Example Nonisothermal Plug Flow Reactor

Most reactions have heat effects, and this means that reactor models must be able to model the heat transfer as well as the mass balances. The following example models a simple reactor oxidizing SO2 to form SO3 (Young and Finlayson, 1973). After some manipulation, the equations are 

These equations are appropriate when radial and axial dispersion are not important. Axial and radial dispersion are actually important in this case, as discussed by Young and Finlayson (1973), but the simpler case is a good vehicle for seeing how to include temperature effects in the problem. The reaction rate equation shows that equilibrium can be reached (then R = 0), and the equilibrium constant depends on the temperature. Thus, the conversion depends intimately on the temperature. 

Step 1 The MATLAB program requires you to write a function (m-file) that calculates the right-hand side of Eq. (8.24), given the input, z, X, and T, which are the axial location in the reactor and the conversion and temperature at that axial location, respectively. Thus, (1) to solve the problem you use the variables 

The function will have available to it the axial location, z, and the variables y(l) and y(2). (2) You hrst move y(l) into X and y(2) into T (for clarity in the program) and then 

Step 2 You test this m-file by setting the input variables and calling the m-file  

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Example 9.11 Modeling of a nonisothermal plug flow reactor Tubular reactors are not homogeneous, and may involve multiphase flows. These systems are called diffusion convection reaction systems. Consider the chemical reaction A -> bB described by a first-order kinetics with respect to the reactant A. For a nonisothermal plug flow reactor, modeling equations are derived from mass and energy balances... 

Example 9.9 Modeling of a nonisothermal plug flow reactor... 

Example 5.3 Solution of Nonisothermal Plug-Flow Reactor. Write general MATLAB functions for integrating simultaneous nonlinear differential equations using the Euler, Euler predictor-corrector (modified Euler), Runge-Kutta, Adams, and Adams-Moulton methods. Apply these functions for the solution of differential equations that simulate a nonisotherm plug flow reactor, as described below. ... 

Example 5.3 Solution of Nonisothermal Plug-Flow Reactor... 

To identify the additional information necessary to design nonisothermal reactors, we consider the following example, in which a highly exothermic reaction is carried out adiabaticaUy in a plug-flow reactor. 

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. 

Calculation of the volume of a nonisothermal chemical reactor usually needs the use of numerical integration. For example, consider the first order reaction A B in liquid phase, taking place in an adiabatic plug flow reactor. Pure <4 enters the reactor, and it is desired to have the conversion X, at the outlet. The volume of this reactor is given by... 

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