Time-optimal diafiltration processes for Cephalosporin C separated from fermentation broth under constant yield and constant concentration

Cephalosporin C (CPC) fermentation broth is a typical fluid which is filtrated hardly. In order to optimize the CPC diafiltration process under constant yield and constant concentration, a mathematic model is developed to estimate the operation time, where the membrane permeation performance is given by the gel polarization model. The expressions of t_min and the optimal conditions are put forward respectively. Based on the model, the optimization processes for CPC diafiltration to achieve desired yield and concentration have been investigated. Under the conditions of C₀ = 0.1 and the steady state, the values C_G = 0.65 and β = 28.65 m³ m^-2 h^-1 are extrapolated based on the experiment results. The optimal range of pre-concentration ratio 0.5 ≤ a ≤ 0.8 is confirmed. Compared with the overall process time under C ₀/C_G = 1/6.5, the fluctuation range of that is more than 40% in the range of 0.08 < C₀/C_G < 0.23. Under the time-optimal conditions, both of the desired CPC yield ξ and the average concentration of CPC in filtrate C_t can be controlled properly.