Mathematical modeling of filtration processes and poro-elasticity

The filtration processes may lead to the appearance of large gradients of pore pressure. It produces a set of main-caused results partially, the seismic activity may be increased. If there are cracks in the formation the pore pressure gradients may excite the shear strains inducing the slipping down processes along the crack. Besides local stress influences the processes near the wells essentially including the fluid-fracturing phenomenon. In this article the set of processes in the saturated porous media is considered according to the quasi-stationary Biot model if both the standard poro-elasticity problem and double-porosity one being examined.