Mathematical Model of Multiphase Nonisothermal Filtration in Deformable Porous Media with a Simultaneous Chemical Reaction

The authors have developed a mathematical model of multiphase nonisothermal filtration with chemical reactions and phase transitions in deformable porous media. A modified Biot approach was used to describe filtration through a deformable porous medium. Equations for the stress-strain state have been formulated in terms of displacements, and the elastic rheology of a porous skeleton in nonisothermal form was used in the model. The dependence of the permeability on porosity has been written in the form of a Kozeny-Carman equation. A test problem of combustion in a low-permeability sample of a bituminous reservoir has been solved. Results of the work can be used to numerically substantiate experiments on the technology of interbedding combustion in low-permeability beds.