An Equivalent Homogeneous Continuum Approach to Modeling Solute Transport and Water Flow in Regularly Structured Porous Media

Theoretical investigations and numerical and laboratory experiments were conducted to evaluate the feasibility and limitations of describing solute transport and water flow in regularly structured porous media with an equivalent homogeneous continuum approach. For the analysis of solute transport, it is shown that distinguishing between resident and flux concentration detection modes is of fundamental importance to obtain physically meaningful solutions of the governing equations in situations when large local variations in pore water velocities occur. Effects of using erroneous detection modes are demonstrated theoretically and experimentally for porous media with bimodal velocity distributions. Using a time moment method, relationships between diffusion-controlled or first-order kinetic type mobile-immobile transport models and an "equivalent" monocontinuum dispersion model are derived and criteria for the validity of the latter approach are obtained. A generalization of the moment analysis results is presented which relates the effective dispersivity tor the monocontinuum system with arbitrary bimodal structure to primary geometrical and physical properties of the system. Effects of local transverse mixing within zones of the bicontinuum are demonstrated experimentally to appreciably affect the validity of monocontinuum degeneration unless a time-dependent dispersion coefficient is adopted. The moment method is also used to evaluate constraints on the description of transport through layered media with flow transverse to the stratification as equivalent homogeneous porous media. Experimental results are employed to demonstrate the method. Finally an analysis at the feasibility of describing flow in variably saturated porous media with heterogeneities perpendicular to the mean flow field are investigated. Comparison of numerically simulated flow in a dual medium system with predictions based on analytically calculated average conductivity saturation-pressure relationships indicates that the averaging procedure may provide satisfactory results under a variety of imposed boundary conditions.

Related material