formulation of general relative permeability …

FORM ULATION OF G EN ERA L RELA T IV E P ER M EA B IL IT Y CORRELATION

OF FIELD A

A BD U L HAKIM BIN BASRI

Laporan ini dikemukakan sebagai memenuhi

sebahagian daripada syarat penganugerahan

[jazah Sarjana Kejuruteraan Petroleum

Sekolah Kejuruteraan Kimia dan Kejuruteraan Tenaga

Universiti Teknologi Malaysia

MEI 2019

v

“My dearest late father, mom, wife, family, Assoc. ProfZaidi andfriends”

This is for all of you

ix

ACKNOWLEDGEMENT

First and foremost, I have to thank my supervisor, Assoc. Prof Zaidi. Without

his assistance and dedicated involvement in every step throughout the process, this

thesis would have never been accomplished. I would like to thank you very much for

your support and understanding over this past one year.

Getting through my dissertation required more than academic support, and I

have many, many people to thank for listening to and, at times, having to tolerate me

over the process. Most importantly, none of this could have happened without my

family. My wife who always been very supportive. Every time I was ready to quit, you

did not let me and I am forever grateful. This dissertation stands as a testament to your

unconditional love and encouragement.

xi

ABSTRAK

Data kebolehtelapan relatif amat penting untuk hampir semua pengiraan

pengaliran bendalir dalam takungan dan digunakan secara meluas dalam banyak

bidang kejuruteraan petroleum. Pengukuran kebolehtelapan relatif dilakukan pada

sampel teras di makmal dan kedua-duanya memakan masa dan mahal untuk

dihasilkan. Hasil daripada kesukaran dan kos yang terlibat dalam mengukur nilai

kebolehtelapan relatif, kolerasi dan pengiraan empirik sering digunakan untuk

menganggarkan nilai-nilai tersebut. Dalam bidang kajian yang merupakan Lapangan

Minyak A, hanya terdapat satu data SCAL yang boleh didapati daripada satu takungan.

Oleh itu, terdapat keperluan untuk merumuskan kolerasi am untuk digunakan dalam

lapangan minyak yang dikaji atau lapangan minyak yang lain di lembangan melayu

tanpa data SCAL. Penubuhan kolerasi tersebut telah menjadi matlamat utama

penyelidikan ini. Tiga kolerasi yang diterbitkan telah dipilih untuk dianalisa dan

dibandingkan untuk menentukan kolerasi yang paling sesuai untuk lapangan minyak

yang dikaji. Penyelidikan bermula dengan pengumpulan data yang meliputi

pemeriksaan kualiti data dan penapisan data. Analisi terperinci mengenai data dana

rumusan kolerasi dijalankan. Tiga (3) kolerasi iaitu Corey, Chierici dan LET telah

dibandingkan dan dianalisa. Dari semua kolerasi, kolerasi Corey dan Chierici tidak

cukup fleksibel untuk menyelaraskan keseluruhan set pemerhatian eksperimen.

Kolerasi LET mempamerkan fleksibiIiti untuk menyelaraskan seluruh set data

eksperimen dengan memuaskan. Tingkah laku s dimodelkan dengan baik

menggunakan kolerasi LET. Kolerasi ini telah dipilih dan diuji dalam model dinamik

untuk menguji kesahihannya. Keputusan menunjukkan bahawa pemadanan kadar

minyak dan air boleh diterima. Oleh itu, kolerasi ini telah diterima dan telah digunakan

untuk menghasilkan lengkung kebolehtelapan relatif untuk takungan minyak lain di

Lapangan Minyak A.

xii

ABSTRACT

Relative permeability data are essential for almost all fluid flow calculations in

reservoirs and are utilized extensively in many areas of petroleum engineering.

Relative permeability measurements are conducted on core samples in laboratory and

are both time-consuming and expensive to produce. As a result of the difficulties and

cost involved in measuring relative permeability values, empirical correlations and

calculations are often employed in order to estimate the values. In the field of study

which is Field A, there is only one SCAL data available from a reservoir. Hence there

is a need to formulate a general correlation to be used in the field of study or other

fields in Malay basin with no or limited SCAL data. The establishment of such

correlation will be the main objective of this research. The available SCAL data were

manipulated and analyzed to create a suitable correlation to be used for other

reservoirs. Three published correlations were chosen to be analyzed and compared to

determine the most suitable correlations for the field under study. The research started

with data collection which includes data quality checking and screening. Six (6) core

samples for kro-krw and six (6) core samples for krg-kro was were used in this

research. Then detailed analysis of the data and correlation formulation was conducted.

