Modeling Transport and Retention: Simultaneous Evaluation of Dispersion and Retention Parameters

Abstract

Summary Understanding transport and retention in porous media is essential in environmental and industrial processes like aquifer contamination, membrane filtration and water and polymer flooding in oil reservoirs. One of the earliest and most used method to determine transport and retention parameters consists in fitting both tracer and suspension/solution effluent concentrations. However, this method works under the assumption that dispersion coefficients for the suspension/solution and the tracer are equal or the difference between them is negligible. In this article, it is shown that this hypothesis can sometimes lead to misinterpretations. Furthermore, population balance equations for transport and retention are discussed based on the master equations. The obtained system of equations consists of one retention and one population equation for each class of particles. Averaging the aforementioned equations results in a closed system consisting of retention and advection-dispersion-reaction equations. Based on the KT (Kurganov and Tadmor) finite volume method, robust numerical solutions were obtained and applied for solving the inverse problem. Transport and retention parameters are firstly optimized by using the Levenberg-Marquardt algorithm and considering analytical solutions available in the literature (dispersion is neglected). Secondly, the proposed numerical model parameters (including dispersion coefficient) are calculated by setting the parameters obtained in the first step as initial input. Comparisons between analytical and the proposed model confirmed the accuracy of the proposed solutions even when advection is dominant. The aforementioned inverse problem solution was applied for determining fitting parameters for polymer and tracer injection experimental data available in the literature. The results allow concluding that, in general, very similar fitting parameters are obtained when tracer injection experimental data were or not used, suggesting that tracer tests are not necessary. However, in some cases, the results have shown that the polymer dispersion coefficient differs significantly from those obtained for the tracer, suggesting that the same dispersion coefficient used for fitting tracer data would not satisfactorily fit the polymer effluent data. Finally, the simultaneous determination of dispersion and retention coefficients would avoid conducting experimental tests with tracers.