NUMERICAL SIMULATIONS OF TRANSPORT OF NONERGODIC SOLUTE PLUMES IN HETEROGENEOUS AQUIFERS

Transport of non-ergodic solute plumes by steady-state groundwater flo w with a uniform mean velocity, mu, were simulated with Monte Carlo ap proach in a two-dimensional heterogeneous and statistically isotropic aquifer whose transmissivity, T, is log-normally distributed with an e xponential covariance. The ensemble averages of the second spatial mom ents of the plume about its center of mass, [S-ii(t)], and the plume c entroid covariance, R-ii(t) (i = 1,2), were simulated for the variance of Y = log T, sigma(Y)(2) = 0.1, 0.5 and 1.0 and line sources normal or parallel to mu of three dimensionless lengths, 1, 5, and 10. For si gma(Y)(2) = 0.1, all simulated [S-ii(t)] - S-ii(0) and R-ii(t) agree w ell with the first-order theoretical values, where S-ii(0) are the ini tial values of S-ii(t). For sigma(Y)(2) = 0.5 and 1.0 and the line sou rces normal to mu, the simulated longitudinal moments, [S-11(t)] - S-1 1(0) and R-11(t), agree well with the first-order theoretical results but the simulated transverse moments [S-22(t)] - S-22(0) and R-22(t) a re significantly larger than the first-order values. For the same two larger values of sigma(Y)(2) hut the line sources parallel to mu, the simulated [S-11(t)]- S-11(0) are larger than but the simulated R11 are smaller than the first-order values, and both simulated[S-22(t)] - S- 22(0) and R22(t) stay larger than the first-order values. For a fixed value of sigma(Y)(2), the summations of [S-ii(t)] - S-ii(0) and Rii, i .e., X-ii (i = 1,2), remain almost the same no matter what kind of sou rce simulated. The simulated X-11 are in good agreement with the first -order theory but the simulated X-22 are significantly larger than the first-order values. The simulated X-22, however, are in excellent agr eement with a previous modeling result and both of them are very close to the values derived using Corrsin's conjecture. It is found that th e transverse moments may be significantly underestimated if less accur ate hydraulic head solutions are used and that the decreasing of [S-22 (t)] - s(22)(0) with time or a negative effective dispersivity, define d as 1/2 mu d[S-22]/di, may happen in the case of a line source parall el to mu where sigma(Y)(2) is small.