NONLOCAL REACTIVE TRANSPORT WITH PHYSICAL ANTI CHEMICAL HETEROGENEITY- LINEAR NONEQUILIBRIUM SORPTION WITH RANDOM K-D

A nonlocal, first-order, Eulerian stochastic theory was developed by D eng et al. (1993) for the mean concentration of a conservative tracer. Here that result is extended to account for linear nonequilibrium sor ption with random partition coefficient. The resultant theory is nonlo cal in space and time. An important observation is that unlike Deng et al. (1993), nonlocality is manifest not just in the dispersive flux, but in an effective convective flux and in sources and sinks as well. The fully nonlocal theory is solved exactly in Fourier-Laplace space a nd converted to a real-space solution via fast Fourier transform in th e spirit of Deng et al. (1993). Where possible, comparisons are made w ith Bellin et al. (1993) and Dagan and Cvetkovic (1993). Positive, neg ative, and uncorrelated models relating the fluctuating partition coef ficient to the fluctuating log conductivity are used to examine the ev olution of mean concentration via contours and spatial moments up to t he third. The initial sorbed concentration and the deterministic react ion rate can have a significant effect on the moments, especially the second longitudinal moment. The first moment is relatively insensitive to the various correlation structures, but the second and third may e xhibit a sensitivity. In the long time asymptotic limit the first two moments are consistent with Fickian theory; however, in the preasympto tic regime the process is nonlocal and non-Fickian.