Dispersion in porous rocks with fractures

This is a set of Matlab script packages related to the dispersion in porous rocks with fractures, studied in a PhD project by Junxin Guo.

A script package containing extended work on this project is also included on this page.

Summary:

Seismic characterisation of fractures is of great importance for the oil and gas production. For this purpose, in this thesis, I explore the mechanisms for the seismic dispersion, attenuation, and frequency-dependent anisotropy in fractured reservoirs.

Two important mechanisms are investigated, one is the wave-induced fluid flow (WIFF) and the other is the wave scattering by fractures. This study provides numerically validated theoretical models, which lay the basis for developing seismic attributes for fractured reservoir characterisation.

This PhD Thesis was submitted in March 2018 by Junxin Guo.

Thesis outline

Chapter 1: Introduction
Chapter 2: Theoretical background and numerical simulation methodologies
Chapter 3 Dispersion, attenuation, and anisotropy due to WIFF in porous rocks with aligned fractures of finite thickness
Chapter 4 Dispersion, attenuation, and anisotropy due to WIFF in porous rocks containing two orthogonal sets of fractures
Chapter 5 Scattering of seismic waves by aligned fluid saturated fractures with finite thickness
Chapter 6 Coupling effects between WIFF and scattering on the seismic dispersion and attenuation
Chapter 7 Conclusions

The published journal articles are included in the folders.

Note that Chapters 3, 4, 5 and 6 each have their own Matlab scripts package as listed below.

Script packages for Junxin Guo’s thesis: Seismic Dispersion, Attenuation, and Frequency-Dependent Anisotropy of Fractured Reservoirs.

Author(s): Junxin Guo and Boris Gurevich, Curtin University
Version: 0.1
Date: 27/04/2018

Packages:

Name: Dispersion Attenuation Anisotropy in Rocks With Aligned Fractures Of Finite Thickness
Version: 0.1
Date: 27/04/2018
Description: Dispersion Attenuation Anisotropy in Rocks With Aligned Fractures Of Finite Thickness (Chapter 3).

Functions:

anisotropy_Gassmann(C,por,Ks,Kf)
Calcuates the saturated stiffness matrix using anisotropic Gassmann (orthotropy).
anisotropy_velocity(C11,C12,C22,C44,C55,C66,ang,den)
Calculates the velocities in the 1-2 plane. The velocities are dependent on the incident angles.
General_Eshelby_model(Km,Gm,Kmf,Gmf,a1,a2,a3,por,opt)
Calculates the excess compliance matrix of fractures which is filled by any elastic materials in the isotropic elastic background matrix (Mura, 1987, Section 11).
linear_slip(Em,vm,Zn1,Zt1,Zn2,Zt2)
Calculates the effective stiffness matrix for the dry rock with two sets of orthoganal fractures in the 1-2 plane.

Name: Dispersion in porous rocks with Fractures/Dispersion Attenuation Anisotropy in Rocks with Two Orthogonal Fracture sets (Chapter 4)
Version: 0.1
Date: 27/04/2018
Description: Dispersion in porous rocks with Fractures/Dispersion Attenuation Anisotropy in Rocks with Two Orthogonal Fracture sets (Chapter 4)

Functions:

anisotropy_Gassmann(C,por,Ks,Kf)
This function calcuates the saturated stiffness matrix using anisotropic Gassmann (orthotropy).
anisotropy_velocity(C11,C12,C22,C44,C55,C66,ang,den)
This function calculates the velocities in the 1-2 plane. The velocities are dependent on the incident angles.
linear_slip(Em,vm,Zn1,Zt1,Zn2,Zt2)
This function calculates the effective stiffness matrix for the dry
rock with two sets of orthogonal fractures in the 1-2 plane.
Multi_fracture_elastic_properties
This function calculates the elastic properties (and elastic wave velocities) of the saturated rock with two perpendicular sets of fractures (intersecting or non-intersecting) in the low- and high-frequency limits, as well as at intermediate frequency range.

Name: Scattering of seismic waves by aligned fluid saturated fractures with finite thickness (Chapter 5)
Version: 0.1
Date: 27/04/2018
Description: Scattering of seismic waves by aligned fluid saturated fractures with finite thickness (Chapter 5).

Functions:

anisotropy_velocity(C11,C12,C22,C44,C55,C66,ang,den)
Calculates the velocities in the 1-2 plane.
The velocities are dependent on the incident angles.
General_Eshelby_model(Km,Gm,Kmf,Gmf,a1,a2,a3,por,opt)
Calculates the excess compliance matrix of fractures, which is filled by any elastic materials in the isotropic elastic background matrix (Mura, 1987, section 11).
Numerical_example_wave_scattering_crack_density
Calculates the scattering dispersion and attenuation under different crack density.
Numerical_example_wave_scattering_fluid_modulus
Calculates the scattering dispersion and
attenuation under different fluid bulk modulus.
Numerical_example_wave_scattering_fluid_viscosity
Calculates the scattering dispersion and
attenuation under different fluid viscosity.
Numerical_example_wave_scattering_thickness
Calculates the scattering dispersion and attenuation under different fracture thickness.
Prediction_wei_data_scattering_dispersion_attenuation
Compares the theoretical predictions with the experimental results for the scattering attenuation perpendicular and parallel to the fracture plane.
Prediction_wei_data_scattering_dispersion_dispersion
Compares the theoretical predictions with the experimental results for the scattering dispersion perpendicular and parallel to the fracture plane.
PSVatt_dis(f,a,ang,v,e,vis,Km,Gm,Kf,den,M)
Calculates the phase velocity and attenuation of the P and SV wave due to the scattering by the aligned fractures in the rock (2D), programmed based on the paper by Kawahara and Yamashita (1992): Scattering of elastic waves by a fracture zone containing randomly distributed fluid saturated cracks with no fluid flow inside.
PSVatt_dis_fluid_pressure(f,a,ang,v,e,vis,Km,Gm,Kf,den,Popt,M)
Calculates the phase velocity and attenuation of the P and SV wave due to the scattering by the aligned fractures in the rock (2D), programmed based on the paper by Kawahara and Yamashita (1992): Scattering of elastic waves by a fracture zone containing randomly distributed fluid saturated cracks with uniform fluid pressure.
PSVscatering_matrix(M,m,n,k,h,opt)
Calculates the scattering matrix element T_mn^(121) for the P and SV wave according to the paper Kawahara and Yamashita (1992): Scattering of elastic waves by a fracture zeone containing randomly distributed cracks (Appendix C).

