Probabilistic Contaminant Source Identification in Water Distribution Systems with Incomplete Mixing at Pipe Junctions

Mounting a fast and effective response if contamination enters a drinking water distribution system is important. A significant part of any response is identifying the source of contamination. In previous work adjoint methods have been successfully employed for this task. Adjoint methods use system sensor data as inputs into adjoints of forward transport equations to backtrack information through a water distribution system to probabilistically determine the source of contamination. Previous work has assumed complete mixing at pipe junctions. This is not the case in a real-world distribution system leading to discrepancies between the modeled system and the true system. A bulk advective mixing algorithm (EPANET-BAM) has been developed to introduce more realistic mixing at pipe junctions. We develop adjoint theory incorporating incomplete mixing at the pipe junctions and test it using EPANET-BAM.