Inverse Modeling of Chlorine Concentration in Pipe Networks under Dynamic Condition
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Volume 123, Issue 10
Abstract
The Surface Water Treatment Rule under the Safe Drinking Water Act and its amendments require that the water utilities maintain a detectable disinfectant residual throughout the distribution system at all times. A new computer model is presented to directly calculate the chlorine concentrations needed at the source(s) to have specified residuals at given locations in a pipe network in unsteady flow conditions by using an inverse method. Unlike the forward solution method, which calculates the source chlorine concentration by a trial-and-error procedure, the inverse solution technique presented in this paper directly calculates the source concentration required to meet a specified value at a particular point in the network. The dynamic flows and pressures are first calculated by solving the governing equations by an implicit finite-difference scheme subject to appropriate boundary conditions. For chlorine concentrations at various pipe sections and at each node, the one-dimensional transport equation is modified for the advection dominated flow. This modified transport equation is then discretized by using the four-point implicit finite-difference scheme and solved simultaneously together with the junction mass balance equations. A first-order reaction rate for chlorine decay is assumed and a flow-weighted averaging procedure is used to calculate the complete mixing of chlorine at the junctions. For the verification of the inverse method, the computed results are compared with those determined by direct simulations. An excellent agreement is observed between the inverse method and direct simulation technique.
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References
1.
Clark, R. M.(1994). “Modeling water quality changes and contaminant propagation in drinking water distribution systems: A U.S. perspective.”J. Water SRT-Aqua, 43(3), 133–143.
2.
Clark, R. M., Grayman, W. M., Goodrich, J. A., Deininger, R. A., and Skov, K.(1994). “Measuring and Modeling Chlorine Propagation in Water Distribution Systems.”J. Water Resour. Plng. and Mgmt., ASCE, 120(6), 871–887.
3.
Chaudhry, M. H. (1987). Applied hydraulic transients, 2nd Ed., Van Nostrand Reinhold, New York, N.Y.
4.
Chaudhry, M. H. (1993). Open channel flow. Prentice-Hall, Inc., Englewood Cliffs, N.J.
5.
Chaudhry, M. H., and Islam, M. R. (1994). “Water quality modeling in distribution systems.”Proc., Conf. on Improving Efficiency and Reliability in Water Distribution Sys., Valencia, Spain.
6.
Hack, D. J.(1985). “State regulations of chloramines.”J. AWWA, 77(1), 46.
7.
Holloway, M. B. (1985). “Dynamic pipe network computer model,” PhD thesis, Washington State Univ., Pullman, Wash.
8.
Holloway, M. B., and Chaudhry, M. H. (1985). “Stability and accuracy of waterhammer analysis.”Advances in water resources, Vol. 8, CML Publications, 121–128.
9.
Holloway, M. B., Chaudhry, M. H., and Karney, B. W. (1988). “Modeling of unsteady flow in pipe networks.”Proc., Int. Symp. on Comp. Modeling of Water Distribution Sys., 311–322.
10.
Holly, F. M. (1975). “Two-dimensional mass dispersion in rivers.”Hydro. Paper No. 78, Colorado State University, Fort Collins, Colo.
11.
Islam, M. R. (1992). “Numerical solution of advection equation for application in environmental hydraulics,” MS thesis, Washington State Univ., Pullman, Wash.
12.
Islam, M. R. (1995). “Modeling of chlorine concentration in unsteady flows in pipe networks,” PhD thesis, Washington State Univ., Pullman, Wash.
13.
Liou, C. P., and Kroon, J. R.(1987). “Modeling the propagation of waterborne substances in distribution networks.”J. AWWA, 96(1), 54.
14.
Males, R. M., Clark, R. M., Wehrman, P. J., and Gates, W. E.(1985). “Algorithm for mixing problems in water systems.”J. Hydr. Engrg., ASCE, 111(2), 206–219.
15.
Murphy, S. B. (1985). “Modeling chlorine concentration in municipal water systems,” MS thesis, Dept. of Civ. Engrg., Montana State Univ., Bozeman, Mont.
16.
Pudar, S. R., and Liggett, L. A.(1992). “Leaks in pipe networks.”J. Hydr. Engrg., ASCE, 118(7), 1031–1047.
17.
Sevuk, S.(1979). “Steady and unsteady flow simulation in pipe networks.”Adv. Engrg. Software, 1(3), 107.
18.
Watters, G. Z. (1984). Analysis and control of unsteady flow in pipelines, 2nd Ed., Butterworth Publishers, Stoneham, Mass.
19.
White, G. C. (1972). Handbook of chlorination. Van Nostrand Reinhold, New York, N.Y.
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Published In
Journal of Environmental Engineering
Volume 123 • Issue 10 • October 1997
Pages: 1033 - 1040
Copyright
Copyright © 1997 American Society of Civil Engineers.
History
Published online: Oct 1, 1997
Published in print: Oct 1997
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