Modelling Water Flow and Solute Transport in Heterogeneous Unsaturated Porous Media

New results concerning flow velocity and solute spreading in an unbounded three-dimensional partially saturated heterogeneous porous formation are derived. Assuming that the effective water content is a uniformly distributed constant, and dealing with the recent results of Severino and Santini (Advances in Water Resources 2005;28:964–974) on mean vertical steady flows, first-order approximation of the velocity covariance , and concurrently of the resultant macrodispersion coefficients are calculated. Generally, the velocity covariance is expressed via two quadratures. These quadratures are further reduced after adopting specific (i.e., exponential) shape for the required (cross)correlation functions. Two particular formation structures that are relevant for the applications and lead to significant simplifications of the computational aspect are also considered.

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