Optimization of granular bed filtration treating polydispersed suspension

The need for economic optimization of a filter unit leading to its least cost design with respect to filtration velocity, run time, depth and medium size has long been identified but there are no algorithms towards this end. In this study, an algorithm incorporating a NLP (non-linear programming) software (NPSOL-System Optimization Laboratory, Stanford University, Calif.) and response surface methodology (RSM) is presented for optimal design and operation of a filter unit. Also, the simulation model included in the optimization takes into account the polydispersity of the influent. The optimization results obtained using laboratory data have shown that the filter design and operating parameters are highly dependent on the particle size distribution (PSD) of the influent. The cost of the filter unit with influent having the same total particles mass concentration and turbidity but with greater fraction of fine particles was about 46% higher. This demonstrates the importance of incorporating PSD instead of suspended solids (SS), turbidity units (TU) or volume average diameter in the design and operation of filter units. The proposed approach, however, is applicable only for single medium filters. Further research is warranted to extend it to dual and tri media filters.