Packed reactor tubes, heat transfer

Heat Transfer in Packed Reactor Tubes Suitable for Selective Oxidation... 

Extensive experimental determinations of overall heat transfer coefficients over packed reactor tubes suitable for selective oxidation are presented. The scope of the experiments covers the effects of tube diameter, coolant temperature, air mass velocity, packing size, shape and thermal conductivity. Various predictive models of heat transfer in packed beds are tested with the data. The best results (to within 10%) are obtained from a recently developed two-phase continuum model, incorporating combined conduction, convection and radiation, the latter being found to be significant under commercial operating conditions. 

Wellauer T, Cresswell D L, Newson E J., "Heat transfer in packed reactor tubes suitable for selective oxidation", ACS Symp. Series, 196, 527 (1982). 

There are two basic types of packed-bed reactors those in which the solid is a reactant and those in which the solid is a catalyst. Many e.xaniples of the first type can be found in the extractive metallurgical industries. In the chemical process industries, the designer normally meets the second type, catalytic reactors. Industrial packed-bed catalylic reactors range in size from units with small tubes (a few centimeters in diameter) to large-diameter packed beds. Packed-bed reactors are used for gas and gas-liquid reactions. Heat transfer rates in large-diameter packed beds are poor and where high heat transfer rates are required, Jluidized beds should be considered. ... 

There may be radial temperature gradients in the reactor that arise from the interaction between the energy released by reaction, heat transfer through the walls of the tube, and convective transport of energy. This factor is the greatest potential source of disparities between the predictions of the model and what is observed for real systems. The deviations are most significant in nonisothermal packed bed reactors. 

When we want to look at the connection between the flow behavior and the amount of heat that is transferred into the fixed bed, the 3D temperature field is not the ideal tool. We can look at a contour map of the heat flux through the wall of the reactor tube. Fig. 19 actually displays a contour map of the global wall heat transfer coefficient, h0, which is defined by qw — h0(Tw-T0) where T0 is a global reference temperature. So, for constant wall temperature, qw and h0 are proportional, and their contour maps are similar. The map in Fig. 19 shows the local heat transfer coefficient at the tube wall and displays a level of detail that would be hard to obtain from experiment. The features found in the map are the result of the flow features in the bed and the packing structure of the particles. 

The equations describing the concentration and temperature within the catalyst particles and the reactor are usually non-linear coupled ordinary differential equations and have to be solved numerically. However, it is unusual for experimental data to be of sufficient precision and extent to justify the application of such sophisticated reactor models. Uncertainties in the knowledge of effective thermal conductivities and heat transfer between gas and solid make the calculation of temperature distribution in the catalyst bed susceptible to inaccuracies, particularly in view of the pronounced effect of temperature on reaction rate. A useful approach to the preliminary design of a non-isothermal fixed bed catalytic reactor is to assume that all the resistance to heat transfer is in a thin layer of gas near the tube wall. This is a fair approximation because radial temperature profiles in packed beds are parabolic with most of the resistance to heat transfer near the tube wall. With this assumption, a one-dimensional model, which becomes quite accurate for small diameter tubes, is satisfactory for the preliminary design of reactors. Provided the ratio of the catlayst particle radius to tube length is small, dispersion of mass in the longitudinal direction may also be neglected. Finally, if heat transfer between solid cmd gas phases is accounted for implicitly by the catalyst effectiveness factor, the mass and heat conservation equations for the reactor reduce to [eqn. (62)]... 

Figure 17.18. Heat transfer in fixed-bed reactors (a) adequate preheat (b) internal heat exchanger (c) annular cooling spaces (d) packed tubes (e) packed shell (f) tube and thimble (g) external heat exchanger (h) multiple shell, with external heat transfer (Walas, 1959).

Figure 17.19. Reactors for the oxidation of sulfur dioxide (a) Feed-product heat exchange, (b) External heat exchanger and internal tube and thimble, (c) Multibed reactor, cooling with charge gas in a spiral jacket, (d) Tube and thimble for feed against product and for heat transfer medium, (e) BASF-Knietsch, with autothermal packed tubes and external exchanger, (f) Sper reactor with internal heat transfer surface, (g) Zieren-Chemiebau reactor assembly and the temperature profile (Winnacker- Weingartner, Chemische Technologie, Carl Hanser Verlag, Munich, 1950-1954).

The ratio, L/D, of length to diameter of a packed tube or vessel has been found to affect the coefficient of heat transfer. This is a dispersion phenomenon in which the Peclet number, uL/Ddisp, is involved, where D Sp is the dispersion coefficient. Some 5000 data points were examined by Schliinder (1978) from this point of view although the effect of L/D is quite pronounced, no dear pattern was deduced. Industrial reactors have LID above 50 or so Eqs. (6) and (7) of Table 17.18 are asymptotic values of the heat transfer coefficient for such situations. They are plotted in Figure 17.36(b). 

Fixed-bed reactors resemble multitube heat exchangers, with the catalyst packed in vertical tubes held in a tubesheet at top and bottom. Reaction heat can be removed by generating steam on the shell side of the reactor or by some other heat-transfer fluid. However, temperature control is more difficult in a fixed-bed than in a fluulized-bed reactor because localized hot spots tend to develop in the tubes. 

Non-isothermal and non-adiabatic conditions. A useful approach to the preliminary design of a non-isothermal fixed bed reactor is to assume that all the resistance to heat transfer is in a thin layer near the tube wall. This is a fair approximation because radial temperature profiles in packed beds are parabolic with most of the resistance to heat transfer near the tube wall. With this assumption a one-dimensional model, which becomes quite accurate for small diameter tubes, is satisfactory for the approximate design of reactors. Neglecting diffusion and conduction in the direction of flow, the mass and energy balances for a single component of the reacting mixture are ... 

---