Heat transfer and temperature uniformity

Excellent reviews of heat transfer in fluidized beds have been provided in books by Botterill [34] and Molerus and Wirth [35]. Many empirical and semiempirical correlations are available for predicting bed-to-surface heat transfer coefficients. The recommended one is that of Molerus and Wirth [35]  

These two equations mechanistically accoimt for contributions from both particle convection to the fixed surface (large first term on right side of Eq. 4.12) and gas convection (second term commencing with 0.165), the former term being the dominant term for the relatively fine particles of interest in catalytic fluidized-bed reactors. For typical bubbling bed operating conditions at atmospheric pressure and for particles of mean size 50-100 pm, the overall bed-to-immersed-surface heat transfer 

In the freeboard region for bubbling and turbulent beds, the heat transfer coefficient falls off rapidly with increasing height as the particles, responsible for enhancing heat transfer, are disengaged and fall back onto the bed surface. If reactor temperatures exceed approximately 600°C, radiation also contributes appreciably to the overall bed-to-surface heat transfer. For start-up. 

Heat transfer to reactor from heat transfer surfaces + 

Given their lack of robust huhhles, interphase transfer resistances are much less likely to he rate hmiting for either the turbulent fluidization or the DSU regimes. Hence chemical kinetics is usually rate controlling, at least for exothermic reactions, in these two flow regimes. For endothermic catalytic reactions, the supply of sufficient heat is likely to also play a significant role. 

---

Fluidized-bed catalytic reactors. In fluidized-bed reactors, solid material in the form of fine particles is held in suspension by the upward flow of the reacting fluid. The effect of the rapid motion of the particles is good heat transfer and temperature uniformity. This prevents the formation of the hot spots that can occur with fixed-bed reactors. 

The heat pipe achieves its high performance through the process of vapor state heat transfer. A volatile liquid employed as the heat-transfer medium absorbs its latent heat of vaporization in the evaporator (input) area. The vapor thus formed moves to the heat output area, where condensation takes place. Energy is stored in the vapor at the input and released at the condenser. The liquid is selected to have a substantial vapor pressure, generally greater than 2.7 kPa (20 mm Hg), at the minimum desired operating temperature. The highest possible latent heat of vaporization is desirable to achieve maximum heat transfer and temperature uniformity with minimum vapor mass flow. 

In order to achieve rapid heat transfer and temperature uniformity, the reactant gas flow velocity should be high enough at least to form gas bubbles in the catalyst bed. However, the need for large-scale operation and relatively small catalyst particles makes operation in the slug... 

Reliability A stable temperature control, combined with an excellent heat transfer and a uniform temperature profile (no hot spots) in the fluidized bed, easily achieves an onstream time >99% per year. A specially designed raw-material sparger system allows operation spans of two years without maintenance. Larger heat-transfer area allows a higher steam temperature and pressure in the cooling coils, which improves the safety margin to the critical surface temperature where hydrochloric acid dewpoint corrosion may occur. 

A good summary of the behavior of steels in high temperature steam is available (45). Calculated scale thickness for 10 years of exposure of ferritic steels in 593°C and 13.8 MPa (2000 psi) superheated steam is about 0.64 mm for 5 Cr—0.5 Mo steels, and 1 mm for 2.25 Cr—1 Mo steels. Steam pressure does not seem to have much influence. The steels form duplex layer scales of a uniform thickness. Scales on austenitic steels in the same test also form two layers but were irregular. Generally, the higher the alloy content, the thinner the oxide scale. Excessively thick oxide scale can exfoHate and be prone to under-the-scale concentration of corrodents and corrosion. ExfoHated scale can cause soHd particle erosion of the downstream equipment and clogging. Thick scale on boiler tubes impairs heat transfer and causes an increase in metal temperature. 

A large block of material of thermal diffusivity Du — 0.0042 cm2/s is initially at a uniform temperature of 290 K and one face is raised suddenly to 875 K and maintained at that temperature. Calculate the time taken for the material at a depth of 0.45 m to reach a temperature of 475 K on the assumption of unidirectional heat transfer and that the material can be considered to be infinite in extent in the direction of transfer. 

