VARIATIONAL BOUNDS FOR FIRST-PASSAGE-TIME PROBLEMS IN STRATIFIED POROUS-MEDIA

We examine the first-passage-time problem for passive tracer transport in how through porous media. The simplified model used [G. Matheron a nd G. de Marsily, Water Resources Res. 16, 901 (1980)] pertains especi ally to groundwater flow, and assumes that the medium is fully stratif ied. Transport normal to the layering is governed by diffusion alone; transport parallel to the layering is governed by both diffusion and c onvection. The fluid velocity varies randomly from layer to layer. The region of interest is vertically infinite but horizontally finite (of length 2L), with a source inside and sinks on the boundaries. We aver age a path-integral expression for the Green function over velocity fl uctuations and approximate the result in the limits of long distance a nd long time via Feynman's variational method. We calculate the exit t ime distribution and the mean first passage time. The latter is propor tional to L(4/3), consistent with previous work.