Inverse modeling for locating dense nonaqueous pools in groundwater under steady flow conditions

In this work we develop an inverse modeling procedure to identify the location and the dimensions of a single‐component dense nonaqueous phase liquid (DNAPL) pool in a saturated porous medium under steady flow conditions. The inverse problem is formulated as a least squares minimization problem and solved by a search procedure based on the Levenberg‐Marquardt method. Model output is calculated by an existing three‐dimensional analytical model describing the transport of solute from a dissolving distributed noise upon the forward model‐generated concentration field. We further test the algorithm's ability to predict the location and size of a DNAPL pool placed in a controlled three‐dimensional bench‐scale experiment. In this case we apply the Levenberg‐Marquardt algorithm to the minimization of three types of residuals: ordinary residuals, weighted residuals with weights equal to the square of the inverse of the observations, and weighted residuals with weights obtained by adding a constant term to the observed concentrations. The results are sensitive to the location of the observation wells and to the type of residuals minimized. In general, better results in terms of pool location and dimensions were obtained by the minimization of weighted residuals with weights obtained by adding a constant term to the observed concentrations. The results also indicate that the inverse problem is nonunique and nonconvex even in the absence of observation errors. Finally, the sensitivity of the inverse modeling scheme to transport parameter uncertainty was addressed. The inverse solution was found to be extremely sensitive to errors in the dispersion coefficients and relatively insensitive to errors in the mass transfer coefficient.