ON THE VARIANCES OF 2ND SPATIAL MOMENTS OF A NONERGODIC PLUME IN HETEROGENEOUS AQUIFERS

The expressions for the variances of the second spatial moments of a s olute plume, Var[S-ij], were formulated and evaluated for a line sourc e of finite length either normal or parallel to the uniform mean flow velocity, mu, in a two-dimensional heterogeneous and statistically iso tropic aquifer. The evaluations were performed by using the analytical solutions for the velocity covariance derived previously under the fi rst-order approximation to the particle displacement. The main finding is that for the special case of a line source either normal or parall el to the mean flow, not all the variances of the second spatial momen ts decrease but all the coefficients of variation of the second spatia l moments, CV[S-ii], decrease as the initial length of a line source i ncreases. The first-order longitudinal CV[S-11] is independent of the variance of transmissivity, sigma(Y)(2) and the transverse CV[S-22] is inversely proportional to sigma(Y) in the case of a line source norma l to mu. Comparison between the first-order theoretical results obtain ed in this study with previous Monte Carlo simulations shows that the match between the theoretical and simulated CV[S-11] improves as iota( 2) increases and in a less heterogeneous aquifer.