Nonisothermal tubular reactor, design

Numerical methods such as the Runge-Kutta-Gill fourth-order correct integration algorithm are required to simulate the performance of a nonisothermal tubular reactor. In the following sections, the effects of key design parameters on temperature and conversion profiles illustrate important strategies to prevent thermal runaway. 

Tubular reactors are normally used in the chemical industry for extremely large-scale processes. When filled with solid catalyst particles, such reactors are referred to as fixed-bed or packed-bed reactors. In this section we treat general design relationships for tubular reactors in which isothermal homogeneous reactions take place. Nonisothermal tubular reactors are treated in Section 10.4 and packed-bed reactors in Section 12.7. 

We shall recapitulate the governing equations in the next section and discuss the economic operation in the one following. The results on optimal control are essentially a reinterpretation of the optimal design for the tubular reactor. We shall not attempt a full derivation but hope that the qualitative description will be sufficiently convincing. The isothermal operation of a batch reactor is completely covered by the discussion in Chap. 5 of the integration of the rate equations at constant temperature. The simplest form of nonisothermal operation occurs when the reactor is insulated and the reaction follows an adiabatic path the behavior of the reactor is then entirely similar to that discussed in Chap. 8. 

DESIGN OF A NONISOTHERMAL PACKED CATALYTIC TUBULAR REACTOR 745... 

In developing Eqns. (3-26)-(3-28), we assumed that the temperature was constant in any cross section normal to the direction of flow. We did not assume that the temperature was constant in the direction of flow. For a PFR, the reactor is said to be isothermal if the temperature does not vary with position in the direction of flow, e.g., with axial position in a tubular reactor. On the other hand, for nonisothermal operation, the temperature will vary with axial position. Consequently, the rate constant and perhaps other parameters in the rate equation such as an equilibrium constant will also vary with axial position. The design equations for an ideal PFR are valid for both isothermal and nonisothermal operation. 

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. 

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