Plug-flow reactors PFR

A PFR is a reactor model based on two assumptions (i) steady-state operation and 

Equation 4.2.10 is the species-based differential design equations for a PFR, written for species j. To obtain the reactor volume of a PFR, we integrate Eq. 4.2.10, 

Equation 4.2.11 provides a relation among the species flow rate at the inlet and outlet of the reactor, Fand Fthe species formation rate, (r ), and the volume of the reactor, Vr, for a plug-flow reactor. 

For PFRs with single chemical reactions, it has been customary to write the species-based design equation for the limiting reactant A, and Eq. 4.2.10 reduces to 

Equation 4.2.13 is the species-based differential design equation of a plug-flow reactor, expressed in terms of the conversion of reactant A. To obtain the integral form of the design equation, we separate the variables and integrate Eq. 4.2.13  

If Fa is the molal flow rate of A into this volume element, then equation 4.11 is described by  

If the volumetric flow rate, Vo, is referenced to reactor inlet conditions, then 

Note that this equation with space time, t, is analogous to equation 4.7 written for a batch reactor using real time, t. 

The average residence time, t, for a volume element is equal to the space time only in this latter situation when there is no volume change. Also, if temperature gradients exist so that the assumption of isothermal operation is inappropriate, the energy balance equation must be combined with the design equation. Further correction is needed if a significant pressure drop exists in the reactor, which is a situation that can easily occur in a fixed-bed reactor [1,4]. 

In such a fixed-bed reactor, once the catalyst packing density is known (mass catalyst/volume), equation 4.16 is easily modified to give  

Now we apply the general mole balance, assuming that the reactor operates at steady state, 

we write the molar flow rate as Pj=CV and the volume as V=tV, which is substituted into the equation to give 

Because of the similarity between the PFR and the batch reactor, we can by analogy develop an expression of the material balance, which is based on conversion  

Highlight 6.10 provides another example about residence time required for conversion of pentane. 

If we compare Highlights 6.9 and 6.10, we see that we have an identical reaction with an identical reaction rate. However, the residence time required in the 

Note the similarity between the ideal batch and the plug flow reactors, Eqs. (7-45) and (7-56), respectively. In terms of conversion, Eq. (7-56) can be written as 

Equation (7-57) can be integrated to calculate the reactor volume required to achieve a given conversion X,  

An apparent residence time based on feed conditions can be defined for a single-phase PFR as follows  

(7-53) the feed and effluent molar rates Mo and M are expressed in terms of volumetric flow rates go and q (inlet and outlet, respectively) and concentrations. Thus Eq. (7-52) can be rewritten as 

Equation (7-54) allows calculation of the residence time required to achieve a given conversion or effluent composition. In the case of a network of reactions, knowing the reaction rates as a function of volumetric concentrations allows solution of the set of often nonlinear algebraic material balance equations using an implicit solver such as the multi variable Newton-Raphson method to determine the CSTR effluent concentration as a function of the residence time. As for batch reactors, for a single reaction all compositions can be expressed in terms of a component conversion or volumetric concentration, and Eq. (7-54) then becomes a single nonlinear algebraic equation solved by the Newton-Raphson method (for more details on this method see the relevant section this handbook). 

Equation (7-60) is identical to that of the ideal batch reactor, Eq. (7-47), and tlie two reactor systems can be modeled in identical fashion. 

For a constant-density system with no change in number of moles, with the true residence time Xpfr  

Ihe material balance for a reactant A for a differential volume element d V of the PFR perpendicular to the flow direction is given by 

Substitution of the rate equations into Equation 7.9 and integration give the following performance equations. 

Equations 7.10-7.12 are identical in forms with those for the uniformly mixed batch reactor, that is. Equations 3.15, 3.22, and 7.3, respectively. It is seen that the time from the start of a reaction in a batch reactor (t) corresponds to the residence time in a PFR (r). 

A feed solution containing a reactant A (C = 1 kmol m ) is fed to a CSTR or to a PFR at a volumetric flow rate of 0.001 m s and converted to product P in the reactor. Ihe first-order reaction rate constant is 0.02 s .  

Determine the reactor volumes of CSTR and PFR required to attain a fractional conversion of A, = 0.95. 

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TABLE 7-7 Material and Energy Balances of a Plug Flow Reactor (PFR)... 

Plug Flow Reactor (PFR) The material balance over a differential vohime dV) is... 

Plug Flow Reactor (PFR) A plug flow reactor is a tubular reactor where the feed is continuously introduced at one end and the products continuously removed from the other end. The concentration/temperature profile in the reactor varies with position. 

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 ... 

Runaway criteria developed for plug-flow tubular reactors, which are mathematically isomorphic with batch reactors with a constant coolant temperature, are also included in the tables. They can be considered conservative criteria for batch reactors, which can be operated safer due to manipulation of the coolant temperature. Balakotaiah et al. (1995) showed that in practice safe and runaway regions overlap for the three types of reactors for homogeneous reactions (1) batch reactor (BR), and, equivalently, plug-flow reactor (PFR), (2) CSTR, and (3) continuously operated bubble column reactor (BCR). 

If the process is carried out in a stirred batch reactor (SBR) or in a plug-flow reactor (PFR) the final product will always be the mixture of both products, i.e. the selectivity will be less than one. Contrary to this, the selectivity in a continuous stirred-tank reactor (CSTR) can approach one. A selectivity equal to one, however, can only be achieved in an infinite time. In order to reach a high selectivity the mean residence time must be very long, and, consequently, the productivity of the reactor will be very low. A compromise must be made between selectivity and productivity. This is always a choice based upon economics. 

The Plug Flow Reactor (PFR)—Basic Assumptions and Design Equations... 

Plug flow reactor (PFR) with recycle. The recycle reactor is characterized by a non-zero value of R, that is the ratio between the mass flow rate of the recycled stream and the feeding rate Q. The material balance reads for this case as... 

Plug-flow reactor (PFR), based on plug flow and... 

A plug-flow reactor (PFR) may be used for both liquid-phase and gas-phase reactions, and for both laboratory-scale investigations of kinetics and large-scale production. The reactor itself may consist of an empty tube or vessel, or it may contain packing or a fixed bed of particles (e.g., catalyst particles). The former is illustrated in Figure 2.4, in which concentration profiles are also shown with respect to position in the vessel. 

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. 

Plug flow reactor (PFR) a tube reactor in which the reactants are fed continuously at one end and the products are removed continuously from the other end concentration and heat generation change along the length of the tube the PFR is often used for potentially hazardous reactions because of the relatively small inventory in the system. 

In another kind of ideal flow reactor, all portions of the fluid have the same residence time. It is called a plug flow reactor, PFR, or a tubular flow reactor, TFR, because this flow pattern is characteristic of tubes and pipes. As the reaction proceeds, the concentration falls off with distance. 

Quantitatively, the efficiency at a specified conversion level, x, is defined as the ratio of the mean residence time or reactor volume in a plug flow reactor (PFR) to that of the reactor in question,... 

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