Models for computing geomechanical constants of double‐porosity materials from the constituents' properties

[1] In previous work, phenomenological equations for the poroelastic behavior of a double-porosity dual-permeability medium (i.e., low-permeability storage porosity and high-permeability transport porosity both present in the same three-dimensional (3-D) volume) were formulated, and the coefficients in these equations were identified. In the present work, models are given instead that allow all of these coefficients to be determined from the underlying constituents' properties. Two different models are provided for the six geomechanical constants in the isotropic theory. In one model the low-permeability storage porosity is assumed to be a mixture of two porous materials in nonwelded or partially welded contact, and the high-permeability joint porosity develops as a misfit porosity at the interface between the two partially welded constituents. In this model the joint phase is 100% fluid. In the other model the low-permeability storage porosity is modeled as a single uniform porous material, while the high-permeability joint porosity is modeled as a second distinct porous material in welded contact with the first. In this model the joint phase is a porous continuum possessing a skeletal framework representing the asperities and gouge material that are present in real joints. The complete set of formulas needed for forward modeling the geomechanical constants is obtained for both scenarios. Examples are evaluated with these formulas, and comparisons are made to previous results on double-porosity systems analysis.

[1]  M. Biot.  General Theory of Three‐Dimensional Consolidation , 1941 .

[2]  J. Berryman,et al.  Volume averaging, effective stress rules, and inversion for microstructural response of multicomponent porous media , 1998 .

[3]  David J. Hart,et al.  Laboratory measurements of a complete set of poroelastic moduli for Berea sandstone and Indiana limestone , 1995 .

[4]  A. Cheng,et al.  Fundamentals of Poroelasticity , 1993 .

[5]  James G. Berryman,et al.  Effective stress for transport properties of inhomogeneous porous rock , 1992 .

[6]  M. Biot.  MECHANICS OF DEFORMATION AND ACOUSTIC PROPAGATION IN POROUS MEDIA , 1962 .

[7]  M. Biot,et al.  THE ELASTIC COEFFICIENTS OF THE THEORY OF CONSOLIDATION , 1957 .

[8]  John R. Rice,et al.  On the Stability of Dilatant Hardening for Saturated Rock Masses , 1975 .

[9]  J. Berryman,et al.  Exact results for generalized Gassmann's equations in composite porous media with two constituents , 1991 .

[10]  Dimitri E. Beskos,et al.  On the theory of consolidation with double porosity—II , 1982 .

[11]  James G. Berryman,et al.  The elastic coefficients of double‐porosity models for fluid transport in jointed rock , 1995 .

[12]  Kagan Tuncay,et al.  Effective stress principle for saturated fractured porous media , 1995 .

[13]  Karl B. Coyner.  Effects of stress, pore pressure, and pore fluids on bulk strain, velocity, and permeability in rocks , 1984 .

[14]  Dimitri E. Beskos,et al.  On the theory of consolidation with double porosity—III A finite element formulation , 1984 .

[15]  On Constitutive Equations and Effective Stress Principles for Deformable, Double‐Porosity Media , 1996 .

[16]  A. Love.  A treatise on the mathematical theory of elasticity , 1892 .

[17]  J. E. Warren,et al.  The Behavior of Naturally Fractured Reservoirs , 1963 .

[18]  M. Biot.  Theory of Propagation of Elastic Waves in a Fluid-Saturated Porous Solid. II. Higher Frequency Range , 1956 .

[19]  J. Korringa,et al.  On the Dependence of the Elastic Properties of a Porous Rock on the Compressibility of the Pore Fluid , 1975 .

[20]  F. Gaßmann.  Uber die Elastizitat poroser Medien. , 1961 .

[21]  G. I. Barenblast,et al.  Fundamental Equations of Filtration of Homogeneous Liquids in Fissured Rocks , 1960 .

[22]  Derek Elsworth,et al.  FLOW-DEFORMATION RESPONSE OF DUAL-POROSITY MEDIA , 1992 .

[23]  James G. Berryman,et al.  Connecting theory to experiment in poroelasticity , 1998 .

[24]  J. Berryman,et al.  Exact results in linear thermomechanics of fluid‐saturated porous media , 1992 .

[25]  Zvi Hashin,et al.  Effective thermal expansion coefficients and specific heats of composite materials , 1970 .

[26]  Herbert F. Wang,et al.  Pore pressure buildup coefficient in synthetic and natural sandstones , 1993 .

[27]  A. Gangi,et al.  Variation of whole and fractured porous rock permeability with confining pressure , 1978 .

[28]  Herbert F. Wang.  Theory of Linear Poroelasticity with Applications to Geomechanics and Hydrogeology , 2000 .

[29]  J. Rice,et al.  Some basic stress diffusion solutions for fluid‐saturated elastic porous media with compressible constituents , 1976 .

[30]  A. Norris.  On the correspondence between poroelasticity and thermoelasticity , 1992 .

[31]  J. Geertsma.  The Effect of Fluid Pressure Decline on Volumetric Changes of Porous Rocks , 1957 .

[32]  M. Biot.  Theory of Propagation of Elastic Waves in a Fluid‐Saturated Porous Solid. I. Low‐Frequency Range , 1956 .

[33]  A. Skempton.  THE PORE-PRESSURE COEFFICIENTS A AND B , 1954 .

[34]  H. Kümpel.  Poroelasticity: parameters reviewed , 1991 .

[35]  Derek Elsworth,et al.  Modeling of naturally fractured reservoirs using deformation dependent flow mechanism , 1993 .

[36]  James G. Berryman,et al.  Elastic wave propagation and attenuation in a double-porosity dual-permeability medium , 1998 .