Elsevier

Chemical Engineering Journal

Volume 396, 15 September 2020, 124994
Chemical Engineering Journal

Non-uniform size of catalyst particles. Impact on the effectiveness factor and the determination of kinetic parameters

https://doi.org/10.1016/j.cej.2020.124994Get rights and content

Highlights

  • Catalytic beds with non-uniform particle size are common in many processes.

  • The size distribution of catalyst particles affects the effectiveness factor.

  • Assessing the intrinsic kinetic constants must consider particle size distributions.

  • The wider the dispersion in sizes the higher the error in assuming uniformity.

Abstract

The analysis of the effectiveness factor in catalytic particles with non-uniform size, was performed. The procedure proposed by Weisz and Prater to determine the intrinsic kinetic constants from experimental results was extended to cases where the catalyst particle size distribution is considered. The approach was applied to the study of reactions with power law and Langmuir-Hinshelwood-Hougen-Watson type kinetics, the catalyst particles being spheres with volume log-normal size distribution (typical in, e.g., fluid catalytic cracking catalysts). If the catalytic effectiveness factor is calculated assuming uniform particle size Rm (Rm being the volume to area mean radius), it will be always higher than the actual effectiveness factor. If the particle size distribution is not taken into account during the assessment of the intrinsic kinetic constants by means of the Weisz and Prater method, the values of those constants will be erroneous. The higher the dispersion in the particles size distribution, the higher the error in ignoring the impact of the different sizes.

Introduction

The concept of catalytic effectiveness factor depicts the efficiency of utilization of the active sites in the pores of a solid catalyst. Moreover, it allows expressing the chemical reaction rate in the mass balances as a function of the conditions observed in the bulk of the fluid phase, which significantly simplifies the analysis and design of chemical reactors [1]. The calculation of the effectiveness factor in a catalytic bed is typically based on considering uniform catalyst particle size. This view is reasonable provided the particles used are conformed with approximately uniform size [2].

Different methods to determine the particle size distribution of catalyst particles have been extensively reported in the literature. For instance, Barroso-Bogeat et al. [3] used electron microscopy in order to determine the particle morphologies and size distributions in activated carbon–metal oxide hybrid catalysts. Sieving is another method to determine the particle size distributions; traditionally, the particle size distributions of ion exchange resins were measured using a set of sieves [4]. In order to assess the minimum fluidization properties of a set of FCC catalysts, Issangya et al. [5] determined the particle size distributions by using a laser diffraction analyzer. Dishman and coworkers [6] compared the particle sizes of commercial cracking catalysts as determined by light scattering and dry sieving methods, showing that the larger the particle size, the larger the divergence between methods [6]. Grace and Sun [7], [8], [9] studied the effect of the particle size distribution of a FCC catalyst on its performance by separating various fractions of different size; the approach used an elutriation device to separate the particles into different narrow fractions [9].

It has been reported that the size of the catalyst particles in fluidized beds, which can be assumed spherical in shape, is not uniform [10], [11]. For example, it is common to find catalyst particles in the fluid catalytic cracking (FCC) process whose diameters range typically from 40 to 150 μm, generally following a log-normal distribution [5], [7], [11]. This means that the volumetric fraction of the particle size has a Gaussian distribution as a function of the logarithm of the diameter [12]. These non-uniform sizes make the analysis of the effectiveness factor difficult and the criteria to quantify the importance of the diffusion limitations become ambiguous.

The analysis of the effects of the particle size distribution on the diffusion–reaction phenomena in catalysis and, consequently, on the effectiveness factors, has been performed only for first order reactions on catalyst particles having a log-normal size distribution [2].

The classical parameter developed by Weisz and Prater [13] is an experimentally measurable magnitude, which represents the relationship between the observed reaction rate and a characteristic diffusion rate [1]. It has been successfully used in the determination of internal diffusional limitations [14] and intrinsic kinetic constants when diffusion limitations to the mass transfer in the catalyst particles exist, by making use of the results of laboratory experiments, provided the particles of catalyst in the bed have uniform size [15], [16], [17], [18], [19]. If a certain particle size distribution exists, a characteristic dimension must be carefully chosen to be representative of all the particles in order to avoid errors in the estimation of kinetic parameters.

