Input-Output Model of Water Quality in Water Distribution Systems

A novel input-output model of water quality in water distribution systems is presented as a partide backtracking algorithm. The algorithm is a simpler and more efficient version of that described by Zierolf et al. and is extended to consider the case of storage tanks (the tank algorithms will be described elsewhere, although simulation results are given here). The input-output model provides information that is not available using traditional simulation approaches: the various paths that water takes between input source and output node and time, decomposed into their associated time delays and impact coefficients. 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 revealed mathematical form of the input-output behavior may be useful information for certain applications such as feedback control. More generally, the input-output model may be useful in understanding the effects of water quality processes that are flow path-dependent, since those paths are made explicit.