Steady-State Plug Flow Reactors

The approach to be followed in the determination of rates or detailed kinetics of the reaction in a liquid phase between a component of a gas and a component of the liquid is, in principle, the same as that outlined in Chapter 2 for gas-phase reactions on a solid catalyst. In general the experiments are carried out in flow reactors of the integral type. The data may be analyzed by the integral or the differential method of kinetic analysis. The continuity equations for the components, which contain the rate equations, of course depend on the type of reactor used in the experimental study. These continuity equations will be discussed in detail in the appropriate chapters, in particular Chapter 14 on multiphase flow reactors. Consider for the time being, by way of example, a tubular type of reactor with the gas and liquid in a perfectly ordered flow, called plug flow. The steady-state continuity equation for the component A of the gas, written in terms of partial pressure over a volume element dV and neglecting any variation in the total molar flow rate of the gas is as follows ... 

Plug flow reactors with recycle exhibit some of the characteristics of CSTRs, including the possibility of multiple steady states. This topic is explored by Penmutter Stah dity of (%emical Reactors, Prentice-Hall, 1972). 

A steady-state heat balance for a plug flow reactor with no radial temperature gradients is given by ... 

Based on the kinetic mechanism and using the parameter values, one can analyze the continuous stirred tank reactor (CSTR) as well as the dispersed plug flow reactor (PFR) in which the reaction between ethylene and cyclopentadiene takes place. The steady state mass balance equations maybe expressed by using the usual notation as follows ... 

In this work we present results obtained with the YSZ reactor operated in the hatch mode with electrochemical oxygen addition, and with the quartz plug flow reactor operated in the continuous-flow steady-state mode. In the case of continuous flow operation, the molecular sieve trap comprised two packed bed units in parallel in a swing-bed arrangement (Fig. 1), that is, one unit was maintained at low temperature (<70°C) to continuously trap the reactor products while the other was heated for -30 min to 300°C to release the products in a slow stream of He. 

Consider the segment of tubular reactor shown in Figure 8.3. Since the fluid composition varies with longitudinal position, we must write our material balance for a reactant species over a different element of reactor (dVR). Moreover, since plug flow reactors are operated at steady state except during start-up and shut-down procedures, the relations of major interest are those in which the accumulation term is missing from equation 8.0.1. Thus... 

The basic design equation for a plug flow reactor (equation 8.2.7) may be used to describe the steady-state conversion achieved in the plug flow element of the recycle reactor ... 

This section treats the material and energy balance equations for a plug flow reactor. For steady-state operation the energy balance analysis leading to equation 10.1.4 is appropriate. 

For steady-state operation of a plug flow reactor the basic design equation (equation 8.2.9) can be written as... 

For a homogeneous gas-phase reaction occurring in a plug-flow reactor, explain briefly under what circumstances tlr < 1. Consider each factor affecting this ratio separately. Give an example (chemical reaction + circumstance(s)) for illustration. Assume steady-state operation and... 

In this chapter, we develop the basis for design and performance analysis for a plug flow reactor (PFR). Like a CSTR. a PFR is usually operated continuously at steady-state, apart from startup and shutdown periods. Unlike a CSTR, which is used primarily for liquid-phase reactions, a PFR may be used for either gas-phase or liquid-phase reactions. 

The aqueous decomposition of A is studied in an experimental mixed flow reactor. The results in Table P5.25 are obtained in steady-state runs. To obtain 75% conversion of reactant in a feed, C o = 0.8 mol/liter, what holding time is needed in a plug flow reactor ... 

Consider a plug flow reactor at steady state, with a first-order sink. What would be the concentration profile versus distance down the reactor ... 

In the next example, we will compare a complete mixed reactor with a first-order degradation reaction at steady state for a plug flow reactor and a series of smaller complete mixed reactors. 

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. 

In the ideal plug-flow reactor (Figure 11.16) the continuous phase flows as a plug through the reactor i.e., there is no mixing or, in other words, no axial dispersion. Consequently, if a compound is consumed or produced, a concentration gradient will exist in the direction of flow. The mass balance is therefore first set up over an infinite small slice perpendicular to the direction of the flow with volume dV of the bioreactor. Assuming steady state and F =Fq=F, Equation (11.5) then is reduced to ... 

Plug-flow tubular reactor (PFTR) This reactor is operated under steady-state condition. The reactor is of tubular shape, the reactants enter at the inlet and the composition is a function of the distance from the inlet. However, the composition is not a function of time. The ideal plug-flow reactor is characterized by the absence of mixing in the direction of flow and complete mixing in the transverse direction. 

We will consider a dispersed plug-flow reactor in which a homogeneous irreversible first order reaction takes place, the rate equation being 2ft = k, C. The reaction is assumed to be confined to the reaction vessel itself, i.e. it does not occur in the feed and outlet pipes. The temperature, pressure and density of the reaction mixture will be considered uniform throughout. We will also assume that the flow is steady and that sufficient time has elapsed for conditions in the reactor to have reached a steady state. This means that in the general equation for the dispersed plug-flow model (equation 2.13) there is no change in concentration with time i.e. dC/dt = 0. The equation then becomes an ordinary rather than a partial differential equation and, for a reaction of the first order ... 

Batch or Steady-State Plug-Flow Reactor... 

Eq. (2.37) can also be applied to an ideal steady-state plug-flow reactor, even though the plug-flow reactor is operated in continuous mode. However, the time t in Eq. (2.37) should be replaced with the residence time t in the plug-flow reactor, as illustrated in Figure 2.10. 

In a tubular reactor, the reactants are fed in at one end and the products withdrawn from the other. If we consider the reactor operated at steady state, the composition of the fluid varies inside the reactor volume along the flow path. Therefore, the mass balance must be established for a differential element of volume dV. We assume the flow as ideal plug flow, that is, that there is no back mixing along the reactor axis. Hence, this type of reactor is often referred to as Plug Flow Reactor (PFR). 

This reactor has continuous input and output of material through a tube. Assumptions made for the plug flow reactor (PFR) are (1) material passes through the reactor in incremental slices (each slice is perfectly mixed radially but has no forward or backward mixing between slices each slice can be envisioned as a miniature CSTR), (2) composition and conversion vary with residence time and can be correlated with reactor volume or reactor length, and (3) the reactor operates at steady state. 

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