General first-order expressions for solute transport in two- and three-dimensional randomly heterogeneous porous media

The dispersion coefficient is a fundamental parameter in modeling solute transport and can be determined from the particle displacement covariance. Closed-form analytical expressions for the particle displacement covariance and macrodispersion coefficient are only available for first-order analysis for a few correlation models of log-hydraulic conductivity. The methods used to obtain the analytical expressions usually require a specific correlation function of natural-log hydraulic conductivity. In this chapter we derive the general expressions for solute particle displacement covariance and macrodispersion coefficients. These expressions are simple and include only the correlation function of natural-log hydraulic conductivity. They are valid for any statistically isotropic log-hydraulic conductivity correlation function. Results are presented for several frequently used correlation functions of log-conductivity.