................................................... 28 Figure 19. Case 7: Optimal Duration Time ........................................................................................... 28 Figure 20. Case 7: Optimal Initial Concentration for Constant Rate .................................................... 29 Figure 21. Case 7: Optimal Initial Concentration for Constant Rate .................................................... 29 Figure 22. Polymer flooding model in restricted area (Case 6) ............................................................ 30 Figure 23. Field Oil Recovery based on different injection rates ......................................................... 31 Figure 24. NPV vs Evolution of Generations for Case 6 ...................................................................... 32 Figure 25. Case 6: Optimal Initiation Time Schedule based on NPV................................................... 33 Figure 26. Case 6: Optimal Duration Time Schedule based on NPV ................................................... 33 Figure 27. Case 6: Optimal Initial Concentration based on NPV ......................................................... 34 Figure 28. Case 6: Optimal Final Concentration based on NPV .......................................................... 34 Figure 29. FOPT vs Adsorption factor .................................................................................................. 35
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LIST OF TABLES
Table 1: Well Data Settings (Case 1) .................................................................................................... 16 Table 2: Well data Settings and Well Placement Boundaries (Case 2) ................................................ 17 Table 3: Evolution of Generations Settings (Cases 1, 2) ...................................................................... 17 Table 4: Evolution of Generations and Polymer Slug Settings (Cases 3, 4, 5, 6, 7, 8) ......................... 18 Table 5: Polymer Flooding – Summary Results ................................................................................... 24 Table 6. Injection Rate Sensitivities ..................................................................................................... 31
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AIM AND OBJECTIVES
The present project presents a method of optimising polymer flooding with the use of genetic
algorithms. This optimisation is based on appropriate well placement and polymer slug design
to reach an optimal ultimate recovery in an economic efficient way. The main criteria of
selecting the most optimal model is the technical and economic feasibility based on Field Oil
Production Total and Net Present Value calculation, respectively.
By varying parameters like well spacing, polymer initial and final concentration, polymer
injection initiation and duration, the field oil ultimate recovery is calculated based on a range
of solutions generated by genetic algorithms. The most optimal model is selected and NPV is
generated along with sensitivities based on injection rate and adsorption factor.
This computational technique aims in robust results by saving valuable time to the reservoir
engineer in well placement selection and polymer injection scheduling.
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1. INTRODUCTION
1.1. POLYMER FLOODING RECOVERY MECHANISM
1.1.1. Polymer injection technique
Οver the last years, innovative techniques have been applied in οil and gas industry to increase
reservoir recovery. Polymer flooding is an enhanced οil recovery mechanism aiming in better
sweep efficiency of the hydrocarbons by increasing viscosity and hence reducing mobility οf
injected water and minimising viscous fingering effect.
During polymer flooding the most commercially and broadly used polymers are the
polyacrylamides like synthetic partially hydrolysed polyacrylamide (HPAM) and the
polysaccharides like biopolymer Xanthan. HPAM shown in Figure 1 is preferable due to lower
cost, large-scale production and higher viscoelasticity (Sheng, 2013).
Figure 1. HPAM molecular structure
1.1.2. Polymer flooding displacement process
Polymer flooding process starts with the injection of a preflush of low-salinity brine followed
by the polymer solution which displaces the unrecovered oil by increasing the water phase
viscosity significantly and decreasing the effective permeability to water by retention.
Combination of these effects leads to a reduced mobility ratio as defined by the following
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equation (1.1) of the displacing fluid and improvement of microscopic displacement efficiency
and volumetric sweep efficiency. Subsequently a freshwater buffer is injected containing
usually polymer in decreasing amounts (tapering rate) (Lake, 2010).
