Historically, the geomechanical behavior of a hydrocarbon reservoir has been modeled based on the classical theory of poro-elasticity, which considers absolute reversibility of deformation, which is liable to a porous medium when the mechanical state of the rock is altered. The sands associated with heavy oil formations are generally characterized by low levels of cohesion and density, which is viewed in an increased sensitivity of the rock to permanent deformation and hysteresis; hence it is not suitable to model these formations as if their rheological behavior is elastic. This set the need to construct a model, which describes the permanent plastic deformation that rocks from this kind of reservoir have.

The modeling of the stress-strain behavior of plastic porous media aims to evaluate the permanent deformation that the rock suffers and to study the impact of this phenomenon on the behavior of the reservoir permeability porosity and mechanical stability of the layers overlying (compaction, subsidence). Several theoretical research and experimental surveys have defined that most heavy oil reservoirs can be studied as elasto-plastic materials.

The purpose of this paper is to show the couple model of constitutive equations (stress-strain model) and fluid flow equations that describe the dynamic behavior of a heavy oil reservoir during an isothermal process, which deforms elasto-plastically, and thereby, to predict several geomechanical phenomena or consequence as productivity drop due to changes in the permeability, pore collapse, cap rock integrity, subsidence, among others, that allow an approach to the behavior of these kind of reservoirs in order to improve production processes and simulation.

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