Simulation of Stress tests using a Poroelastic model to estimate the Permeability behavior of bedford limestone samples

Abstract

Due to its relevance in Geosciences, the stress effect on the dynamic rock properties has been studied experimentally and theoretically for several decades. These works have been oriented mainly to sand- stones, and relatively few to carbonate rocks, despite its relevance. On the other hand, the descrip- tion of the phenomenon is mathematically and numerically complex since it involves the non-linear coupling of the fluid flow with the rock deformation. This work seeks to analyze that little-explored part of experimental tests in carbonates com bined with its numerical simulation. It presents experi- mental tests carried out on Bedford limestone cores and analyzes the effect of confinement stress and fluid pressure (pore pres sure) on its permeability, by two test types, known as hydrostatic (low shear stress) and not hydrostatic (high shear stress) tests. In this work, a mathematical model is presented to describe the phenomenon, considering a single-phase fluid, an elastic rock response, and its numeri- cal implementation in finite elements. The coupling of fluid flow with stress is regularly modeled by algebraic relationships of porosity and permeability as a function of stress. A permeability-stress relationship used in this work depends linearly on volumetric strain and pore pressure. The experi- mental results show that in general, the permeability increases with fluid pressure and decreases with confinement stress. The reduction with the confinement stress is small in the range of confinement stresses analyzed, but it is noticeably more important in the non-hydrostatic tests (8%) than in the hydrostatic ones (2%). The model fitting to experimental data, specifically to the core pressure drop as a function of time, is carried out through the variation of the permeability-stress relationship parame ters. The fitting parameters value differs from the reported value for sandstones, which may be indicative of the difference in the porous structure and mechanical properties of the rocks.