Mobility ratio = M = 𝑘𝑟𝑤
′ /𝜇𝑤
𝑘𝑟𝑜′ /𝜇𝑜
= 𝜇𝑜 . 𝑘𝑟𝑤
′
𝜇𝑤 . 𝑘𝑟𝑜′ (1.1)
𝒌𝒓𝒘′ = relative permeability to water at residual oil saturation
𝒌𝒓𝒐′ = relative permeability to oil at irreducible water saturation
𝝁𝒘 & 𝝁𝒐= water or polymer slug & oil viscosities
The pοlymer floοding mechanism can be analytically described using the Buckley-Leverett
theοry which can be specified to fractiοnal flow theοry. Αccording to the classical Βuckley-
Leverett theοry (Buckley & Leverett, 1942), the continuity equation for the water phase of one
dimensional linear system can be written as:
𝝏𝑺𝒘
𝝏𝒕 +
𝒒
𝑨𝝋 𝒅𝒇𝒘
𝒅𝑺𝒘 𝝏𝑺𝒘
𝝏𝑿 = 0 (1.2)
The velοcity of a displacement front οf constant saturation is:
𝒖𝜟𝑺𝒘= (
𝒅𝑿
𝒅𝒕)
𝑺𝒘
= 𝒒
𝑨𝝋 𝒅𝒇𝒘
𝒅𝑺𝒘 (1.3)
During polymer injection, two saturation fronts are formed. The first saturation shock forms as
water saturation is increasing since saturation velocity upstream is higher than the downstream.
The second saturation shock forms at the polymer front where polymer is in contact with
connate water. The two fluids are completely miscible and their displacement is sharp or piston-
like. As a result, the velocities of water and polymer are equal at the water – polymer contact.
Therefore,
𝒇𝒘𝒑
(𝑺𝒘𝟑)− 𝒇𝒘(𝑺𝒘𝟐)
𝑺𝒘𝟑− 𝑺𝒘𝟐 =
𝝏𝒇𝒘𝒑
𝝏𝑺𝒘 |𝑺𝒘=𝑺𝒘𝟐
= 𝒇𝒘
𝒑(𝑺𝒘𝟐)
𝑺𝒘𝟐+𝑫𝒑 (1.4)
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where 𝑫𝒑 is the polymer retardation factor.
The solution of the above equation for 𝑺𝒘𝟐 and 𝑺𝒘𝟑 provides the values of the first and second
upstream side water saturation shocks. The solutions can also be determined graphically
(Figure 2) by drawing a straight line from the points (𝑺𝒘𝒄, 𝟎) and (-𝑫𝒑, 𝟎) tangents to the water
and polymer factional flow curves, respectively (Pope, 1980).
Figure 2. Effect of viscosity ratio on fractional flow curves during water and polymer flood
During polymer injection there are four different sharpening fronts in the water phase saturation
profile as shown in Figure 3. After waterflood the injected polymer increases the viscosity of
water and decreases its mobility leading to a better sweep efficiency of the remaining oil. The
piston-like displacement of polymer slug enables the oil bank front to be formed by reducing
the viscous fingering effect. The subsequent postflood of a freshwater buffer protects the
polymer solution from backside dissolution.
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Figure 3. Water saturation profile during polymer flooding
1.1.3. Polymer Flooding Design
Polymer injection is commonly selected when waterflood mobility ratio and reservoir
heterogeneity are high. The main steps during the design of polymer flooding are (Lake, 2010):
1. Selection of the candidate reservoirs based on technical feasibility regardless of funds
satisfying two screening criteria of reservoir temperature less than 350 K and permeability
higher than 0.02 μm2 (where 1 m2 equals 1.013249966e+12 Darcy) to avoid polymer
degradation and plugging, respectively. The project should also be economic feasible by
returning profit.
2. Make a decision on the appropriate approach concerning both mobility control by
decreasing mobility ratio and profile control by improving the permeability at the injectors
and producers.
3. Selection of a polymer type that satisfy EOR requirements such as good thickening, high
solubility in water, low retention, shear, chemical and biological stability and ability to
propagate through the rock intact, without excessive pressure losses or plugging.
4. Estimation of polymer amount like mass and concentration based on a targeted mobility
ratio.
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5. Design of polymer injection facilities containing mixing, filtration and injection equipment.
6. Selection of well pattern and spacing, completion design, reservoir characterisation and
appropriate injection rates. Optimisation of those parameters is very important in this stage
in order to obtain the maximum rate of return on investment.
