Forced unsteady-state operation

This chapter describes a forced unsteady-state operation technique as employed for continuous processes which represent the majority of heterogeneous catalysis applications. The catalyst life in these processes often lasts as long as several years. Traditional operation is in the steady-state, and automatic control systems are... 

However, the reactor performance obtained under optimal steady-state conditions does not determine a potential limit for a heterogeneous catalytic system. This performance can be improved further using forced unsteady-state operation. Such an operation is capable of substantial extending a gamut of the process features and allows for better use of nonlinear properties inherent in a catalytic reaction system. The positive effect can be generated by two major factors [1] ... 

Sufficient conditions for optimality of forced unsteady-state operation which provides J > Js, can be determined on the basis of analysis of two limiting types of periodic control [10]. The first limiting type is a so-called quasisteady operation which corresponds to a very long cycle duration compared to the process response time t. In this case the description of the process dynamics is reduced to the equations x(t) = /t(u(t)), where h is defined as a solution of the equation describing a steady-state system 0 = f(/t(u(t),u(t))). The second limiting type of operation, the so-called relaxed operation, corresponds to a very small cycle time compared to the process response time (tc t). The description of the system is changed to ... 

Several other examples for potential application of reverse-flow operated catalytic reactors are described in Ref. 9. Also, other potential techniques of forced unsteady-state operation which allow for combining chemical reaction and heat exchange in a fixed catalyst bed are discussed. One such technique is sequential switching between inlet and outlet ports of the reaction gas between two or more packed beds (Fig. 2(c)). In this case, the thermal wave travels continuously through a series of packed beds in one direction, as if along a closed ring. However, this operation is more complex and requires more catalyst than the reverse-flow operation. 

However, there is substantial evidence that external forcing of process parameters can improve the reactor performance over the steady-state optimum. In this paper, we will focus on forced unsteady-state operation (FUSO) applied to continuous processes with nearly constant catalyst activity. In particular, we are interested in the effect of dynamic processes occurring on the catalyst surface on the FUSO, and in methods of FUSO optimization. Examples of successful practical application of FUSO will be considered. 

Interaction of the dynamic properties of a catalyst, a micro-scale physic-chemical system, and the dynamic properties of the macro-scale reactor creates an opportunity to improve the performance of catalytic processes using forced unsteady-state operation. Forced dynamic operation makes it possible to generate spatio-temporal patterns of temperature, composition and catalyst states that caimot be attained under steady-state operation. 

Mixing, Multiple Solutions, and Forced Unsteady-State Operation... 

This phenomenon of increased conversion, yield and productivity through deliberate unsteady-state operation of a fermentor has been known for some time. Deliberate unsteady-state operation is associated with nonautonomous or externally forced systems. The unsteady-state operation of the system (periodic operation) is an intrinsic characteristic of this system in certain regions of the parameters. Moreover, this system shows not only periodic attractors but also chaotic attractors. This static and dynamic bifurcation and chaotic behavior is due to the nonlinear coupling of the system which causes all of these phenomena. And this in turn gives us the ability to achieve higher conversion, yield and productivity rates. 

Various schemes of reactor operation under forced unsteady-state conditions are shown in Figs 1-4. An unsteady-state process in a fixed bed reactor can be created by oscillations in the inlet composition or temperature (Fig. 1). As a rule, a simple stepwise periodic control (Fig. 1 (a)) is preferable to other types of inlet... 

Figure 2. Schemes of fixed-bed reactors operated under forced unsteady-state conditions (a) Reverse-flow reactor (b) Rotary reactor (c) Reactor system with periodic changes between the inlet and outlet ports in two fixed beds. The tables show positions of switching valves during two successive cycles C = valve closed O = valve open.

The latter inequality is not always satisfied. The goal of general mathematical theory is in establishing whether the optimal steady-state operation can be improved using forced unsteady-state conditions. Then, if the answer is positive, the optimal operation should be found. The last stage obviously is the cost-analysis of... 

Periodic flow reversal inducing forced unsteady-state conditions [339]. The flow to the reactor is continuously reversed before the steady state is attained. A dual hot-spot temperature profile, characterized by a considerably lower temperature than in the single hot spot that would develop in the traditional flow configuration, forms in exothermic oxidation reactions. An increase in selectivity and better reactor control (lower risk of runaway) is possible over fixed-bed reactor operations, but compared... 

However, there has been limited success in the development and commercial application of unsteady-state process operation. In part this was caused by lack of dramatic improvements worthy of commercial applications. It is extremely difiBcult to achieve such improvements because of tremendous inherent complexity of forced unsteady-state catalytic systems. Not completely understood by this moment, interplay of reaction kinetics, heat and mass transport phenomena, nature and parameters of concentration forcing, etc. causes this complexity. 

Unsteady-state operation of a catalytic reactor can be exploited to enhance the efficiency of a catalytic reaction. A simple way of achieving unsteady-state operation is to force it by periodic reversab of the direction of flow of the reactant mixture. An important parameter in creating this condition is the ratio ap so of the time between flow reversals to the time needed for transition to the steady state. For apuso < U unsteady operation results, and for ttpuso > U pseudosteady-state conditions prevail. 

The strategies described so far are essentially chemistry based in the sense that different environments are created for a reaction to be initiated or enhanced. It is also possible to achieve enhancement by physically manipulating the same environment. One way of accomplishing this is by introducing controlled micromixing or optimizing the sequence of reactant additions. Another way is to operate under forced unsteady-state conditions by periodic reversals of the direction of flow. The main aspects of these strategies were considered in Chapter 13. 

The description of the extent of separation achieved in a closed vessel for a mixture of molecules is treated in Chapter 1. Chapter 2 illustrates how to describe the separation of molecules in open separators under steady and unsteady state operation a description of separation for a size-distributed system of particles is also included. Chapter 3 introduces various forces developing species-specific veiocities, fluxes and mass-transfer coefficients, and illustrates how the spatial variation of the potential of the force field can develop multicomponent separation ability. The criteria for chemical equilibrium are then specified for different types of multiphase separation systems, followed by an illustration of integrated flux expressions for two-phase and membrane based systems. 

Steady-state heat transfer Unsteady-state heat transfer Convective heat transfer (heat transfer coefficient) Convective heat transfer (heat transfer coefficient) Radiative heat transfer (not analogous with other transfer processes) Steady-state molecular diffusion Unsteady-state molecular diffusion Convective mass transfer (mass transfer coefficients) Equilibrium staged operations (convective mass transfer using departure from equilibrium as a driving force) Mechanical separations (not analogous with other transfer processes) ... 

The examples above illustrate the benefits gained by unsteady operation. They are, however, only partially related to the phenomena dealt with in this review. The instabilities described above are externally introduced by forcing operation parameters, whereas oscillatory states in heterogeneous catalysis are inherently unstable. Because these autonomous oscillations usually arise as a Hopf bifurcation, wherein the stable state is completely lost. 

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