ali ahmed jalalh

178 Pages·2006·5.38 MB·English

SAMUELMIKOVINY
DOCTORAL SCHOOL OF EARTH SCIENCES
AND ENGINEERING

Head of Doctoral School:
Dr. h.c.mult, Dr. Ferenc Kovacs
Member of the Hungarian Academy of Sciences

Ph.D. DISSERTATION

DETERMINATION AND ANALYSIS OF POROUS ROCK
COMPRESSIBILITY OF HUNGARIAN ROCK SAMPLES

by

ALI AHMED JALALH

Scientific Supervisor
Dr. BÓDI TIBOR

A DISSERTATION PRESENTED TO MIKOVINY SAMUEL
DOCTORAL SCHOOL OF EARTH SCIENCES AND ENGINEERING
OF THE UNIVERSITY OF MISKOLC IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF MISKOLC

2006
A DISSERTATION PRESENTED TO MIKOVINY SAMUEL
DOCTORAL SCHOOL OF EARTH SCIENCES AND ENGINEERING
OF THE UNIVERSITY OF MISKOLC IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF MISKOLC

PETROLEUM ENGINEERING
Copyright 2006

by

ALI AHMED JALALH
DEDICATION

This document is dedicated to those who love me more than themselves, my parents.
ACKNOWLEDGMENTS

I would like to thank my research advisor Professor Bódi Tibor. I honor him for his
constant support, encouragement and guidance during the course of this study. Professor
Bódi was always available to answer my questions, or to help me in finding the right path
to the answers. When I felt depressed because of some unsuccessful struggle or technical
hassle, Professor Bódi kept his belief in my ability to solve problems and encouraged me to
overcome the difficulties eventually. I could not have finished this research project without
Professor Bódi's guidance and encouragement.
Sincere thanks are due to Prof. Gabor Tackacs for his continuous encouragement and
support as head of the department. My sweet wife and best friend, Fatma, always gives me
her wholehearted support, love, kindness, patience and constant spiritual and help. My
gratitude to her is beyond description. I also wish to express my appreciation to my formal
undergraduate teachers and colleagues, Prof. Sanousi Salem, Prof. Rajab Elkazmi, and
Prof. Emhemid Elshair for generously providing good ideas and continuous
encouragement while I have been pursuing my PhD. studies.
Special thanks for those who helped me during my laboratory work, especially Dr.
Tóth János and the technician Bajor László. Mr. Bajor was always ready to help and
sometimes alerted me if there was uncertainty about the readings.
My endless gratitude goes to my parents, Fatima and Ahmed Jalalh, and to my
brother and sisters.
Finally, the Author would like to thank Allah and his dear family.
TABLE OF CONTENTS

