Batch Reactor Analogy

The ideal plug-flow reactor is characterised by the concept that the flow of liquid or gas moves with uniform velocity similar to that of a plug moving through the tube. This means that radial variations of concentration. 

With respect to reaction rates, an element of fluid will hehave in the ideal tubular reactor, in the same way, as it does in a well-mixed batch reactor. The similarity between the ideal tubular and batch reactors can be understood by comparing the model equations. 

For a batch reactor, under constant volume conditions, the component material balance equation can be represented by 

For a plug-flow tubular reactor, the flow velocity v, through the reactor can be related to the distance travelled along the reactor or tube Z, and to the time of passage t, where 

Equating the time of passage through the tubular reactor to that of the time required for the batch reaction, gives the equivalent ideal-flow tubular reactor 

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For gas-phase reactions this tubular reactor-batch reactor analogy may not be valid since the volmnetric flow rate of the gas, and therefore the gas velocity, can vary along the reactor length as a result of mole number changes accompanying chemical rea-... 

Chapter 1 treated the simplest type of piston flow reactor, one with constant density and constant reactor cross section. The reactor design equations for this type of piston flow reactor are directly analogous to the design equations for a constant-density batch reactor. What happens in time in the batch reactor happens in space in the piston flow reactor, and the transformation t = z/u converts one design equation to the other. For component A,... 

This is the piston flow analog of the variable-volume batch reactor. Equation (2.30). 

As with continuous processes, the heart of a batch chemical process is its reactor. Idealized reactor models were considered in Chapter 5. In an ideal-batch reactor, all fluid elements have the same residence time. There is thus an analogy between ideal-batch reactors and plug-flow reactors. There are four major factors that effect batch reactor performance ... 

The tubular flow reactor is a convenient means of approaching the performance characteristics of a batch reactor on a continuous basis, since the distance-pressure-temperature history of the various plugs as they flow through the reactor corresponds to the time-pressure-temperature protocol that is used in a batch reactor. Although this analogy is often useful,... 

The procedure is analogous with the homogeneous batch reactor. To ensure meaningful results, the composition of fluid must be uniform throughout the system at any instant. This requires that the conversion per pass across the catalyst be small. 

When the density varies with conversion, the analogy between the batch reactor and the PFTR dt dx) is no longer appropriate. In the batch reactor with ideal gases, the density varies with conversion in a constant-pressure reactor but not in a constant-volume reactor. In a flow reactor, the reactor volume is fixed, no matter what the density. In a flow reactor the volumetric flow rate changes with conversion if there is a mole number change with ideal gases. 

Analogous to the batch reactor with Michaelis-Menten kinetics, this equation for the residence time of the PFR can be solved directly when the kinetic constants, the inlet concentration of substrate and the desired conversion are known. 

For a variable volume system, / R / 0 by analogy to batch reactor. 

Another approach to a combined system is the connection of the two systems through a quinone redox couple dissolved in an oil phase, as shown in Fig. 17.2. This system is analogous to the combination of photosystems I and II in the photosynthesis of green plants. Fig. 17.10 illustrates the structure of our model system, in which the oil-phase corresponds to the lipid bilayer membrane of chloroplast. Such a system is structurally identical to a liposome and has the possibility of development for use in a batch reactor. 

Analogous to the batch reactor, a fractional conversion of a reactant A can be defined as ... 

At constant pressure and granted ideal plug flow, the behavior of a tubular reactor at steady state is mathematically analogous to that of a batch reactor A volume element of the reaction mixture has no means of knowing whether it is suspended tea bag-style in a batch reactor or rides elevator-style through a tubular reactor being exposed to the same conditions it behaves in the same way in both cases. As in a batch reactor, what is measured directly are concentrations—here in the effluent—and a finite-difference approximation is needed to obtain the rate from experiments with different reactor space times and otherwise identical conditions. For a reaction without fluid-density variation ... 

Note the analogy to batch reactors that have a unique residence time t and where... 

A tubular prereactor, in series with CSTR system, can offer stability advantages, which will he discussed later. A number of other flow alternatives are also possible with a CSTR-series system but these alternates are not widely utilized. An obvious flow alternative for a reactor system consisting of a series of CSTRs would he to introduce some portion of the total recipe at places other than the front end of the reactor train. These intermediate feeds would, in many respects, be analogous to semicootinuous operation of batch reactors. 

The above derivation is for data taken in a constant-volume batch reactor, with t denoting the residence time. The derivation for flow reactors is closely analogous, with space-time as the corresponding variable. 

We note that for adiabatic conditions the relationship between temperature and conversion is the same for batch reactors, CSTRs, PBRs, and PFRs. Once we have T as a function of X for a batch reactor, we can construct a table similar to Table E8-5.1 and use techniques analogous to those discussed in Section 8.3.2 to evaluate the design equation to determine the time necessary to achieve a specified conversion. 

The first reactor gets a mixture of primary and secondary steam to attain 177 °C (9.35 bar). The vapor from this first reactor is fed into the second reactor, but in addition to this vapor, the second reactor also gets some primary steam to partially make up for the pressure loss in the first reactor. Analogously, the vapor from the second reactor is fed into the third reactor, and so forth. As there must be a pressure drop from reactor to reactor to ascertain flow, the last reactor has only 161 °C (6.34 bar), but by an intricate pipe and valve system the batch period is split up in such a way that each reactor is run at each of the different temperatures for an equal interval of time, so that each charge is treated equally. 

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