Heat transfer, packed beds overall coefficient

Hlavacek (1970) has shown that radiation between the solid catalyst and gas can significantly affect the temperature dynamics in packed bed systems operating in excess of 673 K. Since most packed bed systems usually operate well below these conditions, radiation terms are not explicitly included in the model. However, their effect can to some degree be accounted for in the overall heat transfer coefficients.4... 

TABLE 17.16. Data for the Overall Heat Transfer Coefficient, u (kcal/mzh°C), in Packed Beds... 

Homogeneous one-dimensional model This is the simplest description of a packed bed, with an overall heat-transfer coefficient U. The particle and gas temperatures are identical, and only axial variation in temperature is considered, giving the following mass and energy balance equations for any species C, ... 

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. 

Mechanistic equations describing the apparent radial thermal conductivity (kr>eff) and the wall heat transfer coefficient (hw.eff) of packed beds under non-reactive conditions are presented in Table IV. Given the two separate radial heat transfer resistances -that of the "central core" and of the "wall-region"- the overall radial resistance can be obtained for use in one-dimensional continuum reactor models. The equations are based on the two-phase continuum model of heat transfer (3). 

Forced convection heat transfer is probably the most common mode in the process industries. Forced flows may be internal or external. This subsection briefly introduces correlations for estimating heat-transfer coefficients for flows in tubes and ducts flows across plates, cylinders, and spheres flows through tube banks and packed beds heat transfer to nonevaporating falling films and rotating surfaces. Section 11 introduces several types of heat exchangers, design procedures, overall heat-transfer coefficients, and mean temperature differences. 

The catalyst consists of 0.32 cm diameter spheres that have a bulk density of 0.84 g cm and pack into a fixed bed with a void fraction of 0.4. The mass velocity of the gas through each tube will be 0.075 g cm s , which corresponds to an overall heat transfer coefficient between the tube wall and the reacting fluid of about 10 cal cm s K . ... 

In the packed-bed reactor, the molar concentrations and temperature at the exterior of the catalyst particle are coupled to the respective fluid-phase concentrations and temperature through the interfacial fluxes given in Eqs. (3.3-1) and (3.3-2). Overall mass and heat transfer coefficients are often used to describe these interfacial fluxes, similar in structure to Eqs. (3.2-1) and (3.2-2). Complete solution of the packed-bed reactor model... 

The reactants enter in the annular space between an outer insulated tube and an inner tube containing the catalyst. No reaction takes place in the annular region. Heat transfer between the gas in this packed-bed reactor and the gas flowing counter currently in the annular space occurs along the length of the reactor. The overall heat-transfer coefficient is 5 W/ K. Plot the conversion and temperature as a function of reactor length for the data given in... 

Packed Bed Thermal Conductivity 587 Heat Transfer Coefficient at Walls, to Particles, and Overall 587 Fluidized Beds 589... 

Knowledge of the heat transfer characteristics and spatial temperature distributions in packed beds is of paramount importance to the design and analysis of the packed-bed catalytic or non-catalytic reactors. Hence, an attempt is made in this section to quantify the heat transfer coefficients in terms of correlations based on a wide variety of experimental data and their associated heat transfer models. The principal modes of heat transfer in packed beds consist of conduction, convection, and radiation. The contribution of each of these modes to the overall heat transfer may not be linearly additive, and mutual interaction effects need to be taken into account [23,24]. Here we limit our discussion to noninteractive modes of heat transfer. 

Determining the values of h and from experiments is a challenging task, and a great many empirical correlations have been presented. Most of the data are for heat transfer without reaction, such as for heating air in a steam-jacketed pipe packed with spheres. For these tests, Q is measured from the change in sensible heat of the air, and U is calculated from the usual equation, Q = VAAT. The small steam-film and metal-wall resistances can be subtracted from the overall resistance to obtain an overall bed coefficient, ho. ... 

The model discussed here uses the effective transport concept, this time to formulate the fiux of heat or mass in the radial direction. This flux is superposed on the transport by overall convection, which is of the plug flow type. Since the effective diffusivity is mainly determined by the flow characteristics, packed beds are not isotropic for effective diffusion, so that the radial component is different from the axial mentioned in Sec. 11.6.b. Experimental results concerning D are shown in Fig. 11.7.a-l [61, 62,63]. For practical purposes Pe may be considered to lie between 8 and 10. When the effective conductivity, X , is determined from heat transfer experiments in packed beds, it is observed that X decreases strongly in the vicinity of the wall. It is as if a supplementary resistance is experienced near the wall, which is probably due to variations in the packing density and flow velocity. Two alternatives are possible either use a mean X or consider X to be constant in the central core and introduce a new coefficient accounting for the heat transfer near the wall, a , defined by ... 

