ABSTRACT:
In anisotropic materials Skempton's B parameter becomes a second order tensor. It is well established from laboratory experiments that the Skempton B tensor may deviate significantly from isotropy, which will influence the pore pressure response. The anisotropy of B in essence results from the anisotropy of the rock formation, and as a result the effects of the tensor Skempton cannot be considered without taking the underlying anisotropy into account. In this paper we use an implementation of Amadei's (1983) solution of the stress field around the borehole in an anisotropic formation to study the Skempton-induced pore pressure. Examples are shown where the anisotropic contribution dominates completely over the isotropic part, and where anisotropy nearly nullifies the isotropic contribution.
1. INTRODUCTION
Petroleum operations such as hole drilling, production and injection in general may lead to volumetric changes in the underground – also in volumes not directly influenced by injection, production or fluid invasion from the borehole – leading to a change in pore pressure. In an isotropic formation, the volumetric strain results from a change in the mean stress. The undrained pressure change may be described by the well-known B-factor introduced by Skempton in 1954, relating the induced pore pressure to the mean stress.
Skempton (1954) defined his pore pressure parameters A and B in a triaxial context. The definition may be written as
(Equation)
where A and B are Skempton's coefficients, ?pf is the induced pore pressure, (Equation) is the change in mean stress and ?s1 and ?s3 are the changes in triaxial stress in axial and radial directions.
For isotropic elasticity the pore pressure responds only to the change in the mean stress. As a result, for isotropic elasticity A=1/3.
A was hence originally introduced to characterize non-elastic effects.
For anisotropic elastic media shear stresses may induce volumetric strain, and hence give pore pressure changes. As a result, the Skempton B must be generalized to a second order tensor, defined by
(Equation)
where summation over repeated indices is assumed here and in the following. The tensorial B in principle relates all stress components to the induced pore pressure.
