Optimal dosage strategies for filter aid filtration processes with compressible cakes

We establish optimal time-dependent dosage strategies for compressible filter aid materials, focusing on dead-end filter aid filtration processes operated in constant flow mode. To this end, we apply a direct optimal control approach by repeatedly evaluating a mathematical filtration model with filter aid concentration as the unknown time-dependent control function. Our algorithm iteratively constructs the sought-for trajectory to minimize a cost functional representing previously defined performance goals. We evaluate our optimal control approach for two different model formulations. In the first one, all impurity particles are separated by pure surface filtration on top of the existing filter cake, whereas in the second one, the model is extended toward depth filtration in the filter cake. Particularly for the latter, optimally controlled dosage strategies yield a significant performance improvement of up to 30% reduced filter aid consumption compared with the already optimized but constant filter aid dosage.