A general correlation to predict axial dispersion coefficients in aerated channel reactors
Introduction
Activated sludge process is the most widespread technique for biological wastewater treatment. In large wastewater treatment plants, the aerobic degradation is often performed in channels or closed-loop reactors (Degrémont, 1991). Different types of activated sludge reactors have been presented in the literature (Potier et al., 2005). The channel reactor with bottom aerators is one of the oldest types of systems and is particularly well adapted to large plants. Due to the shape and the size of these units, there is an effect of hydrodynamics on the efficiency of the pollution removal, as concentration gradients are experimentally observed, for nutrients as well as for oxygen (Dudley, 1995). The effect of the flow behavior on the efficiency of wastewater treatment has often been pointed out (Metcalf and Eddy, 2002). Many studies have been made in order to describe the hydrodynamics of these reactors. Because of its design, the flow behavior of the channel reactor is well represented by the plug flow with axial dispersion model, the equivalent perfect mixing cells in series model or alternatively by the perfect mixing cells—in series with the back-mixing model. Nevertheless, these models are nearly equivalent since there is a relation between the Peclet number and the total number of mixing cells for the two first models (Villermaux, 1982) and between the back-mixing ratio and the number of mixing cells for the two last ones (Potier et al., 2005). Because of this, numerous studies have been conducted to predict the coefficient of dispersion as a function of operating and geometrical conditions. This coefficient may be used to estimate an equivalent number of mixing cells and back flowrate (see also Potier et al., 2005). The main objective of these correlations is to predict the axial dispersion coefficient knowing geometrical and operating parameters. Major applications concern the design of industrial plants based on laboratory-scale reactor results (scale-up) or the design of a pilot plant representative of a given industrial reactor in order to conduct a complete study in laboratory (scale-down). Many empirical or semi-empirical correlations have been proposed based on tracer studies. They usually give satisfactory results for the range of operating and geometrical parameters used during the experiments but they often fail when one parameter is outside the range of the experimental conditions for which they have been established. Consequently, the use of these correlations for scale-up and scale-down may induce errors.
In 1988, researchers began to quantitatively link pollutant removal and hydrodynamics. In this context, hydrodynamics was often represented by tanks in series model (Iida, 1988; Chambers and Jones, 1988), or by a plug flow reactor model (San, 1992). In order to simulate the dynamic behavior of a full-scale treatment plant, all the time variations of the wastewater characteristics (e.g. concentration and composition of polluted influent; flowrate) need to be taken into account. In fact, in the absence of any buffer tank upstream of the plant, the flowrate varies regularly. This means that the variations of the Peclet number or of the number of cells J should be considered in the mass balances related to the biological reactions. Tanks-in-series models are usually easier to handle in dynamic simulations than distributed parameter models (Turner and Mills, 1990), although the feasibility of the axial dispersion model approach has also been demonstrated for wastewater treatment plants for such conditions (Makinia and Wells, 2000a, Makinia and Wells, 2000b). Attempts have been made to model multiphase bioreactors using CFD (Dhanasekharan et al., 2005). However, it is not yet possible to couple this approach with a complex kinetic biomodel (Henze, 2000) and simulate the behavior of full-scale plants over a long period of time because of the high computer load required by this approach. Therefore, the global approach studies to improve the prediction of axial dispersion coefficient values, as a function of operating and geometrical parameters, are still useful in this context.
Several correlations have been proposed for the last 40 years. They have been determined for different sizes of channel reactors and under different operating conditions. Table 1, Table 2 give the references and the parameters for which the correlations presented below have been determined. Table 1 concerns the data for which all the values of the parameters are available, whereas Table 2 concerns incomplete data.
Murphy and Timpany (1967) and Murphy and Boyko (1970) studied the hydrodynamics of “spiral flow” oxidation ditch in both industrial and pilot-scale devices. They have been the first ones to propose a correlation giving the axial dispersion coefficient as a function of the gas flowrate and geometrical parameters. This correlation (Eq. (1)) is presented here with the original units:where D is in ft2/h, w is in ft, QG is in ft3/min and V is in 1000 ft3.
They studied various combinations of width and depth as “the characteristic length” and the most successful correlation was obtained when only the width was selected.
Harremoes (1979) tried to make a link between the buoyant jet and the bubble-induced loop in the aeration reactor. They correlated the axial dispersion coefficient to geometrical parameters and gas flowrate using
Fujie et al. (1983) worked to develop a more detailed correlation for several geometrical parameters and bubble sizes (Fujie et al., 1983). It results in a very complex expression (see Eq. (3)) with numerous parameters obtained from 11 experiments.withand
These authors are the only ones who are taking into account the size of the bubbles in the correlation. The major problem is that this parameter is sometimes difficult or time consuming to estimate.
