•Eight rules are proposed to effectively reduce the variable number.•Contaminant balance equations and inlet and outlet concentration constraints are linearized.•qHUk(k=k) and qCUk(k=1) are set to zero based on pinch principles of HEN.•Water pinch principles are used to set flowrate and concentration values for processes above or below the pinch.
A water using process usually has requirement not only on contaminant concentration but also on temperature. Hence an optimal water system should minimize both fresh water and energy utility consumptions. The mathematical model for energy efficient water networks with non-linear constraints has the features of big amount variables, heavy computational burden, and difficulty for solving. In order to reduce variables and non-linear terms, in this paper, eight rules are proposed, based on the necessary conditions of concentration monotonicity and maximum outlet concentration, pinch principles for heat exchanger and water networks, and consideration of rational non-isothermal mixing. In this way, the model is easier to solve. A case study shows that the strategy increase the solving efficiency.