NMR Oil Well Logging: Diffusional Coupling and Internal Gradients in Porous Media by Vivek Anand

206 Pages·2007·7.74 MB·English

by  Vivek Anand

RICE UNIVERSITY

NMR Oil Well Logging: Diffusional Coupling and
Internal Gradients in Porous Media

by

Vivek Anand

A THESIS SUBMITTED
IN PARTIAL FULFILLMENT OF THE
REQUIREMENTS FOR THE DEGREE

Doctor of Philosophy

APPROVED, THESIS COMMITTEE

_______________________________
George J. Hirasaki, A. J. Hartsook Professor, Chair
Chemical and Biomolecular Engineering

________________________________
Walter G. Chapman, William W. Akers Chair,
Chemical and Biomolecular Engineering

________________________________
Andreas Luttge, Associate Professor
Earth Science and Chemistry

HOUSTON, TEXAS

APRIL 2007
i
ii

ABSTRACT

NMR Oil Well Logging:

Diffusional Coupling and Internal Gradients in Porous Media

by

Vivek Anand

The default assumptions used for interpreting NMR measurements with reservoir
rocks fail for many sandstone and carbonate formations. This study provides quantitative
understanding of the mechanisms governing NMR relaxation of formation fluids for two
important cases in which default assumptions are not valid. The first is diffusional
coupling between micro and macropore, the second is susceptibility-induced magnetic
field inhomogeneties. Understanding of governing mechanisms can aid in better
estimation of formation properties such as pore size distribution and irreducible water
saturation.
The assumption of direct correspondence between relaxation time and pore size
distribution of a rock fails if fluid in different sized pores is coupled by diffusion. Pore
scale simulations of relaxation in coupled micro and macropores are done to analyze the
effect of governing parameters such as surface relaxivity, pore geometry and fluid
diffusivity. A new coupling parameter () is introduced which quantifies the extent of
coupling by comparing the rate of relaxation in a coupled pore to the rate of diffusional
transport. Depending on , the pores can communicate through total, intermediate or
iii
decoupled regimes of coupling. This work also develops a new technique for accurate
estimation of irreducible saturation, an approach that is applicable in all coupling
regimes. The theory is validated for representative cases of sandstone and carbonate
formations.
Another assumption used in NMR formation evaluation is that the magnetic field
distribution corresponds to the externally applied field. However, strong field
inhomogenities can be induced in the presence of paramagnetic minerals such as iron on
pore surfaces of sedimentary rocks. A generalized relaxation theory is proposed which
identifies three asymptotic relaxation regimes of motionally averaging, localization and
free diffusion. The relaxation characteristics of the asymptotic regimes such as T /T ratio
1 2
and echo spacing dependence are quantitatively illustrated by random walk simulations
and experiments with paramagnetic particles of several sizes. The theory can aid in better
interpretation of diffusion measurements in porous media as well as imaging experiments
in Magnetic Resonance Imaging (MRI).
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ACKNOWLEDGEMENTS
First and foremost, I would like to acknowledge my advisor Dr. George J.
Hirasaki for his continuous support and inspiration. I will remain indebted to him
throughout my life for the things he has taught me.
I would also like to thank Dr. Walter G. Chapman and Dr. Andreas Luttge for
serving on my thesis committee.
I am very thankful to William Knowles, Jie Yu and Shyam Benegal for their help
with the BET, DLS and Coulter Counter measurements.
I am also thankful to Dr. Vicki L. Colvin’s Lab for providing magnetite
nanoparticles and TEM measurements.
Many thanks go to Jim Howard at Conoco Phillips for proving North Burbank
cores and Chuck Devier at PTS labs for making mercury porosimetry and permeability
measurements.
I greatly appreciate Dr. Marc Fluery at French Institute of Petroleum (IFP) for
sharing his carbonate NMR measurements at high temperatures.
I would like to acknowledge Department of Energy (grant number DE-PS26-
04NT15515) and consortium for processes in porous media for the financial support.
Most importantly, I would like to thank my parents, my family members for their
love and support.
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TABLE OF CONTENTS

