Design equations recycle reactor

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 ... 

The tabulated data at two temperatures were obtained in a recycle reactor with powdered catalyst (Rase, Fixed Bed Reactor Design and Diagnostics, p 312, 1990). Verify that the equations are correct by checking the linearized forms, l/rx = a + b(l/pj Pf/r2 c + Pw... 

In this chapter we deal with single reactions. These are reactions whose progress can be described and followed adequately by using one and only one rate expression coupled with the necessary stoichiometric and equilibrium expressions. For such reactions product distribution is fixed hence, the important factor in comparing designs is the reactor size. We consider in turn the size comparison of various single and multiple ideal reactor systems. Then we introduce the recycle reactor and develop its performance equations. Finally, we treat a rather unique type of reaction, the autocatalytic reaction, and show how to apply our findings to it. 

The PFR design equation for a recycle reactor is also developed in the CD-ROM. 

In this chapter, the analysis of chemical reactors is expanded to additional reactor configurations that are commonly used to improve the yield and selectivity of the desirable products. In Section 9.1, we analyze semibatch reactors. Section 9.2 covers the operation of plug-flow reactors with continuous injection along their length. In Section 9.3, we examine the operation of one-stage distillation reactors, and Section 9.4 covers the operation of recycle reactors. In each section, we first derive the design equations, convert them to dimensionless forms, and then derive the auxiliary relations to express the species concentrations and the energy balance equation. 

A recycle reactor is a mathematical model describing a steady plug-flow reactor where a portion of the outlet is recycled to the Met, as shown schematically in Figure 9.5. Although this reactor configuration is rarely used in practice, the recycle reactor model enables us to examine the effect of mixing on the operations of continuous reactors. In some cases, the recycle reactor is one element of a complex reactor model. Below, we analyze the operation of a recycle reactor wifii multiple chemical reactions, derive its design equations, and discuss how to solve fiiem. 

To derive the design equation of a recycle reactor, we consider a differential reactor element, dV, and write a species balance equation over it for species j ... 

Equation 9.4.5 is the dimensionless design equation of a recycle reactor, written for the mth-independent reaction. To describe the operation of a recycle reactor with multiple chemical reactions, we have to write Eq. 9.4.5 for each of the independent reactions. 

With the concentration relations and an expression for 0i, we can now complete the design formulation of recycle reactors. Substituting the species concentrations and 6 in the individual reactions rates, r s and r s, we obtain a set of first-order, nonlinear differential equations that should be solved simultaneously with the energy balance equation for the initial condition that at t = 0, Z s = 0 and 0 =... 

If one is interested in achieving a specified product distribution, rather than just maximizing a yield, the problem is naturally more complicated. Usually numerical simulations with the reactor design equations is necessary, often combined with formal optimization procedures. A study of choice of reactor t3rpe, together with separation and recycle systems, was presented by Russell and Buzzelli [17] for the important class of reactions... 

Continuous flow stirred-tank reactors are normally just what the name implies tanks into which reactants flow and from which a product stream is removed on a continuous basis. CFSTRs, CSTRs, C-star reactors, and backmix reactors are only a few of the names applied to the idealized stirred-tank flow reactor model. We will use the letters CSTR in this book. The virtues of a stirred-tank reactor lie in its simplicity of construction and the relative ease with which it may be controlled. These reactors are used primarily for carrying out liquid phase reactions in the organic chemicals industry, particularly for systems that are characterized by relatively slow reaction rates. If it is imperative that a gas phase reaction be carried out under efficient mixing conditions similar to those found in a stirred-tank reactor, one may employ a tubular reactor containing a recycle loop. At sufficiently high recycle rates, such systems approximate the behavior of stirred tanks. In this section we are concerned with the development of design equations that are appropriate for use with the idealized stirred-tank reactor model. 

Reaction takes place only within the plug flow element of the recycle reactor, and the gross product stream from this element is divided into two portions one becomes the net product and the second is mixed with fresh feed. The mixture of the fresh feed and recycle stream is then fed to the plug flow element. By varying the relative quantities of the net product and recycle streams, one is able to obtain widely varying performance characteristics. At the limit of zero recycle the system approaches plug flow behavior, and at the limit where only an infinitesimal proportion of net product stream is produced, the system wiU approach CSTR behavior. To develop characteristic design equations that describe the peaformance of recycle reactors, we will follow Levenspiel s treatment (23). The recycle ratio R is defined as... 

