Nonlinear pressure diffusion in a porous medium: Approximate solutions with applications to permeability measurements using transient pulse decay method

摘要

Transient pulse decay has been widely used to measure permeability of tight rocks and synthetic materials. When the pore fluid is a gas (e.g., dry air, Ar, or N-2) as used in a gas permeameter, the pressure diffusion equation governing the pulse decay problem is nonlinear due to a pressure-dependent gas compressibility and molecular slippage effect false known as the Klinkenberg effect). To simplify data analysis in permeability measurement using a gas permeameter, an approximate solution to the nonlinear diffusion equation was obtained using a regular perturbation method. This solution, which is similar to the original exponential solution of Brace et al. [1968] for a case when the compressibility of the pore fluid is a constant, is valid in the limit when the volume of the interconnected pore fluid is much smaller than the volume of the upstream reservoir. Applications of the approximate solution to laboratory measured pulse decay data show that the estimated sample permeability can be overestimated by as much as a factor of two if the transient gas pressure decay experiment is conducted at low pressures and if molecular slippage is not taken into account. The molecular slippage can be effectively eliminated if the pulse decay measurement is conducted at a mean pressure at least 5 times higher than the Klinkenberg slip factor, which is on the order of 1 bar for texturally equilibrated marble and quartzite used in the permeability study of Wark and Watson [1998]. [References: 20]