Néstor J. Mariani

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.

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.

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.

An algorithm for evaluating reaction rates of catalytic reaction networks with strong diffusion limitations

Abstract An h -adaptive mesh procedure to solve the reaction–diffusion problem for multiple reactions in catalytic pellets presenting strong diffusion limitations is developed. The discretization approach selected for this purpose is based on an integral formulation of the conservation equations. The adaptive mesh procedure relies on estimating the error of local reaction rate evaluations. By adding or removing nodes the errors will eventually become bounded within pre-set limits. The algorithm is tried on some test cases derived from the liquid phase catalytic hydrogenation of butadiene and butyne in butene (1, 2- cis and 2- trans ) rich hydrocarbon mixtures.

A BEM FORMULATION FOR EVALUATING CONDUCTIVE HEAT TRANSFER RATES IN PARTICULATE SYSTEMS

A formulation based on the boundary-element method (BEM) to solve the conductive heat transfer problem between a particle and an adjacent heat exchange surface or between two particles is presented. This simple geometric configuration corresponds to a unit cell representing the thermal behavior near the wall or in the bulk of fixed and fluidized beds. The BEM is formulated by employing a variable number of nodes defined by the same quadrature points on which the integral coefficients of the influence matrix are evaluated. It is shown that this is a very efficient choice as compared to standard BEM formulations.

EVALUATION OF OVERALL HEAT TRANSFER RATES BETWEEN BUBBLING FLUIDIZED BEDS AND IMMERSED SURFACES

A mechanistic model to evaluate heat transfer rates between the dense phase of gas fluidized beds and immersed surfaces has been recently presented by the authors. This model, denoted Generalized Heterogeneous Model (GHM), is formulated in terms of effective thermal properties for particles and interstitial gas. It has been conceived with the purpose of achieving a generalized formulation accounting simultaneously for conductive, gas convective and radiant effects. The model was previously tested as regards its capability to predict radiative heat transfer rates in beds at high temperature and gas convective contribution in beds of large particles and high operating pressures. It is the principal object of this contribution to evaluate the performance of the GHM for a wide range of particle sizes, covering from The purely conductive regime to the gas convection dominant regime. Also, the main assumptions incorporated in the model are revised and some modifications are introduced, mainly on the basis of th...

A critical review on heat transfer in trickle bed reactors

Abstract A critical review of the available information about heat transfer between a packed bed with cocurrent downflow of gas and liquid and an external medium was undertaken. Several aspects such as experimental set-ups and methods employed to study heat transfer in trickle bed reactors, models used to interpret experimental data, and literature correlations of heat transfer parameters are addressed. From the analysis of the available experimental information, a refined database has been built, which allows comparing the performance of the existing correlations for the parameters of the extensively employed two-dimensional pseudohomogeneous plug flow model (i.e., effective radial thermal conductivity and wall heat transfer coefficient). In addition, new correlations for effective thermal conductivity have been developed. Identification of gaps in the current knowledge and recommendations for future works are summarized.