TITLE PAGE………………………………………………………………………………i

ABSTRACT………………………………………………………………………………ii

ACKNOWLEDGEMENTS……………………………………………………………....iv

TABLE OF CONTENTS………………………………………………………………….v

LIST OF TABLES………………………………………………………………………..ix

LIST OF FIGURES……………………………………………………………………....xi

Chapter 1. Introduction…………………………………………………………..…….1

Chapter 2. Diffusional Coupling ……………………………………………………….4
2.1 Literature Review…………………………………………………………….4
2.1.1 Nuclear Magnetism………………………………………………..4
2.1.2 Pulse tipping and Free Induction Decay……………………….….5
2.1.3 Longitudinal relaxation……………………………………….…...6
2.1.4 Transverse relaxation………………………………………….…..7
2.1.5 NMR formation evaluation…………………………………..……8
2.1.6 Diffusional coupling…………………………………………......10
2.1.7 Spectral BVI and tapered T ………………………………...12
2,cutoff
2.2 Diffusional coupling between micro and macropore………………………13
2.2.1 Mathematical modeling.…………………………………………14
2.2.2 Magnetization decay in coupled pore..…………...……………...17
2.2.3 Coupling Parameter……………………………………………...19
2.2.3.1 Micropore relaxation…………………………………....22
2.2.3.2 Macropore relaxation…………………………………...25
2.2.4 Estimation of irreducible saturation and ……………………....26
2.2.5 Unification of spectral and sharp T theory……...……….....28
2,cutoff
2.3 Diffusional coupling between pore lining clays and pore body……………31
2.3.1 Pore size distribution of North Burbank sandstone……………...32
vi
2.3.2 Numerical solution of Bloch equation in pore size distribution
…..……………………………………………………………….34
2.3.3 Simulated T distributions ……………………………………….36
2
2.3.4 Coupling regimes in North Burbank sandstone …………………37
2.3.5 Estimation of surface relaxivity……………………………….....41
2.4 Effect of clay distribution on diffusional coupling…………………………42
2.4.1 Synthesis of model shaly sands with laminated and dispersed
clays……………………………………………………………...43
2.4.2 T distribution of shaly sands………..…………………………...45
2
2.4.3 Estimation of irreducible water saturation in shaly sands……….49
2.5 Diffusional coupling in microporous grainstones…………………………..52
2.5.1 Coupling parameter for grainstones……………………………...53
2.5.2 Experimental validation of grain size dependence on pore
coupling…………………………………………………………..55
2.5.3 Estimation of irreducible saturation for the sandstone and
grainstone systems……………………………………………….62
2.6 Effect of temperature on diffusional coupling……………………………...63
2.6.1 Temperature dependence of …………………………………...64
2.6.2 Temperature dependence of T distributions of silica gels and
2
carbonate core ………………………………………...................65
2.6.3 Discussion………………………………………………………..69
2.7 Conclusions…………………………………………………………………71

Chapter 3. Paramagnetic Relaxation in Sandstones: Generalized Relaxation
Theory…………………………………………………………………………………...73
3.1 Introduction and Literature Review………………………………………...73
3.2 Generalized secular relaxation theory……………………………………....77
3.2.1 Characteristic time scales for secular relaxation………...……….77
3.2.1.1 Characteristic time scale for restricted diffusion in a
constant gradient………………………………..………78
3.2.1.2 Characteristic time scale for relaxation in field induced by
paramagnetic sphere..…………………………..……….78
3.2.2 Asymptotic regimes of secular relaxation…………………..……80
3.2.2.1 Motionally averaging regime…………………...………81
3.2.2.2 Free diffusion regime…………………………..……….83
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3.2.2.3 Localization regime…………………..…….…………..85
3.2.3 Parametric representation of asymptotic regimes………………..87
3.3 Relaxation regimes in sedimentary rocks…………………………..………88
3.3.1 Paramagnetic particles at dilute surface concentration…….…….89
3.3.2 Paramagnetic particles at high surface concentration………… ...91
3.4 Random walk simulations……………………………………………….…96
3.4.1 Non-dimensionalization of Bloch equations…………….……….97
3.4.2 Algorithm………………………………………………………...99
3.4.3 Validation of numerical solution…………….…………………101
3.4.3.1 Unrestricted diffusion in constant gradient……….…...101
3.4.3.2 Restricted diffusion in constant gradient………….…..102
3.4.4 Results…………………………………………………………..105
3.5 Conclusions………………………………………………………………..117