1.1.4. Polymer Flooding Control Parameters
1.1.4.1. Concentration Rate
Polymer concentration rate is a crucial factor which determines the chemical and operation
costs along with the displacement process. Berh et al. (2013) applied tapering polymer slug
rate to reduce costs and stabilize the displacement front of polymer solution injected initially
and water back front coming afterwards. The tapering slug schematic is illustrated below
(Figures 4, 5).
Figure 4. Polymer slug Design
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Figure 5. Polymer concentration in injected solution vs polymer injection time
According to the tapered slug schematic, polymer is initially injected with a maximum
concentration remaining constant for a certain period and then is gradually reduced with time
to a minimum value. The parameter 𝒕𝒔 defines the slug length and equals the time when the
initial polymer concentration decreases to the half and also represents the effective injection
time in the case of constant injection rate (area of constant injection rate equals the area under
tapering rate, Figure 5) . At an earlier time T, concentration starts reducing linearly, therefore
tapering time is defined by 2T. The dimensionless parameter a=T/𝒕𝒔 depends upon the slope
of concentration reduction and varies from 0 to 1 indicating the degree of tapering.
AlSofi A.M. and Blunt M.J. (2011) used a parallel design algorithm with a streamline-based
simulator that detects non-Newtonian rheology and controls numerical dispersion to optimise
polymer flood with respect to NPV by determining the most profitable scenario of slug size,
polymer concentration and initiation. Their results demonstrate that the optimal conditions are
a generally high concentration, a close to be continuous slug size and start of polymer flood
quite early in field life.
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1.1.4.2. Adsorption
During transport through porous media, polymer molecules may be bound to the solid surface
by physical adsorption. This interaction between polymer particles and solid surface varies
with polymer type, molecular weight, composition of rock, brine hardness and salinity, the
flow rate and temperature. This phenomenon can cause polymer loss from the slug and reduced
mobility control with a delay of polymer rate and of the oil propagation subsequently (Lake,
2010).
The above effect of polymer adsorption can be analytically described by the Langmuir-type
isotherm as stated below (Sheng, 2013):
𝑪𝒑 = 𝒂𝒑𝑪𝒑
𝟏+ 𝒃𝒑𝑪𝒑 (1.5)
where 𝑪𝒑 is the polymer concentration equilibrium in the rock-polymer system and 𝒂𝒑, 𝒃𝒑
empirical constants.
1.1.4.3. Salinity
Water existing in an oil field is usually brine water with a specific ion concentration and
therefore polymer interactions with salinity defined as total dissolved solids (TDS) and aqueous
phase’s hardness depending on divalent cation content are very important.
The commonly used HPAM has been partially hydrolysed resulting in anionic carboxyl groups
(–COO-) across the polymer backbone (Figure 1). At low salinity, these negative charges are
causing repulsion and stretch of the polymer chain and hence viscosity is increased. If salinity
is high, these repulsion forces are decreased by ionic shielding and therefore the stretch and
viscosity are both reduced (Sheng, 2013).
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1.1.5. Polymer Flooding Practices
Polymer flooding has already been tested in various fields to increase the oil recovery providing
an ultimate recovery expectation of 50% and an incremental oil recovery of 10-15% over water
flooding practice. One such polymer flooding practice was performed in China for the Daqing
field in 1996 after 36 years of research. By 2007, the total production attributed to polymer
flooding reached a 22.3% percentage with a potential ultimate recovery of more than 50%
OOIP with 10-10% OOIP more than water flooding (Dong, 2008).
Other case studies involve the polymer flooding feasibility in the southeast Henan oil field
located in China, where Tielong et al. (1998) conducted a pilot test achieving incremental oil
recovery of 9.8%. Littman et al. (1991) presented also a case of polymer injection in a 200,000
ppm salinity reservoir resulting in oil recovery 8% OOIP over waterflood.
1.1.6. Additional Technologies
Polymer flooding additional technologies have been implemented to help operators during
workout. During mixing and injection chemical stability may be preserved by using good
quality of water, a protective package (chelating agent), stainless steel pipeline and non-metal
tanks. Mechanical stability is maintained by low pipe flow rates, and devices like mixers,
valves, pumps and filters operating in low shear rate to prevent polymer degradation.
