Maximum water quality path entropy for water distribution systems

In this work, flow entropy (FE), flow path entropy (FPE), water quality entropy (WQE) and water quality path entropy (WQPE) of a water distribution system (WDS) were proposed and applied to four cases – a single-source branched network, a single-source looped network, a multi-source branched network and a multi-source looped network. The maximum FE, FPE, WQE, and WQPE for four cases were obtained and compared by solving optimisation models. For single-source branched network the maximum FE, FPE, WQE, and WQPE are the same. For multi-source branched network, the maximum FE is equal to the maximum FPE, and the maximum WQE is equal to the maximum WQPE. However, the maximum FE/FPE is not equal to the maximum WQE/WQPE. For single-source looped network and multi-source looped network, the maximum FE is also equal to the maximum FPE, while the maximum WQE is not equal to the maximum WQPE. The WQE and WQPE decreased with an increase in pipe length, pipe diameter and chlorine decay coefficient. The proposed concepts of FE, FPE, WQE and WQPE can help analyse the WDS from the viewpoints of water quantity as well as water quality.