Deduction of in-situ gas permeability test equation

The gas permeability of porous medium can be estimated by in-situ tests, which can avoid the defects of laboratory tests, that is, the pore structure of samples must be steady, and the sample size is small. The equation used in-situ tests is derived from 1-dimensional radial gas seepage model, and then the pressure field is given based on analysis of 2-dimensional axially symmetric model. The radial outer boundary r_out in the in-situ test equation is the sum of test length and half packer length, and the effective region is the sphere of which the radius is r_out. The judgment of whether or not the tests obey the Darcy's law is deduced: the tests are conducted under at least three different fluxes. Taking the flux as abscissa and the difference of pressure square as ordinate, the test points can be curve-fitted as a straight line which crosses origin.