New Iterative Coupling Between a Reservoir Simulator and a Geomechanics Module

Abstract

Interactions of solid mechanics and fluid flow have been studied by numerous researchers for the past several years. Different methods of coupling such as full coupling, iterative coupling, etc., have been used. Nevertheless, the accuracy and the large run time of the coupled solid-mechanics fluid-flow model are outstanding issues that prevent the application of the coupled model in full-field studies. In this work, a novel relationship of porosity as a function of pressure, temperature and mean total stress is developed for iterative coupling of stress and flow. The new formula not only improves the accuracy of the coupling, but also reduces substantially the number of coupling iterations. The latter feature decreases significantly the CPU time. The new approach was implemented in a modular, iteratively coupled system. The rapid convergence provides the equivalent of a fully coupled method that is necessary to investigate complex coupled problems. The main advantage of this type of coupling is that a geomechanics module can be easily coupled with different reservoir simulators. The paper gives some comparisons of results obtained by the new porosity formula with another formulation.

Introduction

Reservoir simulation has a long history of development and it is used to model a wide variety of reservoir problems. However, using a conventional simulator still cannot explain some phenomena that occur during production such as subsidence, compaction, casing damage, wellbore stability, sand production, etc.^1,2,3. Most conventional reservoir simulators do not incorporate stress changes and rock deformations with changes in reservoir pressure and temperature during the course of production. The physical impact from these geomechanical aspects of reservoir behavior is not small. For example, pore reduction or collapse leads to abrupt compaction of the reservoir rock, which in turn causes subsidence at the ground surface and damage to well casings. There are many reported cases of environmental impact due to fluid withdrawal from the subsurface. Well known examples include the sea floor subsidence in the Ekofisk field or Valhall field in the North Sea⁴; subsidence over a large area in the Long Beach Harbor, California⁵ or in the regions of the Bolivar Coast and Lagunillas in Venezuela⁶. In addition, production loss due to casing damage can be significant (e.g., in the Belridge Diatomite field in California⁷).

The fundamentals of geomechanics are based on the concept of effective stress formulated by Terzaghi in 1936⁸. Based on the concept of Terzaghi's effective stress, Biot⁹ investigated the coupling between stress and pore pressure in a porous medium and developed a generalized three-dimensional theory of consolidation. Skempton¹⁰ derived a relationship between the total stress and fluid pore pressure under undrained initial loading through the so-called Skempton pore pressure parameters A and B. Geerstma¹¹ gave a better insight of the relationship among pressure, stress and volume. Van der Knaap¹² extended Geertsma's work to nonlinear elastic geomaterials. Nur and Byerlee¹³ proved that the effective stress law proposed by Biot is more general and physically sensible than that proposed by Terzaghi. Rice and Clearly¹⁴ solved poroelastic problems by assuming pore pressure and stress as primary variables instead of displacements as employed by Biot. Yet, all the above work has been limited to the framework of linear constitutive relations and single-phase flow in porous media. Rapid progress in computer technology in recent years has allowed the tackling of numerically more challenging problems associated with nonlinear materials and multiphase flow. Due to the complexity of the solutions of multiphase flow and geomechanics models themselves, the solution of the coupled problem is even more complicated and needs further study to improve accuracy, convergence, computing efficiency, etc. In particular, researchers have been debating which coupling approach is best for computing fluid-solid interactions. The term ‘interaction' is understood here as the mechanical force effect rather than the chemical reaction effect between fluid and solid.