Experimental Data from Ideal Reactors

Experimental kinetic data always should be taken in a reactor that behaves as one of tiie tiiree ideal reactors. It is relatively straightforward to analyze the data from an ideal batch reactor, an ideal plug-flow reactor, or an ideal stirred-tank reactor. This is not the case if the reactor is nonideal, e.g., somewhere between a PFR and a CSTR. Characterizing the behavior of nonideal reactors is difficult and imprecise, as we shall see in Chapter 10. This can lead to major uncertainties in the analysis of data taken in nonideal reactors. 

Many kinetic studies will involve heterogeneous catalysts, since they are so widely used commercially. The kinetics of heterogeneously catalyzed reactions always must be studied 

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We shall consider three methods of estimating deviations from ideal reactor performance. The first method is to determine the actual RTD from experimental response data and then calculate the conversion by assuming the flow to be wholly segregated (Sec. 6-8). This model should be a good approximation, for example, for a tubular-flow reactor, where the flow is streamline. It would not describe a nearly ideal stirred-tank reactor, for here the fluid is nearly completely mixed when it enters the reactor. In this case no error is introduced by an approximation of the RTD, since the actual... 

Each of these problems will be considered in turn. Consider the three ideal CSTR s shown in Figure 8.11. The characteristic space times of these reactors may differ widely. Note that the direction of flow is from right to left. The first step in the analysis requires the preparation of a plot o>f reaction rate versus reactant concentration based on experimental data (i.e., the generation of a graphical representation of equation 8.3.30). It is presented as curve I in Figure 8.11. 

Some aspects of reactor behavior are developed in Chapter 5, particularly concentration-time profiles in a BR in connection with the determination of values of and k2 from experimental data. It is shown (see Figure 5.4) that the concentration of the intermediate, cB, goes through a maximum, whereas cA and cc continuously decrease and increase, respectively. We extend the treatment here to other considerations and other types of ideal reactors. For simplicity, we assume constant density and isothermal operation. The former means that the results for a BR and a PFR are equivalent. For flow reactors, we further assume steady-state operation. 

The many preexponential factors, activation energies and reaction order parameters required to describe the kinetics of chemical reactors must be determined, usually from laboratory, pilot plant, or plant experimental data. Ideally, the chemist or biologist has made extensive experiments in the laboratory at different temperatures, residence times and reactant concentrations. From these data, parameters can be estimated using a variety of mathematical methods. Some of these methods are quite simple. Others involve elegant statistical methods to attack this nonlinear optimization problem. A discussion of these methods is beyond the scope of this book. The reader is referred to the textbooks previously mentioned. 

In this case, Vr is the volume of each individual reactor in the battery. In modeling a reactor, n is empirically determined based on the extent of reactor backmixing obtained from tracer studies or other experimental data. In general, the number of stages n required to approach an ideal PFR depends on the rate of reaction (e.g., the magnitude of the specific rate constant k for the first-order reaction above). As a practical matter, the conversion for a series of stirred tanks approaches a PFR for n > 6. 

An ideal PER is experimentally simple, but its behavior is governed by partial differential equations. For a trial set of kinetic parameters for the elementary steps, it is necessary to simulate the reactor and then adjust the parameters to obtain the best fit to the experimental data obtained from the experiments in the transient regime. The analytical solution is so complicated that only a simplified sequence of steps can be considered. Of course, interesting qualitative deductions can be made from the experimental response to an inlet step function. 

In this section we focus on the three main types of ideal reactors BR, CSTR, and PFR. Laboratory data are usually in the form of concentrations or partial pressures versus batch time (batch reactors), concentrations or partial pressures versus distance from reactor inlet or residence time (PFR), or rates versus residence time (CSTR). Rates can also be calculated from batch and PFR data by differentiating the concentration versus time or distance data, usually by numerical curve fitting first. It follows that a general classification of experimental methods is based on whether the data measure rates directly (differential or direct method) or indirectly (integral of indirect method). Table 7-13 shows the pros and cons of these methods. 

The use of thermogravimetric analysis (TGA) apparatus to obtain kinetic data involves a series of trade-offs. Since we chose to employ a unit which is significantly larger than commercially available instruments (in order to obtain accurate chromatographic data), it was difficult to achieve time invariant O2 concentrations for runs with relatively rapid combustion rates. The reactor closely approximated ideal back-mixing conditions and consequently a dynamic mathematical model was used to describe the time-varying O2 concentration, temperature excursions on the shale surface and the simultaneous reaction rate. Kinetic information was extracted from the model by matching the computational predictions to the measured experimental data. 

In accordance with the experimental data, the transition from the flare front of a reaction to the quasi-plug flow mode in turbulent flow (plane front of reaction) is observed at a certain ratio of the linear rates Vj/V2 of the reactant supply to the tubular reactor [14]. With an increase of the radial flow rate V2, in order to form the reaction plane front, it is necessary to increase the rate of the axial flow supply Vj (Figure 4.8). The conditions of the quasi-ideal mode formation do not depend on the strength of the acid and/or base, introduced to the tubular reactor during neutralisation. 

Rate measurements are best performed with experiments that closely approximate the behavior of ideal chemical reactors. The concept of ideal chemical reactors is well developed (Aris, 1989 Levenspiel, 1972a, 1972b Rimstidt and Newcomb, 1993), so that the methods of extracting rates from the experimental data are relatively simple and reliable. Chemical reactors can have many different design elements, some of which are illustrated in Figure 4.2, but as long as their behavior approximates an ideal chemical reactor the following analysis methods are applicable. 

Ideally, kinetic information should be presented without the imposition of a kinetic expression or reactor characteristics, which is defined as a model-free analysis. When plug flow reactor data is analyzed using the differential method (section Differential Analysis of Experimental Flow Data ), the rate is calculated directly from the experimental data without assumption of a kinetic model. Temkin and Denbigh applied a... 

The proper design of commercial pyrolysis reactors requires a suitable expression for the intrinsic rate of the reactions. As intrinsic rate equations cannot yet be predicted, especially for the ultrapyrolysis regime, experimental data is required. This data is best obtained from bench-scale laboratory reactors, rather than from pilot plants or commercial-scale units. In laboratory scale pyrolysis reactors, the design and operating conditions can be chosen to reduce or eliminate the effects of mass and heat transfer, contaminants and catalytic surfaces from the observed measurements, thus allowing for the development of accurate expressions. It is most advantageous if the laboratory reactor is operated isothermally (in space and time), so that the temperature can be considered as an independent variable. Also, the pressure should be ideally kept constant. 

The problem of evaluating the influence of pore diffusion on an experimental result can be simplified through some transformations of the previous equations. Suppose that a reaction rate has been measured in some kind of experimental reactor, preferably an ideal CSTR or a differential PFR. From the experimental data, a rate of reaction per unit of geometrical catalyst volume, designated —Ra,y, can be calculated. The v in the subscript indicates that this is a volumetric raLtc of reaction. The measured rate (—Ra.v) is not necessarily the same as the intrinsic rate, expressed on a volumetric basis (—rA,v)-The measured rate may reflect internal transport effects, whereas the intrinsic rate does not. 

Deviations from the ideal frequentiy occur in order to avoid system complexity, but differences between an experimental system and the commercial unit should always be considered carefully to avoid surprises on scale-up. In the event that fundamental kinetic data are desired, it is usually necessary to choose a reactor design in which reactant and product concentration gradients are minimized (36), such as in the recycle (37) or spinning basket reactor designs (38,39). 

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