Nonlinear pressure diffusion in a porous medium: Approximate solutions with applications to permeability measurements using transient pulse decay method
Y. Liang et al., Nonlinear pressure diffusion in a porous medium: Approximate solutions with applications to permeability measurements using transient pulse decay method, J GEO R-SOL, 106(B1), 2001, pp. 529-535
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 Klink
enberg effect). To simplify data analysis in permeability measurement using
a gas permeameter, an approximate solution to the nonlinear diffusion equa
tion 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 small
er than the volume of the upstream reservoir. Applications of the approxima
te 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 a
nd if molecular slippage is not taken into account. The molecular slippage
can be effectively eliminated if the pulse decay measurement is conducted a
t 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 quar
tzite used in the permeability study of Wark and Watson [1998].