Name:Coupling Effects Between WIFF and Scattering On The Seismic Dispersion And Attenuation (Chapter 6)
Version: 0.1
Date: 27/04/2018
Description: Coupling Effects Between WIFF and Scattering On The Seismic Dispersion And Attenuation (Chapter 6).

Functions:

anisotropy_Gassmann(C,por,Ks,Kf)
This function is used to calcuate the saturated stiffness matrix using {716467cda98819fdee890b93468ddc20789bb7014d5f7dd88adfbce1dfda31d2} anisotropic Gassmann (orthotropy).
General_Eshelby_model(Km,Gm,Kmf,Gmf,a1,a2,a3,por,opt)
This function is used to calculate the excess compliance matrix of
{716467cda98819fdee890b93468ddc20789bb7014d5f7dd88adfbce1dfda31d2} fractures which is filled by any elastic materials in the isotropic
{716467cda98819fdee890b93468ddc20789bb7014d5f7dd88adfbce1dfda31d2} elastic background matrix, Mura, 1987, section 11.
Prediction_numerical_simulations_Eva_scattering_WIFF
This function is used to compare the theoretical predictions with the {716467cda98819fdee890b93468ddc20789bb7014d5f7dd88adfbce1dfda31d2} numerical simulations consdiering both the effects of scattering and WIFF.
PSVatt_dis_fluid_pressure(f,a,ang,v,e,vis,Km,Gm,Kf,den,Popt,M)
This function calculates the phase velocity and attenuation of the P and SV wave due to the scattering by the aligned fractures in the rock (2D), programmed based on the paper by Kawahara and Yamashita (1992): scattering of elastic waves by a fracture zone containing randomly distributed fluid saturated cracks with uniform fluid pressure.
PSVatt_dis_WIFF(f,a,ang,v,e,vis,Km,Gm,P1,P2,Znd,Zn0,Kf,por_f,den,M)
This function calculate the phase velocity and attenuation of the P and SV wave due to the scattering by the aligned fractures in the rock (2D), programmed based on the paper by Kawahara and Yamashita (1992): scattering of elastic waves by a fracture zone containing randomly distributed fluid saturated crack, the solid is considered to be porous medium and the wave-induced fluid flow effects are incorporate.
PSVscatering_matrix(M,m,n,k,h,opt)
This function calculate the scattering matrix element T_mn^(121) for the P and SV wave according to the paper by Kawahara and Yamashita (1992): scattering of elastic waves by a fracture zeone containing randomly distributed cracks (Appendix C).

Packages for the extended research on dispersion and anisotropy in porous rocks with fractures to aligned slit and penny fractures, beyond Guo’s PhD thesis.

Authors: Boye Fu and Boris Gurevich, Curtin University
Version: 0.1
Date: 18/05/2018
Name:Dispersion attenuation anisotropy in rocks with aligned slit and penny fractures
Description: Dispersion attenuation anisotropy in rocks with aligned slit and penny fractures.

Functions:

gff(z)
This function is used in scatteringproblem.m and calculates the incident P wave “-p0S(x)” from Galvin (2009), equation (29).
gff1(z)
This function is used in scatteringproblem.m and calculates the incident P wave “f(w)” from Song (2017), equation (A13).
HKK(u)
This code generates an analytical result for the low-frequency limit of the second order term of ‘k2’ of function in the kernel function “H” from Song (2017), equation (60).
HKK4(u)
This code generates an analytical result for the low-frequency limit of the fourth order term of ‘k2’ of function in the kernel function “H” from Song (2017), equation (60).
lambdaK_generalf(u,z)
This function is used in scatteringproblem.m and calculates the kernel function R(x,y)T(y) from Galvin (2009), equation (29).
lambdaK_generalf8(u,z)
This function is used in scatteringproblem.m and calculates kernel function “Kb” from Song (2017), equation (A13).
scatteringproblem.m
The scripts are generated after Galvin, R. (2007), Elastic wave attenuation, dispersion and anisotropy in fractured porous media. Doctoral dissertation, Curtin University. Please see Song, et al., (2017) for the details of the parameters used in this script.

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Please acknowledge the source of this software if you use it in any publications:

Guo, J., and Boris Gurevich. Script Packages for Junxin Guo’s Thesis: Seismic Dispersion, Attenuation, and Frequency-Dependent Anisotropy of Fractured Reservoirs (Version 0.1). Matlab, Windows, Linux. Perth, Western Australia: Curtin University, 2018.

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