Tubular with plug flow

In this liquid phase reaction, it may be assumed that the mass density of the liquid is unaffected by the reaction, allowing the material balance for the tubular reactor to be applied on a volume basis (Section 1.7.1, Volume 3) with plug flow. 

A special kind of tubular flow reactor has laminar flow. The specific rate of such a case is found and compared with plug flow in problem P3.09.15. 

In any real situation, reactants only flow through the reactor because there is a difference in pressure between the inlet and the outlet. Methods for calculating the pressure drop in pipes and packed beds have been outlined in Chap. 1. Often, the pressure drop is negligible compared with the total pressure and it is usual to assume that a tubular reactor with plug flow operates at constant pressure. 

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 Sect. 3.2, the development of the design equation for the tubular reactor with plug flow was based on the assumption that velocity and concentration gradients do not exist in the direction perpendiculeir to fluid flow. In industrial tubular reactors, turbulent flow is usually desirable since it is accompanied by effective heat and mass transfer and when turbulent flow takes place, the deviation from true plug flow is not great. However, especially in dealing with liquids of high viscosity, it may not be possible to achieve turbulent flow with a reasonable pressure drop and laminar flow must then be tolerated. 

As i the term in brackets above tends to exp (vit/V) for t < V/v), and F becomes zero(7>. Thus, for an infinite number of tanks the fraction of tracer that has escaped is zero for all times less than the residence time V/v. This is exactly the same as for the case of an ideal tubular reactor with plug flow. 

The continuous growth of micro-organisms, as with continuous chemical reactions, may be carried out either in tubular fermenters (plug flow) or in well-mixed... 

In the next two chapters of this book we turn to the chemical reactor that is probably the most challenging the tubular or plug flow reactor. The inherent distributed nature of the unit (variables change with axial and radial position) gives rise to complex behavior, which is often counterintuitive and difficult to explain. The increase in the number of independent variables makes the development and solution of mathematical models more complex compared to the perfectly mixed CSTR and batch reactor. 

Beyne and Froment [1993] simulated a tubular reactor with plug flow and diffiisional limitations inside the catalyst for the process discussed already in Section 3. The main reaction is of the type A B and coke is formed through a polymerization mechanism from a site covered by coke... 

Alternatively, tubular reactors with plug flow (piston flow) (PFR) are used and operated in continuous mode (Figure 1.15). 

The reactor in which chemical reactions lake place is fhe mosl imporlanl piece of equipmenl in each chemical planl. A variety of reactors are used in induslry, bul all of Ihem can be assigned to cerlain basic types or a combination of fhese ideal reactors [53] (1) bafch slirred-lank reactor, (2) continuous slirred-lank reactor, and (3) lubular reactor. The ideal slirred-lank bafch reactor is characterized by complete mixing, while in the ideal tubular reactor, plug flow is assumed. In contrast to the stirred-tank batch reactor with well-defined residence time, the continuous stirred-tank reactor has a very broad residence-time distribution. In... 

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,... 

Fig. 2.2-4 Cumulative residence-time function F t/z) for an ideal continuous stirred tank (1), an ideal tubular reactor with plug flow (2), and laminar flow in a tubular reactor (3).

The experimental study of Froment et al. (loc. cit) was carried out in a tubular reactor with plug flow. Tlie data were obtained as follows total conversion of propane versus a measure of the residence time, lyfF cH.fe conversion of propane into propylene versus 1V(Kcjh,)o reactor volume reduced to... 

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... 

This is the energy equation for a single-phase tubular reactor with plug flow. Note that Eq. 7.1d-4 is coupled with the continuity equation, mainly by the reaction term, but also through the heat capacity term on the left-hand side. The latter is sometimes written in terms of a specific heat that is averaged with respect to temperature and composition, that is, Yj = "c,. 

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

Design of Tubular Reactors with Plug Flow... 

The process A B C is canied out in a tubular reactor with plug flow. Both reactions are of first order. The feed consists of pure A. Given the following data... 

If this conversion were desired in a perfectly mixed flow reactor. Fig. 10.2.b-l gives k F/f ) = 6.5 (abcissa of the intersection of the ordinate level of0.865 and the n = 1 line) that is, for the given k, the reactor volume would have to be 6.5 limes the flow rate rather than only twice, as with plug flow. This example clearly illustrates that results obtained in a batch or plug flow tubular reactor cannot be directly extrapolated to a continuous flow stirred tank reactor—there may be large differences in conversion levels. 

Calculate the effect of recycle on the conversion in tubular reactors with plug flow. NONIDEAL FLOW PATTERNS AND POPULATION BALANCE MODELS 655... 

The Continuity, Energy, and Momentum Equations Kinetic Studies Using a Tubular Reactor with Plug Flow... 

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