## Current Research Interests

### Multiphase Flow in Porous Media

The development and solution, via numerical analysis, of the equations

governing the evolution of non-aqueous phase liquids in the subsurface is the

focus of this research. The objective is to develop mathematical models that

describe the flow, transport and transformation of non-aqueous phase

contaminants, such as trichloroethylene, that constitute a threat to

groundwater quality.

### Least-cost Groundwater Remediation Design

The use of groundwater simulators in combination with linear and non-linear

programming algorithms to obtain the least-cost design of

groundwater-remediation systems is the focus of this research effort. Flow and

transport models of contaminated groundwater reservoirs are coupled to

operations-research programming algorithms. Objective functions (usually based

upon cost) are combined with design constraints to obtain the least-cost

remediation-design While pump-and-treat systems have been the focus to date,

other strategies are also considered. Of particular interest at this time is

the study of problems involving non-aqueous phase contaminants and bioremediation.

### Least-cost Long-term Groundwater Quality Monitoring

The use of groundwater flow and transport models that exhibit random-field

based parameter distributions (for example hydraulic conductivity) in

combination with Kalman-Filter algorithms to formulate least-cost strategies

for the long-term monitoring of groundwater quality is the focus of this

research area. Using these computational tools it is possible to determine

where and when to sample groundwater in order to assure that statistical

objectives are met at minimal cost.

### Latin-hypercube Sampling for Random-field Generation

The use of Latin-hypercube statistical sampling to generate correlated random

fields, such as hydraulic conductivity,that are subsequently used in

Monte-Carlo analysis of state variables such as hydraulic head or

concentration, is the main focus of this work. By using the Latin-hypercube

approach it is possible to obtain the target statistical accuracy needed in

Monte-Carlo analysis with less computational effort. The proposed approach is

being developed as a sub-problem associated with long-term monitoring.

### Numerical Analysis

The development of new numerical techniques for the solution of

partial-differential equations, such as those that describe the evolution of

groundwater contaminants, is the focus of this research area. Finite-element

methods, especially those based upon collocation-like methods, are of primary

concern. The development of new and more efficient algebraic approaches for

the solution of the resulting discrete equations is also of interest. Current

efforts focus on the development of a single-degree of freedom strategy for

solving transport-like equations and non-linear flow equations arising out of

multiphase flow in porous media.

### Assessment of Risk using Fuzzy Sets and Fuzzy Logic

The use of fuzzy knowledge-based systems to describe and evaluate risk,

especially health risk identified with exposure to toxic chemicals is the

focus of this research effort. Using the fuzzy approach expert opinion can be

used to formulate a risk-based model that can subsequently be used to

determine health risks associated with new levels of exposure or new exposure

pathways. The approach specifically avoids the need to explicitly use

questionable statistical data on dose-response relationships that have been

developed using animal studies and high-dose concentrations.

### Intermediate Scale Groundwater Facility

The design and construction of an intermediate-scale model , and the design,

fabrication and installation of sophisticated instrumentation for monitoring

various state variables for the evaluation of various theoretical concepts, is

the goal of this research effort. Experiments designed to evaluate the

efficacy of computer generated optimal remediation and optimal monitoring

designs will be conducted in the facility. Concentration, pressure,

temperature and saturation variables will be monitored using state-of-the art

hardware and software.