development of an expert system for · pdf filereservoir fluid pvt properties correleations...

I

DEVELOPMENT OF AN EXPERT SYSTEM FOR

RESERVOIR FLUID PVT PROPERTIES

CORRELEATIONS

Presented By

Ahmed Moustafa Abd El-Rahman Al-Zahaby

B.Sc. in Petroleum Eng. Al-Azhar University (2007)

A Thesis Submitted to the Department of Mining, Petroleum, and

Metallurgical Engineering

Faculty of Engineering, Cairo University

In Partial Fulfillment of the Requirements for the Degree of

MASTER OF SCIENCE

IN

PETROLEUM ENGINEERING

FACULTY OF ENGINEERING, CAIRO UNIVERSITY

GIZA, EGYPT

2012

II



CORRELEATIONS

Presented By

Ahmed Moustafa Abd El-Rahman Al-Zahaby


A Thesis Submitted to the Department of Mining, petroleum, and




MASTER OF SCIENCE

IN


Under the Supervision of

Prof. Dr. Mohamed Helmy Sayyouh

Professor of Petroleum Engineering

Cairo University

Prof. Ahmed El-Banbi

Professor of Petroleum Engineering

Cairo University


GIZA, EGYPT

2012

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CORRELEATIONS Presented By

Ahmed Moustafa Abd-El Rahman Al-Zahaby


A Thesis Submitted to the Department of Mining, Petroleum, and




MASTER OF SCIENCE

IN


Approved by the

Examining Committee

…………………………………………

Prof. Dr. Mohamed Helmy Sayyouh

Faculty of Engineering, Cairo University, Thesis Main Advisor

…………………………………………

Prof. Dr. Ahmed El-Banbi

Faculty of Engineering, Cairo University, Thesis Main Advisor

…………………………………………

Prof. Dr. M. Khairy

Faculty of Engineering, Cairo University, Member

…………………………………………

Prof. Dr. Ismail Mahgoub

Faculty of Engineering, Cairo University, Member


GIZA, EGYPT

2012

IV

ABSTRACT



CORRELEATIONS

Accurate determination of the crude oil PVT properties is essential for solving many

reservoir engineering, production engineering, and surface production and operational

problems. A large number of PVT correlations for oil exist in the petroleum literature and

numerous studies are also present for with data favoring one correlation over the other. In

the absence of PVT data from laboratory experiments, it is often difficult to choose which

correlation to use to calculate different PVT properties. We approached this problem in

two ways. First, we developed an expert system that checks the input parameters (e.g.

reservoir parameters) against the valid ranges of input data for different correlations, and

then recommends which correlations to use for specific input parameters. Second, we

tested all available PVT correlations for black oil on a database of selected 35 Egyptian

crudes to develop guidelines on which correlations to use for each PVT property for the

specific range of input data. These specific crudes were selected to allow testing of those

guidelines on a wide range of reservoir input data for black oils. Our database included

oils with oAPI ranging from 17 to 51, gas-oil-ratios of 8 to 7,800 scf/STB, formation

volume factor at bubble point of 1.04 to 4.47 bbl/STB, bubble point pressures of 60 to

4739psia, and reservoir temperatures of 40 to 270 ◦F.

The present work included 14 bubble points, 6 solution-gas-oil ratio, 15 formation

volume factors, 13 oil compressibilities, 14 dead oil viscosities, 9 saturated oil viscosities,

10 under saturated oil viscosities ,12 under-saturated densities, 2 total formation volume

factors and 2 saturated density correlations. In addition to 6 dew point pressure

correlations and 8 gas compressibility factors.

V

Based on this study, guidelines for selecting an appropriate correlation for PVT

properties are introduced .These guidelines are recommended in programming of PVT

correlations regardless of their geographic origin.

VI

Dedication

To my dear mother, I am not able to thank you, because

whatever I did, you deserve more.

VII

ACKNOWLEDGEMENT

All praise to Allah, the Almighty, who gave me the confidence to carry out this work.

I wish to express my great gratitude to professor Dr. Mohamed Helmy Sayyouh and Prof.

Ahmed Hamdi El-Banbi, Mining Petroleum, and Metallurgical Department, Faculty of

Engineering, Cairo University for selecting the study subject, supervising the work, and

for valuable guidance during the preparation and for their continuous suggestions and

encouragement.

