Plug flow reactors equations

The basic design equation for a plug flow reactor (equation 8.2.7) may be used to describe the steady-state conversion achieved in the plug flow element of the recycle reactor ... 

Upon simplification the resulting ideal plug flow reactor equation is... 

Tubular Reactor with Dispersion An alternative approach to describe deviation from ideal plug flow due to backmixing is to include a term that allows for axial dispersion De in the plug flow reactor equations. The reactor mass balance equation now becomes... 

In some cases it is possible to perform experiments at conversions low enough to allow neglect of the effect of conversion on the rate. In other words the rate is constant throughout the plug flow reactor. Equation (7.159) can then be integrated to ... 

For reactions in which the rate depends only on the concentration of one species [i.e., —=/(Ca)I, it is usually convenient to report —r as a function of concentration rather than conversion. We can rewrite the design equation for a plug-flow reactor [Equation (2-16)] in terms of the concentration, C, rather than in terms of conversion for the special case when v =Vq. ... 

Reactors do not always run at steady state. In fact, many pharmaceuticals are made in a batch mode. Such problems are easily solved using the same techniques presented above because the plug flow reactor equations are identical to the batch reactor equations. Even CSTRs can be run in a transient mode, and it may be necessary to model a time-dependent CSTR to study the stability of steady solutions. When there is more than one solution, one or more of them will be unstable. Thus, this section considers a time-dependent CSTR as described by Eq. (8.51) ... 

The mass balance for a differential plug-flow reactor (equation 3-17) that operates at high-mass-transfer Peclet numbers allows one to replace dtw, in (3-32) ... 

In Figure 1, overall conversion is assumed to be represented by a second-order equation this does approximately fit experimental desulfurization data. Therefore, the lowest line is simply the second order plug flow reactor equation. 

The effective LHSV is the apparent LHSV divided by 0.8 otherwise the identical second order plug flow reactor equation is plotted for this case. 

Example 5 Percent Approach to Equilibrium For a reversible reaction with rate equation r = L[A — (1 — A)Vl6], the size function kV,./V of a plug flow reactor will be found in terms of percent approach to equilibrium ... 

This is the equation for a plug flow reactor. It can be derived directly from the rate equations with the aid of Laplace transforms. The sequences of second-order reactions of Figs. 7-5n and 7-5c required numerical integrations. 

A reversible reaction A B is conducted in a plug flow reactor. The rate equation is... 

Example 5 Application of Effectiveness For a second-order reaction in a plug flow reactor the Thiele modulus is ( ) = SVQ, and inlet concentration is C50 = 1.0. The equation will he integrated for 80 percent conversion with Simpsons rule. Values of T) are... 

After the rates have been determined at a series of reactant concentrations, the differential method of testing rate equations is applied. Smith [3] and Carberry [4] have adequately reviewed the designs of heterogeneous catalytic reactors. The following examples review design problems in a plug flow reactor with a homogeneous phase. 

By comparing the design equations of batch, CFSTR, and plug flow reactors, it is possible to establish their performances. Consider a single stage CFSTR. 

Equation 8-155 shows that the conversion in the dispersion reactor will always be less than that of the plug flow reactor (C >... 

For a plug flow reactor, differential volume moves along the length. The following equation may express the material balance for a plug flow reactor ... 

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 ... 

The above equations also apply to a plug flow reactor, where 0 is the dimensionless residence time, which varies with distance. 

It should be noted that the analysis for an ideal-batch reactor is the same as that for a plug-flow reactor (compare Equations 5.43 and 5.61). All fluid elements have the same residence time in both cases. Thus... 

Alternatively, the residence time in the plug-flow reactor could be calculated from the batch equations given in Table 5.10. This... 

Maximum selectivity requires a minimum ratio r2/ri in Equation 5.65. A batch or plug-flow reactor maintains higher average concentrations of feed (CFeed) than a mixed-flow reactor, in which the incoming feed is instantly diluted by the PRODUCT and BYPRODUCT. If ax > a2 in Equations 5.64 and 5.65 the primary reaction to PRODUCT is favored by a high concentration of FEED. If ax < a2 the primary reaction to PRODUCT is favored by a low concentration of FEED. Thus, if... 

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

Consider the segment of tubular reactor shown in Figure 8.3. Since the fluid composition varies with longitudinal position, we must write our material balance for a reactant species over a different element of reactor (dVR). Moreover, since plug flow reactors are operated at steady state except during start-up and shut-down procedures, the relations of major interest are those in which the accumulation term is missing from equation 8.0.1. Thus... 

This equation is the basic relation for the mean residence time in a plug flow reactor with arbitrary reaction kinetics. Note that this expression differs from that for the space time (equation 8.2.9) by the inclusion of the term (1 + SAfA) and that this term appears inside the integral sign. The two quantities become identical only when 5a is zero (i.e., the fluid density is constant). The differences between the two characteristic times may be quite substantial, as we will see in Illustration 8.5. Of the two quantities, the reactor... 

Consider j plug flow reactors connected in series and let/i,/2,/3, -fh >/ represent the fraction conversion of the limiting reagent, leaving reactors 1, 2, 3,. J. For each of the reactors considered above, the appropriate design equation is 8.2.7. For reactor z,... 

This equation differs from that for the plug flow reactor (8.2.9) in that for a CSTR the rate is evaluated at effluent conditions and thus appears outside the integral. 

The ratio of equations 8.3.58 and 8.3.57 gives the relative total space time requirement for a cascade of stirred tank reactors vis a vis a plug flow reactor. 

This relation is identical with that which would be obtained from equation 8.2.10 for a plug flow reactor with first-order kinetics. 

Hence the area under the curve of y versus CA multiplied by the ratio of stoichiometric coefficients represents the overall change in valuable product concentration between the inlet and outlet streams in a plug flow reactor or in a batch reactor. For the case of a CSTR the instantaneous yield is evaluated at the effluent composition, and the corresponding equation is... 

---