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Summary 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 and iterative coupling 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 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, and sand production. 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 caused by fluid withdrawal from the subsurface. Well-known examples include the seafloor subsidence in the Ekofisk field or Valhall field in the North Sea, subsidence over a large area in Long Beach Harbor, California, or in the regions of the Bolivar coast and Lagunillas in Venezuela. In addition, production loss caused by casing damage can be significant (for instance, in the Belridge Diatomite field in California).
The fundamentals of geomechanics are based on the concept of effective stress formulated by Terzaghi in 1936. Based on the concept of Terzaghi's effective stress, Biot investigated the coupling between stress and pore pressure in a porous medium and developed a generalized 3D theory of consolidation. Skempton 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. Geerstma gave a better insight into the relationship between pressure, stress, and volume. Van der Knaap extended Geertsma's work to nonlinear elastic geomaterials. Nur and Byerlee proved that the effective stress law proposed by Biot is more general and physically sensible than that proposed by Terzaghi. Rice and Cleary solved poroelastic problems by assuming pore pressure and stress as primary variables, instead of displacements as employed by Biot. Still, all the previously mentioned 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. Because of 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, and so on. 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.
The purpose of this paper is to develop a new formula for porosity as a function of pressure, temperature, and mean total stress, which is used to improve the speed of convergence of the coupling between a geomechanics module and a reservoir simulator when iterative coupling is employed. Only porothermoelastic materials are considered in this study.
Coupling Methods Methods of coupling between reservoir flow and solid deformation found in the literature can be classified into four different types: full coupling, iterative coupling, explicit coupling, 19 and pseudocoupling. In spite of recent advances, the interaction between reservoir fluid flow and solid deformation still offers many problems for research such as accuracy, convergence, and computing efficiency. Definitions of the different coupling types are briefly given in the following.
Full Coupling. In this type of coupling, flow variables such as pressure, temperature, and geomechanical response (such as displacements) are calculated simultaneously through a system of equations with pressure, temperature, and displacements as unknowns. The method is sometimes called implicit coupling because the whole system is discretized on one grid domain and solved simultaneously.
Iterative Coupling. In this type of coupling, reservoir flow variables and geomechanics variables are solved separately and sequentially by a reservoir simulator and a geomechanics module, and the coupling terms are iterated on at each timestep. The coupling iteration is controlled by a convergence criterion that is normally based on pressure or stress changes between the last two iterates of the solution.
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