MODELING THE EFFECTS OF MULTIRATE MASS TRANSFER ON WATER SAMPLING WITH PARTIALLY-PENETRATING WELLS

Nonequilibrium concentration type curves are numerically developed and sensitivity analyses are performed to examine the relationships between effluent concentrations in partially-penetrating monitoring/extraction wells, the vertical plume shape, and the mass transfer characteristics of the aquifer. The governing two-dimensional, axisymmetric nonequilibrium solute transport equation is solved in three stages using an operator-splitting approach. In the first two stages the advection and dispersion terms are solved with the Eulerian-Lagrangian method, based on the backward method of characteristics for advection and the standard implicit Galerkin finite element method for dispersion. In the third step the first-order, immobile-mobile domain mass transfer term is computed analytically for both two-site and lognormally-distributed, multi-rate models.

Effluent concentration variations with time and contour plots of the pore-water concentration distribution in the aquifer are compared for a wide range of field- and laboratory-measured mass transfer rates, various plume shapes, and relevant physical/chemical parameter values, including pumping rate, vertical anisotropy ratio, retardation factor, and porosity. The simulation results show that rate-limited mass transfer can have a significant impact on sample and aquifer pore-water concentrations during three-dimensional transport to a partially-penetrating well. An alternative dimensionless form of the nonequilibrium solute transport equation is derived to illustrate the key parameter groupings that quantify rate-limited sorption effects and show the relative importance of individual parameters. A hypothetical field application example demonstrates the fitting of dimensional type curves to discrete-interval sampling data in order to evaluate the mass transfer characteristics of an aquifer and shows how type curve superposition can be used to model complex plume shapes.