SOLUTE-TRANSPORT MODELING: USE OF VOLUME-WEIGHTED PARTICLES TO IMPROVE THE METHOD OF CHARACTERISTICS

In the traditional method of characteristics for groundwater solute-transport models, advective transport is represented by moving particles that track concentration. This approach can lead to global mass-balance problems (even if the grid spacing is uniform) because in aquifers with complex boundary conditions, particles can originate in cells having different pore volumes and (or) be introduced (or removed) at cells representing fluid sources (or sinks) of varying strengths. Use of volume-weighted particles means that each particle tracks solute mass. In source/sink cells, the changes in particle weights will match the volume of water added or removed through external fluxes. This enables the new method to conserve mass in source/sink cells as well as globally.

This approach also leads to potential efficiencies by allowing the number of particles per cell to vary spatially--using more particles where concentration gradients are high and fewer where gradients are low. The approach also eliminates the need for the model user to have to distinguish between “weak” and “strong” fluid source (or sink) cells. The new model automatically determines whether solute mass added by fluid sources in a cell should be represented by (1) new particles having weights representing appropriate fractions of the volume of water added by the source, or (2) distributing the solute mass added over all particles already in the source cell. The first option is more appropriate for the condition of a strong source. The latter option is more appropriate for a weak source. At sinks, decisions whether or not to remove a particle are replaced by a reduction in particle weight in proportion to the volume of water removed.

A number of test cases, including one that focused on the performance assessment for the WIPP repository in New Mexico, demonstrate that the new method works well and conserves mass. The new algorithm is implemented as a solver option in the U.S. Geological Survey's MODFLOW-GWT solute-transport model.