Dynamic Programming for Optimal Synthesis of Water Networks in Batch Processes

Water minimization in the process industry is becoming increasingly important in chemical industries, especially for the batch plants. This work proposes a dynamic programming (DP) method for the optimal design of water-using networks in batch plants. The proposed methodology is explained as follows. Firstly, water-using units are transformed into the water sources and sinks with specific water requirements and time constraints. Secondly, based on the start and end time of each operation, the whole process is divided into N stages. Also these water sources and sinks are arranged in the diagram with time or stages on the horizontal axis and the concentration on the vertical axis. Thirdly, the backward procedure of DP is used to solve the problems based on the insights of diagram. The target of the process and optimal design of water network are obtained simultaneously. In order to display versatility of the proposed approach two examples from literature are taken into account. Example 1 is a completely batch process with a fixed flowrate problem. Example 2 is a hybrid batch water system comprising various operations (fixed load and fixed flowrate) and operating models (completely batch and semi-continuous). The obtained results match with the results from literature, implying that it can be applicable to design optimal batch water networks.