To obtain the similar expressions for a stirred bed it is first assumed that there exists some fictitious time period during which the bed is assumed to be a packed bed and the heat transfer to the bed is governed by Equation 6.4. After tjf a perfect mixing of the bed is assumed. This assumption yields oscillating instantaneous heat transfer coefficient and the time average of these values yields the overall heat transfer coefficient of the stirred bed Uoo. The value of is calculated by... 

Dixon AG. An improved equation for the overall heat transfer coefficient in packed beds. Chemical Engineering and Processing Process Intensification I996 35 323-331. 

If we use Eq. (4.10.71), we have to keep in mind that pronounced radial temperature gradients may be present in cooled tubular reactors, even if the gradient is small or confined to a small region near the wall. Thus, Eq. (4.10.71) is strictly speaking only valid for an ideal PER with a uniform radial temperature, but for the subsequent examination of the basic principles of the behavior of non-isothermal tubular reactors we neglect this aspect and use an overall heat transfer coefficient Uh. The more complicated radial heat transfer in the case of pronounced radial temperature gradients in tubular reactors such as packed bed reactors will be treated in Section 4.10.7.3. Subsequently, we inspect the adiabatic operation of a tubular reactor first. Thereafter, we take a closer look at a wall[Pg.329]

One-Dimensional Model of a Wall-Cooled Fixed Bed Reactor In some cases, it may be convenient to use a simple one-dimensional model, for example, to get an initial insight into the reactor behavior by a less complicated model. This model also takes into account A ad and aw,int> but we now introduce a mean (constant) bed temperature Tnean and an overall heat transfer coefficient of the bed, the thermal transmittance [/ted. which collects the interplay of heat conduction in the bed (A d) and the heat transfer at the wall (a i t) (Figure 4.10.68). According to this model, heat transfer from a packed bed to a heat transfer medium that cools the outer surface of the wall of a tubular reactor is given by ... 

For heat transfer in packed beds with constant wall temperature, the overall heat transfer coefficient defined by taking the difference between wall temperature and the average temperature of the flowing fluid as the driving force of heat transfer, ho, is obtained as follows. 

When gas phase adsorption takes place in a large column, heat generated due to adsorption cannot be removed from the bed wall and accumulated in the bed because of poor beat transfer characteristics in packed beds of particles. A typical model of this situations is an adiabatic adsorption. The fundamental relations for this case are Eqs. (8-22), (8-38), (8-39) and (8-40), which are essentially similar to those employed by Pan and Basmadjian (1970). Thermal equilibrium between particle and fluid is assumed and oidy axial dispersion of heat is taken into account while mass transfer resistance between fluid phase and particle as well as axial dispersion is considered. This situation is identical with the model employed in the previous section. For further simpliHcation, axial dispersion effect may be involved in the overall mass transfer coefficient of the linear driving force model as discussed in Chapter S. In this case, after further justifiable simplifications such as negligible heat capacity and accumulation of adsorbate in void spaces, a set of basic equations to describe heat and mass balances can be ven as follows. 

The catalyst is a mixture of vanadium and molybdenum oxides on an inert support. Typical inlet reaction tenperatures are in the range of 350°C to 400°C. The catalyst is placed in 25 mm diameter tubes that are 3.2 m long. The catalyst pellet diameter is 5 mm. The maximum tenperature that the catalyst can be exposed to without causing irreversible damage (sintering) is 650°C. The packed-bed reactor should be costed as a shell-and-tube exchanger. The heat transfer area should be calculated based on the total external area of the catalyst-filled tubes required from the simulatioa Because of the high tenperatures involved, both the shell and the tube material should be stainless steel. An overall heat transfer coefficient for the reactor should be set as 100 W/m °C. (This is the value specified in the simulation.)... 

Pumparound sections usually contain from 4 ft to 9 ft of packed depth. The traditional method for calculating bed depth is by use of Equation 6-20. This equation is a simplified representation of a complex group of heat and mass transfer processes. A considerable amount of industrial experience has led to the development of satisfactory empirical equations for the calculation of overall heat transfer coefficients. 

Figure 4.9 Overall heat transfer coefficient (a) and heat transfer parameters (b) of a highly conductive structured catalyst in methanol synthesis as a function of the syngas stoichiometric number in the fresh feed stream (Mp). (Squares) Commercial Lurgi multitubular packed-bed reactor (PB) (circles) copper honeycomb monoliths (HM) (triangles) open-cell foams (OF). In Figure 4.9b, the radial effective thermal conductivity is plotted with solid symbols and the wall heat transfer coefficient, h, with empty ones. Reprinted from Montebelli etal. [162], with permission from Elsevier.

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