Consider a tube heated uniformly at a heat flux q/A fed with saturated water at the base at a velocity Fo. For this velocity and heat flux, nucleate boiling will take place, and a temperature difference aTo will be established. At some distance up the tube vaporization will occur and increase the volumetric flow of material and hence the velocity to, say, Fi. The line for forced convective heat transfer meets the boiling curve below the heat flux of q/A and so nucleate boiling will still be the mode of heat transfer and the temperature difference AT, and hence the heat transfer... 

All types of catalytic reactors with the catalyst in a fixed bed have some common drawbacks, which are characteristic of stationary beds (Mukhlyonov et al., 1979). First, only comparatively large-grain catalysts, not less that 4 mm in diameter, can be used in a filtering bed, since smaller particles cause increased pressure drop. Second, the area of the inner surface of large particles is utilized poorly and this results in a decrease in the utilization (capacity) of the catalyst. Moreover, the particles of a stationary bed tend to sinter and cake, which results in an increased pressure drop, uneven distribution of the gas, and lower catalyst activity. Finally, porous catalyst pellets exhibit low heat conductivity and as a result the rate of heat transfer from the bed to the heat exchanger surface is very low. Intensive heat removal and a uniform temperature distribution over the cross-section of a stationary bed cannot, therefore, be achieved. The poor conditions of heat transfer within... 

Temperature in a fluidized bed is uniform unless particle circulation is impeded. Gas to particle heat flow is so rapid that it is a minor consideration. Heat transfer at points of contact of particles is negligible and radiative transfer also is small below 600°C. The mechanisms of heat transfer and thermal conductivity have been widely studied the results and literature are reviewed, for example, by Zabrodsky (1966) and by Grace (1982, pp. 8.65-8.83). 

Advantages of fluidized beds are temperature uniformity, good heat transfer, and the ability to continuously remove catalyst for regeneration. Disadvantages are solids backmixing, catalyst attrition, and recovery of fines. Baffles have been used often to reduce backmixing. 

The effects of heat transfer are found only within the thermal boundary layer. The fluid outside the thermal boundary layer will be unaffected by the heat transfer, and have a uniform temperature Tin at the entrance where x = 0. 

A transparent gas flows into and out of a black circular tube of length L and diameter D. The gas has a mean velocity um, specific heat at constant pressure cp and density p. The wall of the tube is thin, and the outer surface is insulated. The tube wall is heated electrically and a uniform input of heat is provided per unit area, per unit time. Determine the local wall temperature distribution along the tube length. Assume that the convective heat transfer coefficient h between the gas and the inside of the tube is constant. 

Circulation systems with parallel and crossed cocurrent or countercurrent flow of the heat transfer medium (Fig. 16) arc commonly employed for liquid heat transfer media. The main part of the heat transfer medium is generally circulated with a high-capacity pump in order to achieve uniform heat exchange conditions. A partial stream is passed through a heat exchanger for supplying or removing the heat of reaction. The desired heat transfer medium temperature is at-... 

While the chemical aspects of catalyst performance (resistance to poisoning, activity, and selectivity) are being continually improved, only little has been done to date to improve the hydrodynamic aspects (heat transfer and mass transfer rates, pressure drop, and uniformity of distribution of concentration, temperature, and velocity) of heterogeneous contacting. 

Figure 8 presents the heat transfer coefficient data for the corner of the test section. The circles in Figs. 7, 8 correspond to the calculated heat transfer for non-uniform liquid film thickness, which agree well with the data both for large and small liquid Reynolds numbers. In these calculations the temperature of the outer wall and the heat transfer coefficients were defined in accordance with the experimental procedure. The calculations show that liquid suction occurs toward to the channel s corner and liquid is therefore non-uniformly distributed along the perimeter. 

Heat and mass transfer constitute fundamentally important transport properties for design of a fluidized catalyst bed. Intense mixing of emulsion phase with a large heat capacity results in uniform temperature at a level determined by the balance between the rates of heat generation from reaction and heat removal through wall heat transfer, and by the heat capacity of feed gas. However, thermal stability of the dilute phase depends also on the heat-diffusive power of the phase (Section IX). The mechanism by which a reactant gas is transferred from the bubble phase to the emulsion phase is part of the basic information needed to formulate the design equation for the bed (Sections VII-IX). These properties are closely related to the flow behavior of the bed (Sections II-V) and to the bubble dynamics. 

---