Formulation of mathematical modelling for the design of maximum water recovery (MWR)

Abstract

Mathematical programming technique has become an essential tool for design of optimal water networks due to the limitations of conceptual approaches in dealing with complex industrial water systems involving multiple contaminants. This report presents the development of a Model for Optimal Design of Water Networks (MODWN) applicable for water operations involving multiple contaminants and multiple utilities. The approach is based on the optimisation of a superstructure which represents a set of all possible water flow configurations in a process system. MODWN can be analysed in two stages, i.e. fresh water savings mode (FWS-mode) and economic mode (E-mode). The first stage consists of mixed integer linear program (MILP) formulation that is solved to provide some initial values for the second stage. In the second stage, the model is formulated as a mixed integer nonlinear program (MINLP) that is used to optimise an existing design of water systems. The model considers all levels of water management hierarchy (i.e. elimination, reduction, reuse, outsourcing and regeneration) and cost constraints simultaneously to select the best water minimisation schemes that can achieve the maximum net annual savings at a desired payback period. In addition, MODWN can also be used to solve water network design simultaneously. This work also includes cases where fresh water concentrations for all contaminants are assumed to be either zero or non-zero. The approach has been successfully implemented in case studies involving an urban building (Sultan Ismail Mosque, UTM) for retrofit scenario. The results show that the potential maximum reductions of fresh water of 95.3% and wastewater of 64.7% for Sultan Ismail Mosque, giving an investment payback period of within 5 years. By considering more constraints, the MODWN has successfully yielded more accurate results as compared to the heuristics and graphical approaches, and will be very beneficial for the design and retrofit of real-life urban and industrial water networks.