D. Vortmeyer

Evaluation of steady flow profiles in rectangular and circular packed beds by a variational method

Abstract The Brinkman-equation is solved by an equivalent variational problem in order to obtain steady flow profiles which satisfy the conditions w = 0 and e = 1 at the container wall of a packed bed. The quite large deviations between calculated and measured profiles are fully explained. An analytical expression is developed with sufficient accuracy. The main body of calculations is performed for isothermal flow, however flows under non-isothermal conditions also are considered.

Equivalence of one- and two-phase models for heat transfer processes in packed beds: one dimensional theory

Abstract From a two-phase model for an adiabatic packed bed through which a gas is flowing, a one-phase model is derived without assuming that the solid and gas temperatures are equal. By means of the derivation, a relationship between the axial effective thermal conductivity in the one-phase model and the heat transfer coefficient in the two-phase model is obtained. The validity of this relationship is confirmed using the experimental results of other authors. These results can also be applied to fixed bed chemical reactors if the reaction takes place in or on the surface of the catalyst. Essential to the derivation is the assumption that the thermal capacity of the gas phase can be neglected. For a fluid where this assumption is not valid, a separate derivation, whose assumptions are more restrictive, is presented in the appendix.

A simple and coherent set of coefficients for modelling of heat and mass transport with and without chemical reaction in tubes filled with spheres

Abstract Temperature and concentration profiles are commonly modelled in wall-cooled or -heated packed beds by quasi-homogeneous models. The model coefficients depend on the kind of assumptions with respect to the flow profile and to the wall heat transfer mechanism. The coefficients presently available in literature and handbooks are based on plug flow and a wall heat transfer model which generates a temperature jump at the wall. In this paper we have conducted a comprehensive reevaluation of available experimental work with spherical particles and present a simple and consistent set of coefficients based on an uneven flow distribution and on a wall heat conduction model (Λr(r)-model). All coefficients have been found to be invariable upon bed-to-particle diameter ratio or bed length and applicable without additional adaptation to situations with and without an exothermic chemical reaction. The introduction of a wall heat transfer coefficient is not necessary.

Transverse thermal dispersion and wall channelling in a packed bed with forced convective flow

Abstract An analysis has been performed to study the transverse heat transfer characteristics of a fully-developed forced convective flow in a variable-porosity packed bed bounded between parallel plates, separated at a distance 2 H * and heated asymmetrically. The Brinkman model, with the variable permeability approximated by an exponential function, is used as the momentum equation. The method of matched asymptotic expansions is employed to obtain an analytical solution for the velocity distribution in the packed bed. To account for the higher thermal resistance near the wall of a packed bed, a wall function is proposed for the transverse thermal dispersion process. With the introduction of the wall function, the large temperature drop near the wall of a packed bed observed in forced convection experiments can be reproduced theoretically. In agreement with experimental data, the predicted surface heat flux increases with increasing Peclet number and decreasing d p * / H * .

Discrimination of three approaches to evaluate heat fluxes for wall-cooled fixed bed chemical reactors

Abstract Temperature and concentration profiles were measured in the presence of an exothermic chemical reaction along the axis and the wall of a wall-cooled packed bed reactor. The data allowed the discrimination of three approaches to evaluate wall heat fluxes in solving the equations of the quasi-homogeneous model. All model coefficients were obtained from literature data. At Reynolds numbers of 25 and 32 (related to inlet temperatures around 600 K) the wall heat conduction model turned out to be the superior one.

Ignition/extinction phenomena in a wall cooled fixed bed reactor: Experiments and model calculations including radial porosity and velocity distributions

Abstract Measured ignition/extinction temperatures and temperature profiles in a wall cooled exothermic fixed bed reactor are compared with the solutions of the two dimensional pseudohomogeneous model. Best agreement with experiments was obtained when the governing equations were solved with respect to radial p velocity distribution.

Pressure dependency of effective thermal conductivity of packed beds

The effective thermal conductivities of packed beds with stagnant gas were theoretically computed, and it was found that these are expressed as Each conductivity was illustrated in graph; (ke)COND is highly pressure dependent, (ke)RAD is slightly pressure dependent and (ke)CONTACT is independent of pressure. It is also shown that for fine particles the effective thermal conductivities even at normal pressure is still in the pressure dependent region and is influenced by the gas accommodation coefficient.

Moving reaction zones in fixed bed reactors under the influence of various parameters

Abstract Moving reaction zones are obtained by the solution of the interdependent and unsteady state set of the energy and material balance differential equations for a fixed bed catalytic reactor with a fast exothermic reaction. Parametric studies concerning the influence of gas velocity and reactant concentration, of heat and mass diffusivities, of heat radiation, of the kinetic parameters and of the particle diameter were performed. A comparison with experimental work turned out to be very satisfactory.

The near-wall channelling effect on isothermal constant-pattern adsorption

Abstract A two-dimensional model of adsorption under isothermal constant-pattern conditions with local equilibrium between phases has been developed for the experimental conditions of Le Van and Vermeulen (1984, A.I.Ch.E. Symp. Ser. No. 233, 80, 34) and integrated numerically. The model includes the radial fluid velocity profile due to porosity variation near the wall. The flow distribution was estimated from the extended Brinkman equation. The analysis of the predicted bulk concentration profile reveals that, although the ratio of adsorber diameter to particle diameter is greater than 100, wall channelling plays a significant role in the adsorber performance in the work of Le Van and Vermeulen.

Measured and calculated migrating speeds of reaction zones in a fixed bed reactor, a quantitative comparison

Abstract Calculated and measured migrating speeds of reaction zones in a fixed bed reactor are compared for the catalysed ethane oxidation reaction. While agreement is very good at low moving speeds, deviations become larger with increasing migrating velocity. The deviations are thought to be due to the inadequacy of steady state overall kinetic data when used for dynamic calculations.