Ultrafiltration modeling of multiple solutes system for continuous cross-flow process

A mathematical model suitable for the multiple solutes system in continuous cross-flow ultrafiltration is developed. This model is based on mass balance analysis coupled with the filtration theory (osmotic pressure model, Kozeny–Carman equation), resistance-in-series model and gel polarization model. This model is characterized by the parameters RmRm, PmPm, Kb,KbiKb,Kbi and kiki. These parameters are estimated by using the Levenberg–Marquardt method coupled with the Gauss–Newton algorithm based on the experimental data obtained from the treatment of pretreated palm oil mill effluent (POME) as a feed in the pilot plant scale ultrafiltration system. The pretreated POME is composed of a ternary system with the solutes of carbohydrate constituents, crude protein and ammoniacal nitrogen. The simulation results show a good agreement with the experimental data. The proposed model is suitable for predicting the performance of multiple solutes in an ultrafiltration process. The concentration of each solute present is correlated with the COD value of the permeate stream.