Three (3) correlations which are Corey, Chierici and LET were compared and

analyzed. From all the correlations, Corey and Chierici correlations are not flexible

enough to reconcile the entire set of experimental observations. LET correlation

exhibits flexibility to satisfactorily reconcile the entire set of experimental data. The s-

behaviour is well modeled by LET correlation. This correlation was chosen and tested

in the dynamic model to test its validity. Results showed that acceptable matching of

oil rate and water cut were obtained. Hence the correlations were accepted and will be

used to generate pseudo-relative permeability curves for other hydrocarbon reservoirs

in Field A.

xiii

CONTENT

DECLARATION ii

DEDICATION iii

ACKNOWLEDGEMENT xi

ABSTRAK xii

ABSTRACT xiii

CONTENT xiv

LIST OF TABLES xvii

LIST OF FIGURES xix

ABBREVIATIONS xxii

LIST OF SYMBOLS xxiii

1 INTRODUCTION 1

1.1 Background 1

1.2 Problem Statement 4

1.3 Objectives 5

1.4 Scope of Study 6

1.5 Significance of Study 7

2 LITERATURE REVIEW 9

2.1 Concept of Relative Permeability 9

2.1.1 Relative Permeability 10

2.1.2 Factors affecting relative permeability 11

2.1.2.1 Wettability effect on relative

permeability 11

CHAPTER TITLE PAGE

xiv

2.1.2.2 Effect of fluid saturation and

saturation history 12

2.1.2.3 Effect of viscous and capillary

forces 12

2.2 Two-phase relative permeability 14

2.2.1 Relative Permeability parameters 15

2.2.1.1 EndPoints 15

2.2.1.2 Shape Factor 16

2.3 Estimating two-phase relative permeability 17

2.3.1 Lab Procedures 17

2.3.1.1 Centrifuge method 17

2.3.1.2 Two-phase steady state method 18

2.3.1.3 Two-phase unsteady state method

19

2.3.2 Correlations 20

2.3.2.1 Corey correlation 21

2.3.2.2 Chierici correlation 23

2.3.2.3 LET correlation 24

2.4 Correlation Comparison 25

2.5 Software used for research 28

2.5.1 EC LIPSE 100 Reservoir Simulator 28

2.5.2 Petrel 2017 28

3 METHODOLOGY 31

3.1 Introduction 31

3.2 Data Collection 33

3.2.1 Data Source 33

3.2.2 Data Quality Checking 33

3.2.2.1 Data Screening 33

3.2.2.2 Relative Permeability Adjustment

33

3.2.2.3 End Points 34

3.3 Detailed Analysis and Correlation Formulation 34

3.3.1 End Points 34

xv

3.3.2 Shape Factor 37

3.3.2.1 Corey 37

3.3.2.2 Chierici 38

3.3.2.3 LET 39

3.4 Case Studies 40

3.5 Workflow Generation 41

4 RESULTS AND DISCUSSION 43

4.1 Data Collection 43

4.1.1 Data Source 43

4.1.1.1 Porosity and Permeability 45

4.1.1.2 Water-OiI Relative Permeability 51

4.1.1.3 Gas-OiI Relative Permeability 58

4.1.1.4 Capillary Pressure, Pc 64

4.1.2 Data Quality Checking 65

4.1.2.1 Data Screening 66

4.2 Detailed Analysis and Correlation Formulation 68

4.2.1 End Points 68

4.2.2 Shape Factor 81

4.2.2.1 Corey 81

4.2.2.2 Chierici 87

4.2.2.3 LET 90

4.2.2.4 Correlations Comparison 93

4.3 Case Studies 95

4.4 Workflow Generation 101

4.4.1 Workflow Example 104

5 CONCLUSION 109

5.1 Conclusion 109

5.2 Recommendation 110

REFERENCES 111

xv i

LIST OF TABLES

TABLE NO. TITLE PAGE

Table 2-1: Oil Water Corey Exponent with Wettability (McPhee, Reed, &

Zubizarreta, 2015) 22

Table 2-2: Another Oil Water Corey Exponent versus Wettability (Stiles, 2013) 23

Table 4-1: Porosity and Permeability for Plug samples used in Special Core Analysis