I am grateful to Dr Ismail Mahgoub who allowed me to use some industry resources and

useful materials.

Also my acknowledgments to all my friends and staff members who made my stay here

at Cairo and the British University in Egypt. Last but not the least; I am grateful to my

mother and my father for their understanding and affection throughout my life.

Acknowledgements are also extended to my professor Dr. Selim Zeidan of Faculty of

Engineering Al-Azhar University for his continuous support and careful review of the

manuscript.

VIII

CONTENTS Page

ABSTRACT ......................................................................................................................................................... IV

DEDICATION ..................................................................................................................................................... VI

ACKNOWLEDGEMENT .......................................................................................................................................... VII

CONTENTS .......................................................................................................................................................... VIII

LIST OF TABLES ..................................................................................................................................................... XI

LIST OF FIGURES .................................................................................................................................................. XIII

NOMENCLATURE .............................................................................................................................................. XIV

1.CHAPTER 1 .......................................................................................................................................................... 1

INTRODUCTION ..................................................................................................................................................... 1

2.CHAPTER 2 .......................................................................................................................................................... 4

LITERATURE REVIEW .............................................................................................................................................. 4

2.1 OIL CORRELATIONS ............................................................................................................................................. 5 2.1.1 BUBBLE POINT PRESSURE ....................................................................................................................................... 5

2.1.2. Solution Gas –Oil Ratio .................................................................................................................................... 10 2.1.3. Under-saturated Isothermal Oil Compressibility ............................................................................................. 11 2.1.4. Under-saturated Oil Formation Volume Factor .............................................................................................. 14 2.1.5. Bubble point Oil Formation Volume Factor..................................................................................................... 15 2.1.6. Oil Viscosity: .................................................................................................................................................... 19 2.1.6.1. Under-saturated Oil Viscosity .................................................................................................................... 19 2.1.6.2. Bubble Point (Saturated) Oil Viscosity ....................................................................................................... 21 2.1.6.3. Dead Oil Viscosity....................................................................................................................................... 23 2.1.7. Under-Saturated Oil Density ........................................................................................................................... 25 2.1.8. Saturated Oil Density ...................................................................................................................................... 26 2.2. Gas correlations .............................................................................................................................................. 27 2.2.1. Compressibility Factor of Gas .......................................................................................................................... 27 2.2.1.1. Direct calculations ...................................................................................................................................... 27 2.2.1.2. Indirect calculations ................................................................................................................................... 29 2.2.2. Dew point pressure ......................................................................................................................................... 30 2.2.3. Gas Viscosity µg ............................................................................................................................................... 34 2.2.4. Hydrate Temperature...................................................................................................................................... 35 2.2.5. Critical properties (Tc & Pc) ............................................................................................................................. 36 2.3. Water correlations .......................................................................................................................................... 38 2.3.1. Solution Gas Water Ratio (Rsw): ..................................................................................................................... 38 2.3.2. Formation Water Volume Factor (Bw): ............................................................................................................ 39 2.3.3. Density of Formation Water (ρw): ................................................................................................................... 39 2.3.4. The Coefficient of Isothermal Compressibility of Brine (cw): .......................................................................... 40 2.3.5. Formation Water Viscosity (µw): .................................................................................................................... 41 2.3.6. Formation Water Content of Gas Wfw ............................................................................................................. 43

3.CHAPTER 3 ........................................................................................................................................................ 44

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OBJECTIVES AND STATEMENT OF THE PROBLEM ................................................................................................. 44

3.1 THE PROBLEM .................................................................................................................................................... 44 3.2 OBJECTIVES OF THE STUDY .................................................................................................................................... 44

4.CHAPTER 4 ........................................................................................................................................................ 46

RESERVOIR FLUID CORRELATIONS ....................................................................................................................... 46

