Isothermal Plug Flow Tubular Reactor

CONTINUOUS ISOTHERMAL PLUG FLOW TUBULAR REACTOR 

The plug flow tubular reaetor is a heat exehanger where the reaetion oeeurs in the tubes. Construetion is often varied. For example, the reaetor may eonsist of a tube plaeed in a bath, a tube in a jaeket, or a number of tubes immensed in a heat transfer medium for the reaetor 

The tubular plug flow reaetor is relatively easy to maintain with no moving parts, and it usually produees the highest eonversion per reaetor volume of any of the flow reaetors. Other advantages are  

The prineipal disadvantage of die tubular reaetor is die diffieulty in eontrolling die temperature within die reaetor. This often results in hot spots espeeially when die reaetion is exodiermie. The tubular reaetor ean be in die form of one long tube or one of a number of shorter reaetors arranged in a tube bank (Eigure 4-7). 

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Another view is given in Figure 3.1.2 (Berty 1979), to understand the inner workings of recycle reactors. Here the recycle reactor is represented as an ideal, isothermal, plug-flow, tubular reactor with external recycle. This view justifies the frequently used name loop reactor. As is customary for the calculation of performance for tubular reactors, the rate equations are integrated from initial to final conditions within the inner balance limit. This calculation represents an implicit problem since the initial conditions depend on the result because of the recycle stream. Therefore, repeated trial and error calculations are needed for recycle... 

CONTINUOUS ISOTHERMAL PLUG FLOW TUBULAR REACTOR... 

One of the simplest models used to describe the performance of tubular reactors is the well-known isothermal one-dimensional plug flow tubular reactor (PFTR) model. The mass balance of this model for steady-state conditions, the simultaneous occurrence of M reactions and a constant volumetric flow rate V is ... 

The above discussion can be illustrated for an isothermal packed bed tubular reactor with negligible diffusional resistances ( /= 1.0) and negligible axial dispersion (plug flow) and instantaneous radial dispersion (one-dimensional model) ... 

The isothermal plug-flow mass balance for first-order irreversible chemical kinetics in an ideal packed catalytic tubular reactor with significant external mass transfer resistance yields the following functional form for the conversion of reactant A at high mass transfer Peclet numbers ... 

Example 9.11 Which type of isothermal reactor would produce the narrowest possible distribution of chain lengths in a free-radical addition polymerization continuous stirred tank reactor (CSTR, or backmix), batch (assume perfect stirring in each of the previous), plug-flow tubular, or laminar-flow tubular ... 

Because the characteristic of tubular reactors approximates plug-flow, they are used if careful control of residence time is important, as in the case where there are multiple reactions in series. High surface area to volume ratios are possible, which is an advantage if high rates of heat transfer are required. It is sometimes possible to approach isothermal conditions or a predetermined temperature profile by careful design of the heat transfer arrangements. 

There will be velocity gradients in the radial direction so all fluid elements will not have the same residence time in the reactor. Under turbulent flow conditions in reactors with large length to diameter ratios, any disparities between observed values and model predictions arising from this factor should be small. For short reactors and/or laminar flow conditions the disparities can be appreciable. Some of the techniques used in the analysis of isothermal tubular reactors that deviate from plug flow are treated in Chapter 11. 

Compounds A and B are available in the off-gas stream from an absorption column at concentrations of 20 moles/m3 each. 14 m3/sec of this fluid is to be processed in a long isothermal tubular reactor. If the reactor may be assumed to approximate a plug flow reactor, what volume of pipe is required to obtain 80% conversion of species A ... 

The approach to the design of non-isothermal tubular reactors with plug flow parallels that already outlined for batch reactors (see Sect. 2.4.)... 

In designing and operating a tubular reactor when the heat of reaction is appreciable, strictly isothermal operation is rarely achieved and usually is not economically justifiable, although the aim may be to maintain the local temperatures within fairly narrow limits. On the assumption of plug flow, the rate of temperature rise or fall along the reactor d77dz is determined by a heat balance... 

For the isothermal tubular plug-flow reactor (PFR) discussed previously, the mass balance for the G gaseous components is... 

Species C is the desired product. We want to design an isothermal, isobaric tubular reactor (plug-flow reactor) to be operated at 489°C and 5 atm A stieam of reactant A at a rate of 1 mol/s is available in the plant. 

Ogunye and Ray (1971a,b) have formulated the optimal control problem for tubular reactors with catalyst decay via a weak maximum principle for this distributed system. Detailed numerical examples have been calculated for both adiabatic and isothermal reactors. For irreversible reactions, constant conversion policies are found to not always be optimal. A practical technique for on-line optimal control for fixed bed catalytic reactors, has been suggested by Brisk and Barton (1977). Lovland (1977) derived a simple maximum principle for the optimal flow control of plug flow processes. 

De Pauw and Froment [1975] studied n.Cj isomerization on a Pt/alumina catalyst in an isothermal tubular reactor with plug flow, yielding n.Cj-conversion, x, versus W/F °-data. Therefore, the following objective function was chosen for the parameter estimation ... 

The reaction is carried out in an isothermal tubular reactor with plug flow. Accordingly, when the rate equation for the disappearance of A is substituted into the integrated continuity equation for Ai,... 

To carry out an exothermic reaction in a tubular reactor under nearly isothermal conditions, a small diameter is needed to give a high ratio of surface area to volume. The reactor could be made from sections of jacketed pipe or from a long coil immersed in a cooling bath. The following analysis is for a constant jacket temperature, and the liquid is assumed to be in plug flow, with no radial gradients of temperature or concentration and no axial conduction or diffusion. 

If the reactor operates under almost isothermal conditions, equations 6.17-6.20 are not needed. Under plug flow conditions we can integrate equation 6.17 over the cross-sectional area of the tubular reactor and include the boundary conditions into the differential equation. We finally have... 

It will be shown in Chapter 9 that a mass balance on propane over an isothermal differential volume element of a tubular reactor with plug flow may be written... 

Tubular reactors do not necessarily operate under isothermal conditions in industry, be it for reasons of chemical equilibrium or of selectivity, of profit optimization, or simply because it is not economically or technically feasible. It then becomes necessary to consider also the energy equation, that is, a heat balance on a differential volume element of the reactor. For reasons of analogy with the derivation of Eq. 9.1-1 assume that convection is the only mechanism of heat transfer. Moreover, this convection is considered to occur by plug flow and the temperature is completely uniform in a cross section. If heat is exchanged through the wall the entire temperature difference with the wall is located in a very thin film close to the wall. The energy equation then becomes, in the steady state ... 

Example 9.1-1 Derivation of a Kinetic Equation from Experiments in an Isothermal Tubular Reactor with Plug Flow. Thermal Cracking of Propane... 

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