Water Treatment Units Residence-Time Distributions as Probabilistic Functions

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.