Bounds for Effective Stress Coefficients in Poroelasticity

Biot’s theory of poroelasticity implicitely contains a porosity equation that predicts changes in the porosity due to stress loading to be governed by the difference between the macroscopic solid and fluid pressures. This means that the effective stress coefficient for porosity equals 1. However, there is experimental and theoretical evidence that this porosity effective stress coefficient can be smaller and also greater than unity. In order to model such poroelastic rock behavior we make use of a generalized poroelasticity framework. We analyze a generalized porosity equation that depends on an effective pressure and, in particular, we obtain bounds for the porosity effective stress coefficient. These results are then used to obtain new bounds on various other effective stress coefficients.