Models and Problems for Saturated Porous Media / *Brovko G.L.* // Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika. 2010. № 6. P.
[Moscow Univ. Mech. Bulletin. Vol. 72, N 2, 2017. P. 125-135].

A multiphase model of a liquid- and gas-saturated porous medium is proposed. The model takes into account the finite deformations of a skeleton, arbitrary flows of liquids and gases, and the phase mass transfer between the skeleton and the liquids. Some basic relations are given for the corresponding boundary value problems in the cases of arbitrary and small motions. The constitutive relations describing the properties of the skeleton resistance to deformation (skeleton stresses) and the mutual resistance of components (internal interaction) are considered in detail. The internal actions exerted on the skeleton by a moving liquid (gas) are discussed when these actions may take the form of drag forces, lift (displacing) forces, overturning moments, and rotational (screw) moments.

*Key words*:
saturated porous media, deformable skeleton, liquid and gas phases,
boundary value problems, constitutive relations for skeleton, internal interactions.