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

ii

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

1. INTRODUCTION .............................................................................................................. 2

1.1. POLYMER FLOODING RECOVERY MECHANISM ................................................ 2

1.1.1. Polymer injection technique ........................................................................................ 2

1.1.2. Polymer flooding displacement process ...................................................................... 2

1.1.3. Polymer Flooding Design............................................................................................ 5

1.1.4. Polymer Flooding Control Parameters ........................................................................ 6

1.1.4.1. Concentration Rate .................................................................................................. 6

1.1.4.2. Adsorption ............................................................................................................... 8

1.1.4.3. Salinity ..................................................................................................................... 8

1.1.5. Polymer Flooding Practices ........................................................................................ 9

1.1.6. Additional Technologies ............................................................................................. 9

1.2. GENETIC ALGORITHMS .......................................................................................... 10

1.2.1. General ...................................................................................................................... 10

1.2.2. Application in oil industry......................................................................................... 11

2. POLYMER FLOODING OPTIMISATION WORKFLOW ............................................ 12

2.1. Dynamic model of Field-B ........................................................................................... 12

2.2. Main Issues in B-Field .................................................................................................. 13

2.3. Genetic Algorithm Workflow ....................................................................................... 13

2.4. Base Cases based on Global Population and Modified Population .............................. 16

2.4.1. Waterflood performance (Cases 1,2) ........................................................................ 16

2.4.2. Polymer injection evaluation (Cases 3,4,5,6,7, 8) ..................................................... 17

2.5. Economic evaluation based on NPV ............................................................................. 18

2.6. Sensitivity study for adsorption .................................................................................... 19

3. RESULTS & DISCUSSION ............................................................................................ 20

3.1. Waterflood performance results .................................................................................... 20

3.2. Polymer injection evaluation results ............................................................................. 24

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3.3. Economic evaluation results ......................................................................................... 32

3.4. Adsorption Sensitivity Results ...................................................................................... 35

4. CONCLUSION & SUGGESTIONS FOR FURTHER STUDY ...................................... 36

5. REFERENCES ................................................................................................................. 37

vi

LIST OF ABBREVIATIONS

BHP Bottom Hole Pressure

CAPEX Capital Expenditure

EOR Enhanced Oil Recovery

FOPT Field Oil Production Total

FVDG Field Voidage

GA Genetic Algorithms

GRPD Gas Reinject to Producer

HPAM Hydrolysed Polyacrylamide

LRAT Liquid Rate

NPV Net Present Value

NTG Net to Gross

OOIP Original Oil In Place

ORAT Oil Rate

PVT Pressure – Volume – Temperature

TDS Total Dissolved Solids

vii

LIST OF FIGURES

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

viii

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

1

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

3

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)

4

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.

5

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.

6

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

7

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).

9

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.

13

Figure 6. Field-B Permeability Distribution, Erosional surface and Oil Saturation profile

2.2. Main Issues in B-Field

One of the key things that has to be handled in B-Field is the interconnectivity throughout the

reservoir due to the existence of flow barriers and low permeable channels contributing to low

vertical flow. During injection, the mobile water is moving through the more permeable

channels due to viscous forces leading to viscous fingering effect with poor sweep efficiency.

This problem should be treated by proper well placement of the producers and injectors by

ensuring that oil is moving upwards during water injection and avoiding early water

breakthrough. Polymer injection is going to reduce the mobility of water resulting in better

sweep efficiency. Care should be taken though not to place the wells too far apart due to

pressure limits. At the next stage a proper polymer design should be selected by altering

parameters such as polymer initial and final concentration, injection initiation and duration.

The final results will be evaluated based on ultimate recovery and net present value.

2.3. Genetic Algorithm Workflow

Optimisation procedure with Genetic Algorithms is based on evolution theory and transfer of

genetic material from parents to children so that offspring survival is maximised as depicted

below:

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Figure 7. Genetic Algorithm Process

The procedure of optimising begins with the initial input data of number of wells (one producer

and one injector in the present project) and well coordinates of heal (i1, j1, k1) and toe (i2, j2, k2)

with the appropriate well controls and well style in Straight-line-wells program so that the

trajectory and completion can be designed in a .DATA file evaluated by ECLIPSE.

