Analysis of macrodispersion through volume averaging: comparison with stochastic theory

Velocity variability at scales smaller than the size of a solute plume enha nces the rate of spreading of the plume around its center of mass. Macrosco pically, the rate of spreading can be quantified through macrodispersion co efficients, the determination of which has been the subject of stochastic t heories. This work compares the results of a volume-averaging approach with those of the advection dominated large-time small-perturbation theory of D agan [1982] and Gelhar and Axness [1983]. Consider transport of an ideal tr acer in a porous medium with deterministic periodic velocity. Using the Tay lor-Aris-Brenner method of moments, it has been previously demonstrated [Ki tanidis, 1992] that when the plume spreads over an area much larger than th e period, the volume-averaged concentration satisfies the advection-dispers ion equation with constant coefficients that can be computed. Here, the vol ume-averaging analysis is extended to the case of stationary random velocit ies. Additionally, a perturbation method is applied to obtain explicit solu tions for small-fluctuation cases, and the results are compared with those of the stochastic macrodispersion theory. It is shown that the method of mo ments, which uses spatial averaging, for sufficiently large volumes of aver aging yields the same result as the stochastic theory, which is based on en semble averaging. The result is of theoretical but also practical significa nce because the volume-averaging approach provides a potentially efficient way to compute macrodispersion coefficients. The method is applied to a sim plified representation of the Borden aquifer.