Besides the Weisz and Prater approach, other kinetic characterization techniques, which are known as “tail pipe end”, “catalyst effluent”, or “integral” analysis, were based on assessing the composition of the fluid phase [1], [13], [14], [15], [16] and, consequently, the evolution of the chemistry within the catalyst particle is not known [20]. In recent years, some advanced techniques aimed at visualizing that evolution have been presented [20]. These so-called spatially resolved methods, which are based on various techniques including microscopy, spectroscopy, and probe molecules [20], [21], [22], [23], allow observing the evolution of the concentration profiles within a catalyst under realistic operating conditions. For example, Titze et al. [22] studied the hydrogenation of benzene over nickel dispersed within a nanoporous one-piece glass wafer by means of IR microscopy in order to register the evolution of the concentration profiles of reactants and products during the reaction. Moreover, they adapted the IR microscopy technique so as to directly assess the effectiveness factor of a catalytic reaction in nanoporous catalyst pellets, thus allowing one-shot determinations [23]. Even though with these advanced techniques, either applied to single-piece catalyst wafers or catalyst particles, the analysis is still based on a single and well defined characteristic length for the catalyst. Thus, if parameters obtained in these ways are used in chemical reactor analysis and design where catalyst particles are not uniform in their size, the problems described previously are still present.

It is the objective of this work to address the study of the problem of diffusion and chemical reactions obeying different kinetic expressions in spherical particles with non-uniform size. Particularly, power law and LHHW type kinetics are analyzed. The application of the Weisz and Prater approach to determine intrinsic kinetic constants from simple laboratory experiments under the existence of diffusion limitations is extended under these considerations.

Section snippets

Theoretical background. Uniform catalyst particle size

The reaction A → P is assumed to be irreversible, its kinetic expression being either power law or Langmuir-Hinshelwood-Hougen-Watson (LHHW) type. In the latter case, the first order on the surface concentration of the adsorbed reactant is assumed. The reactant A is the only species that is adsorbed on the surface of the catalyst, without dissociation, on a single type of catalytic sites. The pseudo-steady state hypothesis is assumed for the adsorbed reactant, i.e., the intrinsic adsorption and

Non-uniform catalyst particle sizes

It is common in practice to find beds of catalyst particles with various degrees of dispersion in their sizes. Fig. 3 shows examples of particle size distributions of FCC catalysts that can be found in the literature [7].

In addition to the set of hypotheses mentioned in Section 2, it will be assumed in the following sections that the catalyst particle size distribution, the particle density and the intrinsic activity are the same in the whole volume of the catalytic reactor.

For a reaction

Case of log-normal particle size distribution

The definitions of the previous section are neither restricted to a specific kinetic expression nor to a given particle size distribution. Obviously, in order to know the parameters Rm, ϕm, ηm, and θm, which characterize the diffusion–reaction system in a set of spheres with non-uniform sizes, which are needed to calculate the kinetic constants by means of the Weisz-Prater approach, it is necessary to specify the particle size distribution fvR.

Different authors showed that the volume particle

Conclusions

The impact of log-normal size distributions of catalyst particles over the effectiveness factor and the determination of kinetic parameters in reactions with power law and Langmuir-Hinshelwood-Hougen-Watson type kinetics was analyzed.

In a set of particles with a given size distribution the actual effectiveness factor reflects the contribution from all the particles with different sizes. For a mean particle size defined as Rm=3Vpe/Ape, with Rm being the characteristic dimension in the mean

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work has been carried out with financial support of the University of Litoral (UNL, Santa Fe, Argentina), Secretary of Science and Technology, Proj. CAID 50420150100068LI; University of Mar del Plata (Project ING 448/16); National Scientific and Technical Research Council (CONICET), PIP 593/13; and the National Agency for Scientific and Technological Promotion (ANPCyT), PICT 1208/2016.

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