Reaction Rate Data from Differential Reactors

6 Reaction Rate Data from Differential Reactors 

The subscript e refers to the exit of the reactor. Solving for — r. we have 

The mole balance equation can also be written in terms of concentration 

The term F/ ( X gives the rate of formation of product, Fp. when the stoichio-meu-ic coefficients of A and of P are identical. Adjustments to Equation (7-22) must be made when this is not the case. 

Consequently, we see that the reaction rate, —/a, can be determined by measuring the product concentration, Cp. 

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Section 7.S Reaction Rate Data from Differential Reactors... 

FIGURE 11.2 Deterniination of reaction rate parameters from differential and integral reactor data. 

Consider first the tubular reactor. From the material balance (Table 3.5.1), it is clear that in order to solve the mass balance the functional form of the rate expression must be provided because the reactor outlet is the integral result of reaction over the volume of the reactor. However, if only initial reaction rate data were required, then a tubular reactor could be used by noticing that if the differentials are replaced by deltas, then ... 

There are circumstances under which the measured reaction order and activation energy are not the true values. Consider the case in which we obtain reaction rate data in a differential reactor, where precautions are taken to virtually elimiinate external mass transfer resistance. From these data we constmct a log-log plot cf the rate of reaction as a function of the bulk gas-phase concentration (Figure 12-8). The slope of this plot is the apparent reaction order n and tlhe rate law takes the form... 

To determine reaction rate parameters from the experimental data, the following differential equation was used to describe the reaction system in a constant-volume batch reactor assuming a pseudo-first-order equation for propylene epoxidation ... 

Equations (1) and (2) represent reaction rates and, as such, can represent directly only data from a differential reactor. In many cases, however, data are obtained from an integral reactor. Are the data to be differentiated and compared directly to Eqs. (1) or (2), or are the equations to be integrated with the conservation equations and compared to the integral data ... 

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 ... 

For reactor design calculations it is necessary to know the total devolatilization rate as well as the species production rates. Therefore, one needs to include in the reactor model all the reaction rates that are available for the devolatilization of the particular coal. Kayihan and Reklaitis (8) show that the kinetic data provided by Howard, et al. (5,6) can be easily incorporated in the design calculations for fluidized beds where the coal residence times are long. However, if the residence time of pulverized coal in the reactor is short as it is in entrained bed reactors, then the handling of ordinary differential equations arising from the reaction kinetics require excessive machine computation time. This is due to the stiffness of the differential equations. It is found that the model equations cannot be solved... 

Propose a generalized rate expression for testing the data. Analysis of rate data by the differential method involves utilizing the entire reaction-rate expression to find reaction order and the rate constant. Since the data have been obtained from a batch reactor, a general rate expression of the following form may be used ... 

For elucidation of mechanisms, rate data at very low conversions may be highly desirable. They can be obtained more easily from a batch reactor than from a CSTR or plug-flow tubular reactor. A standard CSTR would have to be operated at very high flow rates apt to cause fluid-dynamic and control problems. The same is true for a standard tubular reactor unless equipped with a sampling port near its inlet, a mechanical complication apt to perturb the flow pattern. If the problem of confining the reaction to a very small flow reactor can be solved—as is possible, for example, for radiation-induced reactions—a differential reactor operated once-through or with recycle may be the best choice. 

The reaction was carried out in a differential reactor with 0.5 g of catalyst at 623 K. From the data below, deteirnine the reaction orders with respect to propone (a) and oxygen (P) and the specific reaction rate, k. 

Stefuca et al. (1990) proposed an ET method offering a rapid, convenient, and general approach to determine kinetic constants of immobilized biocatalysts. Here, a differential reactor (DR) was used for the measurement of the initial reaction rate of sucrose hydrolysis (Vallat et al. 1986). The enzyme column of the ET has been considered as a differential packed-bed reactor, and with a mathematical model, intrinsic kinetic constants of immobilized invertase were calculated from experimental DR and ET data. 

In this chapter we are concerned only with the rate equation for the i hemical step (no physical resistances). Also, it will be supposed that /"the temperature is constant, both during the course of the reaction and in all parts of the reactor volume. These ideal conditions are often met in the stirred-tank reactor (see-Se c." l-6). Data are invariably obtained with this objective, because it is extremely hazardous to try to establish a rate equation from nonisothermal data or data obtained in inadequately mixed systems. Under these restrictions the integration and differential methods can be used with Eqs. l-X and (2-5) or, if the density is constant, with Eq. (2-6). Even with these restrictions, evaluating a rate equation from data may be an involved problem. Reactions may be simple or complex, or reversible or irreversible, or the density may change even at constant temperatur (for example, if there is a change in number of moles in a gaseous reaction). These several types of reactions are analyzed in Secs. 2-7 to 2-11 under the categories of simple and complex systems. 

Initial Rate Method For reversible reactions, we use a modified differential method—the initial rate method. In this case, a series of experiments are conducted at selected initial reactant compositions, and each run is terminated at low conversion. From the collected data, we calculate (by numerical differentiation) the reaction rate at the initial conditions. Since the reaction extent is low, the reverse reaction is negligible, and we can readily determine the orders of the forward reaction from the known initial compositions. The rate of the reversible reaction is determined by conducting a series of experiments when the reactor is charged with selected initial product compositions. The initial rate method is also used to determine the rates for complex reactions since it enables us to isolate the effect of different reactants. 

P5-I6c The thermal decomposition of i.sopropyl isocyanate was studied in a differential packed-bed reactor. From the data in Table P5 -16, determine the reaction rate law parameters. 

Problems P5-3. P5-5, P5-7, and P5 18 all involve batch reactor experiments to find] the reactor order and specific reaction rate. The students can use differed techniques to differential the data or can use regression. These problems cat be alternated from year to year. 

In principle any of the three reactor configurations, BR, PFR or, CSTR, can be operated in such a way that initial reaction conditions can be studied - in the so called differential mode. In feet, the CSTR is inherently a differential reactor at all levels of conversion and the standard data obtained from its operation are differential rates at a fixed level of conversion. Rates at low levels of conversion can sometimes be studied in a CSTR simply by increasing feed flow rates to reduce space time and hence the level of conversion. The problem here is the achievement of thorough mixing of the input with the reactor contents at high throughput rates. 

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