ABSTRACT:

Biot's constant is used in many rock mechanics applications to evaluate different problems, therefore it is crucial to estimate it in the laboratory with reasonable experimental error. Three experimental methods are presented in this paper to evaluate the poroelastic factor of rock specimens. The first technique consists of determining matrix and bulk compressibilities using hydrostatic tests. The second technique involves hydrostatic and depletion tests performed on identical samples providing the poroelastic factor as a function of effective stress. The third technique involves constructing the failure envelope on samples with zero pore pressure and one triaxial test with pore pressure. The last two methods provide comparable results that do not require measurement of sample compressibilities. This paper discusses the detailed experimental procedures of proposed methods. Finally, these approaches are compared to the conventional method.

INTRODUCTION

Poroelasticity plays a vital role in the application of rock mechanics in petroleum engineering such as reservoir engineering, wellbore stability, hydraulic fracturing, and production. Several methods have been introduced in the literature to evaluate the poroelastic factor, Biot constant (a). However, these methods have to measure or assume the grain compressibility, and this introduces an appreciable error to the calculation of the poroelastic factor. Additionally, these traditional methods rely on the fact that the sample porosity consists of 100 % interconnected pores, which is not a valid assumption in the majority of rock formations. Within the proximity of the wellbore, poroelasticity can be examined based on the effective stress concept introduced by Terzaghi (1936 and 1943) and Biot (1941). This concept suggests that pore pressure helps counteract the mechanical stress carried through grain-to-grain contact. The effect of pore pressure is measured by the poroelastic factor a; the relationship is:

[Equation available in full paper] (1)

where ó?is the effective stress, ó is the total (absolute) stress, and Pr is the reservoir pressure.

The poroelasticonstant is:

[Equation available in full paper] (2),

with the bulk compressibility Cb given by:

[Equation available in full paper] (3)

If the rock has no porosity, the matrix compressibility, Cma, is equal to Cb, and á becomes zero. Conversely, with high porosity, the matrix compressibility is small compared to the bulk compressibility, and a approaches unity. Hence, when á =0 the deformation is completely consumed by the grains, as is the case in nonporous media, however when á =l the skeleton is much more compressible than the constitutive grains, as can be assumed in soil mechanics. Therefore the Biot's coefficient is a characteristic of the porous media.

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