A dimensionless correlation (Eq. (4)) based on the Buckingham π-theorem has been established by Khudenko and Shpirit (1986), to estimate the axial dispersion coefficient.
This correlation has been validated from the results of 30 experiments.
Recently, a review of all these correlations and studies, as well as of industrial experiments has been proposed (Makinia and Wells, 2005). Another correlation (Eq. (5)) has been proposed to link the axial dispersion coefficient with operating parameters (Potier et al., 2005):
These last authors have also proposed a solution to take into account the dynamic variations of the hydrodynamics by showing the possible equivalence between three models: piston with axial dispersion, perfect mixing cells in series and perfect mixing cells in series with back-mixing (Potier et al., 2005).
The main objective of this present work is to propose a general correlation of axial dispersion able to fit the whole set of data available in the literature covering a large range of operating and geometrical parameters. The major application is on the one hand to be able to propose laboratory pilot dimensions representative of a given industrial plant and on the other hand to scale-up an industrial plant from results obtained at the laboratory scale with a low level of uncertainty.
Section snippets
Experimental data collection
Data have been collected both from the existing literature and from our laboratory. These data cover a large range of operating and geometrical parameters from small pilots up to large industrial plants.
Axial dispersion coefficient correlation determination model
The determination of a general correlation has been based on the application of the Buckingham π-theorem to some data published for the last 40 years by several authors and 175 of our data (see Table 1). The first step for the application of this theorem is the selection of the different parameters involved in the studied system. In the present case, we split the parameters in four classes:
- 1.
The operating parameters: gas and liquid flowrates (QG and QL).
- 2.
The physical properties of the fluids
Results
A multilinear regression has been done on numerous experiments from the literature and from our laboratory. The main problem was to extract the data from the publications. Data only presented on graph were extracted with the help of specific software of data graph recovery. Uncertainty was sometimes observed in the obtained values. Data in some papers were missing and thus could not be used to carry out the regression. Consequently, it has been decided to determine the parameters from the
Comparison with previous correlation from the literature
The 265 experimental data have also been compared with the calculated values using the different correlations proposed in the literature. Fig. 5 shows the results obtained with the correlation recently proposed by Potier (2005). The calculated coefficient of dispersion is overestimated for two sets of data: those obtained with the first pilot plant and those obtained by Murphy. These two sets of data concern pilots with a small ratio w/h (0.05/0.2=0.025 and 0.5/0.82=0.06). It should also be
Possible application to scale-down and scale-up
In order to scale-down an industrial plant to a laboratory pilot plant and reciprocally to scale-up an industrial plant using laboratory pilot results or smaller industrial plant experiments, it is also necessary to take into account the characteristics of the gas–liquid transfer since the value of the aeration intensity needs to be the same for both the pilot and industrial plants. Roustan and Line (1996) proposed a correlation allowing the estimation of the aeration intensity from the gas
Conclusion
A general correlation for the estimation of axial coefficients of dispersion in an aerated channel reactor has been proposed. This correlation has been developed applying the Buckingham π-theorem to a set of data obtained both at laboratory and industrial scales during its 40 years by several authors and to 175 experiments obtained by our team. It gives an estimation of the axial coefficient of dispersion with a relative error of 18% for a large range of sizes of reactors starting from small
References (25)
- et al.
A generalized approach to model oxygen transfer in bioreactors using population balances and computational fluid dynamics
Chem. Eng. Sci.
(2005) Process testing of aerators in oxidation ditches
Water Res.
(1995)- et al.
Hydrodynamic parameters of diffused air systems
Water Res.
(1986) - et al.
A general model of the activated sludge reactor with dispersive flow—I. Model development and parameter estimation
Water Res.
(2000) - et al.
A general model of the activated sludge reactor with dispersive flow—II. Model verification and application
Water Res.
(2000) - et al.
Evaluation of empirical formulae for estimation of the longitudinal dispersion in activated sludge reactors
Water Res.
(2005) - et al.
Influence of geometrical and operating parameters on the axial dispersion in an aerated channel reactor
Water Res.
(2005) - et al.
Comparison of axial dispersion and mixing cell models for design and simulation of Fischer–Tropsch slurry bubble column reactors
Chem. Eng. Sci.
(1990) - et al.
Optimisation and uprating of activated sludge plants by efficient process design
Water Sci. Technol.
(1988) Water Treatment Handbook
(1991)
Liquid mixing in activated sludge aeration tank
J. Ferment. Technol.
Properties and characteristics of drops and bubbles
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