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A general method for obtaining analytical expressions for the first‐order velocity covariance in heterogeneous porous media

Velocity covariance of seepage flow is the essential quantity in understanding the uncertainty of groundwater flow and contaminant transport in heterogeneous porous media. Nevertheless, a closed‐form analytical expression is available only for first‐order analysis. These available expressions are limited to some specific correlation functions of natural log hydraulic conductivity. The present paper develops a general method for obtaining the first‐order velocity covariance for any statistically isotropic log‐hydraulic conductivity correlation function. The general analytical expressions are derived for both two and three dimensions. The results are demonstrated for several frequently used correlation functions.