Deterministic and Stochastic Analyses of Dispersion in an Unbounded Stratified Porous Medium

Abstract

The dispersion of a conservative solute released instantaneously from a finite or point source in an unbounded, nonrandom periodically stratified porous medium is examined theoretically by applying the moment method of R. Aris (1956) and P. G. Saffman (1962). The governing moment equations are derived for a general stratified medium and then applied to study the detailed time‐dependent variations of various low‐order spatial moments of the three‐dimensional concentration distribution in a particular periodic (sinusoidal) stratified medium, both for the general case when the mean flow direction is inclined to the stratification as well as for the special case of flow parallel to the stratification. The present results confirm the previous results of V. K. Gupta and K. N. Bhattacharya (1986) regarding the asymptotic (large‐time) large‐scale dispersion coefficients for such a periodic medium. The present results which are obtained through a deterministic analysis are compared also with the results which would be obtained by using the previous stochastic theories of G. Matheron and G. deMarsily (1980) and L. W. Gelhar et al. (1979). The comparison reveals several similarities as well as some important differences between the results of the deterministic and stochastic analyses.