NonisothermaL Multiple Reactions

It is expected that, for more complex reactions and conditions (e.g., multiple reactions, nonisothermal conditions, etc.), step distributions of a relatively narrow width (approaching a Dirac delta type) placed at a specific location within the membrane pore... 

Example 7.7 Multiple-reaction, nonisothermal fixed-bed reactor... 

These are two coupled algebraic equations, which must be solved simultaneously to determine the solutions Cj(x) and T(t). For multiple reactions the + 1 equations are easily written down, as are the differential equations for the transient situation. However, for these situations the solutions are considerably more difficult to find We will in fact consider theaolutions of the transient CSTR equations in Chapter 6 to describe phase-plane trajectories and the stability of solutions in the nonisothermal CSTR. 

In this and the previous chapters we considered the effects of nonisothermal operation on reactor behavior. The effects of nonisothermal operation can be dramatic, especially for exothermic reactions, often leading to reactor volumes many times smaller than if isothermal and often leading to the possibility of multiple steady states. Further, in nonisothermal operation, the CSTR can require a smaller volume for a given conversion than a PFTR. In this section we summarize some of these characteristics and modes of operation. For endothermic reactions, nonisothermal operation cools the reactor, and this reduces the rate, so that these reactors are inherently stable. The modes of operation can be classified as follows ... 

The locus classicus of this important principle for chemical engineers is the nonisothermal stirred tank in which a single reaction takes place (for multiple reactions, see pp. 16-17). Consider the reaction... 

P2-8 figure P2-8a shows C l-r versus for a nonisothermal, nonelementarj, multiple-reaction liquid-phase decomposition of reactant A. 

In many catalytic systems multiple reactions occur, so that selectivity becomes important. In Sec. 2-10 point and overall selectivities were evaluated for homogeneous well-mixed systems of parallel and consecutive reactions. In Sec. 10-5 we saw that external diffusion and heat-transfer resistances affect the selectivity. Here we shall examiineHEieHnfiuence of intrapellet res ahces on selectivity. Systems with first-order kinetics at isothermal conditions are analyzed analytically in Sec. 11-12 for parallel and consecutive reactions. Results for other kinetics, or for nonisothermal conditions, can be developed in a similar way but require numerical solution. ... 

The design formulation of nonisothermal plug-flow reactors with multiple reactions follows the same procedure outlined in the previous section—we write design... 

Design and operation of nonisothermal reactors with multiple reactions... 

The design formulation of nonisothermal CSTRs with multiple reactions follows the same procedure outlined in the previous section—we write the design equation, Eq. 8.1.1, for each independent reaction. However, since the reactor temperature, out> is not known, we should solve the design equations simultaneously with the energy balance equation (Eq. 8.1.14). 

Falling Off the Steady State 623 Nonisothermal Multiple Reactions 625 Unsteady Operation of Plug-Flow Reactors... 

In the previous examples, we have exploited the idea of an effectiveness factor to reduce fixed-bed reactor models to the same form as plug-flow reactor models. This approach is useful and solves several important cases, but this approach is also limited and can take us only So far. In the general case, we must contend with multiple reactions that are not first order, nonconstant thermochemical properties, and nonisothermal behavior in the pellet and the fluid. For these cases, we have no alternative but to solve numerically for the temperature and species concentrations profiles in both the pellet and the bed. As a final example, we compute the numerical solution to a problem of this type. 

For the single-reaction, nonisothermal problem, we solved the so-called Weisz-Hicks problem, and determined the temperature and concentration profiles within the pellet. We showed the effectiveness factor can be greater than unity for this case. Multiple steady-state solutions also are possible for this problem, but for realistic values of the... 

General expression for an SBR for multiple reactions with Inflow of liquid and outflow of liquid and vapor Scheme 4 Nonisothermal operation Optimum temperatures/temperature profiles for maximizing yields/selectivltles Optimum temperatures Optimum temperature and concentration profiles In a RPR Parallel reactions Oonsecutive reactions Extension to a batch reactor Explore yourself References Bibliography... 

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