Gas filtration from an underground reservoir at a large initial pressure gradient

Gas filtration from an underground reservoir through a layer of a porous medium due to an instantaneous increase in the gas pressure in the reservoir is studied. The problem is considered in a one-dimensional formulation in the general case where the temperatures of the gas and the porous medium are different and unstable, and in the case of a high specific heat of the solid phase and a high interfacial heat-transfer rate. The dynamics of the gas flow at the inlet and outlet of the underground reservoir is analyzed, the time of unloading of the system is estimated as a function of the permeability of the porous medium. It is shown that, depending on the properties of the porous layer, two characteristic gas flow regimes are possible: a fast discharge regime and a slow regime which is determined mainly by barodiffusion.