Concepts - Temperature Profiles in a PBMR

Comparison of the X(r)- and ccw-model Concepts - Temperature Profiles in a PBMR 

In this section, the 2D analysis is extended to nonisothermal PBMR operation. In particular, differences between the two heat-transfer models, the A(r)- and the Ow-model, are examined. In the first instance, only the computational domain of Fig. 5.11 is considered, with boundary conditions at the membrane wall according to Table 5.3. The standard parameter set of Table 5.4 is used, though with 1-5 vol.% overall oxygen concentration. 

Calculated temperature profiles are shown in Fig. 5.21. By comparison, the 2D model with a heat-transfer resistance at the wall gives slightly higher hot-spot temperatures than the A(r)-model. This implies a somewhat better cooling performance according to the A(r)-model, in spite of the pronounced bypass flow near the membrane and the resulting lower fluid velocity in the core of the bed. In addition to the radially averaged temperature profiles, the results from the one-dimensional model are also depicted in Fig. 5.21a. While the maximal difference between predictions of the two-dimensional models is less than 4K, the one-dimensional model overestimates those results by about 

Comparing the reactor performance, it can be seen that - just as in the isothermal case - 7 to 8% higher conversion values are obtained with the simple ID model (Fig. 5.21b). This higher conversion is responsible for the increased hotspot temperature, and shows once more the limitations of the ID modeL The ethylene selectivity and also the conversion obtained by the 2D models are identical within 1%. 

Up to now, the heat-transfer resistances of the membrane and of the shell side have been neglected. This is reasonable only in exceptional cases, because the highest heat-transfer resistance of the system is expected - due to the reactor construction - at the shell side. Assuming quasistationary heat transfer, the calculation of the overall heat-transfer coefficient between reactor wall and catalyst bed is easy to implement using a series connection of thermal resistances for both the ay,- and 2,(r)-models. Because of the small differences in the predicted temperature profiles and the lower computational cost, the o -model with the overall heat-transfer coefficients has been used in the following calculations. 

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