Impact of Porosity and Velocity Distribution on the Theoretical Prediction of Fixed-Bed Chemical Reactor Performance

Abstract

Due to porosity changes and to the nonslip condition at the wall, the non uniform po rosity profiles in packed beds exhibit steep maxima close to the wall. The govern ing equations of energy and mass conserva tion were solved for fixed bed chemical reactors including these profiles. Under the assumption of non uniform flow the problems become two-dimensional also under adiabatic conditions. In all cases the agreement between available experimental data and theoretical predictions based on realistic flow conditions is improved. In particular measured and calculated moving speeds of migrating reaction zones fit to gether very well for adiabatic fixed bed reactors. Also considerable improvements concerning multiple steady states, temper ature profiles and conversion rates were obtained in situations when the reactor was wall cooled. In fixed bed chemical reactor analysis it is commonto assume uniform flow distribution within the bed. The reality however is different. Due to a change of the average porosity near the wall [ 1,2,3],(Figure 1.) -ε=1 at the wall -the flow velocity increases until close to the wall and is reduced again because of the non slip condition (Figure 2.) The artificial flow pro file is described by the Brinkman equation I =-150^ -L75 ρ »2 ψΙ.Α. Α. ( η iiL,àz a e 3 dp 2 9 £ 3 dp r dr 9 dr B.C. Ζ=0 : ρ=ρ 0 ;Γ=0: s 0 ; Γ « R : U = 0;

The Measurement of Void Fraction Profiles in Packed Beds

“…Carbonell [2] also used a two zone model for his analysis of the dispersion phenomena. In more recent work Vortmeyer et al [5,6] tried to use the complete radial void fraction profile, and so did Chang [3]. They followed the same itinerary outlined by Lerou and Froment [1] and Marivoet et al [21].…”

“…Carbonell [2] and Chang [3] used the structure of the bed to explain dispersion phenomena. Vortmeyer et al introduced the structural characteristics of the bed to improve their models for creeping flow in reactors [4] and for the theoretical prediction of fixed bed chemical reactor performance [5,6]. Cohen and Metzner [1] accounted for nonuniformities of the bed in the pressure drop relationship for both linear and non-Newtonian fluids.…”

Forced Convection in Packed Tubes and Channels with Variable Porosity and Thermal Dispersion Effects

“…It has been found that these lumped parameter models often overpredict the temperature of hot spots in the reactors [37,38], which implies that the models underestimate the heat transfer rate at the wall. Some investigators [42][43][44][45][46] have attributed the disparity of the theoretical and experimental results in a wall-cooled catalytic reactor to the assumption of a flat velocity profde (Plug flow) in the lumped parameter model, which does not take into consideration the nonuniform velocity distribution near the wall due to the channeling effects. Other investigatorS (39) attribute the disparity between theory and experiments to unrealistic assumptions of a constant effective radial thcnnaI conductivity, a constant wall heat transfer coeffICient, and the widely scattered wall Nusselt number as shown in Fig.2.…”

Application of computational fluid dynamics to fixed bed adsorption calculations: Effect of hydrodynamics at laboratory and industrial scale

“…Axial and radial dispersion coefficients have to be known, as well as the porosity profile within the bed of adsorbent. Numerical studies have reported the role of by-pass flows near the wall inside reactors or adsorbers using two-dimensional models [9][10][11][12][13]. In particular, Tobis and Vortmeyer [14] used a two-dimensional model to study the near-wall channelling effect on an instantaneous isothermal adsorption.…”