Publications
Examining the effects of variability in short time scale demands on solute transport
Variations in water use at short time scales, seconds to minutes, produce variation in transport of solutes through a water supply network. However, the degree to which short term variations in demand influence the solute concentrations at different locations in the network is poorly understood. Here we examine the effect of variability in demand on advective transport of a conservative solute (e.g. chloride) through a water supply network by defining the demand at each node in the model as a stochastic process. The stochastic demands are generated using a Poisson rectangular pulse (PRP) model for the case of a dead-end water line serving 20 homes represented as a single node. The simple dead-end network model is used to examine the variation in Reynolds number, the proportion of time that there is no flow (i.e., stagnant conditions, in the pipe) and the travel time defined as the time for cumulative demand to equal the volume of water in 1000 feet of pipe. Changes in these performance measures are examined as the fine scale demand functions are aggregated over larger and larger time scales. Results are compared to previously developed analytical expressions for the first and second moments of these three performance measures. A new approach to predict the reduction in variance of the performance measures based on perturbation theory is presented and compared to the results of the numerical simulations. The distribution of travel time is relatively consistent across time scales until the time step approaches that of the travel time. However, the proportion of stagnant flow periods decreases rapidly as the simulation time step increases. Both sets of analytical expressions are capable of providing adequate, first-order predictions of the simulation results.