Particle backtracking algorithm for water distribution system analysis

A novel input-output model of water quality in water distribution systems is presented as a particle (water parcel) backtracking algorithm (PBA). The PBA is a simpler and more efficient version of that described by Zierolf et al. in 1998 and is extended to allow storage tanks and multiple water sources and quality inputs. For simplicity the algorithm details are described for networks with a single water quality input at the water source, and the necessary extensions to allow multiple water sources and quality inputs are described separately. The PBA provides information that is not available using traditional simulation approaches: the various paths that water takes between a particular input source and output node, and their associated time delays and impact on output node water quality. Such information constitutes a complete description of the input-output behavior under typical assumptions of first-order chemical decay or production reactions. Thus the output behavior can be calculated for any source quality input, and the explicit mathematical form of the input-output behavior is useful information for certain applications such as feedback control. More generally, the PBA is a tool to understand flow-path-dependent water quality processes in distribution systems, since those paths and their characteristics are made explicit and thus available for analysis. The potential utility of input-output analysis is illustrated by several examples.