All attempts to modelize and wastewater treatment process must go through the imperative knowledge of its mixing characteristics. Such a knowledge calls for the realization of tracing experiments, classically one per basin; an operation that becomes rapidly tedious, especially when it has to be repeated for a series of reactors.
The transfer function theory would allow to avoid such a multiplication of tracing operations. The transfer function which characterizes every system is indeed equal, under well defined initial conditions, to the Laplace transform of the distribution of residence times (R.T.D.) in this same reactor. The R.T.D. can then be calculated from the transfer function by a deconvolution process.
The main interest of this method consists in the fact that, unlike the R.T.D. the transfer function can be evaluated from any input/output signals whatsoever. Thus, the hydraulic pattern of a series of reactors can be easily and, more important, individually studied by means of tracer concentrations measured during only one tracing experiment at the exit of each basin.
The only difficulty in applying this method lies in the choice of the deconvolution procedure used to estimate the R.T.D. Four different methods of calculation are proposed and compared:
* deconvolution by Fourier transforms.
* deconvolution by multilinear regression.
* deconvolution by the algebraic resolution of a set of n equations with n unknowns.
* adjustment by the least-square method to an n order ARX model.
The last mentioned gives the best results. This method provides, for each pond, different parameters like Peclet number, percentage of dead-space or short-circuits. From these results, correlations between dispersion numbers and other state variables can be evaluated. Finally several hydraulic models (completely-stirred, dispersive plug flow, completely mixed tanks in series) may be simulated and compared with observed R.T.D.s.