Abstract
Fluid-saturated rocks are multi-phasic materials and the mechanics of partitioning the externally applied stresses between the porous skeleton of the rock and the interstitial fluids has to take into consideration the mechanical behaviour of the phases. In these studies the porosity of the multi-phasic material is important for estimating the multi-phasic properties and most studies treat the porosity as a scalar measure without addressing the influence of pore shape and pore geometry. This paper shows that both the overall bulk modulus of a porous medium and the Biot coefficient depend on the shape of the pores. Pores with shapes resembling either thin oblate spheroids or spheres are considered. The Mori–Tanaka and the self-consistent methods are used to estimate the overall properties and the results are compared with experimental data. The pore density and the aspect ratio of the spheroidal pores influence the porosity of the geomaterials. For partially saturated rocks, the equivalent bulk modulus of the fluid–gas mixture occupying the pore space can also be obtained. The paper also examines the influence of the pore shape in estimating the Biot coefficient that controls the stress partitioning in fluid-saturated poroelastic materials.
Highlights
Fluid-saturated rocks are multi-phasic materials and the mechanics of partitioning the externally applied stresses between the porous skeleton of the rock and the interstitial fluids has to take into consideration the mechanical behaviour of the phases
The main purpose of this paper is to examine the important role that the pore shape plays in controlling the overall elastic moduli of fluid-saturated porous media
The conventional approaches for the estimation of overall elastic properties of porous media largely focus on a scalar measure of porosity
Summary
The effective properties of rocks can be estimated by one of the effective medium methods, such as the MoriTanaka[1,2,3] or the self-consistent m ethod[4]. The volume fraction of the pores filled with fluid is nS , where S is the degree of saturation. The bulk moduli of the fluid and the solid phase are denoted by Kf and Ks , respectively, whereas the bulk modulus of air is Ka ≪ Kf. The overall bulk modulus Ku of such a three-phase medium in the undrained state can be expressed as. Where Af and Aa are the total strain localization factors for the fluid phase and the air phase, respectively. Where Tf , Ta are, respectively, the partial strain localization factors for the fluid phase and the air. The overall bulk modulus of the drained medium is obtained by setting the bulk modulus of the fluid phase Kf in (4) equal to zero, which gives
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