Ideal Tubular Reactor

If changes in volume due to reaction are negligible, then [F, = C,v moles of //time = (moles of //volume) (volume/time)]  

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

Clearly, the space-time, t, in the ideal tubular reactor is the same as the residence time in the batch reactor only if volume changes are neglectable. This is easy to see from Equation (3.4.2) by substituting C,-v for F,- and recalling that for volume changes 

A PFR operating isothermally at 773 K is used to conduct the following reaction O O O O 

If a feed of pure methylacetoxypropionate enters at 5 atm and at a flow rate of 0.193 ft7s, what length of pipe with a cross-sectional area of 0.0388 ft is necessary for the reaction to achieve 90 percent conversion (from C. G. Hill, An Introduction to Chemical Engineering Kinetics Reactor Design, Wiley, 1977, pp. 266-267)  

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We now formalize the definition of piston flow. Denote position in the reactor using a cylindrical coordinate system (r, 6, z) so that the concentration at a point is denoted as a(r, 9, z) For the reactor to be a piston flow reactor (also called plug flow reactor, slug flow reactor, or ideal tubular reactor), three conditions must be satisfied ... 

With respect to reaction rates, an element of fluid will behave 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. 

At steady-state conditions, the mass balance design equations for the ideal tubular reactor apply. These equations may be expressed as... 

Tanks-in-series reactor configurations provide a means of approaching the conversion of a tubular reactor. In modelling, they are employed for describing axial mixing in non-ideal tubular reactors. Residence time distributions, as measured by tracers, can be used to characterise reactors, to establish models and to calculate conversions for first-order reactions. 

The ideal tubular reactor is one in which elements of the homogeneous fluid reactant move through a tube as plugs moving parallel to the tube axis. This flow pattern is referred to as... 

It should be emphasized that for ideal tubular reactors, it is the total volume per unit of feed that determines the conversion level achieved. The ratio of the length of the tube to its diameter is irrelevant, provided that plug flow is maintained and that one uses the same flow rates and pressure-temperature profiles expressed in terms of reactor volume elements. 

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. 

Jackson (1968) proposed an algebraic structure for the reactor representation consisting of parallel ideal tubular reactors that were interconnected with side streams at various sink and source... 

The diffusion length was varied from 10 to 100 pm for the whole range the selectivities did not indicate good mixing [41]. This shows that pure laminar diffusion cannot compare with the ideal tubular reactor. Hence, such mixers may not be adequate for fast to very fast reactions, when side reaction selectivities are considered. 

M 39] [P 37] Using an azo-type competitive reaction, the selectivities were compared for the P- and V-type micro mixers having straight and oblique fluid injection, respectively [41]. In this way, laminar- and turbulent-flow mixing achieved by vertical interdigital microstructured mixers can be compared. The selectivities of the turbulent V-type mixer are better to some extent as compared with the P-type device however, neither approaches the characteristics of the ideal tubular reactor. The micro devices, however, are better than a conventional jet mixer. 

The flow patterns, composition profiles, and temperature profiles in a real tubular reactor can often be quite complex. Temperature and composition gradients can exist in both the axial and radial dimensions. Flow can be laminar or turbulent. Axial diffusion and conduction can occur. All of these potential complexities are eliminated when the plug flow assumption is made. A plug flow tubular reactor (PFR) assumes that the process fluid moves with a uniform velocity profile over the entire cross-sectional area of the reactor and no radial gradients exist. This assumption is fairly reasonable for adiabatic reactors. But for nonadiabatic reactors, radial temperature gradients are inherent features. If tube diameters are kept small, the plug flow assumption in more correct. Nevertheless the PFR can be used for many systems, and this idealized tubular reactor will be assumed in the examples considered in this book. We also assume that there is no axial conduction or diffusion. 

Plug Flow Reactor A plug flow reactor (PFR) is an idealized tubular reactor in which each reactant molecule enters and travels through the reactor as a plug, i.e., each molecule enters the reactor at the same velocity and has exactly the same residence time. As a result, the concentration of every molecule at a given distance downstream of the inlet is the same. The mass and energy balance for a differential volume between position Vr and Vr + dVr from the inlet may be written as partial differential equations (PDEs) for a constant-density system ... 

In a multichannel monolith with cocurrent downflow, each channel will have the same residence time and a residence-time distribution close to an ideal tubular reactor. But due to nonuniform flow distribution, the gas-liquid ratio, the volume reactant per volume catalyst, and, consequently, the conversion can be very different in different channels. 

Now if we consider the idealized tubular reactor with uniform... 

We first consider nonideal tubular reactors. Tubular reactors may be empty, or they may be packed with some material that acts as a catalyst, heat-transfer medium, or means of promoting interphase contact. Until now when analyzing ideal tubular reactors, it usually has been assumed that the fluid moved through the reactor in piston-like flow (PFR), and every atom spends an identical length of time in the reaction environment. Here, the velocity profile... 

For example, in one version of the Wacker process used for the oxidation of ethylene to acetaldehyde with soluble palladium-copper complexes, a tubular reactor containing ceramic rings is used to promote gas-liquid contacting and to impart a gas-liquid flow pattern that approaches ideal tubular reactor behavior. 

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... 

Sane of the results obtained experimentally are oatiared in table III with those predicted by the model. The agreeroent is excellent and, as e 5)ecbed, the amounts of dinitroanthraquinene formed in this reactor system are higher than in the plug flew reactor. Using this model we were able to shew that for this nitration a cascade of at least 20 stirred vessels are required in order to obtain the same product-mixture as with the ideal tubular reactor (fig. 2). 

We have simulated the complete (stirred tank and tube) reactor system combining our model for the cascade reactor, with only one stirred tank, with the model for the adiabatic ideal tubular reactor. An example of the excellent fit between simulated and eiq)eriinentally found resiUts is given in fig. 3. ... 

With this reactor stan we have beai able to achieve our gocil of cbtciinlng the product-mix of the ideal tubular reactor. 

When multiple reactions occur in the gas phase, the mass balance for component i is written for an ideal tubular reactor at high mass transfer Peclet numbers in the following form, and each term has units of moles per volume per time ... 

Non-ideal simulations satisfy the Danckweits boundary condition for the outlet concentration gradient. Real and ideal tubular reactor performance at various mass transfer Peclet numbers is compared when the product of the effectiveness factor, the interpeilet Damkohler number, and the catalyst filling factor is 5. 

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