4.1 OIL CORRELATIONS ............................................................................................................................................. 46 4.1.1. INTRODUCTION ............................................................................................................................................. 46 4.1.2. PROGRAMMING OF PVT OIL PROPERTIES CORRELATIONS...................................................................................... 46 4.1.3. EVALUATION OF PVT OIL CORRELATIONS ............................................................................................................ 47 4.1.3.1. BUBBLE POINT PRESSURE ........................................................................................................................... 47 4.1.3.2. SOLUTION GAS –OIL RATIO ........................................................................................................................ 47 4.1.3.3. UNDER-SATURATED ISOTHERMAL OIL COMPRESSIBILITY ................................................................................... 47 4.1.3.4. UNDER-SATURATED OIL FORMATION VOLUME FACTOR .................................................................................... 48 4.1.3.5. BUBBLE POINT OIL FORMATION VOLUME FACTOR ........................................................................................... 48 4.1.3.6. OIL VISCOSITY .......................................................................................................................................... 48 4.1.3.6.1. UNDER-SATURATED OIL VISCOSITY .......................................................................................................... 48 4.1.3.6.2. BUBBLE POINT (SATURATED) OIL VISCOSITY .............................................................................................. 48 4.1.3.6.3. DEAD OIL VISCOSITY ............................................................................................................................. 49 4.1.3.7. UNDER-SATURATED OIL DENSITY ................................................................................................................. 49 4.1.3.8. TOTAL FORMATION VOLUME FACTOR ............................................................................................................ 49 4.2 GAS CORRELATIONS ............................................................................................................................................ 69 4.2.1. DATA DESCRIPTION ........................................................................................................................................ 70 4.3 WATER CORRELATIONS ........................................................................................................................................ 82

5.CHAPTER 5 ........................................................................................................................................................ 89

DEVELOPMENT OF AN EXPERT SYSTEM ............................................................................................................... 89

5.1INTRODUCTION............................................................................................................................................... 89

5.2PVT EXPERT SYSTEM DEVELOPMENT .............................................................................................................. 90

5.2.1.KNOWLEDGE ACQUISITION ......................................................................................................................... 90

5.2.2.SYSTEM FORMULATION .............................................................................................................................. 90

5.3PVT EXPERT SYSTEM UTILISATION .................................................................................................................. 91

5.4APPLICATION OF EXPERT SYSTEM ON SOME OF THE EGYPTIAN OIL PVT SAMPLES ......................................... 93

6.CHAPTER 6 ........................................................................................................................................................ 96

RESULTS AND DISCUSSIONS ................................................................................................................................. 96

6.1 GUIDELINES FOR SELECTING THE APPROPRIATE PVT PROPERTIES BASED ON THE RESULTS OF RELIABILITY ANALYSIS PERFORMED

ON EGYPTIAN OIL SAMPLES ............................................................................................................................................ 96 6.1.1. COMPARISON OF BUBBLE POINT PRESSURE CORRELATIONS ..................................................................................... 96 6.1.2. COMPARISON OF SOLUTION GAS OIL RATIO CORRELATIONS. .................................................................................... 97 6.1.3. COMPARISON OF BUBBLE POINT OIL FORMATION VOLUME FACTOR CORRELATIONS. .................................................... 97 6.1.4. COMPARISON OF UNDER-SATURATED OIL FORMATION VOLUME FACTOR CORRELATIONS. ............................................. 97

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6.1.5. COMPARISON OF UNDER-SATURATED OIL VISCOSITY CORRELATIONS. ........................................................................ 97 6.1.6. COMPARISON OF GAS SATURATED OIL VISCOSITY CORRELATIONS. ............................................................................ 98 6.1.7. COMPARISON OF THE COEFFICIENT OF UNDER-SATURATED ISOTHERMAL OIL COMPRESSIBILITY CORRELATIONS. ................. 98 6.1.8. COMPARISON OF GAS SATURATED OIL DENSITY CORRELATIONS. ............................................................................. 98 6.1.9. COMPARISON OF UNDER-SATURATED OIL DENSITY CORRELATIONS. .......................................................................... 99 6.2 GUIDELINES FOR SELECTING THE APPROPRIATE PVT PROPERTIES BASED ON RESULTS OF RELIABILITY ANALYSIS PERFORMED ON

WORLDWIDE GAS CONDENSATE SAMPLES .......................................................................................................................... 99 6.2.1. COMPARISON OF GAS COMPRESSIBILITY FACTOR CORRELATIONS. ............................................................................. 99 6.2.2. COMPARISON OF DEW POINT PRESSURE CORRELATIONS. ........................................................................................ 99

7.CHAPTER 7 ...................................................................................................................................................... 100

CONCLUSIONS AND RECOMMENDATIONS ......................................................................................................... 100

7.1 CONCLUSIONS: ................................................................................................................................................ 100 7.2 RECOMMENDATIONS: ....................................................................................................................................... 101

REFERENCES ....................................................................................................................................................... 102

APPENDIX A ....................................................................................................................................................... 114

EMPIRICAL PVT CORRELATIONS USED FOR CORRELATIONS ............................................................................... 114

APPENDIX B ............................................................................................................................................................

