The kinetic modeling of the perchloroethylene reaction-extraction process has been carried out on the basis of batch extraction data. In this paper, modeling results of both second order as well as the pseudo-first order model has been presented. Multiple parameter estimates have been found which minimize the model-data discrepancies. Novel methods have been devised to illustrate multiple estimates of the kinetic parameters. Ill-posedness of the kinetic modeling problem has been analyzed using the expression for extractability and the Hessian matrix of the model-data discrepancy function. Root Mean Square Errors (RMSE) for various types of coals have been evaluated to represent the model-data discrepancy function. It was found that the RMSE was between 2-8% of the estimated initial concentration of extractable organic sulfur, depending upon the type of coal. A novel method, called ''RMSE Contours'' has also been developed to present the sensitivity of parameters to the kinetic models. The second order model has been compared with the simpler pseudo-first order model. It has been successfully demonstrated that the organosulfur extractability of continuous processes can be consistently simulated regardless of the sensitivity of parameters to the model.