Unsteady-state flow reactor

Equipment in which homogeneous reactions are effected can be one of three general types the batch, the steady-state flow, and the unsteady-state flow or semibatch reactor. The last classification includes all reactors that do not fall into the first two categories. These types are shown in Fig. 4.1. 

A.2. Imaging Unsteady-State Flows in Fixed-Bed Reactors... 

Khadilkar, M. R., Al-Dahhan, M. H., Dudukovic, M. P., Parametric study of unsteady-state flow modulation in trickle-bed reactors. Chemical Engineering Science, 1999, 54, 2585... 

Equations (1.1) to (1.3) are diflerent ways of expressing the overall mass balance for a flow system with variable inventory. In steady-state flow, the derivatives vanish, the total mass in the system is constant, and the overall mass balance simply states that input equals output. In batch systems, the flow terms are zero, the time derivative is zero, and the total mass in the system remains constant. We will return to the general form of Equation (1.3) when unsteady reactors are treated in Chapter 14. Until then, the overall mass balance merely serves as a consistency check on more detailed component balances that apply to individual substances. 

Although catalytic wet oxidation of acetic acid, phenol, and p-coumaric acid has been reported for Co-Bi composites and CoOx-based mixed metal oxides [3-5], we could find no studies of the wet oxidation of CHCs over supported CoO catalysts. Therefore, this study was conducted to see if such catalysts are available for wet oxidation of trichloroethylene (TCE) as a model CHC in a continuous flow fixal-bed reactor that requires no subsequent separation process. The supported CoOx catalysts were characterized to explain unsteady-state behavior in activity for a certain hour on stream. 

A semicontinuous reactor is a reactor for a multiphase reaction in which one phase flows continuously through a vessel containing a batch of another phase. The operation is thus unsteady-state with respect to the batch phase, and may be steady-state or unsteady-state with respect to the flowing phase, as in a fixed-bed catalytic reactor (Chapter 21) or a fixed-bed gas-solid reactor (Chapter 22), respectively. 

Although there is steady flow of feed, the reactor is in unsteady-state operation during the time t, since the outlet concentration cA (and hence fA) is continuously changing (cA decreasing from cAo, and fA increasing from 0). 

Plug flow reactor Partial differential equations in one spatial variable (unsteady state)... 

The use of magnetic resonance imaging (MRI) to study flow patterns in reactors as well as to perform spatially resolved spectroscopy is reviewed by Lynn Gladden, Michael Mantle, and Andrew Sederman (University of Cambridge). This method allows even unsteady-state processes to be studied because of the rapid data acquisition pulse sequence methods that can now be used. In addition, MRI can be used to study systems with short nuclear spin relaxation times—e.g., to study coke distribution in catalytic reactors. 

The complete unsteady-state model for adsorption-desorption and surface reactions of the plug flow laboratory reactor was based on the following equations NH3 mass balance on the catalyst suiface ... 

In Example 6.6, we saw that there is little difference between a plug flow reactor and 10 or more reactors-in-series when the constituent is undergoing a first-order reaction under steady-state conditions. This is not true for all circumstances. One example would be a conservative tracer under unsteady boundary conditions, as discussed in this section. 

Whereas the operation of batch reactors is intrinsically unsteady, the continuous reactors, as any open system, allow for at least one reacting steady-state. Thus, the control problem consists in approaching the design steady-state with a proper startup procedure and in maintaining it, irrespective of the unavoidable changes in the operating conditions (typically, flow rate and composition of the feed streams) and/or of the possible failures of the control devices. When the reaction scheme is complex enough, the continuous reactors behave as a nonlinear dynamic system and show a complex dynamic behavior. In particular, the steady-state operation can be hindered by limit cycles, which can result in a marked decrease of the reactor performance. The analysis of the above problem is outside the purpose of the present text ... 

In conclusion to this section, research in the RTD area is always active and the initial concepts of Danckwerts are gradually being completed and extended. The population balance approach provides a theoretical framework for this generalization. However, in spite of the efforts of several authors, simple procedures, easy to use by practitioners, would still be welcome in the field of unsteady state systems (variable volumes and flow rates), multiple inlet/outlet reactors, variable density mixtures, systems in which the mass-flowrate is not conserved, etc... On the other hand, the promising "generalized reaction time distribution" approach could be developed if suitable experimental methods were available for its determination. 

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