Wastewater minimisation using central reusable water storage in batch plants

This paper presents a continuous-time mathematical formulation for freshwater and wastewater minimisation in multipurpose batch plants with and without a central reusable water storage facility. The minimisation of wastewater is achieved through the exploitation of recycle and reuse opportunities. A superstructure that entails all the possible recycle and reuse possibilities is used as the basis for the formulation. Initially, the formulation is based on a predefined schedule characterized by a priori specification of starting or finishing times. The formulation is then extended to embed wastewater minimisation within an established scheduling framework in which starting and finishing times become optimization variables. In both forms the formulation can readily be extended to multiple contaminant media, although this will be the subject of another publication. Fixing the outlet concentration and the contaminant mass load for each water using operation in the absence of central reusable water storage initially renders the formulation a nonconvex mixed integer nonlinear program (MINLP) which is linearized exactly to yield a convex mixed integer linear program (MILP). On the other hand, allowing the outlet concentration to vary within predefined bounds while fixing both the water requirement and contaminant mass load yields a MINLP formulation for which global optimality cannot be guaranteed in complex problems. The developed formulation is applied to a published literature example as well as case studies involving production scheduling.