The Straight-line-wells program completes the wells as straight lines and allows the variation

of different constraints in terms of controls and styles. The coordinates of well’s heal and toe

are representing by the (i, j, k) values. The fluid option can be oil, water or gas. The controls

settings include BHP, LRAT, ORAT, FVDG or GRPD. The BHP mode determines the

downhole pressure limits for each well. The well’s style defines the nature of the well. In this

project XYZ style represents a horizontal or high angle well with six degrees of freedom for

the i, j, k components. Well angles and costs can also be evaluated from the program. A view

of the Straight-line-wells program is shown below (OptiRes Manual, 2016).

15

Figure 8. Straight-line-wells program interface

The genetic algorithm uses these well pairs to produce an initial random population which is

essential to establish diversity among them. Then each of the individuals is executed by

interpreting the location and completion based on an objective function (ultimate recovery,

NPV) and the favourable are considered as parent chromosomes for the next generation. The

algorithm reproduces the next generation of individuals through random mating, selection,

crossover and mutation. The new generation is evaluated for another time in terms of objective

function and this procedure continues to an acceptable value or the algorithm reaches its

generation limit.

The dominant controlling parameters in Genetic Algorithm are the sample size for the first

iteration (ni), maximum number of iterations (it), number of parents (nr), number of children

per iteration (ns) and number of models calculated according to the following equation:

no. models = ni + (it · ns) (2.1)

Polymer optimisation is based on well placement optimisation as the initial step and polymer

slug design as the next stage. For well placement there are 12 degrees of freedom controlled

by the spatial selection of wells’ heal (i1, j1, k1) and toe (i2, j2, k2) in the whole grid space or in

16

specific areas due to restrictions based on geological analysis of the model. Subsequently,

polymer slug parameters design is conducted incorporating four additional degrees of freedom.

These parameters include polymer initiation time (T1), polymer injection duration (T2), initial

polymer concentration (C1) and final concentration (C2).

2.4. Base Cases based on Global Population and Modified Population

Since the optimiser is ignorant of the problem that is solving, it proposes possible solutions at

random, unless certain restrictions are introduced. For the aim of this project, two methods of

population generation are considered by altering the well location freedom. The first option of

global population allows the optimiser to place the wells at the whole grid area with random

completions. At the next step the modified population model will set a limited area for each

well to be placed based on the ultimate recovery results.

2.4.1. Waterflood performance (Cases 1,2)

The first stage of this project is the injection of water simulation along the entire grid area using

the global population method. The well placement data settings of the initially submitted base

case model including the heal (i1, j1, k1) and toe (i2, j2, k2) for each well, the production and

injection rates controls, bottom hole pressure range and well styles are summarised below. In

this case the control settings include the LRAT (Liquid Rate for Producer) and RATE (Injected

Rate of Water for Injector) set at 10000 bbls/day and the Bottom Hole Pressure Limits set at

1000 psia minimum value for Producer and 5000 psia maximum value for Injector. The wells

are both horizontal (XYZ style). Case 1 includes the water injection along the whole grid area.

Table 1: Well Data Settings (Case 1)

Wells i1 j1 k1 i2 j2 k2 Fluid Control Value

(Bbl.)

BHP

(Psia)

Style

PROD1 9 19 1 9 19 70 OIL LRAT 10000 1000 XYZ

INJ1 19 9 1 19 9 70 WATER RATE 10000 5000 XYZ

17

At the subsequent stage, the population is modified in order to focus the optimiser in a limited

range of solutions, by restricting the well placement area according to the evaluation of the

most optimal models based on ultimate recovery of Case 1. The best model of Case 1 becomes

the base case now with well data settings and region boundaries presented in Table 2 below

followed by the evolution of generations settings of the two Cases (Table 3).

Table 2: Well data Settings and Well Placement Boundaries (Case 2)

Wells i1 j1 k1 i2 j2 k2

PROD1

[Boundaries]

4

[1-9]

22

[15-23]

69

[64-74]

10

[5-15]

14

[9-19]

12

[7-17]

INJ1

[Boundaries]

28

[15-30]

2

[1-6]

63

[57-67]

24

[19-29]

5

[1-10]

16

[11-21]

Table 3: Evolution of Generations Settings (Cases 1, 2)

Altered Parameters Case 1

Global Population

Case 2

Modified Population

Sample Size ni 32 32

Max no. Iterations It 20 25

No. Children/Iteration ns 16 16

No. Couples nr 8 8

No. Models 352 432

2.4.2. Polymer injection evaluation (Cases 3,4,5,6,7, 8)

After finding the optimal well placement design for water flooding, polymer injection is

conducted in the same bounded area to increase recovery. The polymer slug method is

depended of design parameters like polymer initial and final concentration, initiation and

duration of injection. Tapered and constant polymer injection rate are applied combined with

primary and secondary injection to find the optimal model based on ultimate recovery (Cases

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3, 4, 5, 6, 7). A polymer injection is also conducted in the whole grid area (Case 8) to estimate

the optimal model design.

