TEMPORAL MOMENT-GENERATING EQUATIONS - MODELING TRANSPORT AND MASS-TRANSFER IN HETEROGENEOUS AQUIFERS

We present an efficient method for determining temporal moments of con centration for a solute subject to first-order and diffusive mass tran sfer in steady velocity fields. The differential equations for the mom ents of all orders have the same form as the steady state nonreactive transport equation. Thus temporal moments can be calculated by a solut e transport code that was written to simulate nonreactive steady state transport, even though the actual transport system is reactive and tr ansient. Higher-order moments are found recursively from lower-order m oments. For many cases a small number of moments sufficiently describe the movement of a solute plume. The first four moments describe the a ccumulated mass, mean, spread, and skewness of the concentration histo ries at all locations. Actual concentration histories at any location can be approximated from the moments by applying the principle of maxi mum entropy, a constraint consistent with the physical process of disp ersion. The forms of the moment-generating equations for different mas s transfer models provide insight into reactive transport through hete rogeneous aquifers. For the mass transfer models we considered, the ze roth moment in a heterogeneous aquifer is independent of the mass tran sfer coefficients. Thus, if the velocity field is known, the mass tran sported past any point, or out any boundary, can be calculated without knowledge of the spatial pattern of mass transfer coefficients and, i n fact, without knowledge of whether mass transfer is occurring. Also, for both first-order and diffusive mass transfer models, the mean arr ival time depends on the distribution coefficient but is independent o f the values of the rate coefficients, regardless of the spatial varia bility of groundwater velocity and mass transfer coefficients.