Modeling the transport and retention of polydispersed colloidal suspensions in porous media

Abstract

Colloid suspensions commonly exhibit a distribution of sizes, but most transport models only consider a single colloid size. A mathematical model was therefore developed to describe the advective and dispersive transport and first-order retention and release of a stable or aggregating polydispersed colloid suspension in porous media. The colloid size distribution was described using a unimodal or a bimodal lognormal probability density function (PDF), and Brownian aggregation was considered by making lognormal PDF parameters a function of time. Filtration theory was used to predict the retention rate coefficients for the various colloid sizes. The amount of retention for a stable polydispersed suspension was highly dependent on the colloid size distribution parameters, especially for a bimodal lognormal PDF. Increasing the distribution variance produced hyper-exponential retention profiles and an increase or a decrease in colloid retention depending on whether the medium colloid size was close to the optimum size for transport. Aggregation produced a similar decrease in the breakthrough concentrations with injection time as ripening, especially when the sticking efficiency was low. Aggregation effects were much more pronounced at higher input concentration levels, which also produced retention profiles that were increasingly hyper-exponential. Simulation results indicate that the colloid size distribution of stable and aggregating polydispersed suspensions always becomes more uniform and approaches the optimum transport size with increasing distance, suggesting that consideration of polydispersed suspensions is of primary importance near the injection surface.