An Analytical Solute Transport Model for In Situ Estimation of Retardation

This paper presents an analytical model for evaluating a contaminant's in-situ retardation coefficient from concentration data obtained from an extraction well in a region of initially uniform contamination. Effective retardation estimates are required to effectively evaluate contaminant transport. This estimate often relies on literature values for the distribution coefficient, Kd, and site-specific estimates for effective porosity, bulk density, and chemical composition of the porous medium. When more accuracy is required, column or field studies may be performed to define a contaminant breakthrough curve which is used to determine retardation. These data can, in many instances, be difficult and expensive to obtain and interpret. In practice, in-situ retardation coefficients have been frequently evaluated using the results of injection well data and analytical solutions to the governing transport equation in radial coordinates or multi-dimensional numerical modeling of the transport equation using data from extraction wells. This study presents a solution and method to use extraction well data and the in-situ contaminant, rather than injection well data and an introduced tracer. Since the solution is based on extraction well data, no tracers or chemicals need to be injected into an aquifer and data from potential remediation wells can be used to obtain these values. In addition to the solution, an integral solution to the instantaneous concentration at the extraction well is presented which allows retardation estimates to be made using only extraction well data and not requiring an observation well. The solution method presented is a numerical inversion of a Laplace transform solution using the Stehfest algorithm to provide non-dimensional results in real time and space.