Abstract

Geomechanics is often represented in conventional reservoir simulators by pressure dependent treatment of porosity and/or permeability. The paper gives a systematic treatment of the subject and shows different methods for pressure-dependent approximations.

Although there is no single method that would provide the best approximation under all circumstances, reasonable approximations exist in several situations. For porosity coupling, the primary factor is the type of deformation. Accurate approximations are given for the cases of uniform depletion with different deformation assumptions. For permeability coupling, new methods have been developed and tested against coupled simulations.

The results show clearly that large errors can result from simple approaches, in estimating both reservoir pressure decline and well productivity/injectivity.

Introduction

In coupled geomechanical and reservoir modelling, one can correctly represent the dependence of reservoir porosity and permeability on effective stress or deformation of porous media. However, because of the complexity and cost of coupled modelling, it is often necessary to approximate these effects in conventional (uncoupled) reservoir simulators. Most commercial models offer options for pressure-dependent porosity (or rock compressibility) and permeability.

In spite of the popularity of the approach, confusion exists about how to best translate the rock mechanics lab data (measured as a function of effective stress) to functions of pressure only, and little is known about the errors resulting from this simplification. This paper gives a systematic discussion of the subject and provides methods for the computation of rock compressibility and pressure depemdent permeability for uncoupled modelling from the true geomechanical data. Both aspects of the coupling (i.e., coupling via porosity and via permeability) will be treated. The methodology utilizes a combination of analytical considerations and comparisons of coupled and uncoupled simulations.

In all reservoirs, the changes in pressure P and temperature T induced by recovery operations are accompanied by changes of stress state. In some problems reservoir undergoes deformation caused by outside forces (e.g., from another reservoir or aquifer zone). In the first (more common) case the P and T changes are the driving forces causing deformation and stress changes, while in the second the deformations are the driving forces causing changes in pressure.