Dynamic optimization of a dead-end filtration trajectory: Non-ideal cake filtration

A control strategy aimed at minimizing energy consumption is formulated for non-ideal dead-end cake filtration with an inside-out hollow fiber ultrafiltration membrane system. The non-ideal behavior was assumed to originate from cake compression, non-linear cake resistance and a variable pump efficiency. Constant gross power, constant flux and constant pressure filtration were considered as alternatives for the optimal operating strategy. It was found that the ratio between the initial and final total resistance determines whether a large difference between these strategies occurs. This is mainly determined by the specific cake resistance, the final state and the membrane resistance. When there is a large difference between the operating strategies, the pump characteristics determine which suboptimal strategies are attractive. For a pump with a low head and a large capacity, constant flux filtration is nearly optimal, whereas for a pump with a large head and a small capacity optimal operation is closer to constant pressure filtration. Under the investigated conditions there was no significant difference (image 0.5%) between the constant gross power and the optimal operating strategy.