PLUG-FLOW REACTOR WITH RECYCLE The Basic Design Equation... 

The parameter of the recycle reactor R is directly related to the parameter of the partially emptying reactor V. Thus for design purposes, one can treat this as a recycle reactor, determine R for optimal operation by the procedure described earlier, and then determine V from Equation 10.51 to operate the reactor in the VV or PEER mode. 

Here again the development of the design equation proceeds along the same lines as for the recycle reactor described in Chapter 10. Thus, considering Figure 21.8, the following mass balance can be written over a differential cathode area element dA ... 

To evaluate the appropriate form of Equation (7.18) we must employ the design equation used to obtain the kinetic data. We studied the kinetics of adsorption using a batch reactor with recycle operation in the differential mode. The reactor consists of a packed column with the adsorbent between two layers of glass beads. Pore diffusion and mass transfer resistances were minimized by using small particle sizes (180 to 120 pm) and high flow rates. The design equation written for the aforanentioned metal cation extraction is... 

In other words, as R goes to infinity, that is, when the amount of effluent stream 2 leaving the reactor is too small in comparison to the amount recycled RQp the design equation converges to that for an MFR ... 

Parallel reactions (nonreacting products) The general case Effect of reaction order One of the reactants undergoes a second reaction Parallel-consecutive reactions Plug-flow reactor with recycle The basic design equation Optimal design of RPR Use of RPR to resolve a selectivity dilemma Semibatch reactors... 

H.1 In Appendix 1.2 three versions of the core model of the reactor/flash unit plant are developed. One is a full-composition model (Eqs. 1-9 through 1-31) that provides the relations needed to calculate every stream variable and every vessel holdup in the plant design. The second model (Eqs. 1-33 through 1-40) is a reduced-composition model, obtained from the full model by elimination of all variables and equations not needed to implement the control loops in this chapter. Thus only the necessary manipulated and disturbance variables, the dependent variables in the differential equations (predominantly reactor and recycle tank compositions), and the controlled (output) variables remain in the second model. The third model (Eqs. 1-47 through 1-55) is a reduced version of the original model equations in which component mass holdups have been used instead of vessel concentrations as the dependent variables. 

Equation (4-41) is the design equation for a recycle reactor. This equation shows that the behavior of a recycle reactor can be varied continuously between an ideal PFR (R = 0) and an ideal CSTR (R— oo)by changing the recycle ratio. As the recycle ratio increases, the reactor behaves more like a CSTR,... 

The required volume can be calculated by solving the design equation for a recycle reactor, Eqn. (4-41), recognizing that -rA = LCa = jfcCAo(l - jca). The per pass conversion can be calculated from Eqn. (4-39). 

The equations that have been developed for design using these pseudo constants are based on steady-state mass balances of the biomass and the waste components around both the reactor of the system and the device used to separate and recycle microorganisms. Thus, the equations that can be derived will be dependent upon the characteristics of the reactor and the separator. It is impossible here to... 

Reaction occurs in the loop as well as in the stirred tank, and it is possible to eliminate the stirred tank so that the reactor volume consists of the heat exchanger and piping. This approach is used for very large reactors. In the limiting case where the loop becomes the CSTR without a separate agitated vessel, Equation (5.35) becomes q/Q > 10. This is similar to the rule-of-thumb discussed in Section 4.5.3 that a recycle loop reactor approximates a CSTR. The reader may wonder why the rule-of-thumb proposed a minimum recycle ratio of 8 in Chapter 4 but 10 here. Thumbs vary in size. More conservative designers have... 

As will be shown later the equation above is identical to the mass balance equation for a continuous stirred-tank reactor. The recycle can be provided either by an external pump as shown in Fig. 5.4-18 or by an impeller installed within the reaction chamber. The latter design was proposed by Weychert and Trela (1968). A commercial and advantageously modified version of such a reactor has been developed by Berty (1974, 1979), see Fig. 5.4-19. In these reactors, the relative velocity between the catalyst particles and the fluid phases is incretised without increasing the overall feed and outlet flow rates. 

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