Practical application of the cake-complete, pore-plugging model for sizing normal flow filters

Considerable process development efforts are spent selecting and sizing normal flow filters-typically beginning with small-scale experiments on flat sheet membrane samples and then scaling up to pleated membrane capsules and cartridges. Experimentally measuring filter capacity requires long test times; therefore, many scientists perform a short, small-scale test and fit the data to a mechanistic model which is used to extrapolate the filter's capacity. For more than a decade, the most commonly used fouling model has been the standard (or gradual pore-plugging) model. In 2006, Bolton et al. proposed a new model which combined both cake formation and complete pore-plugging (the "cake-complete" model). The authors used this model to fit data sets generated under constant flow and constant pressure conditions on microporous and ultrafiltration membranes. They concluded that the new model could more consistently predict filter performance as it was able to provide good fits of all data sets over a wide range of plugging behavior. This work describes a reliable method for solving the constant flow and constant pressure forms of the cake-complete model and for predicting the initial values of the plugging constants. Additionally, algorithms for determining required filter area to satisfy process conditions (batch volume and batch time) are proposed.