Heat transfer in a packed bed

The Rowe-Claxton empirical equation has been found to conform to many experimental studies of heat transfer in a packed bed, such as the reactor typically used in the catalytic processes described earlier. It is first necessary in this situation to define die voidage of the system, AV, where... 

In the chromatographic method a pulse or step change in sor-bate concentration is introduced into the carrier stream at the inlet of a packed adsorption column and the diffusional time constant is determined from the dispersion of the response signal at the column outlet. Since heat transfer in a packed bed is much faster than in a closed system the chromatographic method may, in principle, be used to follow somewhat faster sorption processes. 

In this paper the coupled elliptic partial differential equations arising from a two-phase homogeneous continuum model of heat transfer in a packed bed are solved, and some attempt is made to discriminate between rival correlations for those parameters not yet well-established, by means of a comparison with experimental results from a previous study (, 4). 

Heat Transfer in a Packed Bed (Effective Thermal Conductivity) In a bed of solid particles through which a reacting fluid is passing, heat can be transferred in the radial direction by a number of mechanisms. However, it is customary to consider that the bed of particles and the gas may be replaced by a hypothetical solid in which conduction is the only mechanism for heat transfer. The thermal conductivity of this solid has been termed the effective thermal conductivity k. With this scheme the temperature T of any point in the bed may be related to and the position parameters r and z by the differential equation... 

A. A. Mohamad, S. Ramadhyani, and R. Viskanta, Modeling of Combustion and Heat Transfer in a Packed Bed With Embedded Coolant Tubes, Int. J. Heat Mass Transfer (37/8) 1181,1994. 

Figure 7.33 Conceptual model for heat transfer in a packed bed. [After S. Yagi and D. Kunii, Amer. Inst. Chem. Eng, JL, 3, 375, with permission of the American Institute of...

Ashley et al. [161] modified a model for heat transfer in a packed bed to describe the performance of an intermittently stirred bed by assuming an instantaneous redistribution of biomass and energy within the bed at regular intervals. The model was used to explore whether mixing could decrease the maximum temperature achieved within the bed in comparison with static packed bed operation, in which the maximum temperature occurs at the outlet air end of the bed at the time of peak heat production. Interestingly, using... 

These equations are precisely analogous to those used to describe heat transfer in a packed bed or in a double crossflow heat exchanger, and many of the earliest solutions such as that of Anzelius were derived for the analogous heat transfer problem. 

Lamine AS, Gerth L, Le Gall H, Wild G. Heat transfer in a packed bed reactor with cocurrent downflow of a gas and a liquid. Chem. Eng. Sci. 1996 51 3813. 

Moreira MPP, Thomeo JC, Freire JT Analysis of the heat transfer in a packed bed with cocurrent gas-liquid upflow, Ind Eng Chem R s 44 4142—4146, 2005. 

A wide class of forced unsteady-state processes have already been realized on the commercial scale using specific dynamic phenomenon, that takes place during performance of an exothermic reaction in a fixed bed of catalyst. This phenomenon is referred to in the literature as wrong-way behavior of a fixed bed reactor [20]. Substantial differences in characteristic times of heat and mass transfer in a packed bed reactor result in a surprising rise of temperature inside the reactor after... 

Example 4.6 Entropy production in a packed duct flow Fluid flow and the wall-to-fluid heat transfer in a packed duct are of interest in fixed bed chemical reactors, packed separation columns, heat exchangers, and some heat storage systems. In this analysis, we take into account the wall effect on the velocity profile in the calculation of entropy production in a packed duct with the top wall heated and the bottom wall cooled (Figure 4.7). We assume... 

Palancz. B., Modelling and simulation of heat and mass transfer in a packed bed of solid particles having high diffusion resistance, Comput. Chem. Eng.. 9(6). 567-582 (1985). 

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 ... 

The heat transfer in fluidized beds of monodisperse particle has been extensively investigated in the past. Heat transfer in a packed/fluidized bed with an interstitial fluid may involve many mechanisms as shown in Fig. 1 (Yagi and Kunii, 1957). These mechanisms can be classified into three heat transfer modes in fluidized beds fluid—particle or fluid—wall convection particle-particle or particle—wall conduction and radiation. Different heat transfer models are developed for these mechanisms, as described in the following. 

Effective thermal conductivities and heat transfer coefficients are given by De Wasch and Froment (1971) for the solid and gas phases in a heterogeneous packed bed model. Representative values for Peclet numbers in a packed bed reactor are given by Carberry (1976) and Mears (1976). Values for Peclet numbers from 0.5 to 200 were used throughout the simulations. 

