Modeling approach to describe fouling removal during relaxation

Filtration tests were designed with fixed filtration durations and varying relaxation lengths to study the influence of relaxation time on flux recovery and fouling removal. A mathematical model was used to estimate the development and removal of fouling during the filtration and relaxation phases. During the relaxation phases, a relaxation-time dependent back transport constant was introduced to properly simulate removal of the cake layer. It was found that the rate of removal of cake was highest in the beginning of relaxation period and decreased during relaxation. This shows that the rate of removal depends on the amount of cake to be removed, but can also be explained by cake not being removed as single flocs or colloids, but as fragments of flocs released in the beginning or relaxation, followed by release of colloids more strongly adhered to the surface or due to an initial swelling of the cake layer during the relaxation. Based on this, a model was proposed to simulate the development in amount of cake during filtration and removed during relaxation. With this, the development in amount of cake and permeability could be simulated for different filtration and relaxation times to identify the setting with the highest net flux.