Nonlocal Reactive Transport with Physical and Chemical Heterogeneity: Linear Nonequilibrium Sorption with Random Kd

Abstract

A nonlocal, first‐order, Eulerian stochastic theory was developed by Deng et al. (1993) for the mean concentration of a conservative tracer. Here that result is extended to account for linear nonequilibrium sorption with random partition coefficient. The resultant theory is nonlocal 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 and converted to a real‐space solution via fast Fourier transform in the spirit of Deng et al. (1993). Where possible, comparisons are made with Bellin et al. (1993) and Dagan and Cvetkovic (1993). Positive, negative, and uncorrelated models relating the fluctuating partition coefficient to the fluctuating log conductivity are used to examine the evolution of mean concentration via contours and spatial moments up to the third. The initial sorbed concentration and the deterministic reaction 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 exhibit a sensitivity. In the long time asymptotic limit the first two moments are consistent with Fickian theory; however, in the preasymptotic regime the process is nonlocal and non‐Fickian.