Fluid Flow through a Conventional Gas Reservoir:
Conventional diffusivity equation.
Add the non-linear quadratic pressure-gradient term to account for the gas compressibility and reservoir heterogeneity effect.
Treat porosity and permeability as a function of reservoir pressure.
Consider gas viscosity and gas compressibility as a function of reservoir pressure and temperature.
Can we still solve the above problem in terms of "pressure" (meant for liquid flow solution) only - without introducing the concept of "pseudo-pressure" and "pseudo-time" (meant for gas); and get the reasonable results?
At reservoir conditions, the quadratic term may not make much difference. In very sharp pressure changes, such as flow trough perforations and maybe in fractures, there is likely a need to account for that. Are you looking at an analytical solution, or a numerical application? Practically, in reservoir simulation flow through perforations is handled as a variable skin. Flow in fractures is handled through a dual permeability formulation.
Also bear in mind that in resource plays, where the reservoir is also a source rock, or in coal bed methane, there is absorbed gas liberated and described by diffusion. Many reservoir simulation packages account for that as well.
In tight rocks it is also useful to account for rock compressibility. That is an interesting phenomenon, because with a decrease of pore pressure and increase of net stress, permeability decreases. Pore space also decreases adding a drive mechanism. Those two elements, counter each other, but depending on rock setting and well/completion design, one may prevail over the other.
"Investigating the Expected Long-Term Production Performance of Shale Reservoirs" Vassilellis, George D., Gaffney, Cline & Associates Inc. Moos, Daniel, GeoMechanics International GMI Li, Chao, Gaffney, Cline & Associates Inc. Seager, Rawdon John H., Gaffney, Cline & Associates Inc. 138134-MS SPE Conference Paper - 2010
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