Numerical Simulation of Coupled Fluid-Flow/Geomechanical Behavior of Tight Gas Reservoirs with Stress Sensitive Permeability
Authors: Osorio Jose G. , Chen Her-Yuan , Teufel Lawrence W. 
Published: December 2007

Abstract
This paper presents a 3D finite-difference, fully implicit model to represent the physical phenomena that occur during the production from tight-gas reservoirs with stress-sensitive permeability.
The reservoir is treated as a multiphase poroelastic system consisting of a deforming solid skeleton and a moving compressible pore fluid. The governing equations describing the deformation of the solid part of the rock and the motion of the pore fluid are fully coupled. The model takes into account the effect that rock deformation has on reservoir-rock properties. This feature, and the pressure dependence of the gas properties, leads to a highly non-linear system of finite-difference equations.
Simulation results show that the permeability reduction due to changes in the stress state and pore pressure can significantly affect the production of tight-gas reservoirs.

Introduction
Variation of the pore pressure and the stress state associated with the production of fluids from an oil/gas reservoir gives rise to a change in volume of both reservoir fluids and reservoir rock. The volume variation of the reservoir rock depends on the mechanical properties of the rock material and the magnitude of the changes in pore pressure and stress state. In some cases, the volumetric deformation of the rock has appreciable effects on some of the physical properties of the reservoir rock, such as porosity and permeability.
In conventional reservoir simulation, the permeability is considered to remain constant with time. However, published laboratory works indicate that the permeability of tight-gas reservoirs may be strongly stress-sensitive. Vairogs et al. concluded that low-permeability rocks are affected by stress to a greater degree than those having higher levels of permeability. This agrees with the results published earlier by McLatchie et al. A study by Thomas and Ward showed that the permeability of cores from the Pictured Cliffs and Fort Union formations were affected significantly by confining pressure. Jones and Owens performed laboratory tests on more than 100 tight-gas-sand core samples from five formations. They found that the confining pressure simulating the reservoir effective stress reduces permeability of tight-gas sands two to more than 10 times, depending on the permeability and rock type. Warpinski and Teufel studied the permeability and deformation behavior of low-permeability, gas-reservoir rocks and provided laboratory results showing that tight-gas-sand cores can lose up to 90% or more of their permeability when subjected to the reservoir effective stress.
These laboratory studies show that the permeability of gas-reservoir rocks may change significantly with variation of the pore pressure and the stress state. On the other hand, field observations show that the stress state changes throughout the reservoir as well as with time. These two evidences suggest that it is necessary to consider permeability variation in reservoir simulation.