Energy Balances of Reactors

A continuous stirred tank reactor battery CSTR) Material balances  

S are participants in the reaction the tetters aiso are used to represent concentrations 

Cj = ni/K o ilV, concentration n, = mols of component i in the reactor n j = molal flow rate of component i V, = voiume of reactor V = volumetric flow rate Vi = stoichiometric coefficient 

An overall conversion rate may depend on rates of mass transfer between phases as well as chemical rates. In the simplest case, mass transfer and chemical transformation occur in series advantage is taken of the equality of these two rates at steady state conditions to eliminate interfacial concentrations from the rate equations and thus to permit integration. Item 8 of Table 17.2 is an example. 

Rates of fluid phase reactions catalyzed by solids also can be represented at least approximately by powers of the concentrations. A more fundamental approach, however, takes into account mechanisms of adsorption and of reaction on the catalyst surface. A few examples of resulting equations are in item 9 of Table 17.2. 

Vf = volume of reactor V = volumetric flow rate v, = stoichiometric coefficient 

All chemical reactions are accompanied by some heat effects so that the temperature will tend to change, a serious result in view of the sensitivity of most reaction rates to temperature. Factors of equipment size, controllability, and possibly unfavorable product distribution of complex reactions often necessitate provision of means of heat transfer to keep the temperature within bounds. In practical operation of nonflow or tubular flow reactors, truly isothermal conditions are not feasible even if they were desirable. Individual continuous stirred tanks, however, do maintain substantially uniform temperatures at steady state when the mixing is intense enough the level is determined by the heat of reaction as well as the rate of heat transfer provided. 

In many instances the heat transfer aspect of a reactor is 

TABLE 17.3. Some Isothermal Rate Equations and Their Integrals 

Equations readily solvable by Laplace transforms. For example  

Inversion of the transforms can be made to find the concentrations A, B, and C as functions of the time t. Many such examples are solved by Rodiguin and Rodiguina (Consecutive Chemical Reactions, Van Nostrand, New York, 1964.  

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Material and energy balances of a nonflow reactor are summarized in Table 7-5. Several catch operations are summarized in Fig. 7-5. 

TABLE 7-5 Material and Energy Balances of a Nonflow Reactor... 

Material and energy balances of common types of reactors are summarized in several tables of Sec. 7. For review purposes some material balances are restated here. For the /ith stage of a CSTR batteiy,... 

If the batch reactor operation is both nonadiabatic and nonisothermal, the complete energy balance of equation 12.3-16 must be used together with the iiaterial balance of equation 2.2-4. These constitute a set of two simultaneous, nonlincmr, first-flijer ordinary differential equations with T and fA as dependent variables and I as Iidependent variable. The two boundary conditions are T = T0 and fA = fAo (usually 0) at I = 0. These two equations usually must be solved by a numerical procedure. (See problem 12-9, which may be solved using the E-Z Solve software.)... 

The energy balance of ethanol in this type of reactor (CSTR type) is flux in - flux out = disappearance by reaction... 

The relation between the temperature of the reactor, T, and the fraction of fuel burned, y/f can be expressed from an energy balance of the reactor system. This yields... 

The solution to the reactor model differential equations (7.166) and (7.180) to (7.182) simulates the molar flow rates and the pressure drop and energy balance of the reactor. The solution of the catalyst pellet boundary value differential equations (7.172) and (7.173) provides the effectiveness factors r]j for each reaction labeled j = 1,..., 6 for use inside the differential equations (7.180) to (7.182). 

The reaction entropy ACS is a result of the different opportunities of the species to save thermal energy between the absolute zero level of temperature and the temperature level of the reactor. Concerning the energy balance of a fuel cell (Figure 2.1), the heat <2FCrev has to be transferred reversibly from the fuel cell to the environment. 0FCrev is defined as a positive value if the reversible change in entropy is... 

Table 1 Energy balance of Figure 7 heating system, 600 MWth nuclear reactor case...

Heat Transfer Parameters. Attempts in this investigation to use heat transfer parameters ( X. h ) calculated from correlations based on data without reactidn 6,7) led to the result that the energy balance of the reactor at the measured temperatures was not satisfied. On the other hand, the simultaneous estimation of heat transfer and kinetic parameters by regression analysis of polytropic measurements allows these parameters to influence each other. It was observed that the parameters calculated by these two methods were quite different (5,46). Therefore in this report the heat transfer parameters were determined from experimental results by a third method with a minimum of additional assumptions ... 

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