NONERGODIC SOLUTE TRANSPORT IN 3-DIMENSIONAL HETEROGENEOUS ISOTROPIC AQUIFERS

The general expressions for the time-dependent ensemble averages of th e second spatial moments [A] and the effective dispersivities gamma, d efined as (1/2 mu)(d[A]/dt) where mu is the magnitude of the mean flow velocity mu, are evaluated in order to study the effect of initial pl ume size on [A] and gamma in three-dimensional heterogeneous isotropic aquifers under the first-order approximation to the particle displace ment. The results confirm previous findings that [A] and gamma general ly approach their respective ergodic limits X and alpha as the size of a source increases, where X and alpha are the single particle displac ement covariance and the associated dispersivity, and that the transve rse lengths of a source are more important than the longitudinal lengt h for the ergodic condition to be met. The longitudinal dispersion of a nonergodic plume becomes Fickian or the effective asymptotic longitu dinal dispersivity is constant at late time as long as one of the init ial lateral lengths of the plume is nonzero, while the transverse disp ersion is always non-Fickian and the effective asymptotic transverse d ispersivities are always zero regardless of the initial plume size. Th e most important and interesting findings are, when the longitudinal l ength I, of an initial plume is larger than the lateral lengths l(2) a nd l(3), both effective longitudinal and transverse dispersivities gam ma(ii) (i = 1, 2, 3) increase to their respective peaks at early time, then gamma(ii) decreases toward an asymptotic constant, whose value d epends on the values of l(2) and l(3) (gamma(11) --> 0 if l(2) = l(3) = 0), whereas gamma(22) and gamma(33) decrease to below zero (i.e., be come negative), increase again, and finally approach zero independent of the lateral lengths of the source. Comparison of the current study with a numerical simulation shows good agreement between the calculate d and simulated longitudinal second spatial moments.