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Elements of Rock Physics and Their Application to Inversion and AVO Studies

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The ultimate aim of the oil exploration industry is to determine the distribution of rock types and underground fluids. At this stage, we can actually determine the distribution of several underground physical properties with a certain accuracy. The challenge for the rock physicist is to translate those physical properties (P-velocity, S-velocity, density) into rock types and fluids (gas-, or oil-, or water-bearing sand, shale). If performed correctly, dry holes can be avoided and millions of dollars can be saved. Ultimately, an integrated approach is required. This book deals with a series of topics in rock physics, including elasticity, pore pressure, incompressibility of rocks and the Gassmann equation, fluid substitution, forward modelling and empirical equations, rock physics applications to AVO studies and inversion studies, and the Differential Effective Medium (DEM) method. It is generally addressed to the practitioner (geophysicist, geologist), and in some instances, detailed instructions are furnished to perform a particular task. Some chapters, on the other hand, are theoretical and more mathematical, and are expected to be of interest to both practitioners and students alike. Other chapters include innovative ideas that could, for instance, be tested by oil companies that have substantial amounts of data at their disposal.

This book will serve as a useful guide to practitioners (geologists, petrophysicists, geophysicists and reservoir engineers) and students/academics.

Author(s): Robert S. Gullco, Malcolm Anderson
Publisher: CRC Press/Balkema
Year: 2022

Language: English
Pages: 189
City: Leiden

Cover
Half Title
Title Page
Copyright Page
Table of Contents
About the authors
Introduction
1 Petrophysics review
Definition of effective and total porosity, clay and  shale
The effective porosity model
The total porosity model
Estimation of the shale point in a Density/Neutron crossplot
Calculation of the effective porosity and the shale volume fraction (V[sub(sh)]) from the Neutron and Density logs, in oil- or water-bearing sands
Using the Gamma Ray log to calculate shale volume fraction: Comparison with the Neutron/Density approach
Evaluating gas-bearing sands using the Neutron, Density and Gamma Ray logs
Reference
Appendix 1.1: Gas density and hydrogen index at reservoir conditions
Hydrogen index of a gas
Gas density at reservoir conditions
2 Elements of elasticity theory
Definition of stress, strain, elasticity and elastic moduli
The concept of normal and shear stresses
The shear modulus
Relationship between seismic velocities and elastic moduli
References
3 Pore pressure review
Introduction
Normal and abnormal pressures: Most common causes of abnormal pressure
Overburden pressure and Net Overburden Pressure
The Gluyas-Cade correlation of porosity vs. depth for clean, uncemented sands
Calculation of the pore pressure: The Eaton and Bowers equations
The Eaton equation reads
The Bowers formula
Lithological problems
Pore pressure calculations in limestones, and the difficulty of doing this with velocity data alone
Calculation of the fracture pressure
The Eaton formula (1969, 1997) for calculating the pore pressure
An oil exploration application of pore pressure
Sealing and non-sealing faults
References
4 Incompressibility of rocks and the Gassmann equation
Incompressibility moduli and the relationships between them
The Gassmann equation
The relationship between the porosity and the net overburden pressure
Summary
Reference
5 Fluid substitution
The fluid substitution problem
Physical properties of fluids
A simple fluid substitution exercise
1. Calculate the bulk modulus (K[sub(b)]) and the shear modulus (µ) of the wet rock
2. Calculate the dry modulus (K[sub(dry)])
3. Calculate the effective fluid compressibility and the density under the new fluid saturation conditions
4. Given the new value of K[sub(f)], calculate the new value of the bulk incompressibility K[sub(b)] of the rock, assuming 70% gas in the pore space
5. Calculate the new seismic velocities and the new bulk density
Reuss lower bound and Voigt upper bound and Hashin-Shtrikman upper and lower bounds
Marion’s hypothesis
Reference
6 Forward modelling and empirical equations
Forward modelling and empirical equations
The Wyllie equation
Estimation of the shear velocity from the compressional velocity
Input data for the Monte Carlo simulation
Estimation of the elastic parameters of the ideal rock using the Hashin-Shtrikman bounds
Correlations used to estimate the bulk and shear moduli
The Murphy et al. (1993) correlation
The critical porosity hypothesis (Nur, 1992)
The Krief et al. (1990) correlation
Comparison with real data
Summary
References
Appendix 6.1: Estimation of the incompressibility of the solid part of the rock in shaley sands
7 Applications of rock physics to AVO analyses
Reflection coefficients
Simulation of the AVO responses
Some of the problems in using amplitudes as surrogates for reflection coefficients
Scaling of the amplitudes
The possibility of estimating the proportions of lithological types in a relatively small volume
Probability that a point in a gradient-intercept diagram belongs to an interface of interest
General comments and summary
References
8 Applications of rock physics to inversion studies
Introduction
Standard outputs of an inversion (apart from the density)
Making use of well data to identify facies and assessing the feasibility of an inversion study
Using the properties of the normal distribution
Using cluster analysis to identify facies
Scaling the well data to make it compatible with the seismic data
A quick recapitulation of the steps involved in analysing well data
Populating the seismic cube with facies
Estimation of the effective porosity of a “sand” facies
A theoretical example involving inversion in carbonates
References
Appendix 8.1: Mixtures of normal distributions
Appendix 8.2: Some comments on the use of Bayes’ theorem
9 Modelling carbonates using Differential Effective Medium theory
Introduction
Preliminary remarks
The case of spherical pores
The case of penny cracks (representing fractures)
Discussion
Final remarks
References
Appendix 9.1: Exact solution of the DEM differential equation in the case of spherical inclusions filled with fluid
The impossibility of simulating a granular medium using “pure” DEM theory
Appendix 9.2: Integration of the DEM equations in the case of penny cracks, when the pore space is empty (i.e. dry)
Appendix 9.3: The probability that penny cracks will be interconnected