46

Table 4-2: Sample No. 21A kro-krw 52






Table 4-8: Sample No. 21D kro-krg 59





Table 4-15: Capillary Pressure, Pc Data 64

Table 4-13: Table of end points for the water-oil samples 66

Table 4-14: Table of end points for the gas-oil samples 67

Table 4-16: End-Points Correlations Summary 81

Table 4-17: Sample 25A Normalized Relative Permeability 82




xvii

Table 4-21 Corey Relative Permeability Table 86

Table 4-22 Chierici Relative Permeability Table 89

Table 4-23 LET Relative Permeability Table 92

Table 4-24 RQI Range Selected 96

Table 4-25 End Point Values for each RQI Ranges 96

Table 4-26 Relative Permeability Table (1) 104




xviii

LIST OF FIGURES

Figure 1-1: Example of Oil-Water Relative Permeability Curve 2

Figure 1-2: Illustration of two-phase reservoir system 3

Figure 2-1: Two-phase relative permeability curves (Ahmed, 2006) 14

Figure 2-2: Schematic of steady state displacement experiment for water-oil system

19

Figure 2-3: Schematic of unsteady state displacement experiment for water-oil

system 20

Figure 2-4: History match of differential pressure (Lomeland et a I., 2005) 25

Figure 2-5: History match of production (Lomeland et al., 2005) 26

Figure 2-6: Relative permeability curve (Lomeland et al., 2005) 26

Figure 3-2: Relative Permeability curve endpoints for Oil-Water System 36

Figure 3-3: Relative Permeability curve endpoints for Oil-Gas System 36

Figure 4-1: Sampling point in the open hole logs 44

Figure 4-2: Sampling point in the core slab 44

Figure 4-3: Poro Perm Plot by Facies 50

Figure 4-4: Sample No. 21A kro-krw 52






Figure 4-10: Sample No. 21D kro-krg 59



FIGURE NO. TITLE PAGE

xix



Figure 4-17: Pc vs Sw Plot 65

Figure 4-15: kro-krw Comparison Plot 66

Figure 4-16: kro-krg Comparison Plot 67

Figure 4-18: Swi vs Porosity 68

Figure 4-19: Swi vs Permeability 69

Figure 4-20: Swi vs RQI 69

Figure 4-21: Sorw vs Porosity 70

Figure 4-22: Sorw vs Permeability 70

Figure 4-23: Sorw vs Rock Quality Index 71

Figure 4-24: Sorg vs Porosity 72

Figure 4-25: Sorg vs Permeability 72

Figure 4-26: Sorg vs Rock Quality Index 73

Figure 4-27: krorwvs Porosity 74

Figure 4-28: krorwvs Permeability 74

Figure 4-29: krorw vs Rock Quality Index 75

Figure 4-30: krorw vs Porosity 75

Figure 4-31: krorw vs Permeability 76

Figure 4-32: krorw vs Rock Quality Index 76

Figure 4-33: krwr vs Porosity 77

Figure 4-34: krwr vs Permeability 78

Figure 4-35: krwr vs Rock Quality Index 78

Figure 4-36: krgr vs Porosity 79

Figure 4-37: krgr vs Permeability 79

Figure 4-38: krgr vs Rock Quality Index 80

Figure 4-39: O-W Relative Permeability Plot for all samples 85

Figure 4-40: Corey Normalized O-W Relative Permeability Plot 85

Figure 4-41: Corey Normalized (semilog) O-W Relative Permeability Plot 86

Figure 4-42: Chierici Normalized O-W Relative Permeability Plot 88

Figure 4-43: Chierici Normalized (semilog) O-W Relative Permeability 89

Figure 4-44: LET Normalized O-W Relative Permeability Plot 91

Figure 4-45: LET Normalized (semilog) O-W Relative Permeability 92

xx

Figure 4-46: Correlation comparison - Normalized O-W Relative Permeability Plot

94

Figure 4-47: Correlation comparsion- Normalized (semilog) O-W Relative

Permeability 95

Figure 4-48: Relative Permeability Plot for each RQI Ranges 97

Figure 4-49: A01, A02 and A03 Swi Matching 97

Figure 4-50: A04 and A05 Swi Matching 98

Figure 4-51: Well A-01 History Matching 99





Figure 4-56: Relative Permeability workflow 103

Figure 4-57: kro-krw Plot 108

xx i

ABBREVIATIONS

SCAL

RCA

RQI

Special Core Analysis

Routine Core Analysis

Rock quality index

xxii

LIST OF SYMBOLS

k - Permeability

kro - Relative permeability of oil

krw - Relative permeability of water

krg - Relative permeability of gas

Swi - Irreducible water saturation

Sgc - Critical gas saturation

Sorw - Residual oil saturation

Sorg - Residual oil saturation to gas

Q - Fluid flowrate

A - Cross-sectional area

dp/dl - Pressure gradient

\i - Viscosity

cp - Centipoise

Nc - Capillary number

g - Interfacial tension

9 - Rock porosity in fraction

Swn - Normalized water saturation

