Reactor integral

Although the composite curves can be used to set energy targets, they are not a suitable tool for the selection of utilities. The grand composite curve is a more appropriate tool for understanding the interface between the process and the utility system. It is also, as is shown in later chapters, a useful tool for study of the interaction between heat-integrated reactors and separators and the rest of the process. 

Motivation Unit tests require a substantial investment in time and resources to complete successfully. This is the case whether the test is a straightforward analysis of pump performance or a complex analysis of an integrated reactor and separation train. The uncertainties in the measurements, the likelihood that different underlying problems lead to the same symptoms, and the multiple interpretations of unit performance are barriers against accurate understanding of the unit operation. The goal of any unit test should be to maximize the success (i.e., to describe accurately unit performance) while minimizing the resources necessary to arrive at the description and the subsequent recommendations. The number of measurements and the number of trials should be selected so that they are minimized. 

The differential reactor is the second from the left. To the right, various ways are shown to prepare feed for the differential reactor. These feeding methods finally lead to the recycle reactor concept. A basic misunderstanding about the differential reactor is widespread. This is the belief that a differential reactor is a short reactor fed with various large quantities of feed to generate various small conversions. In reality, such a system is a short integral reactor used to extrapolate to initial rates. This method is similar to that used in batch reactor experiments to estimate... 

In a small integral reactor at each step of the stepwise increasing temperature, one point on a conversion versus temperature curve is received. These are all at the same feed rate and feed composition, constant pressure, and each is at a different but practically constant temperature along the tube length within every step. Since the reactor is small the attainment of steady-state can be achieved in a short time. The steadiness of conditions can be asserted by a few repeated analyses. 

Here, since the measurements were done in an integral reactor, calculation must start with the Conversion vs. Temperature function. For an example see Appendix G. Calculation of kinetic constants starts with listed conversion values as vX and corresponding temperatures as vT in array forms. The Vectorize operator of Mathcad 6 tells the program to use the operators and functions with their scalar meanings, element by element. This way, operations that are usually illegal with vectors can be executed and a new vector formed. The v in these expressions indicates a vector. 

Commercial or production reactors for heterogeneous catalytic processes are versions of the so-called integral reactors, so the fundamental process of design is integration. In particular, the necessary catalyst-filled reactor volume must be calculated that will give a desired production rate. This then includes finding conditions to achieve the desired production, at a certain selectivity and minimal operating costs and investment, to maximize the return on investment. 

Figure 4-18. Fixed bed (integral) reactor. (Source V. W. Weekman, Laboratory Reactors and Their Limitations/ A CbEJ, Vol. 20, p. 833, 1974. Used with permission of the AlChEJ.)...

Each experimental run gives the reaction rate at the composition of the exit fluid. Tubular reactors can be operated as differential reactors (i.e., at high throughputs and low conversions) or as integral reactors (i.e., at low throughputs and high conversions). Differential reactors give the rate as ... 

The reaction of Example 7.4 is not elementary and could involve shortlived intermediates, but it was treated as a single reaction. We turn now to the problem of fitting kinetic data to multiple reactions. The multiple reactions hsted in Section 2.1 are consecutive, competitive, independent, and reversible. Of these, the consecutive and competitive t5T>es, and combinations of them, pose special problems with respect to kinetic studies. These will be discussed in the context of integral reactors, although the concepts are directly applicable to the CSTRs of Section 7.1.2 and to the complex reactors of Section 7.1.4. 

The use of integrated reactor and heat-transfer models is essential for scale-up. Figure 11.7 shows an early reactor design for the same chemistry that was developed without the use of integrated models. Other unoptimized designs with temperature spikes have also been reported [12,44]. Integrated models were used to... 

Parameter estimation. Integral reactor behavior was used for the interpretation of the experimental data, using N2O conversion levels up to 70%. The temperature dependency of the rate parameters was expressed in the Arrhenius form. The apparent rate parameters have been estimated by nonlinear least-squares methods, minimizing the sum of squares of the residual N2O conversion. Transport limitations could be neglected. 

An impression of the activity of the different catalysts is given in figure 1. The activity order Cu>Co>Fe corresponds with literature [4]. The N2O pressure dependency for Co-ZSM-5 is given in figure 2. Due to the integral reactor behaviour the relation between conversion and partial pressure shows a curvature, but the reaction order equals 1 for Co, and slightly lower... 

Steady-state reactors with ideal flow pattern. In an ideal isothermal tubular pZi/g-yZovv reactor (PFR) there is no axial mixing and there are no radial concentration or velocity gradients (see also Section 5.4.3). The tubular PFR can be operated as an integral reactor or as a differential reactor. The terms integral and differential concern the observed conversions and yields. The differential mode of reactor operation can be achieved by using a shallow bed of catalyst particles. The mass-balance equation (see Table 5.4-3) can then be replaced with finite differences ... 

In integral reactors conversions and yields are quantities obtained by integration over the whole length of the reactor. 

Chemical analysis of the reaction mixture is easy in integral reactors because of the high... 

Kinetic analysis of the data obtained in differential reactors is straightforward. One may assume that rates arc directly measured for average concentrations between the inlet and the outlet composition. Kinetic analysis of the data produced in integral reactors is more difficult, as balance equations can rarely be solved analytically. The kinetic analysis requires numerical integration of balance equations in combination with non-linear regression techniques and thus it requires the use of computers. 

When differential data (r s for known c s) are available, the above equation can directly be used to calculate fc-values if reaction orders a are known or assumed. For data from integral reactors the balance equation ... 

In order to explore composition modulation of the final stage of a converter further, Briggs et al. (1978) added a second integral reactor, also holding about 30 g of the vanadia catalyst. With the preconverter in place, this system was operated on a typical feed from sulfur burning, with a S02 02 N2 composition in vol% of 10.8 15.2 74, and from a smelter effluent with a composition of 8.0 6.2 85.8. The cycled beds of vanadia catalyst were held in a fluidized sand bath at 401°C for the former feed and at 405°C for the latter one. The space velocity for both the air and the S03/S02 mixture was about 24 min 1 (STP). Table II summarizes the experimental results for the cycle periods tested. 

PFR OS integral reactor. In Figure 3.8, the entire vessel indicated from sampling points Sjn to Sout, over which a considerable change in fA or cA would normally occur, could be called an integral PFR. It is possible to obtain values of kinetics parameters by means of such a reactor from the material balance equation 2.4-4 rearranged as... 

In the case of a PFR, it is usually easier to vary Tin a controllable and measurable way if it is operated as a differential reactor rather than as an integral reactor. In the latter case, it may be difficult to eliminate an axial gradient in Tover the entire length of the reactor. 

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 ... 

This method has been applied (M5) for modeling the vapor-phase rate of dehydration of secondary butyl alcohol to the olefin over a commercial silica-alumina cracking catalyst. Integral reactor data are available at 400, 450, and 500°F. Two models considered for describing this reaction are the single site... 

Fig. 13.1 Two basic types of integrated reactor—separator systems. In A the membrane is used as an add-on to the reactor, whereas in B the membrane is fully integrated.

Recycle Reactor. As with integral analysis of an integral reactor, when we use a recycle reactor we must put a specific kinetic equation to the test. The procedure requires inserting the kinetic equation into the performance equation for recycle reactors... 

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