Nonisothermal CSTR design equations

The design equations for a chemical reactor contain several parameters that are functions of temperature. Equation (7.17) applies to a nonisothermal batch reactor and is exemplary of the physical property variations that can be important even for ideal reactors. Note that the word ideal has three uses in this chapter. In connection with reactors, ideal refers to the quality of mixing in the vessel. Ideal batch reactors and CSTRs have perfect internal mixing. Ideal PFRs are perfectly mixed in the radial direction and have no mixing in the axial direction. These ideal reactors may be nonisothermal and may have physical properties that vary with temperature, pressure, and composition. 

The steady-state design equations (i.e., Equations (14.1)-(14.3) with the accumulation terms zero) can be solved to find one or more steady states. However, the solution provides no direct information about stability. On the other hand, if a transient solution reaches a steady state, then that steady state is stable and physically achievable from the initial composition used in the calculations. If the same steady state is found for all possible initial compositions, then that steady state is unique and globally stable. This is the usual case for isothermal reactions in a CSTR. Example 14.2 and Problem 14.6 show that isothermal systems can have multiple steady states or may never achieve a steady state, but the chemistry of these examples is contrived. Multiple steady states are more common in nonisothermal reactors, although at least one steady state is usually stable. Systems with stable steady states may oscillate or be chaotic for some initial conditions. Example 14.9 gives an experimentally verified example. 

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). 

The design formulation of nonisothermal CSTRs consists of ( / + 1) simultaneous, nonlinear algebraic equations. We have to solve them for different values of dimensionless space time, t. Below, we illustrate how to design nonisothermal CSTRs. 

Equations (3.71) and (3.82) are the basic design equations for the design of nonisothermal CSTR. For tubular and batch reactors, the same equations are slightly modified to put them in a suitable differential equation form. 

Basic PFR equation Design equations Nonisothermal operation Perfectly mixed flow reactor (MFR) Basic CSTR equation Nonisothermal operation Multiple steady states MSS In a CSTR Adiabatic CSTR... 

Nonisothermal stirred tanks are governed by an enthalpy balance that contains the heat of reaction as a significant term. If the heat of reaction is unimportant so that a desired Tout can be imposed on the system regardless of the extent of reaction, then the reactor dynamics can be analyzed by the methods of the previous section. This section focuses on situations where Equation 14.3 must be considered as part of the design. Even for these situations, it is usually possible to control a steady-state CSTR at a desired temperature. If temperature control can be achieved rapidly, then isothermal design techniques again become applicable. Rapid means on a time scale that is fast compared to reaction times and composition changes. 

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