Predicting changes in groundwater quality in a complex hydrologic system generally requires simulation of the field problem through the use of a deterministic model. In the most general case, a complete physical-chemical description of moving groundwater includes chemical reactions in a multicomponent fluid and requires the simultaneous solution of the differential equations that describe the transport of mass, momentum, and energy in porous media.

The difficulties in solving this set of equations for real problems have forced hydrologists and reservoir engineers to consider simplified subsets of equations for the general problem. The equation of motion for single-component groundwater flow, which describes the rate of propagation of a pressure change in an aquifer, has been solved for many different initial and boundary conditions. To describe the transport of miscible fluids of differing density, such as salt water and fresh water, the mass-transport equation and the equation of motion have been coupled and solved numerically. Numerical solutions have also been obtained for the heat-transport equation and the equation of motion, particularly for convection problems.

A case history of groundwater contamination at Brunswick, Georgia, illustrates the use of the mass- and momentum-transport equations in predicting and controlling movement of contaminants.