Integral reactor concentration

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 ... 

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. 

In integral analysis concentration-versus-time (or equivalently concentration-versus-distance from the inlet of the integral flow reactor) data are known. Kinetic expressions to be determined are incorporated into the differential material balance equations ... 

Since the concentration varies significantly during the runs, the experimental reactor should be considered to be an integral reactor. 

The CSTR is not an integral reactor. Since the same concentration exists everywhere, and the reactor is operating at steady state, there is only one reaction rate at the average concentration in the tank. Since this concentration is low because of the conversion in the tank, the value for the reaction rate is also low. This is particularly significant for higher-order reactions compared with integral reactor systems. 

The parameters for PFRs include space time, concentration, volumetric flow rate, and volume. This reactor follows an integral reaction expression identical to the batch reactor except that space time has been substituted for reaction time. In the plug flow reactor, concentration can be envisioned as having a profile down the reactor. Conversion and concentration can be directly related to the reactor length, which in turn corresponds to reactor volume. 

Oh, Se H., Hegedus, L. L., Baron, K. and Cavendish, J. C., "Carbon Monoxide Oxidation in An Integral Reactor. Transient Response to Concentration Pulses in the Regime of Isothermal Multiplicities" Proc. ISCRE5 ACS Symposium Series 65,... 

To extend their analysis to integral reactors and singlesample batch reactors, three modifications are appropriate. First, use a more appropriate reactor concentration to analyze the data than the initial concentration. The simplest, and an effective one 1s... 

Initial reaction rates obtained with a pure feed in which only reactants are present can be used for the discrimination between rival kinetic models, i.e. to identify whether adsorption, desorption, or surface reactions are the rate-determining steps. When pure A is fed to an integral reactor, for example, initial rates are observed at the inlet, where the product concentration is still zero. Comparing possible rate equations, which are often simpler in case of absence of products, with experimental data obtained at different concentrations of A, helps to reveal the appropriate [33,35]. 

Several interesting features of the above simple relationships are noteworthy. If an inert liquid phase is introduced into an all-gas-phase differential reactor, keeping the inlet gas-phase composition constant, the reaction rate would, in general, be distributed between gas and liquid phases thus reducing the overall effective concentration of the reactant. In the limiting case, if the feed liquid is saturated with the reactant, the reaction rate will be unaffected by the introduction of liquid, ln an integral reactor, the overall reaction rate (as a space time yield) would increase if the feed liquid is saturated with the reactant. The conversion is always decreased by the introduction of liquid because of the contribution of the term QL(rG/Bi5L) in the denominator of Eq. (4-19). 

For an integral reactor, conventional derivations— for first-order reactions—lead to an expression for (dN/dt)/ l/[A ) anywhere along the reactor, with [A] being the reactant concentration... 

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 kinetics are given for both the differential (Schwab) reactor, in which the reactant concentration is essentially constant over the whole catalyst bed, and the integral reactor, in which the reactant concentration decreases significantly as it passes over the bed. 

The best, but also the most laborious, method to determine the lifetime is a longterm test in an integrated reactor. Here the catalyst is operated under intensified conditions (high conversion, high temperature, high concentration, etc.) in so-called stress tests that allow statements about the lifetime to be rapidly made. This method is especially suitable for comparing different variants of a catalyst. 

The integral reactor is often experimentally easier to handle and provides a faster overview of the kinetics. However, the reaction rates ry must be derived by differentiation of the measured concentration-time curves, which is a source of errors. Furthermore, the reaction concentrations and temperatures are often not unambiguously assignable to the thus-obtained r values. 

There are two fundamental types of experimental reactors for measuring solid-catalyzed reaction rates, integral and differential. The integral reactor consists essentially of a tube of diameter less than 3 cm filled with, say, IF g of catalyst. Each run comprises steady-state operation at a given feed rate, and based on several such runs, a plot of the conversion X/ versus IF/F o is prepared. Differentiation of this curve gives the rate at any given (i.e., concentration) as... 

Summarizing, the effect of the porosity profile on the integral reactor performance is rather small for the conditions studied. This can, however, change for systems with kinetics more sensitive to the educt concentration (higher reaction orders). In comparison with the ID model results it was found that the simple model overpredicts the achievable intermediate yields in the PBMR. Consequently, radial mass-transfer limitations can not be neglected if more precise predictions are required. 

Figure 4.14. Integral reactors classification and concentration profile for a continuous tubular reactor.

Fig. 4.14. A special type of integral reactor (pseudo-integral reactor) is one constructed with taps at various distances along the length so that samples may be removed and the actual concentration profile measured. A disadvantage of integral reactors is that the balance equations are a system of coupled differential equations. The measured conversion often is due to a complex interaction of transport and reaction processes. For quick, empirical, and pragmatic process development, the integral reactor may be well suited, especially now that fast digital computers and effective integration algorithms facilitate parameterization.

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