Study on fluid flow in nonlinear elastic porous media: Experimental and modeling approaches

A theoretical model for describing the changes in the porosity and permeability with fluid pressure in elastic deformed porous media was presented firstly. Secondly, the changes in porosity and permeability of sandstones were studied by experimental approach, and the exponential correlations between porosity, permeability and fluid pressure in porous media were obtained by regression based on these experimental data. Thirdly, based on the theory of nonlinear deformation of porous media and the continua theory on porous media and fluids, a fluid filtration mathematical model considering nonlinear elastic deformation of porous media was developed. To get insights into the performances of fluid flow in the media, exact analytical solutions of the nonlinear model were obtained by traveling-wave transmission. The main parameters were input to analyze the difference of the solutions and their effects on the characteristics of the fluid pressure distribution with space and time. It is found that the effect of nonlinear elastic deformation may lead to the nonlinear distribution of fluid pressure in porous media at one-dimensional case at a one-dimensional case. However, the distribution of fluid pressure in porous media is linear only when the pressure-dependent factors of pressure rock permeability, porosity, fluid density and viscosity satisfy a special correlation.

Research Highlights
► The exponential correlations between porosity, permeability and fluid pressure in porous media were obtained.
► A mathematical model considering nonlinear elastic deformation of porous media and fluid percolating was developed.
► The exact analytical solution of the nonlinear percolating model was obtained by traveling-wave transmission.
► The solution method is different from Boltzmann transformation and perturbation method.