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 understand ing the uncertainty of groundwater flow and contaminant transport in hetero geneous porous media. Nevertheless, a closed-form analytical expression is available only for first-order analysis. These available expressions are li mited to some specific correlation functions of natural log hydraulic condu ctivity. The present paper develops a general method for obtaining the firs t-order velocity covariance for any statistically isotropic log-hydraulic c onductivity correlation function. The general analytical expressions are de rived for both two and three dimensions. The results are demonstrated for s everal frequently used correlation functions.