Mathematical Simulation of Interphase Mass Exchange in Course of Filtration of Immiscible Liquids in Deformable Porous Media

This work is devoted to issues related to the need to develop a new mathematical model and methods of obtaining of its analytical solutions on the example of constructing and search of mathematical solutions of phenomenological model of physical-chemical mechanics and mass transfer in multiphase systems of oil reservoirs with highly viscous oil. A model of the interaction of gas and oil with the formation of a gas-oil mixture less viscous than the original oil is constructed based on a mass transfer model in a porous media with double porosity, or dual-porosity fracture-matrix systems, taking into account the deformations of the medium under the influence of swelling of the gas-oil mixture during gas dissolution and applied mechanical load (Wilson–Aifantis model). It is shown that in the simplest case the model is reduced to the nonlinear Khristianovich equation, and its self-similar solution is given.