Reaction Rates in Reactors

under reaction conditions, one of the adsorbed species dominates on the surface and the fractional coverage of this intermediate on the catalytic sites is much greater than any other species, then it is said to be the most abundant reaction intermediate (MARI). Technically, it may not be the most abundant surface intermediate (MASI) because some adsorbed species may not be participating in the reaction sequence [2], although these two terms tend to be used interchangeably [1]. 

A chain reaction is a closed sequence which is created by the formation of active centers due to the thermal decomposition of a molecular species or to some external source such as light or ionizing radiation. A chain reaction must consist of at least four steps one for initiation, one for termination and at least two for chain propagation, with the last steps being the principal pathway for product generation. 

In flow reactors, various quantities are related to the reaction rate. One important one is the space velocity, which is defined by the volumetric flow rate of the reactant stream, Vo, specified at the inlet conditions of temperature and pressure with zero conversion (unless otherwise noted), and the catalyst volume, Vc, to be  

In designing reactors, the reactor volume, Vj-, which is required to hold a given mass or volume of catalyst, is routinely used  

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Model Reactions. Independent measurements of interfacial areas are difficult to obtain in Hquid—gas, Hquid—Hquid, and Hquid—soHd—gas systems. Correlations developed from studies of nonreacting systems maybe satisfactory. Comparisons of reaction rates in reactors of known small interfacial areas, such as falling-film reactors, with the reaction rates in reactors of large but undefined areas can provide an effective measure of such surface areas. Another method is substitution of a model reaction whose kinetics are well estabUshed and where the physical and chemical properties of reactants are similar and limiting mechanisms are comparable. The main advantage of employing a model reaction is the use of easily processed reactants, less severe operating conditions, and simpler equipment. 

Note The Reactor 1 conditions are a compromise between the need for a temperature as high as 350 C for a maximum conversion of COS/CS2 and a lower temperature to achieve better approach to equilibrium for H2S/SO2. The reaction rate in Reactor 2 is low owing to the lower H2S/SO2 concentration. Only a small amount of remaining H2S/SO2 is converted in Reactor 3. 

The reaction rate in a continuous reactor is dependent on monomer conversion but it does not vary with time once steady-state... 

While true, this result is not helpful. The derivation of Equation (1.6) used the entire reactor as the control volume and produced a result containing the average reaction rate, In piston flow, a varies with z so that the local reaction rate also varies with z, and there is no simple way of calculating a-Equation (1.6) is an overall balance applicable to the entire system. It is also called an integral balance. It just states that if more of a component leaves the reactor than entered it, then the difference had to have been formed inside the reactor. 

All these steps can influence the overall reaction rate. The reactor models of Chapter 9 are used to predict the bulk, gas-phase concentrations of reactants and products at point (r, z) in the reactor. They directly model only Steps 1 and 9, and the effects of Steps 2 through 8 are lumped into the pseudohomoge-neous rate expression, a, b,. ..), where a,b,. .. are the bulk, gas-phase concentrations. The overall reaction mechanism is complex, and the rate expression is necessarily empirical. Heterogeneous catalysis remains an experimental science. The techniques of this chapter are useful to interpret experimental results. Their predictive value is limited. 

The solution to this equation, which is detailed in Section 10.4.1, gives the concentration at position I down a pore that has its mouth located at position (r, z) in the reactor. The reaction rate in Equation (10.3) remains based on the bulk gas-phase volume, not on the comparatively small volume inside the pore. 

We first explain the setting of reactors for all CFD simulations. We used Fluent 6.2 as a CFD code. Each reactant fluid is split into laminated fluid segments at the reactor inlet. The flow in reactors was assumed to be laminar flow. Thus, the reactants mix only by molecular diffusion, and reactions take place fi om the interface between each reactant fluid. The reaction formulas and the rate equations of multiple reactions proceeding in reactors were as follows A + B R, ri = A iCaCb B + R S, t2 = CbCr, where R was the desired product and S was the by-product. The other assumptions were as follows the diffusion coefficient of every component was 10" m /s the reactants reacted isothermally, that is, k was fixed at... 

In what follows, the above balance for unmixedness is applied to individual reactor cases. The relation for reaction rate in terms of I is then considered, and finally this is applied for simple and complex reactions. 

The experimental method used for this kinetie study is reaetion ealorimetry. In the ealorimeter, the energy enthalpy balance is continuously monitored the heat signal can then be easily converted in the reaction rate (in the case of an isothermal batch reactor, the rate is proportional to the heat generated or consnmed by the reaction). The reaction orders and catalyst stabihty were determined with the methodology of reaction progress kinetic analysis (see refs. (8,9) for reviews). 

High reaction rate in Equation 5.71 is favored by a high concentration of enzymes (CE ) and high concentration of feed (CA). This means that a plug-flow or ideal-batch reactor is favored if both the feed material and enzymes are to be fed to the reactor. 

