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The path integral for classical statistical dynamics is used to determine theproperties of one-dimensional Darcy flow through a porous medium with acorrelated stochastic permeability for several spatial correlation lengths.Pressure statistics are obtained from the numerical evaluation of the pathintegral by using the Markov chain Monte Carlo method. Comparisons betweenthese pressure distributions and those calculated from the classicfinite-volume method for the corresponding stochastic differential equationshow excellent agreement for Dirichlet and Neumann boundary conditions. Theevaluation of the variance of the pressure based on a continuum description ofthe medium provides an estimate of the effects of discretization. Log-normaland Gaussian fits to the pressure distributions as a function of positionwithin the porous medium are discussed in relation to the spatial extent of thecorrelations of the permeability fluctuations.

Pressure statistics from the path integral for Darcy flow through random porous media