Recycle differential reactors

The principle of the differential reactor with recycle is illustrated in Fig. 5.4-18. 

Figure 5.4-18. Differential reactor with recycle of the reaction mixture.

The apparatus used are mostly stirred-tank-, tubular-, and differential recycle reactors. Also, optical cells are used for spectroscopic measurements, and differential thermal-analysis apparatus and stopped flow devices are applied at high pressures. 

The measurement of a small concentration gradient requires more analytical work, and often gives less accurate kinetic data. For this reason, in the differential recycle reactor a fraction of the reaction mixture leaving a thin catalyst bed is recycled and added again to the feed (Fig. 3.3-4). This results in a larger difference of concentration, c0, or mole fraction, x , between the feed and c or x at the reactor outlet, which is used to determine the reaction rate from the material balance ... 

On the one hand, the differential reactor with recycle permits kinetic measurements of high accuracy. On the other hand, a transfer equipment is required to recycle a fraction of the reaction mixture. This can be difficult when the pressure is high. For this purpose, a jet loop reactor was developed which is equipped with an ejector to recycle the fluid. The design of the jet loop reactor is described in Chapter 4.3.4. 

Under the above modeling assumptions, the dynamic model of the reactor-column-recycle system consists of the material balance for the total molar holdup of the reactor, condenser, and reboiler, and component-wise balances for the reactant A and product Pi in the reactor, condenser, reboiler, and column trays, having a total of 2N + 9 differential equations. Specifically,... 

The limitation to low conversion is the major disadvantage of differential operation. This is not critical if the influence of the catalyst properties on deactivation is studied. If, on the other hand, one is interested in the mechanism and the kinetics of coke formation and in the deactivation of the main reactions, it is necessary to reach higher conversions. A solution to this problem is to combine the electrobalance with a recycle reactor. The recycle reactor is operated under complete mixing, so that the reactor is gradientless. Since in a completely mixed reactor the reactions occur at effluent conditions and not at feed conditions, a specific experimental procedure is necessary to obtain the deactivation effect of coke. 

Truly differential reactors of this type provide the most useful kinetic data. However, as indicated above they suffer from problems of analysis, etc. The addition of a recycle stage permits one to overcome these problems since the conversion per pass remains differential but the overall conversion becomes large enough to be measured and reflects accurately the influence of products as well as that of the reactants. A drawback, however, concerns the design of experiments. At the beginning of the investigation, trial and error is necessary for obtaining the desired concentrations at the exit. In external recycle reactors the recycle stream... 

Tiltscher H., Schelchshom J., Wolf H., Dialer K., Differential Recycle Reactors for Investigation of Heterogeneous Systems at High Pressures and Temperature Ger. Chem. Eng. 313-320. 

In performance, a differential recycle reactor resembles a batch reactor in that conversion progresses with time. The difference is that in a batch reactor the reaction occurs in all of the fluid, whereas in a differential recycle reactor it does so only in a small fraction because at any time most of the fluid is in the recycle loop rather than the reactor itself. The rate is given by... 

A guideline for choosing a suitable method is to avoid approximations as much as possible. Thus, plots of concentration, or a function of concentrations, versus time or reactor space time are preferred for evaluation of experiments with batch, tubular, and differential recycle reactors, in which concentrations are directly measured and rates can only be obtained by a finite-difference approximation (see eqns 3.1, 3.2, 3.5, 3.6, and 3.8). On the other hand, plots of the rate, or a function of the rate, versus concentration or a function of concentrations serve equally well for evaluation of results from CSTRs or differential reactors without recycle (gradientless reactors), where concentrations and rate are related to one another by algebraic equations that involve no approximations (see eqns 3.3, 3.4, or 3.7). 

Rate methods are much less suited for evaluation of results from batch, tubular, and differential recycle reactors because for these the rate must be obtained by a finite-difference approximation (see eqns 3.1, 3.5, and 3.8). In particular the method based on eqn 3.11 should not be used for such a purpose because of its high sensitivity to even minor experimental errors. 

Concentration methods. For results from batch, tubular, or differential recycle reactors at constant fluid density, the most common procedures are based on integrated forms of the rate equation. 

Fractional-life methods. If a reaction is known to be first order and at constant fluid density, its apparent rate coefficient can be found very quickly. For batch and differential recycle reactors, the relationship between the rate coefficient and the time ty required for all but a fraction y of the reactant to be consumed is... 

Concentration methods. Results from constant volume-batch or differential recycle reactors for a reaction nkA + bB — product(s) give a linear plot of ln(CB ICk) versus t with slope kapp(nACf - nBCf) and intercept ln(CB°/CA°) if the reaction is first order in both A and B [41], However, this procedure is inapplicable to experiments with stoichiometric amounts of A and B (i.e., nBCA° = nACB°), and is highly error-sensitive for amounts that are close to or extremely different from stoichiometric. 

Reactions orders and rate coefficients can be established with methods that use either rate or concentration data. Batch, tubular plug-flow, and differential recycle reactors yield concentrations as directly measured quantities, and calculation of rates... 

Carbon monoxide oxidation by pure oxygen on a porous catalyst of the type CuO on A12Os was studied in a laboratory differential recycle reactor. Under certain experimental conditions sustained oscillations of the catalyst bed temperature and CO concentrations in the reactor described in article I of Eckert et al. were observed and reported in article II of the series. 

A more general form of eqn 3.12 for first-order reactions in batch or differential recycle reactors is... 

Reactions orders and rate coefficients can be established with methods that use either rate or concentration data. Batch, tubular plug-flow, and differential recycle reactors yield concentrations as directly measured quantities, and calculation of rates requires finite-difference approximations. To avoid these, concentration methods should be used. In contrast, continuous stirred-tank reactors allow rates to be calculated from material balances without approximation. Here, evaluation based on rates is equally suited. 

Entrapment in polyacrylamide gel Active immobilized enzyme theoretical treatment of and experimental results for the use of the immobilized enzyme in a packed-bed differential recycle reactor 818... 

Figure 3.38. Derivation of mass balance equations in the case of an ideal tube reactor. Here, differential mass conservation dV = A dz for s and x for a tubular reactor with recycle, leading to Equ. 3.85 at steady state.

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... 

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. 

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