Simplified procedure for design of catalytic combustors with periodic flow reversal

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Abstract

An extended simplified model, applicable to every cycle period, for the simulation of the behaviour of an adiabatic reverse-flow reactor for the treatment of waste gases is presented and compared to the complete model. This model is based on the analogy with the steady countercurrent reactor and consists of simple equations that relate the main input and dimensional parameters of the reactor. Such a model permits the setting up the guidelines for the design of the reactor and to obtain some indications for its control system, allowing the prediction of the limiting operating conditions for autothermal operation.

Introduction

The search for processes and treatments with low fuel consumption is drawing more and more attention in recent years: not only for energy saving, but also because of its environmental implications, due to the requirement of reducing CO2 emissions in the atmosphere.

Concerning the treatment of lean mixtures of waste gases, for which no recovering process can compete economically with combustion, the catalytic reverse-flow combustor seems to be a promising technology. A standard (even if catalytic) combustion requires large amounts of auxiliary fuel and this affects both the process costs and the environmental impact. The reverse-flow reactor, by accumulating the heat of reaction in the catalytic bed, does not require any bulky gas-gas heat exchanger and reduces strongly (or even eliminates) the need for auxiliary fuel.

For this reason, in the past 20 years, this kind of reactors have been deeply investigated; a complete review has been made by Matros [1].

The evaluation of the transient and pseudo-steady-state (pss) behaviour of the forced unsteady-state reactors, needed for the selection of optimum cycle time, bed size and initial catalyst temperature, is computationally very demanding, even if a simplified monodimensional model is adopted. A long simulation time is required, because about one hundred cycles are generally necessary before the pss is reached; finding the limit conditions which cause extinction, in particular, requires very long simulations and a trial and error approach.

As shown in previous studies [2], [3], [4] the use of a complete model permits us to predict the behaviour in the period before the attainment of the pss, during which large emissions can occur under certain conditions, and to find evidence for and an understanding of the characteristics of the system, but it is very unpractical for routine design and sizing of the bed. In addition, a numerical solution makes it very difficult to understand deeply the process and does not allow to single out easily the parameters that influence its performance, limiting the possibility of finding the optimal configuration.

For the above reasons some authors have developed simplified models for the reverse-flow adiabatic reactors. A simplified high-switching frequency model has been proposed by Boreskov and Matros [5], Matros et al. [6], Eigenberger and Nieken [7], and Nieken et al. [8], [9].

Matros and Bunimovich [10] presented a model for high-frequency flow reversal, in which the system of partial differential equations is reduced to a system of ordinary differential equations, that, through further simplifications, can be solved analytically for the maximum temperature in the bed.

Nieken et al. [11] analysed the two limiting cases of a very large switching period, for which the temperature profile approaches that of the stationary travelling reaction front, and of a very short switching period; in the latter case, the behaviour of the reactor is similar to that of a countercurrent reactor. By simplification of the pseudo-homogeneous model (that can be considered very good if the particle size is small), they obtained simple quasi-analytical expressions for the most important parameters of the pss temperature profile (Tmax and dT/dx). A good agreement was observed between the complete two-phase model and the simplified quasi-homogeneous model.

Haynes et al. [12] demonstrated that the high switching frequency model can be derived from the full dynamic quasi-homogeneous model by expressing the process variables as a Taylor series in time, and compared its performances with those of the complete model.

A different approach was proposed by Sun et al. [13], who neglected axial conductivity in the bed, but allowed heat transfer between gas and solid, by considering different gas and solid temperatures. They succeeded in reducing the model to a simple system of ordinary differential equations, but finally a numerical solution is needed. A design procedure for the reverse-flow reactor was also given.

Züfle and Turek [14] discussed the analogies between the reverse-flow reactor and two other apparatuses: the conventional adiabatic fixed bed reactor with external heat exchangers and the countercurrent reactor; they developed a model different from that of the previous authors, based on the partition of the bed in a cascade of electrically heated elements and the subsequent discretization of the variables. The solution is more complex, and an additional system parameter, the centre of gravity of the energy release caused by exothermic chemical reaction, is required; but, through an iterative procedure, it is possible to obtain again the main parameters of the pss profiles.

Design rules have been proposed in generalised form by Haynes et al. [12]: from given values of conversion the bed length and the gas velocity can be calculated. It is important to note that in all the previous studies the cycle period was not taken into consideration, while Thullie and Burghardt [15] pointed out that the maximum cycle time is the most relevant parameter, because lower frequencies cause extinction of the reactor, and proposed a very simplified procedure to estimate it.

The aim of this work is the development of a simple design procedure, pursuing further the approach proposed by Nieken et al. [11]. The validity of their model is extended to any cycle period and, under simplifying assumptions, these results are exploited to predict the limiting operating conditions for autothermal operation: minimum bed length, maximum cycle period, minimum inlet concentration, minimum and maximum flow rate.

The simplified quasi-homogeneous model has been validated comparing its predictions with those of a dynamic two-phase model. For all the simulations, the combustion of low concentrations of methane has been considered.

Section snippets

Complete dynamic model

The complete monodimensional model is described by the following balance equations.Energy balance for the gas phase:∂τG∂s=−ρG,0ρG∂τG∂z+keffεcp,GLu0ρG2τG∂z2+haLcp,Gu0ρGS−τG)−4Lhw,ovDRcp,Gu0ρGG−τE).

Mass balance for the gas phase:∂YG∂s=−ρG,0ρG∂YG∂z+DeffεLu02YG∂z2kGaLu0(YG−YS).

Energy balance for the solid phase:∂τSs=λSεcp,SLu0ρS2τS∂z2+kGaL(−ΔH)ρGεy0cp,S(1−ε)u0ρSMT0(YG−YS)−haLεcp,S(1−ε)u0ρSS−τG).

Mass balance for the solid phase:

For the catalytic part of the reactor, a first order rate

Results

Fig. 4 compares the prediction of the maximum reactor temperature as given by the simplified and the complete model, in order to show the good quality of the simplified one.

The prediction of the influence of y0 and u0 on the maximum temperature of the bed is particularly important, because, on one hand, high temperatures endanger the activity of the catalyst and, on the other hand, low temperatures lead to extinction of the reaction. It should be noted that the prediction of the simplified

Conclusions

The development of a simplified model for the prediction of the behaviour of a reverse-flow reactor for the combustion of waste gases has allowed us to set up some fundamental principles for the design and the control of the reactor; particular attention has been given to the autothermal behaviour and stability of the reactor, considering the treatment of waste gases with low calorific value. As shown in a previous paper the same results can be obtained by a numerical investigation based on the

Acknowledgements

This study has been financially supported by the European Union (Contract ENV4-CT97-0599).

References (18)

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