Biological degradation can be prevented by using a protective package (bactericide) like
formaldehyde.
Water treatment is also a concern since polymer existing in produced water increases the
viscosity and worsens the oil – water separation and moreover the untreated water affects the
environment. The process of water treatment in this case involves natural settling by gravity,
flocculation and pressure boosting pump. After this treatment the produced water can be
reinjected in the new well patterns (Dong, 2008).
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1.2. GENETIC ALGORITHMS
1.2.1. General
Genetic Algorithms were initially proposed by Holland (1975) based on the Darwinian theory
of biological evolution drawing on concepts from natural selection and genetics to produce a
range of solutions for complex functions.
Genetic Algorithms are codifying in binary code each potential solution of a complex problem
on a parent chromosome who represents an individual composed by genes. After inserting the
data of the problem, genetic algorithms start to generate an initial random population aiming
in high diversity among them. Then the process in finding the most optimal solution based on
each parent chromosome fitness value begins according to evolutionary procedure that occurs
in cycles. Each of these cycles is termed as generation and includes the stages of evaluation,
selection, crossover and mutation.
During evaluation stage, each individual is assessed based on a fitness value and the most
optimal individuals compared to the other individuals in the population become “parents” for
the next generation. The most fitted of the individuals have better chance to be selected. At the
next stage, the reproduction can be implemented by two mechanisms: crossover and mutation.
The crossover combines genes from two different individuals to produce new offspring as a
mix of genes while mutation reproduces a new individual by substituting a randomly selected
gene with a new generated one. With these procedures genetic diversity among the population
is increased drastically.
The new population generation is checked for another time in terms of fitness value and this
procedure is performed until an optimal solution is achieved or the algorithm reaches the
generation limit (Emerick, 2009).
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1.2.2. Application in oil industry
New computational techniques are already been used in oil industry to contribute to the
reservoir characterisation process by analysing the complex and great amount of data and
generate more realistic models.
Genetic Algorithm is a stochastic approach optimisation method which can be applied to multi-
objectives and handle conflicts among them. Consequently, it is a robust technique providing
a range of solutions, highly efficient and easy to use.
Practical applications of Genetic Algorithms in oil industry involve the reservoir
characterisation by analysing well logs, seismic data, conducting history matching of
production data, modelling of fluid flow in porous media and analysing of production-injection
operation systems (Velez-Langs, 2005).
One important use of Genetic Algorithms that is researched also in this project is the
optimisation of well placement. Morales et al. (2010) used Genetic Algorithms to optimise well
placement in the Qatar’s North gas condensate Field and find the possible local cumulative
production optimal positions. They resulted in an efficient horizontal well placement giving a
considerable gas and condensate production increase.
Hou et al. simulated polymer flooding performance in Taking Shengli oilfield with Genetic
Algorithms resulting in good match between model quantitative characterization and actual
data.
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2. POLYMER FLOODING OPTIMISATION WORKFLOW
In the present project a polymer flooding optimisation through well placement and polymer
solution design is carried out to obtain a better degree of recovery in an economical efficient
way. The software that is used for optimisation is OptiRes Version 4.0.00 an in-house software
of Heriot-Watt University (OptiRes Manual, 2016) working in conjunction with Eclipse to
demonstrate the outputs. The optimisation is applied in a real tight turbidite sand system named
Field-B. In the next sections a better understanding of the field can be obtained and decisions
should be made to succeed optimum recovery.
2.1. Dynamic model of Field-B
The present model is a dipping layered system with an erosional surface with grid cell size of
164 x 164 x 20 ft discretised into 30 x 22 x 91 grid blocks. The reservoir has a NTG value of
0.35 and constant porosity of 0.32. The permeability varies from 10.59 to 896.30 mD indicating
a highly heterogeneous system. From PVT data at surface conditions oil density is 52 lb/ft3, oil
viscosity is 20.051 cP, water viscosity is 0.65 cP, Rs is 0.032 scf/bbl and Bo is 1.04 rb/bbl.