The size and compactness of particles of arbitrary shape: application to catalyst effectiveness factors

Buffham, B.A.

doi:10.1016/s0009-2509(00)00425-5

Cited by 17 publications

(17 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…From the expansion of the effectiveness factor at low reaction rates, a different coefficient, γ, also encompasses geometric and activity gradient effects. 4,7 Based on previous results from Buffam, 12 Keegan et al, 1 Mariani et al,4,13 and some examples provided here, it has been observed that Γ and γ are frequently very strongly correlated. In these cases, it will be more convenient to adjust the 1D geometric model with Γ, which is more easily evaluated than γ.…”

Section: Discussionsupporting

confidence: 58%

“…Buffham 12 proposed a magnitude called compactness (here denoted as Q) as a shape factor: Therefore, Q is proportional to the value of Γ in the case of uniform activity and a smooth surface (cf. eq 21.b with Ω av ) 0).…”

Section: Discussion and Use Of The Second-order Expansionmentioning

confidence: 99%

“…Buffham 12 compared the effectiveness factor of a first-order reaction for different catalyst geometries. Three kinds of comparisons were made.…”

Section: Discussion and Use Of The Second-order Expansionmentioning

confidence: 99%

“…Equation 12 can now be used to obtain an approximate expression for the penetration depth , which can be defined as the distance from S p at which r(Y) reaches a residual value r(Y*) ) 0.1,…”

Section: Asymptotic Behavior At High Reaction Ratesmentioning

confidence: 99%

See 3 more Smart Citations

Behavior of Catalytic Pellets at High Reaction Rates. The Effect of Edges

Keegan

Mariani

Martı́nez

et al. 2005

Ind. Eng. Chem. Res.

View full text Add to dashboard Cite

The diffusion and reaction problem in catalytic pellets of any shape subject to diffusive transport limitations is undertaken in this contribution. Effective reaction rates in three-dimensional (3D) catalysts can be evaluated through a series solution written in terms of powers of (1/Φ) when strong diffusion limitations are present. In a recent paper, Keegan et al. [Chem. Eng. J. 2005, 110, 41] have clearly demonstrated for smooth catalysts that the second-order term [in (1/Φ) 2 ] depends essentially on the shape of the pellet. In this context, the purpose of this paper is to develop expressions of the second-order term for two-dimensional (2D) or 3D catalytic bodies showing edges. While the first-order term allows definition of the proper size of a catalyst, the second-order term provides a characterization for the shape of the catalyst. The possibility of using this characterization of catalyst shape in a geometrical one-dimensional (1D) model to approximate the behavior of given 2D or 3D pellets is analyzed. Also, the direct use of the two-term truncated series for complementing the numerical evaluation of the conservation equation is described.

show abstract

Section: Discussionsupporting

confidence: 58%

Section: Discussion and Use Of The Second-order Expansionmentioning

confidence: 99%

“…Buffham 12 compared the effectiveness factor of a first-order reaction for different catalyst geometries. Three kinds of comparisons were made.…”

Section: Discussion and Use Of The Second-order Expansionmentioning

confidence: 99%

Section: Asymptotic Behavior At High Reaction Ratesmentioning

confidence: 99%

See 2 more Smart Citations

Behavior of Catalytic Pellets at High Reaction Rates. The Effect of Edges

Keegan

Mariani

Martı́nez

et al. 2005

Ind. Eng. Chem. Res.

View full text Add to dashboard Cite

show abstract

“…For example, the bioavailability of pharmaceuticals often depends on both the particle size and shape. In heterogeneous catalysis, shape is important because it affects catalyst effectiveness (Buffham, 2000). For paint, opacity is a function of size, whereas coating layer properties are a function of the shape distribution (Lohmander, 2000b); for example, a broader shape factor distribution produces a coating with higher mechanical strength.…”

Section: Introductionmentioning

confidence: 99%

Statistics of multiple particle breakage accounting for particle shape

Hill

2004

AIChE Journal

View full text Add to dashboard Cite

show abstract

Surface textures of detrital pyroxenes in coastal dune sands (western Gulf of Mexico, Mexico): Implications for their preservation and geoenvironmental processes

Kasper‐Zubillaga

Martínez‐Serrano

Buchs

et al. 2023

The Depositional Record

View full text Add to dashboard Cite

This work investigates how the surface textures and morphology of pyroxene grains evolve during their source‐to‐sink history. This study applies to detrital clinopyroxenes concentrated in coastal dune sands of the Gulf of Mexico which were sourced in the Trans Mexican Volcanic Belt then transported and deposited in environments subject to limited chemical weathering. The composition and morphology of the pyroxenes was characterised using single‐grain geochemical analysis and surface texture imagery with a novel approach based on the compactness property to assess the shape of minerals. This reveals heterogenous diopside‐augite populations, displaying mineral morphologies dominantly controlled by impact breakage along cleavages, little physical abrasion along their edges and with limited evidence for chemical weathering. Mechanical surface textures dominate over mechanical/chemical and chemical surface textures. These mechanical surface textures are preserved primarily as flat cleavage surfaces and rounded edges inherited from fluvial‐intertidal and aeolian transport, respectively. Mechanically/chemically induced surface textures are preserved as elongated depressions. Chemical surface textures are sparse and mostly represented by mammillated textures that suggest local dissolution under subaqueous conditions. The scarcity of chemical surface textures is attributed to frequent fragmentation of the clinopyroxenes along cleavages and limited chemical weathering during transport of the observed populations. Clinopyroxene grains in the coastal dune sands primarily retain surface characteristics from fluvial transport. Although the breakage of minerals along cleavages can obscure their original morphology under a weathering‐limited erosion regime, this study shows how surface textures and morphology of pyroxene grains is used to determine episodes of transport and deposition close to volcanic environments. The use of the compactness property as a shape descriptor measurement of particles provides an alternative approach to observe how clinopyroxene remains unaltered despite the high energy conditions of the coastal area.

show abstract

The size and compactness of particles of arbitrary shape: application to catalyst effectiveness factors

Cited by 17 publications

References 17 publications

Behavior of Catalytic Pellets at High Reaction Rates. The Effect of Edges

Behavior of Catalytic Pellets at High Reaction Rates. The Effect of Edges

Statistics of multiple particle breakage accounting for particle shape

Surface textures of detrital pyroxenes in coastal dune sands (western Gulf of Mexico, Mexico): Implications for their preservation and geoenvironmental processes

Contact Info

Product

Resources

About