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Ind. Eng. Chem. Res. 2000, 39, 838-842
Extension of a Model for Bulk Crushing Strength of Spheres to Solid Catalysts of Different Shapes Yongdan Li,*,† Dongfang Wu,† Jianpo Zhang,† Liu Chang,† Dihua Wu,‡ Zhiping Fang,‡ and Yahua Shi§ Department of Catalysis Science and Technology and State Key Lab on C1 Chemical Technology, School of Chemical Engineering, Tianjin University, Tianjin 300072, China, SINOPEC Technology Company, China Petrochemical Corporation, A-6 Huixin Dongjie, Chaoyang District, Beijing 100029, China, and Research Institute of Petroleum Processing, Beijing 100083, China
The applicability of a model developed for the bulk crushing strength of spherical catalysts has been extended to differently shaped nonspherical catalysts such as extrudates. A broken percentage for a spherical catalyst and a percentage of fine particles for other shaped ones generated during the bulk crushing strength measurement are discussed and used as indices for strength. A good correlation has been obtained between the model-predicted values and the experimental results of differently shaped extruded catalysts. It has also been found that the slope factor in the model does not change with the size of the sieve; it is thus suggested that one group of data obtained with an appropriate sieve is informative for strength analysis. 1. Introduction The mechanical strength of a solid catalyst is one of the key parameters for efficient performance of an industrial converter.1-3 The scientific basis for strength measurement has been an important research field, which has been aimed at providing reliable guidance for the development and selection of catalysts and the design of converters for a specific chemical process.4-16 It has been proposed in previous communications that solid catalysts composed of mixed metal oxides or oxidesupported metals are typically brittle materials and their strength failure is due to brittle fracture.9-11 This nature of catalyst strength leads to a large scattering range of the single-particle strength (SPS) data. It has been well-demonstrated that the distribution of the SPS data can be described by a Weibull equation, which provides a method for the calculation of the probability of strength failure under a specific loading condition.9-16 Thus, a preliminary scheme in theory has been established to predict the strength reliability of solid catalysts.10,11 Recently, a model for the bulk crushing strength (BCS) of a spherical catalyst was proposed,16 and a conclusion was drawn that the percentage of broken spheres in a catalyst bed, dm/m, under a specific pressure obeys the following relationship,
dm/m ) 1 - exp(-BPM)
(1)
where P is the axial piston pressure applied on the top of the catalyst bed and B and M are the parameters of the model. It has been illustrated by experimental results that the model describes well the behavior of strength failure of a bed of spherical catalyst during BCS measurement.16 This model has a very close meaning to the reliability of a fixed-bed converter, and therefore along with the BCS test method it is expected * To whom correspondence should be addressed. E-mail:
[email protected]. † Tianjin University. ‡ China Petrochemical Corporation. § Research Institute of Petroleum Processing.
to be useful in mechanical reliability simulation and prediction of practical fixed-bed converters. The model is, however, deduced from a tetrahedral packing of spheres. The percentage of broken spheres is adopted as a strength failure index, that is, BCS criterion. It represents the fracture condition of catalyst particles in the bed; nevertheless, it is complex to be measured. For instance, the spheres were checked one by one, by hand and human eyes after the bed was pressed during the experiment in ref 16. In fact, this index is not measurable for complex-shaped samples such as extrudates. A common one is called for. Ouwerkerk17 said that, for nonspherical material such as extrudates, BCS criterion may be set according to a change in, for example, the length-to-diameter ratio. It sounds like a good idea, but it is not practical for extruded catalysts because the length of these particles varies in a rather large range before BCS measurement. In the literature,18-21 the authors suggested using the weight percentage of fine particles generated during the pressing of the bed as BCS data, which are measurable for all the catalysts with different shapes. However, it is likely that the criterion covers up the scientific mechanism of strength failure. In this work, the percentage of fine particles is adopted as BCS criterion for nonspherical catalyst samples and is discussed on the basis of the BCS data. Commercial solid catalysts have a wide spectrum of shapes. In this work, several extruded catalysts are used as the model sample, the validity, and applicability of the BCS model with the percentage of fine particles used as a criterion is discussed. 2. Experimental Section Five samples were used in this work. They are differently shaped commercial catalyst supports with identical chemical compositions, γ-Al2O3, and are available in the Chinese market. Sample 1 is spherical in shape, while others are extruded cylindrical or trilobite pellets. Table 1 gives their physical properties. Before BCS measurements were performed, all samples were
10.1021/ie990418+ CCC: $19.00 © 2000 American Chemical Society Published on Web 03/06/2000
Ind. Eng. Chem. Res., Vol. 39, No. 3, 2000 839 Table 1. Physical Properties of the Catalyst Samples geometric size no sample 1 2 3 4 5
Al2O3 Al2O3 Al2O3 Al2O3 Al2O3
shape spheres trilobite extrudates trilobite extrudates cylindrical extrudates cylindrical extrudates
diameter (mm) length (mm) 5.7-6.6 2.30a 1.44a 2.04 1.38
5-30 3-20 8-30 4-30
a
pretreated under the following conditions. After the sample was heated in air at 200 °C for 4 h and cooled to room temperature, it was sieved to eliminate fine particles by a sieve of 1.25 mm. For sample 1, broken and defected spheres were sought out and removed before BCS measurements were performed. A pretreated sample (125 mL) was charged in the BCS tester, which is described in ref 16 in detail. A uniform loading was applied on the top of the catalyst bed via a piston of a hydraulic system. After being pressed at a specific loading, the sample was taken from the container and sieved by three sieves, 1.25, 0.9, and 0.45 mm, respectively. The original sample and fine particles generated by crushing were weighed with a balance with a precision of 0.1 g. The accumulative weight percentage of fine particles below a specific sieve was used as BCS data. For sample 1, the weight percentage of broken spheres after pressing was also determined by choosing with hands and eyes. The experiment was repeated at different applied pressures to generate a series of data points for each sample. Then, the data were treated by linear regression to obtain M and B in the model and the correlation coefficients, in the same way as detailed in ref 16. Equation 1 can be written as
1 (1 - dm/m ) ) M Ln P + Ln B
Ln Ln
(2)
Figure 1. (a) Logarithm plot of the bulk crushing strength for sample 1: 4, percentage of broken particles; O, percentage of fine particles