In this project, primary initiation relates to polymer flooding beginning at the earliest stage of

field production, while secondary initiation refers to a later stage injection performance.

The altered parameters including evolution of generations and polymer slug design settings are

presented in the following table:

Table 4: Evolution of Generations and Polymer Slug Settings (Cases 3, 4, 5, 6, 7, 8)

Altered Parameters Case 3

Case 4

Case 5

Case 6 Case 7 Case 8

Sample Size ni 32 32 32 32 32 24

Max no. Iterations it 25 25 20 20 20 35

No. Children/Iter. ns 16 16 16 16 16 16

No. Couples nr 8 8 8 8 8 8

No. Models 432 432 352 352 352 584

Concentration

Schedule Tapered

Rate

Secondary

Constant

Rate

Secondary

Tapered

Rate

Primary

Tapered

Rate

Secondary

Constant

Rate

Secondary

Tapered

Rate

Secondary

Initiation (days) T1 0-100 0-100 0-1 0-100 0-100 0-100

Max. Duration (days) T2 0-500 0-500 0-500 0-500 0-500 0-500

Initial Concentration

(lb/stb) C1 0-1 0-0.8 0-2 0-2 0-1.5 0-2

Final Concentration

(lb/stb) C2 0-0.1 0-0.8 0-0.1 0-0.1 0-1.5 0-0.1

2.5. Economic evaluation based on NPV

The feasibility of polymer flooding besides the technical part is directly related to the costs of

the polymer, the additional polymer process facilities and the operating costs of the injectors.

Economic evaluation of the project can be conducted by the optimiser.

The NPV calculation using the optimiser is based on the below equation:

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NPV = ∑ ((𝟏 − 𝒕𝒂𝒙) · 𝟏

(𝟏+𝒅𝒊𝒔𝒄𝒐𝒖𝒏𝒕)𝒊 ∑ 𝑽𝒐𝒍𝒖𝒎𝒆(𝒑) · 𝑵𝒆𝒕𝑹𝒆𝒗𝒆𝒏𝒖𝒆 𝒑𝒆𝒓 𝒖𝒏𝒊𝒕(𝒑)𝒗𝒂𝒓𝒏𝒐𝒑=𝟏 ) −

𝒕𝒔𝒕𝒆𝒑𝒏𝒐𝒊=𝟏

𝑪𝑨𝑷𝑬𝑿 − 𝒅𝒓𝒊𝒍𝒍𝒊𝒏𝒈 (2.2)

𝑽𝒐𝒍𝒖𝒎𝒆(𝒑) = volume produced or injected over a year

𝑵𝒆𝒕𝑹𝒆𝒗𝒆𝒏𝒖𝒆 𝒑𝒆𝒓 𝒖𝒏𝒊𝒕(𝒑) = “cash in” for 𝑽𝒐𝒍𝒖𝒎𝒆(𝒑) (-ve for a cost)

𝒅𝒊𝒔𝒄𝒐𝒖𝒏𝒕 = fraction for one year (i.e. 0.1 or 0.08) and includes inflation

𝒕𝒂𝒙 = government tax

𝑪𝑨𝑷𝑬𝑿 & 𝒅𝒓𝒊𝒍𝒍𝒊𝒏𝒈 = fixed costs

2.6. Sensitivity study for adsorption

Sensitivities are conducted on the most optimal model based on adsorption. The polymer

settings for absorption are inputted in Eclipse to run sensitivities.

Eclipse uses the below Langmuir adsorption equation developed in 1916 by Irving Langmuir

to relate the molecules coverage or adsorption on a solid surface to gas pressure or

concentration of a medium above that surface at a standard temperature.

