A Review of Techniques for Measuring the Biot Coefficient and Other Effective Stress Parameters for Fluid-Saturated Rocks

Abstract

Predicting the behavior of a saturated rock with variations in pore fluid pressure during geo-energy production and storage, deep geological disposal of nuclear wastes, etc. is carried out using the isothermal theory of poroelasticity that incorporates Biot's effective stress principle. Several experimental methods for determining Biot's effective stress parameter have been documented in the literature. The original definition of Biot's effective stress is constantly being extended to account for non-linear and inelastic behavior of the rock. The objective of this study is to review the fundamentals of the original experimental approach for determining Biot's coefficient and other developments, their advantages and disadvantages, and include several case studies. Current techniques are based on different premises: jacketed and unjacketed bulk moduli or compressibility values; volume changes of the bulk and pore fluid from a drained triaxial test on a saturated sample; isotropic-isochoric compression tests on a saturated sample; matching volumetric strains or failure envelopes for dry and saturated samples; variations of rock properties, such as volumetric strain, permeability, compressional and shear wave velocities, with respect to confining stress and pore pressure; estimation of the Biot coefficient from other poroelastic parameters; and approximation of the dry bulk modulus or unjacketed bulk modulus of the rock from mineralogical compositions or ultrasonic wave velocities. This article discusses variations in Biot's effective stress coefficients produced using the different techniques and how factors such as pore geometry, test conditions, stress path, and test temperature affect the Biot's coefficient.

On the Poroelastic Biot Coefficient for a Granitic Rock

“…This methodology was also successfully applied to estimate the Biot coefficient for Grimsel granite, which also has a low permeability and a transversely isotropic elastic fabric (Selvadurai et al [43]). A review of the experimental methodologies for estimating the Biot coefficient for rocks and references to other investigations are presented by Kasani and Selvadurai [44]. In conventional definitions of the Biot coefficient, the porous medium is considered to be elastic.…”

“…Values for the Biot coefficient for a variety of rocks were compiled by many investigators (Berryman [96]; Wang [97]; Rice and Cleary [91]; Cosenza et al, [90] Lau and Chandler [87]; Mavko et al [58]; and Kasani and Selvadurai [44]). Table 5 provides values reported in the literature for the Biot coefficient for low permeability materials such as marble, granite, and other crystalline low permeability rocks.…”

Cavity Flow Permeability Testing of an Intact Granite

“…An air flow technique was applied to estimate the permeability of low permeability materials such as cement grout, concrete and ceramics; further references and a review of the experimental techniques are given in [178][179][180][181][182][183] . Transient techniques are complicated because other properties relevant to the interpretation of the tests have to be determined, including the compressibility of the porous skeleton, the compressibility of the solid material composing the porous skeleton, the compressibility of water, the porosity of the porous medium, the Biot coefficient (see [178][179][180][181][182][183][184][185][186][187] ), the air voids that can be present in the fluid region that is pressurized to attain the transient flow, and the appropriate mathematical formulation and modelling (i.e. the diffusion equation approach or a poroelasticity approach) used to interpret the experiments.…”

Theoretical Developments for the Interpretation of Cavity Flow Permeability Tests Conducted on Intact Lac du Bonnet Granite

“…Other contributions relevant to transient tests are also given in [23,24]. Transient techniques are complicated because other properties relevant to the interpretation of the tests have to be determined, including the compressibility of the porous skeleton, the compressibility of the solid material composing the porous skeleton, the compressibility of water, the porosity of the porous medium, the Biot coefficient the air voids that can be present in the fluid region that is pressurised to attain the transient flow, and the appropriate mathematical formulation and modelling (i.e., the diffusion equation approach or a poroelasticity approach) used to interpret the experiments [25][26][27][28][29][30][31][32][33][34][35][36][37]. With the advent of high-precision pumps that can provide flow rates as low as 0.000070 mL/min, steady-state experiments can be performed on low permeability materials such as the Cobourg limestone and the granites from the Canadian Shield.…”