page

ACKNOWLEDGMENTS...............................................................................................VII
LIST OF TABLES............................................................................................................XI
LIST OF FIGURES........................................................................................................XIII
1. INTRODUCTION.........................................................................................................1
1.1 STATEMENT OF PROBLEM..............................................................................1
2. BACKGROUND AND LITERATURE REVIEW.....................................................4
2.1 COMPRESSIBILITY OF POROUS ROCKS.......................................................4
2.2 MATHEMATICAL EXPRESSIONS FOR COMPRESSIBILITY.......................6
2.3 RELATIONSHIPS BETWEEN COMPRESSIBILITIES....................................10
2.4 EFFECTIVE STRESS COEFFICIENTS.............................................................16
2.5. LITERATURE REVIEW....................................................................................23
3. POROELASTICITY MEASUREMENTS................................................................25
3.1 INTRODUCTION TO POROELASTICITY THEORY.....................................25
3.2 LABORATORY MEASUREMENTS OF COMPRESSIBILITIES...................30
4. DESCRIPTION OF EQUIPMENT AND SAMPLES TEST PROCESSES..........40
4.1 PRINCIPLE OF APPARATUS COMPONENTS...............................................40
4.1.1 Oven...........................................................................................................40
4.1.2 Control Panel..............................................................................................41
4.2 EXPERIMENTAL TECHNIQUE.......................................................................44
4.2.1 Preparation of Samples..............................................................................44
4.2.2 Measuring Porosity....................................................................................44
4.2.2.1 Helium Porosimeter................................................................................44
4.2.2.2 Porosity by Saturation Method................................................................46
4.3 COMPRESSIBILITY APPARATUS OPERATION...........................................47
4.3.1 Leak-off Test..............................................................................................47
4.3.2 Transducer Calibration...............................................................................47
4.3.3 Equipment Composite Correction..............................................................49
4.3.3.1 Equipment Correction Calculations........................................................50
4.4 MEASUREMENTS OF PORE VOLUME COMPRESSIBILITY......................52
4.4.1 Pressurization of Samples..........................................................................52
4.4.2 Laboratory Calculations of Pore Volume Compressibility........................53
5. RESULTS AND DISCUSSion....................................................................................56
5.1 ROCK IDENTITY CARDS.................................................................................56
5.2 EFFECTIVENESS OF CYCLING, TIME, AND TEMPERATURE..................63
5.2.1 Cycling.......................................................................................................63
5.2.2 Time...........................................................................................................63
5.2.3 Temperature...............................................................................................63
5.3 COMPRESSIBILITY MEASUREMENT RESULTS.........................................64
5.3.1 Zsana Field Samples..................................................................................65
5.3.2 Hajduszoboszlo Field Sample....................................................................66
5.3.3 Algyo Field Samples..................................................................................67
5.3.4 Földes Field Samples.................................................................................70
5.4 DISCUSSION......................................................................................................74
6. NEW CORRELATIONS OF ROCK COMPRESSIBILITY..................................78
6.1 INTRODUCTION................................................................................................78
6.2 MODIFIED HORNE’S CORRELATION APPROACH (Mod-Horne)..............82
6.3 NEW ROCK COMPRESSIBILITY CORRELATION.......................................86
6.3.1 NEW LIMESTONE ROCKS COMPRESSIBILITY CORRELATION..........86
6.3.2 NEW SANDSTONE COMPRESSIBILITY CORRELATION........................89
7. USE OF COMPRESSIBILITY DATA IN OIL AND GAS CALCULATIONS AND
FOR IMPROVING RESERVOIR ANALYSIS....................................................92
7.1 AN EXAMPLE OF A GAS RESERVOIR..........................................................92
7.1.1 Introduction................................................................................................92
7.1.2 Aspects of the new (Fetkovich) Material Balance Equation......................93
7.1.4 Notes on sample calculations.....................................................................96
7.2 OIL RESERVOIR EXAMPLES..........................................................................97
7.2.1 Introduction................................................................................................97
7.2.2 A New Concept of Pore Volume...............................................................98
7.2.3 Modified Fluid Formation Volume Factors...............................................99
7.2.5 Examples of Application............................................................................99
8. CONCLUSIONS........................................................................................................102
LIST OF REFERENCES................................................................................................104
NOMENCLATURES......................................................................................................111
APPENDIX A.................................................................................................................113
LABORATORY DATA SHEETS OF COMPRESSIBILITY MEASUREMENTS
AND CALCULATION.......................................................................................113
APPENDIX B..................................................................................................................150
TWELVE FITTING FORMULAS WITH TWO PARAMETERS USED IN THE
RESEARCH........................................................................................................150
DATA MODELING EQUATIONS USED BY CurveExpert 1.38 PROGRAM....150
APPENDIX C..................................................................................................................153
DERIVATION OF GENERAL GAS MATERIAL BALANCE.............................153
DERIVATION OF BLACK OIL MATERIAL BALANCE...................................159
BIOGRAPHICAL SKETCH...........................................................................................166
IX
LIST OF TABLES
Table page

Table 4.1 Control and indicator function of the control panel..........................................41
Table 4.2: Output of Corex helium porosimeter results....................................................46
Table 4.3: Collected input data for porosity estimation by saturation method..................46
Table 4.4 Display the collected readings used for equipment correction..........................50
Table 4.5: Correction equipment calculation I results.......................................................51
Table 4.6: Pore volume measurement data........................................................................53
Table 4.7: Statistical fitting results....................................................................................54
Table 4.8: Pore-volumecompressibility measurement correction calculations.................54
Table 4.9: Result of a linear statistical fitting approach estimation and results of uniaxial
compressibility as a function of effective pressure..................................................55
Table 5.2: Magnified captured photograph of limestone textures from the Zsana field...57
Table 5.3: Sandstone sample textures captured photograph magnified 200X and other
laboratory measurements.........................................................................................58
Table 5.4: Magnified photographs of sample rock textures and other laboratory
measurements...........................................................................................................62
Table 5.5: Magnified captured of sample’s rock textures used in the study and other
laboratory measurements.........................................................................................62
Table 5.6: Summary of the obtained measured compressibility of Zsana field samples at
average reservoir effective stress.............................................................................66
Table 5.7: Summary of measured compressibility of Hajduszoboszlo Field Sample at
various measurement runs........................................................................................67
Table 5.8: Summary of measured compressibility of Algyo Field Samples.....................67
Table 5.9: Summary of measured compressibility of Földes field samples......................71
Table 6.1 Descriptive statistical data of Horne and published rock compressibility of
limestone..................................................................................................................82
X I
Table 6.2: Statistical correlation data of Mod-Horne and published rock compressibility of
limestone..................................................................................................................84
Table 6.3: Statistical correlation data of Horne and published rock compressibility of
sandstone..................................................................................................................85
Table 6.4: Statistical correlation data of Mod-Horne and published rock compressibility of
sandstone..................................................................................................................85
Table 6.4a: Statistical data of the new fitting curve of published rock compressibility of
limestone..................................................................................................................87
Table 6.4b: Statistical data of nonlinear regression of new fitting curve and published rock
compressibility of limestone....................................................................................87
Table 6.5a: Descriptive statistical data of the new fitting curve of published rock
compressibility of limestone....................................................................................90
Table 6.5b: Statistical data of nonlinear regression of new fitting curve and published rock
compressibility of sandstone....................................................................................90
Table 6.6: Sum-of-squares (SS) and degree of freedom (DF) of the models used, for
limestone samples....................................................................................................91
Table 6.7: Sum-of-squares (SS) and degree of freedom (DF) of the models used, for
sandstone samples....................................................................................................91
Table 7.1: Reservoir Data,.................................................................................................93
Table 7.2: Main data of the reservoir..............................................................................100
X II
LIST OF FIGURES
Figure page