Figure 1736. Effective thermal conductivity and wall heat transfer coefficient of packed beds. Re = dpG/fi, dp = 6Vp/Ap, s -porosity, (a) Effective thermal conductivity in terms of particle Reynolds number. Most of the investigations were with air of approx. kf = 0.026, so that in general k elk f = 38.5k [Froment, Adv. Chem. Ser. 109, (1970)]. (b) Heat transfer coefficient at the wall. Recommendations for L/dp above 50 by Doraiswamy and Sharma are line H for cylinders, line J for spheres, (c) Correlation of Gnielinski (cited by Schlilnder, 1978) of coefficient of heat transfer between particle and fluid. The wall coefficient may be taken as hw = 0.8hp.

Basic A, Dudukovic MP. Hydrodynamics and mass transfer in rotating packed beds. In Heat and Mass Transfer in Porous Media Conference Proceedings, 1992 651-662. 

Second, the efficiency of conventional reformer decreases at small scales due to heat transfer limitations and parasitic heat losses. The transfer of heat from the combustion products to the reactants is an inherently inefficient process, and in any practical system, especially for smaller scales, it is not possible to transfer all of the energy released by combustion into the process being heated. In UMR the heat transfer is more efficient as the packed bed is internally heated. The improvements in heat transfer to the packed bed are expected to result in a higher process efficiency. 

Further, we should realize that the relations in Equation 4.9 hold for single particles. In a packed bed the heat and mass transfer is enhanced due to the presence of the adjacent particles. For this enhancement Martin [4] derived the following relation ... 

In the recent years different numerical models for the conversion of wood in a packed bed have been presented, e. g, [3-6], Existing models mostly describe the as a porous media by an Eulerian approach, with the cons vation equations for the solid and the gas phase solved with the same mesh. This approach implies that heat and mass transfer can only be taken into account according to the dimensions of the bed but not within the particles itself. Temperature and species distributions are assumed to be homogenous over the fuel particles. Thus, the influence of the particle dimensions on the conversion process can only be captured by simplified assumptions or macrokinetic data. 

Due to the Langrangian formulation applied to the solid phase, the use of an effective thermal conductivity as usually applied to porous media is not necessary. In a packed bed heat is transported between solid particles by radiation and conduction. For materials with low thermal conductivity, such as wood, conduction contributes only to a minor extent to the overall heat transport. Furthermore, heat transfer due to convection between the primary air flow through the porous bed and the solid has to be taken into account. Heal transfer due to radiation and conduction between the particles is modelled by the exchange of heat between a particle and its neighbours. The definition of the neighbours depends on the assembly of the particles on the flow field mesh. 

In order to assess transport mechanisms due to convection various correlation for heat and mass transfer coefficients in a packed bed have been derived. For the present application the transfer coefficient in the bed is related to the transfer coefficient of a single particle in a gas flow according to [15]. Due to the outflow of the gases during pyrolysis and char conversion the calculated transfer coefficient is decreased, thus Stefan correction is included to calculate the transfer coefficient at a finite flow over the boundary. 

A numerical model is presented to describe the thermal conversion of solid fuels in a packed bed. For wood particles it can be shown, that a discretization of the particle dimensions is necessary to resolve the influence of heat and mass transfer on the conversion of the solid. Therefore, the packed bed is described as a finite number of particles interacting with the surrounding gas phase by heat and mass transfer. Thus, the entire process of a packed bed is view as the sum of single particle processes in conjunction with the interaction of the gas flow in the void space of a packed bed. Within the present model, neighbour particles exchange heat due to conduction and radiation with each other. 

Takeuchi et al. 7 reported a membrane reactor as a reaction system that provides higher productivity and lower separation cost in chemical reaction processes. In this paper, packed bed catalytic membrane reactor with palladium membrane for SMR reaction has been discussed. The numerical model consists of a full set of partial differential equations derived from conservation of mass, momentum, heat, and chemical species, respectively, with chemical kinetics and appropriate boundary conditions for the problem. The solution of this system was obtained by computational fluid dynamics (CFD). To perform CFD calculations, a commercial solver FLUENT has been used, and the selective permeation through the membrane has been modeled by user-defined functions. The CFD simulation results exhibited the flow distribution in the reactor by inserting a membrane protection tube, in addition to the temperature and concentration distribution in the axial and radial directions in the reactor, as reported in the membrane reactor numerical simulation. On the basis of the simulation results, effects of the flow distribution, concentration polarization, and mass transfer in the packed bed have been evaluated to design a membrane reactor system. 

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