Because of the dilution that results from the mixing of entering fluid elements with the reactor contents, the average reaction rate in a stirred tank reactor will usually be less than it would be in a tubular reactor of equal volume and temperature supplied with an identical feed stream. Consequently, in order to achieve the same production capacity and conversion level, a continuous flow stirred tank reactor or even a battery of several stirred tank reactors must be much larger than a tubular reactor. In many cases, however, the greater volume requirement is a relatively unimportant economic factor, particularly when one operates at ambient pres-... 

An exothermic reaction with the stoichiometry A 2B takes place in organic solution. It is to be carried out in a cascade of two CSTR s in series. In order to equalize the heat load on each of the reactors it will be necessary to operate them at different temperatures. The reaction rates in each reactor will be the same, however. In order to minimize solvent losses by evaporation it will be necessary to operate the second reactor at 120 °C where the reaction rate constant is equal to 1.5 m3/kmole-ksec. If the effluent from the second reactor corresponds to 90% conversion and if the molal feed rate to the cascade is equal to 28 moles/ksec when the feed concentration is equal to 1.0 kmole/m3, how large must the reactors be If the activation energy for the reaction is 84 kJ/mole, at what temperature should the first reactor be operated ... 

Still another advantage of fluidized bed operation is that it leads to more efficient contacting of gas and solid than many competitive reactor designs. Because the catalyst particles employed in fluidized beds have very small dimensions, one is much less likely to encounter mass transfer limitations on reaction rates in these systems than in fixed bed systems. 

As shown in Example 22-3, for solid particles of the same size in BMF, the form of the reactor model resulting from equation 22.2-13 depends on the kinetics model used for a single particle. For the SCM, this, in turn, depends on particle shape and the relative magnitudes of gas-film mass transfer resistance, ash-layer diffusion resistance and surface reaction rate. In some cases, as illustrated for cylindrical particles in Example 22-3(a) and (b), the reactor model can be expressed in explicit analytical form additional results are given for spherical particles by Levenspiel(1972, pp. 384-5). In other f l cases, it is convenient or even necessary, as in Example 22-3(c), to use a numerical pro-... 

Since the overall reaction rate in the loop reactor is limited by mass transport at the phase boundary, one would expect that the Ru concentration has a weaker influence on the rate of reaction than in the batch reactor. We have carried out experiments at a Ru concentration of 0.005 M as well as at 0.01 M and observed nearly a doubling of the overall reaction rate, giving rise to a reaction order of 0.96 with regard to Ru. The result is somehow surprising, since it can be explained only in terms of a kinetic control of the reaction, like in the batch reactor. On the other hand, previous experiments clearly indicate a mass transport limitation at the L/L-interphase. So the question which arises is how it can be possible that a multiphase reaction system is limited by both mass transport and kinetics ... 

Since MeOH or MeOAc carbonylation is generally a very selective reaction, the reactor composition at any time throughout the reaction can be calculated from the amount of CO consumed. From these measurements the relationship between reaction rate and reactor composition can be established. By obtaining IR data at the same time, the nature and amount of catalyst species present can be measured to relate to rate and reaction composition. At the same time, useful data about the water gas shift reaction can be obtained from the increase in the CO2 peak. 

EXAMPLE 5J REACTION RATE IN A MIXED FLOW REACTOR... 

The chemical engineer almost never has kinetics for the process she or he is working on. The problem of solving the batch or continuous reactor mass-balance equations with known kinetics is much simpler than the problems encountered in practice. We seldom know reaction rates in useful situations, and even if these data were available, they frequently would not be particularly useful. 

It is evident that in many situations the reaction rate will be directly proportional to the surface area between phases whenever mass transfer hmits reaction rates. In some situations we provide a fixed area by using solid particles of a given size or by membrane reactors in which a fixed wall separates phases Ifom each other. Here we distinguish planar walls and parallel sheets of sohd membranes, tubes and tube bundles, and spherical solid or liquid membranes. These are three-, two-, and one-dimensional phase boundaries, respectively. 

Reaction rate in heterogeneous catalysis from active sites to reactor level... 

Lbe = the mass transfer coefficient between the bubble and emulsion phase (m3 gas interchange volume/m3 of reactor) (1/s) yb = the volume fraction of the bubble occupied by solids ( rh,vs) = the reaction rate in bubbles per unit volume of solids, based on the reactant... 

The reaction is carried out over a silver gauze or low surface supported catalyst at 600—700°C, indicating a very fast chemical reaction. This implies that determination of the intrinsic reaction rate in laboratory reactors is complicated by the interference of heat and mass transfer limitations. To avoid this problem, studies have been made at much lower temperatures, which in turn run the risk of being non-representative. 

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