Abstract: Groundwater contamination and soil remediation analyses often employ the modeling of transport as well as geochemical and biological processes. Many numerical models have been used for solving these coupled advection-dispersion-reaction (ADR) problems. One key aspect in these models' development is the choice of suitable reaction terms in the governing equations. Electing an appropriate analytical form is crucial to the accurate prediction of system behavior, but this can be daunting in the absence of accurate site properties a priori. Once chosen, the reaction function's parameters must be calibrated, which can be especially challenging with complex models. The research presented here investigates avoiding the direct choice of reaction functions. Instead, using only existing observations, the approach develops reaction terms by optimally conjoining a set of hyperplanes in the reaction space to approximate the unknown reaction. First, a genetic algorithm (GA) finds a near-optimal set of junction nodes and slopes for the hyperplanes. Next, sequential quadratic programming (SQP) computes the optimal node/slope set in the neighborhood of the GA's solution. The GA and the SQP ally with the ADR simulation to provide the most elementary functional approximation satisfying prediction and reliability requirements. Results are shown demonstrating the effectiveness of this inverse approach. Also presented is an integral goodness of fit metric indicating which member of a family of analytic functions the reaction approximation most closely resembles. This methodology provides the most reliable reaction the data allow and indicates the analytic form most likely present. Additionally, the work addresses the application of optimal experimental design (OED) for obtaining data in an efficient manner. Designs can be used for multiple purposes, such as for collecting samples that improve reaction parameters and for accurately monitoring contaminant transport using existing models. The nondominated sorting genetic algorithm, NSGA-II, is used to develop the Pareto surface of these objectives and the design's cost. Costs explicitly include the designer's discount rate, a factor which can significantly influence the selection of well installation and sampling times. As the temporal domain is of interest to both design cost and reaction kinetics, the methodology explicitly addresses the time dependency of the OED problem.