Continuous-time formulation for the synthesis of water-using networks in batch plants

Water minimization is conducted by exploiting all possibilities of water reuse and recycle to reduce the freshwater consumption, as well as the wastewater generation. Because the starting and finishing times of batch water-using tasks are dependent on the production schedule as the inherent time dependence in batch processes, storage facilities are commonly equipped for the temporary storage of reusable water to partially bypass the time limitation. With a fixed production schedule, this paper presents a mathematical formulation for the synthesis of water-using networks in batch plants. Superstructures that incorporate all possible flow connections are built for modeling the batch water system. The proposed formulation is based on a continuoustime representation where different design objectives have been considered for an applicable network configuration. The design problems for the minimization of freshwater consumption, storage capacity, and the amount of connecting flows are formulated as nonlinear programs (NLPs), whereas the design problem for minimizing the number of connections will be a mixed-integer nonlinear program (MINLP). Representative examples from literature are provided to demonstrate the effectiveness of proposed formulation. Furthermore, the application of a fictitious contaminant is also developed, to address the forbidden match between assigned water-using tasks.