ERROR CALCULATIONS DETAILS FOR OIL DATA BASE ......................................................................................... 169

XI

LIST OF TABLES

Table No. Page

Table 4- 1: Data Range for the Egyptian PVT Data ........................................................... 52

Table 4- 2: Reported Input Parameters Ranges for Bubble Point Pressure Correlations 53

Table 4- 3: Reported Input Parameters Ranges for Solution Gas Oil Ratio Correlations . 54

Table 4- 4: Reported Input Parameters Ranges for Under-Saturated Isothermal Oil

Compressibility Correlations ............................................................................................ 55

Table 4- 5: Reported Input Parameters Ranges for Formation Volume Factor Correlations

........................................................................................................................................... 56

Table 4- 6: Reported Input Parameters Ranges for Total Formation Volume factor

Correlations ...................................................................................................................... 57

Table 4- 7: Reported Input Parameters Ranges for under-saturated Oil Viscosity

Correlations ...................................................................................................................... 58

Table 4- 8: Reported Input Parameters Ranges for Bubble Point Oil Viscosity Correlations

........................................................................................................................................... 59

Table 4- 9: Reported Input Parameters Ranges for Dead Oil Viscosity Correlations ....... 60

Table 4- 10: Data Range for the World-Wide PVT Gas Condensate Samples .................. 73

Table 4- 11: Reported Input Parameters Ranges for Dew Point Pressure Correlations .. 74

Table 4- 12: Reported Input Parameters Ranges for Gas Viscosity µg Correlations ........ 75

Table 4- 13: Reported Input Parameters Ranges for Gas Z Factor Correlations .............. 76

Table 4- 14: Reported Input Parameters Ranges for Critical Properties Correlations ..... 77

Table 4- 15: Reported Input Parameters Ranges for Isothermal compressibility of a gas,

cg Correlation .................................................................................................................... 79

Table 4- 16: Reported Input Parameters Ranges for Hydrate temperature Correlations 79

Table 4- 17: Reported Input Parameters Ranges for Bw Correlations ............................. 84

Table 4- 18: Reported Input Parameters Ranges for cw Correlations ............................. 85

XII

Table 4- 19: Reported Input Parameters Ranges for Water density ρw Correlations ..... 86

Table 4- 20: Reported Input Parameters Ranges for methane solubility in brine

Correlations ...................................................................................................................... 87

Table 4- 21: Reported Input Parameters Ranges for Brine viscosity µw Correlations .... 88

XIII

LIST of FIGURES

Figure No. Page Figure 4- 1: Cross-plot between estimated and experimental bubble point pressure, psia.

........................................................................................................................................... 61

Figure 4- 2: Cross-plot between estimated and experimental solution gas-oil ratio,

scf/STB for the range of 0-200 scf/STB. ............................................................................ 62

Figure 4- 3: Cross-plot between estimated and experimental solution gas-oil ratio,

scf/STB for the range of 0-3000scf/STB. ........................................................................... 63

Figure 4- 4: Cross-plot between estimated and experimental bubble point oil formation

volume factor (bbl/STB). ................................................................................................... 64

Figure 4- 5: Cross-plot between estimated and experimental the coefficient of under-

saturated isothermal oil compressibility data, psia -1. ................................................... 65

Figure 4- 6: Cross-plot between estimated and experimental under-saturated oil

viscosity data, cp. ............................................................................................................. 66

Figure 4- 7: Cross-plot between estimated and experimental saturated oil viscosity

data, cp. ............................................................................................................................ 67

Figure 4- 8: Cross-plot between estimated and experimental under saturated oil

formation volume factor, bbl/STB. ................................................................................... 68

Figure 4- 9: Cross-plot between calculated and experimental Z-factor for Pappy method.