Chapter 4. Paramagnetic Relaxation in Sandstones: Experiments………………..119
4.1 Paramagnetic particles in aqueous dispersions……………………………119
4.1.1 Ferric Ion………………………………………………………..119
4.1.2 Polymer coated magnetite nanoparticles……..………………...120
4.1.3 Magnetite nanoparticles coated with citrate ion….…………….125
4.1.4 Characteristic time scales for paramagnetic particles in
dispersion………………………………………..……………...129
4.2 Paramagnetic particles on silica surface…………………………………..132
4.2.1 Fine sand coated with ferric ions……………………………….132
4.2.2 Fine sand coated with magnetite nanoparticles……...................136
4.2.3 Fine sand with dispersed 2.4 m magnetite………………….....140
4.2.4 Coarse sand coated with magnetite nanoparticles……………...142
4.3 Paramagnetic relaxation in sandstones…………………………………....144
4.3.1 Motionally averaging regime……………………...……………144
4.3.2 Free diffusion regime……………………………..…………….145
4.3.3 Localization regime…………………………………………….148
4.4 Parametric representation of asymptotic regimes in experimental
systems……………………………………………………………….……153
4.5 Conclusions………………………………………………………………..159
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Chapter 5. Conclusions………………………………………………………………161

Chapter 6. Future Work……………………………………………………………..166

REFERENCES……………………...………………………………………...……….168
Appendix A. Numerical solution of Bloch equations in coupled pore model…………174
Appendix B. Relaxation time of micropore in coupled pore model…………………...181
Appendix C. Characteristic parameters for the sandstones and grainstone systems…..185
Appendix D. Characteristic parameters for the experimental systems of Chapter 4. …187
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LIST OF TABLES
Table 2.1: Characteristic parameters for the simulations for three NB cores……………39

Table 2.2: Physical Properties of Fine Sand, Kaolinite and Bentonite clays…………….44
Table 2.3: Physical properties of the grainstone systems………………………………..55
Table 4.1: Characteristic Time scales for the ferric ions and magnetite nanoparticles...131

Table 4.2: Longitudinal and transverse relaxation times of water-saturated fine sand
coated with ferric ions at different surface concentrations (area/ferric ion)..…………..134

Table 4.3: Longitudinal and transverse relaxation times of water-saturated fine sand
coated with 25 nm magnetite at different surface concentrations………………………137

Table 4.4: Longitudinal and transverse relaxation times of water-saturated fine sand
coated with 110 nm magnetite at different surface concentrations…………………......137

Table 4.5: Longitudinal and transverse relaxation times of water-saturated fine sand with
dispersed 2.4 m magnetite………………………………………………………….....140

Table 4.6: Longitudinal and transverse relaxation times of water-saturated coarse sand
coated with 25 nm magnetite at different surface concentrations………………………144

Table 4.7: Characteristic time scales for relaxation in coarse sand coated with 25nm
(7102nm2/particle) and fine sand coated with 110nm magnetite (1.5106nm2/particle)
……………………………………...…………………………………………………...147

Table 4.8: Characteristic time scales for relaxation in fine sand coated with 25 nm and
110 nm magnetite at high surface concentrations. ………………….………………….149

Table 4.9: Characteristic time scales for relaxation in fine with dispersed 2.4 µm
magnetite…………………………………………………………………………..........149

Table 4.10: Logmean longitudinal and transverse relaxation times of water saturated
North Burbank cores……………………………………………………………………151
Table A.1: Model parameters for magnetization decay simulations…………………...179
Table C.1: Characteristic parameters for North Burbank sandstone …………………..185

Table C.2: Characteristic parameters for chalk…………………………………………185

Table C.3: Characteristic parameters for silica gels……………………………………185
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Table C.4: Characteristic parameters for molecular sieves…………………………….186

Table C.5: Characteristic parameters for silica gels at 30, 50, 75 and 95oC …..……….186

Table C.6: Characteristic parameters for reservoir carbonate core at 25, 50, 80oC…….186

Table D.1: Characteristic parameters for fine sand coated with 25 nm magnetite at
different surface concentrations.  and 1 TD are dimensionless.…………………….187
2,sec

Table D.2: Characteristic parameters for fine sand coated with 110 nm magnetite at
different surface concentrations.  and 1 TD are dimensionless……………………..188
2,sec

Table D.3: Characteristic parameters for coarse sand coated with 25 nm magnetite at
different surface concentrations.  and 1 TD are dimensionless……………………..188
2,sec

Table D.4: Characteristic parameters for fine sand with dispersed 2.4m magnetite at
different concentrations.  and 1 TD are dimensionless……………………………...189
2,sec

Table D.5: Characteristic parameters for North-Burbank sandstones.  and 1 TD are
2,sec
dimensionless…………………………………………………………………………...189