In the last century, there has been strong emphasis on numerical formulations related to the interaction between rock deformation and multiphase fluid flow behavior in hydrocarbon reservoirs. The emphasis of this work has been to develop a coupled model for a petroleum well used within a reservoir simulator. The coupled interaction between geo-mechanics and fluid production can significantly influence both the stress state and fluid flow in the reservoir. As a consequence, coupled theory can provide a unique advantage in simulation interaction between porous media and fluid flow. In addition, the coupled well model can be used to model compaction and subsidence problems in the near wellbore area. Applying the advantage of the finite element method, the governing equations will be solved. Initial results show the influences of geomechanical parameters which have been investigated.
The coupled formulations of deformation and fluid flow are governed by the principal equations, the mass conservation equation, the momentum equation and Darcy?s equation. These physical laws are presented by partial differential equations that can be solved by either analytical methods or numerical methods. In the last century, many researchers have investigated coupled methodologies for application to reservoir simulation particularly in the area of formation subsidence, compaction and hydraulic fracturing. For example, the coupled formulations of deformation and fluid flow were first analyzed by Terzaghi [1,2] as a problem for material consolidation. Subsequent to this, Biot [3] focused on extending the Terzaghi?s theory into 3 dimensions. Also focusing on a linear stress-strain relationship and single-phase fluid flow, both Terzaghi?s and Biot?s analyses are linear, but have not yet been extended for non-linear systems. Following that work, coupled models have existed not only in petroleum engineering but also in civil engineering, geotechnical engineering and rock mechanics. This would include the work of Sandhu and Wilson [4], Ghaboussi and Wilson [5], Gambolati and Freeze [6], Noorishad et al. [7], these are some of the earliest coupled hydromechanical models. In recent years, Gutierrez et al. [8] presented the general equations and theory of a fully coupled analysis for hydrocarbon reservoir compaction and subsidence. They showed that compaction drive could not be properly represented by simply adjusting the value of rock compressibility used in traditional reservoir simulation.
