Principles of Mathematical Petrophysics

273 Pages·2014·19.52 MB·English

by  John H. Doveton

Principles of Mathematical Petrophysics
International Association for Mathematical Geosciences
STUDIES IN MATHEMATICAL GEOSCIENCES
1. William B. Size, Editor
Use and Abuse of Statistical Methods in the Earth Sciences
2. Lawrence J. Drew
Oil and Gas Forecasting: Reflections of a Petroleum Geologist
3. Ricardo A. Olea, Editor
Geostatistical Glossary and Multilingual Dictionary
4. Regina L. Hunter and C. John Mann, Editors
Techniques for Determining Probabilities of Geologic Events and Processes
5. John C. Davis and Ute Christina Herzfeld, Editors
Computers in Geology—25 Years of Progress
6. George Christakos
Modern Spatiotemporal Geostatistics
7. Vera Pawlowsky-Glahn and Ricardo Olea
Geostatistical Analysis of Compositional Data
8. P.J. Lee
Statistical Methods for Estimating Petroleum Resources
9. John H. Doveton
Principles of Mathematical Petrophysics
Principles of

Mathematical
Petrophysics
John H. Doveton
Kansas Geological Survey
3
3
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Library of Congress Cataloging-in-Publication Data
Doveton, John H., 1944–
Principles of mathematical petrophysics / John H. Doveton.
pages cm
Includes bibliographical references and index.
ISBN 978–0–19–997804–5 (alk. paper)
1. Petrology—Mathematical models. 2. Mineralogy—Mathematical
models. 3. Rocks. I. Title.
QE431.6.P5D68 2014
552.00151—dc23
2014001402
9 8 7 6 5 4 3 2 1
Printed in the United States of America
on acid-free paper
Dedicated with thanks and remembrance of good times to the Mathematical
Geology Section and the Energy Research Section of the Kansas Geological
Survey, without whose work and inspiration, this book would not have been
possible.

CONTENTS

Foreword to the Series xi
Preface xiii
Acknowlegements xv
1. Fluid Saturation Evaluation 1
The Archie equations 1
The Humble equation and its variants 4
Sensitivity analysis of Archie equation parameters 8
Non-Archie sandstones 10
Shaly sandstone analysis 13
Double-layer shaly sandstone models 15
Dual-water shaly sandstone models 20
The Archie equation in carbonate rocks 23
Porosity partitioning in dual-porosity systems 26
The porosity exponent in a triple-porosity system 31
Dielectric logging measurement of the porosity exponent 31
Petrographic evaluations of the porosity exponent in carbonates 32
The saturation exponent, n 33
Wettability effects on the saturation exponent 36
Archie redux 38
2. Porosity Volumetrics and Pore Typing 44
Porosity of spherical packs 44
Clastic “effective” porosity 44
Neutron-density shale volumetrics 45
Gamma-ray estimations of shale volume 47
Correction of total porosity for shale contents 50
Allocation between shale morphology types 51
Carbonate porosity 55
Vug porosity evaluation from acoustic and resistivity logs 56
NMR logging of vuggy porosity 62
3. Permeability Estimation 67
Permeability is a vector 67
Prediction of permeability from porosity 67
Flow-zone indicator (FZI) discrimination of hydraulic units 69
Application of FZI to permeability prediction 73
Permeability predictions from porosity and “irreducible” water
saturation 77
NMR estimation of permeability in clastic pore systems 79
Permeability estimation in carbonates dominated by interparticle
porosity 81
Evaluation of permeability in dual- and triple-porosity systems 82
A Wilderness of mirrors 88
4. Compositional Analysis of Mineralogy 94
Some matrix algebra 94
Compositional-solution evaluation 97
Underdetermined systems 99
Overdetermined systems 102
Optimization models for compositional solutions 103
Multiple-model solutions of rock composition 105
Elucidation of clay minerals 106
Compositional analysis from geochemical logs 113
Inversion mapping of compositions 117
5. Petrophysical Rocks: Electrofacies and Lithofacies 122
Facies and electrofacies 122
Dunham textures and electrofacies 123
Petrophysical recognition of lithofacies 124
Zonation by cluster analysis 128
Theoretical, empirical, and interpretive electrofacies methods 131
Principal component analysis (PCA) of electrofacies 134
Classification by a parametric electrofacies database 146
Supervised electrofacies analysis methods 147
Electrofacies classification by discriminant function analysis (DFA) 148
Nonparametric discriminant analysis 152
Neural-network prediction of lithofacies from logs 157
Beyond product facies to the petrophysical prediction of process
facies 162
6. Pore-System Facies: Pore Throats and Pore Bodies 171
The petrofacies concept 171
Equivalent hydraulic radius of tubes 172
Capillary pressure evaluation of pore-throat sizes 172
The Winland equation 176
The flow-unit concept 178
Petrofacies case-study applications of the Winland equation 179
Carbonate petrofacies pore-throat size distributions 185
Pore-body size distributions from NMR measurements 198
NMR facies in sandstones 200
NMR pore-size interpretation in carbonates 204
NMR-partitioned porosity and Dunham textural classes 205
NMR facies in carbonates 209
[viii] Contents
7. Saturation-Height Functions 217
Integration: the saturation-height model 217
The basics of reservoir saturation profiles 218
Saturation-height modeling in sandstones from capillary pressure
measurements 221
Height functions for bulk-volume water 225
Permeability-height functions 230
Saturation-height modeling in carbonates 233
Saturation-height modeling based on magnetic resonance logs 238
Putting it all together: the static reservoir model 241
Index 245
Contents [ix]