Asymptotic model for deep bed filtration

• Analytical asymptotic model for non-linear deep bed filtration.
• Explicit formulae to treat long-term laboratory data on colloidal suspension flow.
• Data treatment from the period 5–10 times longer than that used by classical method.
• Fewer laboratory tests required to adjust micro scale population balance model.
• Accuracy–uncertainty criteria of colloidal flow laboratory and asymptotic modelling.

Asymptotic solution for non-linear stage of colloidal suspension flow in porous media is developed. The expansion is performed behind the concentration front; the zero order approximation coincides with the short-time solution of the linearised system. Using the first order approximation allows significantly enhancing the validity time period for the analytical model if compared with the linearised solution, allowing using the long-term experimental breakthrough concentration history for the model adjustment. Laboratory injection tests for three size colloids are performed. The asymptotic solution is used to tune the model parameters from the breakthrough histories of two size particles; good quality of matching is observed. The breakthrough concentration history for the third size particles is compared with the prediction by the adjusted model; good quality prediction is observed. The above serves for validation of the asymptotic method for the model tuning and prediction of non-linear colloidal suspension flow in porous media.

Evolution of pore size distribution for size exclusion deep bed filtration in porous media.Figure optionsDownload as PowerPoint slide