kair - Permeability to air

krin - Normalized relative permeability

kro-krw - Oil-water relative permeability

krg-kro - Gas-oiI relative permeability

xxiii

CHAPTER 1

INTRODUCTION

1.1 Background

Permeability is a property of the porous medium that measures the capacity and

ability of the formation to transmit fluids (Ahmed, 2001). The rock absolute

permeability, often given the symbol k is a very important rock property because it

controls the directional movement and the flow rate of the reservoir fluids in the

formation. If it takes a lot of pressure to squeeze fluid through a rock, that rock has

low permeability. If fluid passes through the rock easily, it has high permeability.

Relative permeability, a dimensionless quantity, is the ratio of effective

permeability to absolute permeability. Relative permeability is a crucial empirical

parameter in describing the flow of multiple immiscible fluids within a porous medium

(Honarpour and Mahmood, 1988).

E f f e c t i v e Permeabil ity, k o / k w / k gRelative P e r m e a b i l i t y , k r o / k r w / k r g = ------------------------ -— ---------------------------------------------— -------------- ----------------------

Absolute Permeability, k

1

The relative permeability to one phase changes with the relative saturation of

that phase. It is equal to one at 100% saturation of the phase and gradually decreases

to reach zero at the critical or irreducible saturation of that phase. Figure 1.1 shows the

general oil water relative permeability curve.

Figure 1-1: Example of Oil-Water Relative Permeability Curve

In hydrocarbon reservoirs, no one phase can reach the saturation of 100%.

Consequently, in a multiphase system, the relative permeability of any phase cannot

reach the value of one. However, most core analysis laboratories evaluate the relative

permeability as referenced to the maximum effective permeability of the oil phase

rather than referencing to the porous medium's absolute permeability. This leads to

reporting the value of one for the maximum relative permeability to the oil phase. In

any reservoir study, this should be noticed and all relative permeability values should

be adjusted before further proceeding. In two-phase system, the fluids consists of oil

and water, oil and gas or gas and water, while in three-phase system, the fluids consists

of oil, water and gas. An example of an oil-water system is shown in Figure 1-2.

2

Connate/Irreducible Water Siw

Pore Volume — < Residual Oil Sorw

Mobile Oil

Grain Volume^=i

Figure 1-2: Illustration of two-phase reservoir system

Relative permeability data are essential for almost all fluid flow calculations in

reservoirs and is utilized extensively in many areas of petroleum engineering such as

determining the residual fluid saturations, calculating the fractional flow and frontal

advance and making engineering estimates of productivity, injectivity and ultimate

recovery. The data are more particularly used for matching, predicting and optimizing

oil and gas reservoir performances through numerical simulations.

Relative permeability measurements are conducted on core samples in

laboratory and are both time-consuming and expensive to produce. Consequently,

relative permeability measurements are mainly requested for projects where secondary

and/or tertiary recovery is being considered. As a result of the difficulties and cost

involved in measuring relative permeability values, empirical correlations and

calculations are often employed in order to estimate the values. In the past decades,

several correlations have been developed to predict relative permeability of oil

reservoirs. In 1954, Corey introduced a correlation to estimate relative permeability of

water-oil and gas-oil systems, based on relative permeability measurements on a large

number of cores from several formations. Honarpour, Koederitz and Harvey (2000)

utilized the relative permeability data obtained from oil and gas fields in various parts

of the world, to develop a new correlation for prediction of relative permeabilities.

