Concentration and temperature transients in heterogeneous porous media Part I: Linear transport

The transport of solute/heat in porous media is modeled by the convection-d ispersion equation. In the study of such transport processes, while the res ident concentration has always been used to develop the governing different ial equations, the flux concentration has been the most commonly measured q uantity in experiments. Hence, earlier studies have emphasized that care mu st be exercised in the quantitative interpretation of experiments to avoid inconsistent use of solutions with the actual conditions of experiments. Th ey have further demonstrated that performing an actual variable transformat ion in the homogeneous medium differential equation of resident concentrati ons shows that the flux concentration also satisfies the convection dispers ion equation including those with linear reaction. Hence, the physical mean ings of solutions with respect to these two concentrations are inferred fro m boundary conditions. The earlier studies have also provided a classificat ion of solutions of homogeneous medium models based on these two concentrat ion variables. This work first generalizes the theory of dependent variable transformation for dispersive transport and further extends it to include the heterogeneous medium models that assume a diffusive transport between t he fracture and matrix phases. Then, two new solutions of the heterogeneous medium solutions are derived. Hence, the experimentalist is furnished with the heterogeneous medium model solutions in which at least one of them is consistent with the actual conditions of an experiment. Secondly, in this w ork, the concept of block geometry functions (BGFs) is extended to include frequency distributions of multiple block sizes more likely to exist in het erogeneous media than a single block. It was found that BGFs of various dis tributions with lambda(min) less than 0.1 differ only slightly, and hence, may be represented by the BGF of the mean block size. Otherwise care must b e exercised to include the block size distribution effect. In addition, num erical Laplace inversion of complete solutions having those slightly differ ing BGFs is found to lead to significant differences for cases where mobile and immobile phase fractions are close. Finally, interpretation of tracer return profiles in a heterogeneous system by employing a nonlinear regressi on technique is illustrated. Simulated field data are matched by a four-par ameter theoretical model and sensitivity of results to parameter values is investigated. (C) 2000 Published by Elsevier Science B.V.