........................................................................................................................................... 80

Figure 4- 10: Cross-plot between calculated and experimental dew point pressure of gas

condensate, psia. .............................................................................................................. 81

Figure 4- 11: Cross-plot between estimated and experimental dew point pressure of gas

condensate, psia. .............................................................................................................. 81

Figure 5- 1: PVT expert system utilisation. ...................................................................... 92

Figure 5- 2: An extract of the PVT Expert System database used in selection. ............... 94

Figure 5- 3: An extract of the PVT Expert System output results. ................................... 95

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List of abbreviations

Scf standard cubic feet

Bbl barrels

STB Stock Tank Barrel

PVT Pressure, Volume and Temperature

CVD constant volume depletion

CCE constant composition expansion

Nomenclature

Bo Oil Formation Volume Factor bbl/STB

Rso Solution Gas-oil ratio scf/STB

Pb Bubble point pressure psia

API Gravity of stock tank oil degree

Mc7plus C7 plus molecular weight lb/lb. mole

Bgi Gas formation volume factor bbl/Mscf

Boi Oil formation volume factor Bbl/STB

γgR reservoir gas specific gravity

xc7plus % of C7plus (C7+) -

γg sp separator gas specific gravity in

Rspd

Separator producing gas condensate ratio above the

dew point pressure

scf/STB

ρc7 densityc7plus g/cc

GCR Gas condensate ratio SCF/STB

Gi

Original gas in-place

MMscf

γSTO

The specific gravity of the stock –tank oil

AGP The additional gas produced and related to the mass of

the gas produced from the second separator and the

stock tank.

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VEQ The equivalent volume; is the volume of second

separator gas and stock-tank gas plus the volume in

scf that would be occupied by a barrel of stock-tank

liquid if it were gas.

SCF/STB

oAPI API stock tank oil gravity

Mwo Molecular weight of the stock-tank liquid lb/lb. mole

µ Viscosity cp

co oil compressibility psia

-1

γg Gas specific gravity STB

γo Oil specific gravity -

ρr Reduced density -

P System pressure psi

Pci Critical pressure of component i, psi

Pd Dew point pressure psi

Pi Initial reservoir pressure psi

PPc Pseudo-critical pressure psi

PPr Pseudo-reduced pressure -

Pwf Bottom hole flowing pressure psi

Psp Separator Pressure, psia Mscf/D

Tsp Separator temperature ̊F

R Instantaneous gas oil ratio scf/STB

O oil density g/cc

Rs Solution gas oil ratio Mscf/STB

Rsi Initial solution gas oil ratio Mscf/STB

Rv Vaporized oil gas ratio STB/Mscf

Rvi Initial vaporized oil gas ratio STB/Mscf

1:

viscosity of the gas at atmospheric pressure and

reservoir temperature

cp

a0-a15 coefficients of the equations are given in the tables -

So Oil saturation fraction

Swi Initial water saturation fraction

T System temperature °R

Tb Boiling point temperature °R

Tci critical temperature of component i °R

XVI

Tf Formation temperature °R

TPC Pseudo-critical temperature °R

Ppr (Pr): pseudo-reduced pressure of the gas mixture -

Zco 2

Mole fraction of carbon dioxide in reservoir fluid

(gas plus liquid) phases

Fraction

ZH2S

Mole fraction of hydrogen sulfide in reservoir fluid

(gas plus liquid) phases

Fraction

Zi

Mole fraction of component i in reservoir fluid (gas

plus liquid) phases

Fraction

Xi

Mole fraction of component i in reservoir liquid

phase

Fraction

yi

Mole fraction of component i in reservoir liquid

phase

Fraction

Z Single gas phase deviation factor -

Z2p Two phase Z factor -

Zd gas deviation factor at dew point -

Zi gas deviation factor at initial condition -

γg dry gas specific gravity

γw Wet gas specific gravity

γo Specific gravity of the stock-tank liquid

Tpr (Tr): pseudo-reduced temperature of the gas mixture -

μg Gas viscosity cp

ρg Gas density lb/ft3

IAWPS

The International Association for The Properties of

Water and Steam

1

1. CHAPTER 1

INTRODUCTION

Ideally, PVT properties are experimentally measured in the laboratory. When

such direct measurements are not available, PVT correlations from the literature are

often used.

Fundamentally, there are two different types of correlations in literature. The first group

of correlations is developed using randomly selected datasets. We would like to call

such correlations generic correlations. The second group of correlations is developed

using a certain geographical area or a certain types of oil. Correlations using randomly

selected datasets may not be suitable for certain type of oils, or certain geographical

areas. Even though the authors of the generic correlations want to cover a wide range of

data .Such correlations still work better for certain types of oils.