θ = 𝒂 ·𝑷

𝟏 + 𝒂·𝑷 (2.3)

θ = coverage percent of the surface

𝑷 = gas pressure or concentration in a solution

𝒂 = Langmuir adsorption constant

The polymer adsorption is treated as an instantaneous effect and is described in ECLIPSE by

the 3 keywords PLYADS, PLYROCK, PLYMAX and PLMIXPAR. PLYADS keyword

describes the polymer adsorption by the rock formation. With PLYROCK the rock properties

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are specified with dead pore space set at 0 value meaning that the total pore space can be filled

with the polymer slug. The residual resistance factor set at 1 value represents the decrease in

rock permeability to aqueous phase when polymer adsorption reaches the maximum. PLYMAX

keyword defines the polymer/salt concentrations for the mixing parameter calculation of the

fluid component viscosities. PLMIXPAR describes the Todd – Longstaff mixing parameter

which relates the segregation degree between the polymer slug and water and is set at 1 value

to indicate a completely mixed polymer solution (ECLIPSE 2014.1 Manual).

To conduct adsorption sensitivity in the Case 6 optimal model the saturated concentration of

injected polymer adsorbed by the rock varies from 0.0 lb/lb to 1 lb/lb.

3. RESULTS & DISCUSSION

3.1. Waterflood performance results

The below Figure 9 presents the distribution of the potential solutions during waterflood in the

whole grid area and in the more restricted area for Cases 1 and 2, as they are calculated by the

optimiser based on the ultimate recovery objection function. A convergence of Case 2 can be

observed to a value of 28.3 Mbbls with a recovery factor of 19.1 %. Compared to the base case

input with an FOPT of 21.3 Mbbls and 14.4 % recovery factor, an improvement in both values

is noticeable after algorithm optimisation.

21

Figure 9. Evolution of Generations vs FOPT for global (Case 1) and modified population (Case 2)

during water flooding

The boundaries of Case 2, were selected based on the converged wells coordinates’ values of

Case 1 and convergence of Case 2 wells coordinates was noticeable after the first 100 models.

The well locations convergence for Cases 1 and 2 are shown below in Figures 10 and 11,

respectively.

22

Figure 10. Well Coordinates Convergence for Case 1

23

Figure 11. Well Coordinates Convergence for Case 2

The optimal model of Case 2 is shown in Figure 12 as was obtained from Floviz 2015.1

Schlumberger Simulation Launcher. As described above, the reservoir is highly heterogeneous

with highly varying permeability across it. During water flooding, water as being denser than

oil has the tendency to slump down due to gravitational forces, while viscous forces move the

fluid faster in the more permeable paths. Capillary forces are ignored here. In this case,

viscosity is the main factor that contributes to fluid flow and mobility control by preventing

viscous fingering effect plays an important role to target a better sweep efficiency.

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Figure 12. Water flooding model in restricted area (Case 2)

3.2. Polymer injection evaluation results

The below table summarises the highest solutions of the different Cases 3, 4, 5, 6, 7 and 8 of

polymer flooding models produced by the Genetic Algorithm implementation.

Table 5: Polymer Flooding – Summary Results

Base Case

Case 3 Tapered-

Secondary

Case 4 Constant-

Secondary

Case 5 Tapered-

Primary

Case 6 Tapered-

Secondary

Case 7 Constant-

Secondary

Case 8 Tapered-

Secondary

FOPT (Mbbls) 21.30 28.24 28.30 28.75 28.70 28.80 28.65

Recovery

Factor (%) 14.4 19.1 19.1 19.4 19.4 19.5 19.4

Water Cut (%) 65.7 40.3 38.4 34.4 34.4 32.7 34.4

From the above table Case 5 represents the polymer slug design based on tapered-primary

injection schedule, resulting in 28.75 Mbbls FOPT and 19.4% recovery factor, Case 6 is based

on tapered-secondary injection program providing 28.70 Mbbls FOPT and 19.4% recovery,

while Case 7 uses constant-secondary method with a subsequent FOPT of 28.80 Mbbls and

19.5% recovery. In all of the cases a convergence is observable above 100 generations.

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Compared to Base Case model a 5% higher recovery can be observed for polymer flooding

Cases 5, 6, 7, and 8 but related to water flooding of Case 2 recovery is improved 0.3 %. A

better understanding of this result is discussed more detailed below in the model overview.

