STATISTICAL MOMENTS OF REACTIVE SOLUTE CONCENTRATION IN A HETEROGENEOUS AQUIFER

Neglecting local solute dispersion, we prove that under realistic cond itions the ensemble moments of the local concentration satisfy a mean convection dispersion equation (CDE) for both conservative and instant aneously adsorbing solutes, provided that the solute velocity field is stochastically stationary. Thus the same algorithm can be used to mod el the ensemble mean concentration and its uncertainty. For uniform in itial conditions the solution of the mean CDE contains all the informa tion about the local concentration probability distribution function, which is not Gaussian. The governing equation for k-point ensemble mom ents of the concentration is similar in form to the mean CDE, with the same effective dispersion coefficient and convective velocity. The sp ecial case of an impulse initial condition is used to illustrate that volume averaging can significantly change the concentration coefficien t of variation except at the plume front. The persistence in the longi tudinal direction of concentration moments and concentration k-point m oments is caused by large longitudinal megadispersion. Finally, it is suggested that ''ergodicity'' should be interpreted operationally in t erms of an acceptably small coefficient of variation of the concentrat ion field so that this concept can be applied to experimental field da ta.