Breakage of macroporous alumina beads under compressive loading: simulation and experimental validation
Introduction
Porous alumina beads in the millimetre size range are commonly used as catalyst carrier in the oil and chemical industries. During transport to and from the reactor as well as in operation, the catalyst beads experience mechanical stresses, which could be sufficiently high to cause breakage of the particles. The formation of small fragments and fines leads to operational problems such as excessive pressure drop and segregation of fines and fragments, resulting in blockages or flow maldistributions. Therefore, for the reliable operation of reactors, it is necessary to quantify the extent of breakage of the beads and to improve their resistance to degradation. In a number of catalytic reactions, such as reforming, the presence of macropores (>50 nm) in the catalyst carrier beads is desirable to enhance the transport of the reagents within the catalyst. However, an increase in the porosity may reduce the particle strength causing excessive attrition. Therefore, the effect of the volume of macropores on the single particle properties and on the bulk crushing behaviour is addressed in this paper for three laboratory-scale samples of spherical porous alumina catalyst carrier beads in the size range of 1.70–2.00 mm with different levels of macroporosity: low (1), medium (2) and high (3). The single particle crushing strength and Young's modulus of the three samples are determined experimentally as well as the bulk crushing strength (BCS) of one of the samples for which an adequate supply was available. The bulk crushing test is simulated using the distinct element analysis (DEA) in order to relate the bulk mechanical behaviour of the assembly to individual particle properties. The DEA code used here is the TRUBAL code developed by Cundall and Strack [1]to model the behaviour of granular solids, which has subsequently been modified to model particle breakage. The predictions of the computer simulation are compared with the experimental results.
Section snippets
Determination of the crushing strength distribution
The side crushing strength (SCS) test is used to determine the resistance to fracture of a particle subjected to compressive loading. In a basic compression test, individual beads are compressed between two horizontal rigid platens using a mechanical testing machine. However, in an assembly, the particles are supported by particles underneath and are loaded by particles above them, thus leading to multiple particle contact points. The tensile stresses and the crushing strength distributions are
Determination of Young's modulus
The contact deformation of the three samples was measured under compressive loading between two stainless steel platens using a mechanical testing machine. Young's modulus of elasticity was then estimated based on Hertz analysis of elastic contacts 5, 6, where the dependence of the radius of the contact area, a, on the applied load, P, is given by:where Ee and Re are the effective Young's modulus and radius of curvature, respectively. The contact area, a, can be expressed as a
Determination of the BCS
In a BCS test, a bed of particles is quasi-statically compressed in a piston cylinder arrangement using a mechanical testing machine. The particles within the assembly undergo both fragmentation and wear. After unloading, the amount of fines and broken particles produced during the compressive loading is quantified by sieving in order to determine the size distribution of the product and the mass of broken particles. The BCS is defined as the pressure at which the amount of either fines or
Generation of the assemblies
Each assembly of particles of samples 1, 2 and 3, corresponding to low, medium and high macroporosity as given in Table 2, was randomly generated in a cubic box of 33 mm side length. Each assembly contains 4000 particles and three particle sizes. The particles radii are 0.90, 0.95 and 1.00 mm and their respective numbers are 1072, 1856 and 1072. This gives a size distribution which is close to the experimental part. The material properties of the beads and of the upper and lower platens are
Conclusions
An attempt has been made to relate the BCS of catalyst carrier beads to the single particle crushing strength distribution of individual beads and other mechanical properties such as Young's modulus, yield stress and fracture toughness. These properties are in turn affected by the presence of macropores in the beads.
The strength of three samples with different levels of macroporosity was compared under quasi-static loading. Individual particle testing shows that Young's modulus decreases with
List of symbols
a contact area (m2) BCS bulk crushing strength (Pa) E Young's modulus (Pa) Ee effective Young's modulus (Pa) Fn normal contact force (N) Fy yield force (N) H hardness (Pa) Kc fracture toughness (Pa m0.5) MPCS multiple particle crushing strength (N) P load (N) R particle radius (m) Re radius of curvature (m) s contact displacement (m) SCS side crushing strength (N) Vw volume of wear (m3) Y plastic yield stress (Pa)
Acknowledgements
The work reported here is part of an ongoing research programme supported by the Institut Français du Pétrole and Rhodia.
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- 1
Present address: Department of Physics, Cavendish Laboratory, University of Cambridge, UK.
- 2
Present address: Elf Atochem CRRA, rue Henri Moissan, BP63, 69493 Pierre Bénite, France.