The Secret to Successful Solute-Transport Modeling

Modeling subsurface solute transport is difficult—more so than modeling heads and flows.  One reason is that the classical governing equation does not always adequately represent what we see at the field scale.  In such cases, commonly used numerical models are solving the wrong equation.  A second reason is that the transport equation is hyperbolic in nature if, where, and when advection is dominant, and parabolic where hydrodynamic dispersion is dominant.  No single standard numerical method works well for all conditions, and for any given complex field problem, where seepage velocity is highly variable in space and/or time, no one method will be optimal everywhere within the solution domain.  Whereas we normally expect a numerically accurate solution to the governing ground-water flow equation, numerical errors in concentrations from numerical dispersion and/or oscillations may be large in some cases—even if the mass-balance error is small.  The accuracy, precision, and efficiency of the numerical solution to the solute-transport equation is more sensitive to the numerical method chosen than for typical ground-water flow problems.  However, numerical errors can be kept within acceptable limits if sufficient computational effort is expended.  But impractically long simulation times may promote a tendency to ignore or accept numerical errors.  Examples illustrate both the value and some practical limitations of numerical solute-transport modeling.  One approach to effective solute-transport modeling is to keep the model relatively simple and use it to test and improve conceptual understanding of the system and the problem at hand.  It should not be expected that all concentration variations observed in the field can be reproduced.  High predictive accuracy likewise cannot be expected.  Given a knowledgeable analyst, a reasonable description of a hydrogeologic framework, and the availability of solute concentration data, the secret to successful solute-transport modeling may simply be to lower expectations.