Cases 3 and 4 doesn’t vary compared to Case 2 due to low polymer injected concentration.

The above Cases 6 and 7 related to tapered and constant polymer injection rate are plotted in

the following figures which provide a better illustration of the dispersion of results that are

provided by the optimiser, where fit and poor resolutions are subjective to the evolution of

generations. Analytical results of all Cases are provided in the Appendix section.

Figure 13. Case 6 vs 7: Evolution of Generations vs Oil Recovery

26

Figure 14. Case 6: Optimal Initiation Time

Figure 15. Case 6: Optimal Duration Time

27

Figure 16. Case 6: Optimal Initial Concentration for Tapered Rate

Figure 17. Case 6: Optimal Final Concentration for Tapered Rate

28

Figure 18. Case 7: Optimal Initiation Time

Figure 19. Case 7: Optimal Duration Time

29

Figure 20. Case 7: Optimal Initial Concentration for Constant Rate

Figure 21. Case 7: Optimal Initial Concentration for Constant Rate

From the above figures, it can be observed that the tapered and constant rate polymer injection

provide almost the same oil recovery production with convergence. The polymer injection is

30

preferable to start as soon as possible at field’s production life in both cases, while duration

tends to be at high values. Concerning the polymer concentration for tapered rate of Case 6 is

optimum to inject at high initial concentration above 1 lb/stb and low final concentration below

0.05 lb/stb, while Case 7 promotes a concentration at around 1-1.5 lb/stb during the whole

injection period.

The model overview of Case 6 is shown below as was obtained from Floviz 2015.1.

Figure 22. Polymer flooding model in restricted area (Case 6)

The main purpose of polymer injection is to increase the injected water viscosity and thus

reducing the mobility ratio aiming in better sweep efficiency and minimising of viscous

fingering effect. Compared to water flooding in Figure 12 it is obvious that more area is swept

and the possibility of an additional producer to recover the swept oil in certain areas that the

already existed one cannot be obtain should be considered. This might be the case that the

recovery factor is not so high compared to water injection in the same area.

Another important factor in this case is that the wells’ control parameter change from rate to

bottom hole pressure and after 1500 days the producer rate is less than 10,000 stb/day as shown

in Figure 23. A sensitivity was conducted in this model of Case 6 to vary the rate parameters

of both injector and producer. The results are shown in the below table.

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Table 6. Injection Rate Sensitivities

Injection

Rate

(bbls/day)

6,000 7,000 8,000 9,000 10,000

FOPT

(Mbbls) 26.33 27.35 28.26 28.88 28.75

Production

Rate

(bbls/day)

9,000 10,000 11,000

FOPT

(Mbbls)

26.53 28.88 29.50

From the above table it is estimated that the most optimal injection rate is 9,000 bbls/day given

a FOPT of 28.88 Mbbls, while production rate is 11,000 bbls/day with a FOPT of 29,50 Mbbls.

The lower injection rate of 9,000 bbls/day compared to 10,000 bbls/day to reach better recovery

can be attributed to the fact that the high rate injected polymer solution flows out of the target

zones finding high permeable in other directions. Another important consideration during

polymer flooding is that the injected polymer solution finds resistance to flow of the low

permeable channels during displacement and becomes plugged there leading to oil trapped. In

general, lower injection rate contributes to a longer production period, while high rates

accelerate the shear degradation (break up of polymer chain) leading to poor displacement.

Injection rates should be monitored during the whole field production period.

Figure 23. Field Oil Recovery based on different injection rates

32

3.3. Economic evaluation results

The optimiser was set up to find the optimal solutions based on NPV objective fitness value.

The NPV was calculated for the polymer flooding Case 6. Convergence is obvious with the

optimal model peaking a NPV of 419 MMUSD as shown below. This high NPV value can be

attributed to low initial Capex since two wells are drilled and estimation is only for the first 9

years of production. The polymer facilities contribute to 2 more MMUSD of the initial Capex

considering the mixture and injection facilities, as well as an estimated polymer cost of 2

USD/lb.

Figure 24. NPV vs Evolution of Generations for Case 6

33

Figure 25. Case 6: Optimal Initiation Time Schedule based on NPV

Figure 26. Case 6: Optimal Duration Time Schedule based on NPV

34

Figure 27. Case 6: Optimal Initial Concentration based on NPV

Figure 28. Case 6: Optimal Final Concentration based on NPV

Based on NPV objective function the polymer injection should start as early as possible like

the FOPT based results, but this time the duration should be shorter at approximately 300 days.