Chierici (1984) suggested a two-parameter exponential relationship to predict relative

permeabilites of water-oil and gas-oil systems. In the current study, these three

3

correlations are used and compared. Fine tuning of the correlation might be done to fit

the field of study.

Analysis done by Cocco (2002) concluded that each depositional environment

has its distinct relative permeability correlations. There are differences in the average

values and variances, as well as in the strength of the correlations between the variable.

Hence it is necessary to sample core plugs in the reservoir under study. Relative

permeability also depends on a combined effect of pore geometry, fluid distribution,

wettability, and fluid saturation (Okasha, Funk and Balobaid, 2001). Hence relative

permeability is unique to the field or regions. This study was conducted to formulate

the most suitable correlations for the field of study.

1.2 Problem Statement

Relative permeability is one of the most essential parameters in reservoir

engineering studies. In reservoir simulation, relative permeability is the parameter

used by reservoir simulators to define the relative movements of different reservoir

fluids. The concept of relative permeability is quite simple. However, proper

evaluation is not an easy task. Relative permeability is evaluated in laboratory as part

of the SCAL (Special Core Analysis) program. Both steady and unsteady state

displacement are used to evaluate relative permeability at different saturation values.

These measurements are being carried out on small core plugs obtained from the

available whole cores. In addition to lab work uncertainties, core coverage is an

important factor that affects the reliability of the evaluated relative permeability. Due

to operation concerns, it is very difficult to have adequate core coverage for any

reservoir. Strict precautions and high costs make it even more difficult to obtain

adequate coverage of SCAL. These factors raise the importance of careful and

effective handling of the available SCAL data to obtain reasonably representative

relative permeability data for any reservoir study.

Since obtaining relative permeability data from laboratory experiments is

rather delicate, time consuming, and costly, a series of empirical models has been

4

developed in literature to estimate them when experimental data from core samples is

not available. The empirical correlations are also employed to reproduce

experimentally determined relative permeability curves as verification. These methods

were based on experimental data and mathematical derivations or heuristic concepts

to predict relative permeability.

In the field of study, there is only one SCAL data available from a reservoir.

Hence there is a need to formulate a general correlation for other reservoirs in the field.

The available SCAL data can be manipulated and analysed to create a suitable

correlations to be used for other reservoirs. Since relative permeability is such a strong

controlling factor in determining reservoir performance, accurate determination of

water-oil and gas-oil relative permeability character for a formation matrix is essential

for accurate prediction and optimization purposes. Although a variety of correlations

to predict relative permeability are available, considerable variance can be present in

the predicted results, and experimental measurements still provide the most accurate

method of determination. Three published correlations were chosen to be analysed and

compared to determine the most suitable correlations for the field of study. Fine tuning

of the correlations might be done if none of the correlations satisfy the criteria. There

is also no general workflow of formulating the relative permeability correlation

available. Hence a general workflow will be generated in the study for the use of other

users.

1.3 Objectives

The main objectives of this study are:

i) To develop a general relative permeability correlation to be used in the

field of study or other fields in Malay Basin with no or limited SCAL

data.

ii) To establish a workflow in order to guide users on proper way of

formulating relative permeability correlations.

5

iii) To perform a case study whereby the correlation formulated is applied

in a specific field.

1.4 Scope of Study

i) Data collection and quality checking

a. Six (6) core samples for kro-krw (labelled as

21 A/2 5 A/3 5 A/4 3 A/4 7 A/51 A).

b. Six (6) core samples for krg-kro (labelled as

21 D/2 5 D/3 5 D/4 3 D/51 D).

ii) Detailed analysis and correlation formulation

a. Finding a trend using few properties to find endpoints general

formula to be used in the correlation.

b. Three correlations were generated and analysed based on the

published papers.

c. Fine tuning the generated correlations to fit the field of study.

iii) Correlation workflow generation

a. Detail workflow was generated for formulating general relative

permeability correlation.

iv) Field application

a. Formulated correlation was applied and tested in a reservoir in the

field of study to prove concept.

6

1.5 Significance of Study

i) Relative permeability is essential for dynamic simulation to forecast the

reservoir performance more effectively.

ii) The formulated relative permeability correlation can be used in other

reservoirs in the field having limited or no SCAL data.

iii) The generated workflow can be used as a guide for other users in

formulating the correlations in other regions.

7

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