Two-Dimensional Heterogeneous Models

The preceding considerations led De Wasch and Froment [106] to the following mathematical model  

Curve 5 corresponds to no-heat transfer through the solid and this predicts a hot spot that is far too important. Such a model is no improvement at all with respect to the two-dimensional pseudo-homogeneous model of Sec. 11.7. It is interesting also to note that, for the conditions used in these calculations, the solid temperature only exceeds the gas temperature by 1 or 2°C This is generally so in industrial reactors. Finally, the radial mean temperatures of the two-dimensional models are significantly different from the temperature predicted by the one-dimensional models. Provided the physical data are available the two-dimensional models would definitely have to be preferred for the simulation of this reactor. 

1 Showthat Leva s pressure drop equation for packed beds, (Eq. 11.5.a-t). yields a parabolic pressure profile when the fluid density is constant. 

The reaction is carried out isothermally in a packed bed reactor with plug flow at 275°C. The feed contains 0.155 moles water per mole of reactant. Water is not adsorbed on the catalyst and acts purely as an inert diluent Given the following 

Calculate the length of the reactor required to reach an exit conversion of (i) 40 percent, (ii) 70 percent. 

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The reformer tube operation was simulated on the basis of a set of continuity-, energy- and momentum equations using one and two dimensional heterogeneous models. Intraparticle gradients in the rings were accounted for by the use of the generalized modulus concept. 

A two-dimensional heterogeneous model is developed for the catalyst tubes, without catalyst deactivation, taking into consideration the steam reforming... 

Ri, Rj, R3 are ratesof reaction for reactions(1), (2), (3) respectively. The two-dimensional heterogeneous model equations takes the form,... 

Attempts have been made to develop two-dimensional heterogeneous models (McGreavy and Cresswell, 1968, 1969, Deasch and Froment, 1971). McGreavy and Cresswell proceded by adding to the one-dimensional heterogeneous model the terms accounting for radial heat and mass transfer in the bed. 

De Wasch AP, Froment GF (1971) A two dimensional heterogeneous model for fixed bed catalytic reactors. Chem Eng Sci 26 629-634... 

Adams II, Thomas A. and Barton, Paul I. (2009). A dynamic two-dimensional heterogeneous model for water gas shift reactors. International Journal of Hydrogen Energy 34, 8877-8891. 

Other applications of convective reforming are associated with recovery of the process gas heat in ammonia and methanol plants [395] [479] and lately also in ATR-based syngas units for GTL plants as discussed in Chapter 2. Design and simulation of such a reformer is shown in [519], where the two-dimensional heterogeneous model has been applied using the kinetics in [525]. A homogeneous model has also been used, and almost identical temperature profiles have been foimd. 

Radial conversion (a) and temperature (b) profiles in two-dimensional heterogeneous model with porosity and velocity profiles, (c) Comparison of radially averaged axial temperature profiles for 2D pseudo-homogeneous and heterogeneous models, djdp = 5.8 Rep = 175 [Papageorgiou and Froment, 1995]. 

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