35

The injected polymer initial concentration above 0.5 lb/stb provides a high NPV, while final

concentration should be at around 0.02-0.04 lb/stb. In general, the NPV objective function is

in accordance with FOPT except for the duration time schedule that should be shorter according

to NPV fitness value.

3.4. Adsorption Sensitivity Results

Adsorption sensitivity was conducted in Case 6 polymer flooding optimal model by varying

the adsorption factor from 0.00 lb/lb to 1.00 lb/lb. The results are shown below.

Figure 29. FOPT vs Adsorption factor

From the above diagram, it is observable that by increasing the adsorption factor, the oil

recovery decreases. As polymer flows through the porous media, a significant reduction in

polymer concentration is observed due to adsorption and plugging leading to permeability

reduction. This reduced adsorption is caused by inaccessible pore volume with brine passing

through small pores while polymer bypasses. Injection rate is also important in this case since

36

it influences the water permeability decrease caused by the polymer with higher injection rates

leading to less polymer particles adsorption.

4. CONCLUSION & SUGGESTIONS FOR FURTHER STUDY

The main objective of this study was to prove the feasibility of well placement and polymer

flooding optimisation by appropriate constraints of the well coordinates and polymer slug

design parameters. This has been successfully demonstrated by the OptiRes software using

Genetic Algorithms to create various models based on ultimate recovery objective function

which indicates the degree of sweep efficiency of Field-B. The Genetic Algorithm is able to

process a wide range of scenarios providing automatic results and free up valuable time of the

engineer to extract manually these scenarios.

The polymer flooding well placement and slug design that algorithm suggested increased the

oil recovery compared to the base case at about 5%, while compared to water flooding the

recovery increased by 0.3%. The optimal polymer slug design based on ultimate recovery

suggested that polymer injection is preferable to start as soon as possible in field production

life with a high duration while initial concentration is high and final concentration should be

low in tapered injection rate. The same response was given by the NPV fitness value except

for the duration time that in this case is more restricted.

Injection rate played an important role in this case with 9,000 bbls/day given a better recovery

due to improved sweep efficiency. Increase of adsorption factor decreased the oil recovery.

For further study, well placement should be consider the possibility of an additional producer

to recover the polymer injection swept oil that the existing one is not able to do. An appropriate

selected well-pattern that provides an optimal and economic efficient recovery. This should be

in consideration with both technical and economic feasibility.

37

Other factors that affect the injection of polymer should be also considered for further study.

Such factors may be the brine salinity with provided data about brine concentration as well as

the injected polymer solution viscosity as influenced by the polymer molecular weight, the

degree of HPAM hydrolysis and the temperature.

5. REFERENCES

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Uncertainty. SPE-145110-MS, Enhanced Oil Recovery Conference, 19-21 July, Kuala

Lumpur, Malaysia.

Behr, A., et al., 2013. Optimisation of Polymer Flooding with a Tapered Concentration Slug.

EAGE. 17th European Symposium on IOR (P10).

Buckley, S.E. & Leverett, M.C., 1942. Mechanism of Fluid Displacement in Sands. Trans

AIME, 146, pp. 107-116.

Dong, H. Z., et al., 2008. Review of Practical Experience & Management by Polymer Flooding

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ECLIPSE 2014.1 Manual. 2014: Schlumberger.

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Hou, J., et al., 2009. Integrating genetic algorithm and support vector machine for polymer

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Lake, L.W., 2010. Enhanced Oil Recovery. Society of Petroleum Engineers, pp. 128, 189, 314-

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Littmann, W., Kleinitz, W., Kleppe, G., Lund, T., 1991. A commercial scale xanthan polymer

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Morales, A., et al., 2010. A Modified Genetic Algorithm for Horizontal Well Placement

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Pope, G.A., 1980. The Application of Fractional Flow Theory to Enhanced Oil Recovery. SPE-

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Sheng, J.J., 2013. Enhanced Oil Recovery Field Case Studies. Elsevier Inc., pp. 63-64, 67-68

Tielong, C., et al., 1998. A pilot test of polymer flooding in an elevated-temperature reservoir.

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APPENDICES