Guillermo F. Barreto

Evaluation of heat transfer parameters in packed beds with cocurrent downflow of liquid and gas

The results of an experimental investigation on heat transfer from a packed bed with cocurrent gas–liquid downflow to the wall are presented and analyzed in this contribution. The measurements cover the range of operating variables corresponding to the so-called trickle regime in beds presenting aspect ratios (tube to particle diameter ratio) from 4.67 to 34.26. Water and air were employed as model fluids. The heat transfer process was first analyzed by means of a two-dimensional pseudohomogeneous plug-flow model with two parameters, the effective radial thermal conductivity (ker) and the wall heat transfer coefficient (hw). ker is well correlated with liquid and gas Reynolds numbers and particle diameter, except for the lowest experimental aspect ratio (4.67). Instead, a meaningful correlation of hw stands only for aspect ratios larger than 15. These results are analyzed and the evidence points out to sustain the hypothesis that the model fails at low aspect ratios because an apparent contact resistance (1/hw) can no longer accommodate the effects of significant fluid bypassing and finite size of the near-wall region. The experimental set of data were also used to develop a correlation for the overall heat transfer coefficient (hT), which can be employed satisfactorily to predict heat transfer rates in the whole range of variables here investigated.

A One-Dimensional Equivalent Model to Evaluate Overall Reaction Rates in Catalytic Pellets

The problem of finding a one-dimensional (ID) model to approximate the behaviour of actual three-dimensional (3D) catalyst pellets is undertaken. It is shown that the ID model proposed by Burghardt and Kubaczka (Chem Eng Proc 35: 65–74, 1996), called here the generalized cylinder (GC) model, is most suitable for this purpose, provided that its main parameter (the shape power σ) is fitted to the behaviour of the actual pellet at low reaction rates. Calculations from the GC model are expected to be precise at around 1% for most geometrical cases of practical interest. The evaluation of σ for a given pellet geometry involves the solution of a Poisson equation. An approximate method that greatly simplifies this task for finite cylinders of any cross-section shape is developed. The procedure assumes knowledge of σ just for the cross-section (at most, a 2D problem). This is readily available for some practical cases, but if not, a suitable numerical procedure based on the boundary element method (BEM) is proposed. BEM is also suitable for the general 3D case.

Analysis of operating variables on the performance of a reactor for total hydrogenation of olefins in a C3C4 stream

Abstract The effect of process and operating variables in the catalytic hydrogenation of unsaturate traces in C 3 C 4 streams, intended for aerosol propellant use, has been analysed. The results from catalytic tests carried out on a commercial Pd/Al 2 O 3 catalyst have been used to estimate the kinetic parameters of rate expressions. The set of rate expressions is used in a mathematical model of a three-phase fixed-bed catalytic unit operated in up-flow mode. The mathematical model allowed studying the effect that variables such as temperature, pressure, hydrogen mass flow and feed composition will exert on the reactor performance. The volatility of the hydrocarbon mixture is found to be a paramount factor in the process, as H 2 becomes diluted in the vapour phase and, consequently, the amount of H 2 dissolved in the liquid stream and the hydrogenation rates decrease significantly. A temperature rise turned out to be detrimental for the reactor performance, as the increased hydrocarbon volatility overcomes the effect on the kinetic coefficients. This conclusion precludes the usual operating practice of rising temperature to compensate for catalytic activity decay. Instead, increasing the H 2 input and/or the operating pressure were shown to be effective alternatives for this purpose.

Effectiveness factor of a catalyst pellet in a trickle bed reactor: Limiting reactant in the gas phase

Abstract The influence of both internal and external wettings on the effectiveness factor of a partially wetted catalyst pellet in a trickle-bed reactor when the limiting reactant is in the gas phase is analyzed. A new parameter, not considered up to now, measuring the gas-liquid interfacial area inside and on the pellet surface, is introduced to study different forms of wetting. The reaction in the dry zone is also taken into account and its influence on the effectiveness factor for both the pores mouth and pores end dry is studied. An approximate analytical expression for the effectiveness factor, giving close results to the numerical solution, is proposed.

Evaluation of Structural Properties of Cylindrical Packed Beds Using Numerical Simulations and Tomographic Experiments

This contribution is focused on the analysis of the structure of packed beds of spherical particles at relatively low aspect ratios (i.e., particle to tube diameter ratio) as those arising in multitubular fixed bed reactors. On one hand, the computed tomography (CT) technique is employed to evaluate the position of each particle in the packing and from this information local properties such as particle center distribution and radial porosity profile were obtained. On the other hand, results from a previously developed algorithm to simulate packings were compared with those from our CT data and from literature sources. The agreement was very satisfactory.

Approximation of the effectiveness factor in catalytic pellets

The 1D model proposed by Burghardt and Kubaczka [Chem. Eng. Proc. 35 (1996) 65] to approximate the behavior of 3D catalytic pellets has been recently found able to provide accurate results for evaluating effective reaction rates when its parameter σ is suitable adjusted [Chem. Eng. Res. Des., submitted for publication]. This parameter represents the contraction of the cross-section available for diffusion. A formulation coupling a first-order Galerkin approximation with a truncated asymptotic expansion is proposed here to evaluate the effectiveness factor of single reactions in the range of interest −1/5 <σ< 5 [Chem. Eng. Res. Des., submitted for publication]. The formulation provides a 3% level of precision for essentially all normal kinetics of practical interest and a large range of abnormal kinetics. In particular, this conclusion includes reaction rates approaching a zero-order reaction, for which large deviations arise from the use of previous approximations proposed in the literature. On the other hand, the extent of abnormal kinetics being accurately approximated is significantly enlarged.

On the validity of the addition of independent contributions for evaluating heat transfer rates in gas fluidized beds

Abstract Different approaches for the approximate prediction of heat transfer rates between gas fluidized beds and immersed surfaces are analyzed in this work. They concern the interstitial gas and radiant contributions that have been frequently accounted for by adding approximate terms to the particle convective component which is usually the principal component. A generalized heterogeneous model considering simultaneously the three mechanisms and their interactions is presented and used to assess the validity of some previous approximations. This analysis is carried out by scanning practical ranges of the main decision variables: operating pressure, temperature and particle size.

Effect of the geometric characteristics of commercial catalysts for steam reforming

Abstract An analysis is made of the effect of the geometric characteristics of commercial catalysts for natural gas reforming on useful catalyst life and tube l Recently available catalysts are manufactured in the form of multiholed cylinders so as to obtain larger external surface areas for reactant access int

The gas contribution to heat transfer between fluidized beds of large particles and immersed surfaces

Abstract The gas contribution to heat transfer between large particle fluidized beds and immersed surfaces is analysed through a heterogeneous model for the dense phase. An approximate solution of the governing balances provides a conceptually appropriate and precise enough expression for the gas heat transfer coefficient, h g . For most practical conditions h g amounts to 75—85% of the limiting heat transfer coefficient at the surface wall, h wg . The results are compared with previous correlations for experimental conditions at which they were formulated. The analogous mass transfer process is included in this analysis as a particular case of the proposed theory.

Computing radial packing properties from the distribution of particle centers

The relationship between the distribution of particle centers in random beds of uniformly sized spheres and radial properties, in particular radial voidage profiles, is undertaken in this work. To this end, closed expressions for six geometrical quantities related to the intersection of spheres with cylindrical surfaces are presented. The relations to compute radial properties are then expressed in terms of those geometrical quantities and it is shown that for realistic types of particle center distribution, the calculations can be carried out without resorting to simplifying assumptions or numerical integration. The significance of radial profiles of particle surface area is also discussed.