David A. Benson Colorado School of Mines Hydrologic Science and Engineering Program Dept. of Geol. and Geol. Eng. Golden, CO 80401 (303) 273-3806 dbenson@mines.edu
 Curriculum Vitae Class Materials Geol 702, 783; G.E. 484/684 Current Research Fractional Derivatives and Contaminant Transport Past Research Soil Vapor Extraction Modeling

## Current and Past Research

My current research deals with little-known yet powerful mathematical tools called fractional derivatives. In essence, the classical Gauss divergence theorem doesn't work well with a misbehaving flux vector like solute advection and dispersion in natural porous or fractured media. The classical divergence takes an integer (first) derivative whereas a fractional-order derivative is a much better choice. Download some papers (including my 1998 dissertation) on the subject.

### VENT2D and VENT3D

My Master's work centered on the creation of realistic numerical models for simulating vaporous contaminant transport in soil. Since nonaqueous-phase liquids (NAPLs) are often present in soil, one cannot justify a simple (linear) retardation coefficient for volatile organic compound movement in the vapor phase. Rather, one must explicitly calculate the phase partitioning via Raoult's or Henry's Laws. The resulting 2-D and 3-D models (VENT2D and VENT3D) are perfectly suited to modeling soil vapor extraction (SVE) as a means of remediating contaminated soil. Since VENT3D was coded and debugged in 1997, VENT2D is available to the general public free of charge. A VENT2D FTP site contains all of the necessary files and an introduction to the model.

VENT3D is a fast, 3-D vapor transport model with NAPL partitioning that uses a third-order transport algorithm with gradient checking for sharp fronts. You can download a reduced-size VENT3D demo here.

### SALTWATER INTRUSION MODELING

A colleague of mine (Anne Carey @ Ohio State University) was doing her Ph.D. research on seawater intrusion and we noticed that some numerical models simply did not do a very good job. It turns out that nobody (to my knowledge) had looked at the error induced by approximation of a highly variable velocity vector field. Lots of previous research looked at error in the approximation of the concentration gradient vector. Read the abstract of our article in the Journal of Contaminant Hydrology (v. 34 no. 3) entitled "Numerical Flux in Highly Variable Velocity Fields Exemplified by Saltwater Intrusion." Those of you doing contaminant transport in the unsaturated zone may want to take a look at this, since it applies to you too.