Exact solutions for suspension-colloidal transport with multiple capture mechanisms

We discuss one-dimensional (1D) non-linear problems of suspension-colloidal transport in porous media with two simultaneous particle capture mechanisms. The first mechanism corresponds to low retention concentration and constant filtration function. The second mechanism corresponds to large retention concentration with blocking (Langmuir) filtration function. The 1D flow problems are non-linear; however, they allow for exact solutions. The exact solutions are obtained for the general two-capture case, and also for piecewise-linear approximation of the filtration function. The proposed filtration function describes the breakthrough curves (BTCs) that monotonically increase with time and stabilise at some value lower than the injected concentration; those BTCs are observed for numerous suspension-colloidal flows. The tuning method for determining the model coefficients is developed. Close agreement between the laboratory and modelling data validates the proposed form of filtration function.