Stochastic analysis and simulation of transport of a contaminant plume in nonuniform groundwater flow

The effect of the size of a solute plume on macrodispersion in two-dimensional nonuniform groundwater flow caused by recharge is investigated. The first-order analytical expressions of the non-stationary velocity covariance are presented under a uniform recharge condition. These expressions are used to evaluate the ensemble averages of the second spatial moments of a finite plume. The first-order theoretical results are verified with Monte Carlo simulations. The results for a line source of different lengths normal to the mean flow and β = 0.05, where β characterizes degree of flow nonuniformity, are presented. It is shown that spreading of a solute plume increases and uncertainty about the mass center of a plume decreases as the size of the plume increases. The ergodic limit is approached as the size of a plume increases and the medium becomes less heterogeneous. For the small value of σ(Y)2 = 0.1, the simulated results are almost identical to the first-order results. As σ(Y)2 increases, the simulated second spatial moments are generally larger than the corresponding first-order results, especially in the transverse direction.