Specialized correlations represent the properties of a certain type of oil or geographical

area (for which they are developed) better than the general purpose correlations.

The best source of oil property data is the laboratory PVT (pressure-volume-

temperature) analysis of a reservoir fluid sample. However, in the absence of

experimentally measured properties of reservoir fluids, these physical properties must be

estimated from correlations.

Many correlations for estimating crude oil PVT properties have been published in the

past 50 years. Most of these correlations yield reasonably accurate results when applied

at the original limitations.

Here our work presents the details of the error statistics for each correlation. For

comparison, error analyses were carried out for this study and for some of the more

frequently used published correlations in the industry.

We believe that the results obtained by using these correlations will improve the use of

material balance calculations as well as the recovery efficiency of a reservoir.

2

A computer simulation program for oil PVT correlations model was written in a

programming language to predict all the properties over a wide range of input data and

also to provide the most appropriate correlation to be used for any reservoir data range

based on the limitations of each correlation which has been mentioned in the literature

with all database of limitations as briefly explained in chapter 4.

In our work Chapter 1 gives a brief introduction about our crude oil, gas and water

properties determination and how the correlation is useful in the petroleum literature.

Chapter 2 is a literature review about the published correlations of oil, gas and water

properties. In order to get reliable results of this work a special care is given to the

limitations of the input parameters of each correlation.

Chapter 3 presents the statement of the problem and objectives of the current study.

Chapter 4 gives an overview about oil correlations and data range for the Egyptian PVT

data and data bank ranges for each published correlation. Also, there are cross-plots

between estimated and experimental properties. Results of reliability analysis were

performed on Egyptian oil samples.

Chapter 4 also presents gas correlations and how it is preferred for the petroleum

science, where data range for the world wide above 119 PVT gas condensate samples

are tested. Also, there are cross-plots between estimated and experimental properties of

gas condensate properties.

In chapter 4 water correlations are considered and how understanding of the properties

of the produced water is very important in reducing the cost of handling the produced

water and increase added value of the produced oil in addition to cost reduction.

Chapter 5 explains in details the development process of the Expert System.

Chapter 6 summarizes the results of reliability analysis performed on Egyptian oil

samples and worldwide gas condensate samples.

3

Chapter 7 summarizes conclusion and recommendation of the evaluation studies of

correlations. As more correlations are developed, the researchers evaluate the previously

published correlations with the new ones. Others carried out studies to select the most

accurate correlation for a particular reservoir in a geographic area.

4

2. CHAPTER 2

LITERATURE REVIEW

In this chapter we present the most popular black oil correlations developed

during the period from 1947 to 2010. The chapter provides the essential background

required for the comparison and listed all ranges of the inputs according to the original

condition of each correlation as published in the original paper.

There have been a number of empirical correlations developed for medium and light

crude oils. However, their applicability is limited to specific oils due to the complex

formulation of the crude oils. Moreover, their applicability to heavy oils is very much in

question. Egbogh1 used the pour point as an additional input parameter for dead oil

viscosity correlations .De Ghetto et al.2

first defined the heavy oils in terms of oAPI

gravity. Later, he divided the heavy oil into two groups: heavy oil(10 < oAPI <22.3)and

extra heavy oil (oAPI <10).Hossain and Sarica

3 mentioned that Lohrenz and Bray also

used the crude oil chemical composition to develop an empirical correlation for oil

viscosity .

Standing 4

,in 1947 used a total of 105 data points on 22 different crude oils from

California to develop his correlations. Lasater 5

, in 1958 presented a bubble point

correlation using 158 measured bubble point data on 137 crude oils from Canada,

Western and Mid-Continental United States and South America. Vasquez and Beggs 6

,in 1989 developed correlations for the solution gas to oil ratio and formation

volume factor using 600 laboratory PVT analysis. Glasso7,

in 1980 used data from 45

oil samples mostly from the North Sea region to develop his correlations. Al-Marhoun8

,in 1988 used 160 bubble point data on 69 Middle Eastern crude samples to

develop a bubble point pressure correlation. Ahmed 9used the combined reported data

of Glasso and Marhoun to develop a correlation for determining the oil formation

volume factor.

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