(575aq) Simulation and Sensitivity Analysis of a Multitubular Fixed Bed Catalytic Reactor to Produce Phthalic Anhydride

Introduction. The objective of this paper is to find numerical solutions of one-dimensional and two-dimensional models under the reaction mechanism proposed by Calderbank [1], using the kinetics parameters adjusted by Anastasov [2] for the anhydride phthalic reaction. These models were used with the purpose of carrying out comparisons among each one of the models, with the experimental temperature profiles (for axis tube r = 0) of an industrial reactor; and in this way, determine the one with highest prediction grade. Finally it will be studied the effect of the temperature of the coolant and feed temperature by means of parametric sensitivity analysis using the two-dimensional models.

One-dimensional and Two-dimensional models. The equations corresponding to each one of the models are well-known and can be found in reference [3]. Such set of equations constituyen a system of non lineal ODE together with a system of algebraic equations for the one-dimensional heterogeneous case, and a system of PDE for the two-dimensional case. The solution of the one-dimensional system was made by the Runge-Kutta method together with iteration, for the solution of the algebraic system, supposing initially that the temperature of the bulk and pellet are the same. For the case of the two-dimensional model, the system was solved using a combination of methods including Crank-Nicholson, relaxation and a false transient algorithm [4]. The results obtained for the axis of the tube are shown next:

Parametric sensitivity analysis For the calculation of the sensitivities (η) the definition used was the one given by Anastasov [5], with the purpose of studying the effect of the entrance temperature (To) and the coolant temperature (Tc). The results are shown next:

The temperature of the coolant was varied between 200 and 400°C (the industrial value is between 350 and 390°C). There were also carried out two different simulations for To=Tc and To=150°C. The sensitivities calculated for this case show values that vary approximately between 1.1 and 2, obtaining the maximum values of η (1.8-2) in the area where the coolant temperature is between the 300 and 320 °C. For the entrance temperature, it was observed for the three coolant temperatures, that from about 320°C, a remarkable change occurred in the sensitivities (Figure 4), since they pass from almost zero to a considerably increasing amount; a behavior showed in the change of slope for the three curves, obtaining sensitivities between 1.5 and 2.1, for all the cases. It is important to mention that the apparent non-dependence, between the coolant temperature and the entrance temperature of the mixture, is broken approximately when the two values are the same (i.e. To=Tc), but for lower mixture temperatures than the coolant, it was found that as the entrance temperature increases a shift of the hot spot exists toward the entrance of the reactor.

Bibliography

[1] Chandrasekharan K. Calderbank P.H. (1976). Chemical Engineering Science, 32, 1435-1446.

[2] Anastasov. A. (2003) Chemical Engineering Science, 58, 89-98.

[3] Froment G., Bischoff K. Chemical reactors analysis and design. John Willey & Sons (1994).

[4] Nikolov A., Anastasov A. (1992). Chemical Engineering Science, 47, 1291-1298.

[5] Anastasov A. (2002) Chemical Engineering Science, 86, 286-297.