Filtration modelling of oil and gas reservoir is one of the main tools available to petroleum engineering.
In this paper exact and approximate conservation laws and analytical solutions of filtration models are constructed, including multiphase flow models in nanoporous reservoirs that violate Darcy's law.
Constructed conservation laws and particular solutions allow evaluating of technological parameters of oil field development. The structure of the obtained solutions is analyzed and the sensitivity of solutions to the source data is evaluated.
Qualitative and numerical-analytical methods for investigating mathematical models of filtration in inhomogeneous anisotropic media are developed. These methods allow taking into account the fractal, topological and geometric features of the structure of the filter media.