Water Treatment Units Residence-Time Distributions as Probabilistic Functions |
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Authors: | Velitchko G. Tzatchkov Steven G. Buchberger Alejandra Martin-Dominguez |
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Affiliation: | 1Senior Research Scientist, Dept. of Hydraulics, Mexican Institute of Water Technology, Paseo Cuauhnahuac 8532, Jiutepec, Mor. CP 62550, Mexico (corresponding author). E-mail: velitchk@tlaloc.imta.mx 2Professor, Dept. of Civil and Environmental Engineering, Univ. of Cincinnati, P.O. Box 210071, Cincinnati, OH. E-mail: steven.buchberger@uc.edu 3Department of Drinking Water Treatment Coordinator, Mexican Institute of Water Technology, Paseo Cuauhnahuac 8532, Jiutepec, Mor. CP 62550, Mexico. E-mail: alejandra_martin@tlaloc.imta.mxx
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Abstract: | A probabilistic approach to obtain theoretical residence-time distribution (RTD) functions for series of reactors with possible stagnation, bypassing, and recycle is presented. It is shown that most known RTD functions can be obtained from probability arguments alone, thus avoiding abstract Laplace transform mathematical techniques and providing additional physical insight. Several new RTD models for reactors in series are derived, based exclusively on using the binomial probability distribution to describe the passage of a particle through the treatment train with bypassing and stagnation possible at each individual reactor. The proposed RTD models are validated with travel time computer simulation of a large number of particles through the series of reactors. A MSExcel based computer procedure was programmed to obtain the nonideal flow parameters by minimizing the squared sum of the differences between tracer test data and the derived unit’s RTD function. The least squares parameter estimation procedure was used to fit theoretical RTDs to tracer data collected from real water treatment units with different hydraulic behavior at two locations in Mexico. |
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Keywords: | Residence time Nonuniform flow Water treatment plants Reactors Mathematical models Probability Probability density functions |
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