Dates of Involvement:
September 14, 2009- Present
Roseanna M. Neupauer, Ph.D., P.E., M. ASCE
Contaminants in Water Distribution Systems
The threat of accidental or deliberate releases of contaminants into water distribution systems is a series concern. If a contaminant is released into a system, sensors placed throughout the distribution system relay information about the dispersion of the contaminant throughout the system. Sensory data can provide information about the source and release time of the contaminant. It is extremely important that a source of pollutant be identified efficiently. Several different methods have been used to analyze sensory data most using optimization and numerical algorithms.
Dr. Nuepauer’s (2009) work has previously approached this problem using backward probabilistic modeling to identify source and release time of a contaminant. This research matched probability density functions with sensory data modeled by releasing a slug of contaminant at varying nodes throughout the network.
Additionally, Dr. Nuepauer (2009) was able to examine the sensitivity of a distribution system to varying parameters. The sensitivity analysis was completed by analyzing how a performance measure, P, varied with respect to a parameter alpha, α. The sensitivity of the system, dP/dα, was calculated by examining the adjoint state of the adjoint equation. This method proved to be more computationally efficient than directly calculating the sensitivity.
In both projects the transport of solutes in a single pipe was modeled as an advective-dispersive-reactive process given by the following:
In the equation above, Ci(xi,t), Qi, Ai, and Ei are the concentration, flow rate, cross-sectional pipe area, and longitudinal dispersion coefficient respectively. However, both project heavily employed the adjoint state of the above equation given by the following:
In the previously stated equation, ψi represents the adjoint state and τ represents backward time or . The work done on this project has assumed that flow is constant with steady demands. Furthermore, the contaminant was assumed to be instantaneously. These assumptions simplified the problem greatly by implying that flow direction in a given pipe is consistent over time. Furthermore, the probabilistic method focused on the sudden release of a slug of contaminant.
The current goal of the project is to expand on Dr. Nuepauer’s previous work by relaxing some of the assumptions previously made. The same methods will by expanded in an attempt to determine state sensitivity, source location, and release time if the flow is transient with changing demands and time-dependent sources releases.
About Cody Cichowitz:
Cody Cichowitz is currently a junior in applied mathematics focusing in water resources and hydrology. He enjoys learning seeing math applied to a water related issues. He spends his summers as a whitewater rafting guide on the Arkansas River. This experience has motivated his interest in hydrology. He is currently planning on participating in the five-year BS/MS program.
Neupauer, R. M. (submitted, 2009). Adjoint sensitivity analysis of contaminant concentrations in water distribution systems.
Neupauer, R. M., Records, M. K., Ashwood, W. H. (submitted, 2009). Backward probabilistic modeling to identify contaminant sources in water distribution systems.