Figure 2.1: Illustration of the two types of stresses.............................................................5
Figure 2.2: Illustration of the overburden confining pressure P and internal pore-pressure
c
P of porous body.......................................................................................................5
p
Figure 2.3: Pore strain ε (a) and pore compressibility C .................................................8
b pc
Figure 2.4: ΔV measured (Pore volume change) (left) and Pore volume compressibility
p
C (right) as a function of confining pressure...........................................................9
pc
Figure 2.5: Sandstone modeled as (a) an assemblage of discrete grains in contact, and (b) a
solid matrix containing voids...................................................................................11
Figure 2.6: Measured values [Zimmerman, 1986] of C for Bandera sandstone, compared
bp
with the values predicted from C measurement....................................................14
pc
Figure 2.7: Dynamically measured values [King, 1969] of C for a Berea sandstone,....15
bc
Figure 2.8: Measured values [Greenwald, 1980] of C for a Boise sandstone,................16
bp
Figure 2.9: Lower bounds in effective stress coefficient from n .....................................19
b
Figure 2.10: Lower bounds in effective stress coefficient from n ...................................19
p
Figure 2.11: Comparison of direct and indirect measurements [Fatt, 1958a] of n for a
b
Boise sandstone........................................................................................................20
Figure 2.12: Force-balance arguments [after Greenwald, 1980] for the derivation of the
mean-stress relationship...........................................................................................21
Figure 3.1: Infinitesimally small cube of rock material, "cut out" of a larger piece of rock
that is subjected to various forces............................................................................27
Figure 3.2: Schematic diagram of a purely dilatational deformation................................28
Figure 3.3: Schematic diagram of a purely deviatoric deformation..................................28
Figure 3.4: Schematic diagram of system used to measure compressibilities of porous
rocks.........................................................................................................................31
Figure 3.5: Device used by [Zimmerman, 1986a] to measure changes in the pore volume,
and to control the pore pressure...............................................................................32
XI II
Figure 3.6: Apparatus used to saturate the cores with the pore fluid [after Greenwald,
1980]........................................................................................................................33
Figure 3.7: Schematic diagram of system used to measure C ........................................34
pc
Figure 3.8: Schematic diagram of the apparatus used by Sampath [1982] to measure Cpc
using nitrogen as the pore fluid................................................................................35
Figure 3.9: Schematic diagram of method used by Greenwald [1980] to attach strain
gauges to cores.........................................................................................................37
Figure 3.10: Schematic diagram of apparatus used to measure pore and bulk
compressibilities......................................................................................................38
Figure 3.11: Schematic diagram of apparatus used by Green and Wang [1986] to measure
induced pore pressures.............................................................................................39
Figure 3.12: Schematic diagram of apparatus used by Laurent et al. [1993]....................39
Figure 4.1: The main three components of the compressibility apparatus:.......................40
Figure 4.2: Control panel controls and indicators (see Table 4.1)....................................41
Figure 4.3: Compressibility apparatus II's plumbing schematic.......................................43
Figure 4.4: Corex’s helium porosimeter used for measuring porosity..............................45
Figure 4.5: Heise gauge (Dead Weight Tester) used for potentiometer calibration..........48
Figure 4.6: Cross plot illustrating measured and calculated pore volume changes versus
effective pressure.....................................................................................................51
Figure 4.7: Thicknesses of core rubber sleeves used in this study....................................51
Figure 5.1: Compressibility plots for different cycle values at different temperatures,
Sample Sz-005.........................................................................................................64
Figure 5.2: Group of compressibility values of all Zsana field samples versus effective
pressure....................................................................................................................65
Figure 5.3: Pore volume compressibility of Sample Zs-005 from different cycle values at
same laboratory temperature....................................................................................65
Figure 5.4: Pore volume compressibility plots of Sample H for different cycle...............66
Figure 5.5: Pore volume compressibility of Samples A.1.1, A.1.2 and A 985 /5.2, A 985
/1.2 at same laboratory temperature.........................................................................68
Figure 5.6: Measured pore volume compressibility of a group of sandstone sample
readings at the same laboratory temperature...........................................................68
Figure 5.7: Measured pore volume compressibility readings of sandstone samples 30.S,
43.S and 82.S...........................................................................................................69
XI V