Mathematical model and numerical simulation of multiphase-flow in permeable rocks considering diverse deformation

• We presented a model describing formation deformation during oil production.
• A numerical simulator was developed for predicting multiphase-flow in deformable reservoirs.
• Simulations were carried out to study elastic, elastic–plastic and plastic rock deformations.
• The rock deformation results in a sharp pressure-drop in the vicinity of a production wellbore.

Formation deformation of oil reservoirs is a widespread phenomenon for unconsolidated or abnormal high-pressure formations due to the depletion of reservoir pressure in the process of oil recovery. It may not only result in formation damage, but also have an adverse influence on production performance. In this paper, the deformation behavior of formation and formation damage are analyzed by elastic, elastic–plastic and plastic theory of solid porous media, and a set of expressions is derived to describe the change in porosity and permeability caused by linear or nonlinear deformation. Based on the comprehensive study on deformation of reservoir rock and multiphase flow in porous media, a new three dimensional and three phase-flow mathematical model that is used to predict the changes of porosity and permeability is presented, and the model is solved by the finite-difference method and self-adaptive iterative technique. A field-scale numerical simulator written in FORTRAN code is developed to predict the change trend of porosity and permeability in elastic and elastic–plastic deformation range.The runs of an oil field example with five-spot patterns are calculated on the simulator, and the formation damage and its influence on the pressure profiles in the vicinity around production well are studied under the condition of linear and nonlinear deformation of a reservoir. This work implies that the deformation of oil formation may be elastic, elastic–plastic or plastic in actual oil formation during the oil exploitation. The declines of porosity and permeability induced by the deformation are completely recoverable only for elastic deformation. Furthermore, elastic–plastic and plastic deformation may occur in the vicinity of production wells in unconsolidated formations. It is found that the increase of deformation coefficients presented in this work results in a sharp pressure-drop funnels on the vertical cross profile, which can be interpreted by the permeability decline induced by rock deformation.