Thiele modulus

2020 ◽  
Author(s):  
P. Claus, D. Hönicke
Keyword(s):  
Thiele Modulus

Evaluating the effectiveness factor from a 1D approximation fitted at high Thiele modulus: Spanning commercial pellet shapes with linear kinetics

2009 ◽  
Vol 64 (11) ◽  
pp. 2762-2766 ◽  
Author(s):  
Néstor J. Mariani ◽  
Clarisa Mocciaro ◽  
Sergio D. Keegan ◽  
Osvaldo M. Martínez ◽  
Guillermo F. Barreto
Keyword(s):  
Effectiveness Factor ◽  
Thiele Modulus ◽  
Linear Kinetics

scholarly journals Approximations for the Concentration and Effectiveness Factor in Porous Catalysts of Arbitrary Shape: Taylor Series and Akbari-Ganji’s Methods

2021 ◽  
Vol 8 (4) ◽  
pp. 527-537
Author(s):  
Ramu UshaRani ◽  
Lakshmanan Rajendran ◽  
Marwan Abukhaled
Keyword(s):  
Taylor Series ◽  
Arbitrary Shape ◽  
Reaction Diffusion ◽  
Diffusion Problem ◽  
Effectiveness Factor ◽  
Michaelis Constant ◽  
Thiele Modulus ◽  
Porous Catalysts ◽  
Analytical Approaches ◽  
Analytical Expressions

A mathematical model of reaction-diffusion problem with Michaelis-Menten kinetics in catalyst particles of arbitrary shape is investigated. Analytical expressions of the concentration of substrates are derived as functions of the Thiele modulus, the modified Sherwood number, and the Michaelis constant. A Taylor series approach and the Akbari-Ganji's method are utilized to determine the substrate concentration and the effectiveness factor. The effects of the shape factor on the concentration profiles and the effectiveness factor are discussed. In addition to their simple implementations, the proposed analytical approaches are reliable and highly accurate, as it will be shown when compared with numerical simulations.

scholarly journals A Potential–dependent Thiele Modulus to Quantify the Effectiveness of Porous Electrocatalysts

2021 ◽  
Author(s):  
Charles Wan ◽  
Katharine Greco ◽  
Amira Alazmi ◽  
Robert Darling ◽  
Yet- Ming Chiang ◽  
...  
Keyword(s):  
High Surface ◽  
High Surface Area ◽  
Reaction Rates ◽  
Effectiveness Factor ◽  
Mathematical Framework ◽  
Electrochemical Reactors ◽  
Thiele Modulus ◽  
Thermochemical Processes ◽  
Increase Productivity ◽  
Catalyst Utilization

<p>Electrochemical reactors often employ high surface area electrocatalysts to accelerate volumetric reaction rates and increase productivity. While electrocatalysts can alleviate kinetic overpotentials, diffusional resistances at the pore-scale often prevent full catalyst utilization. The effect of intraparticle diffusion on the overall reaction rate can be quantified through an effectiveness factor expression governed by the Thiele modulus parameter. This analytical approach is integral to the development of catalytic structures for thermochemical processes and can be extended to electrochemical processes provided the relationship between reaction kinetics and electrode overpotential is incorporated. Here, we derive a potential-dependent Thiele modulus to quantify the effectiveness factor for porous electrocatalytic structures. We apply this mathematical framework to spherical microparticles as a function of applied overpotential across catalyst properties and reactant characteristics. The relative effects of kinetics and mass transport are related to overall reaction rates, revealing markedly lower catalyst utilization at increasing overpotential. Subsequently, we generalize the analysis to alternative catalyst shapes and provide guidance on the design of porous catalytic materials for use in electrochemical reactors.</p>

Optimal catalyst activity distribution in fixed-bed reactor with catalyst deactivation

1989 ◽  
Vol 54 (2) ◽  
pp. 375-387 ◽  
Author(s):  
Jozef Markoš ◽  
Alena Brunovská
Keyword(s):  
Catalyst Deactivation ◽  
Active Catalyst ◽  
Catalyst Activity ◽  
Fixed Bed ◽  
Fixed Bed Reactor ◽  
Catalytic Reactor ◽  
Reactor Performance ◽  
Thiele Modulus ◽  
Activity Distribution ◽  
Parameter Ratio

In this paper the influence of the active catalyst location in a pellet on fixed-bed catalytic reactor performance is described. The optimal activity distribution as a function of an economic parameter (ratio of product and catalyst costs), Thiele modulus and Damkohler number is estimated.

scholarly journals A Thiele Modulus Approach for Nonequilibrium Adsorption Processes and Its Application to CO2 Capture

2020 ◽  
Vol 59 (15) ◽  
pp. 6874-6885 ◽  
Author(s):  
Rick T. Driessen ◽  
Sascha R.A. Kersten ◽  
Derk W.F. Brilman
Keyword(s):  
Co2 Capture ◽  
Thiele Modulus ◽  
Adsorption Processes

Diffusional limitations of anaerobic biofilms

1987 ◽  
Vol 14 (5) ◽  
pp. 631-637 ◽  
Author(s):  
K. J. Kennedy ◽  
R. L. Droste
Keyword(s):  
Kinetic Parameters ◽  
Biofilm Thickness ◽  
Thiele Modulus ◽  
Diffusion Limitations ◽  
Start Up ◽  
Empirical Determination ◽  
Film Reactor ◽  
Apparent Kinetic Parameters ◽  
Intrinsic Kinetic

Using an empirical determination of apparent kinetic parameters in the bulk mixed liquor, the intrinsic kinetic parameters of anaerobic biofilms developed at 35 °C during start-up and steady-state downflow stationary fixed film reactor operation were estimated. The apparent kinetic parameters of anaerobic biofilms are not significantly influenced by internal diffusion limitations. The apparent kinetic parameters of mature biofilms showed no significant trends with increased biofilm thickness up to 2.6 mm and increased apparent Thiele modulus up to 3.1. Key words: anaerobic, biofilm kinetics, Thiele modulus, wastewater, filter.

Mass Transfer with Chemical Reactions in Porous Catalysts: A Discussion on the Criteria for the Internal and External Diffusion Limitations

2013 ◽  
Vol 334-335 ◽  
pp. 279-283
Author(s):  
S. Gültekin
Keyword(s):  
Mass Transfer ◽  
Chemical Reactions ◽  
Effective Diffusivity ◽  
Effectiveness Factor ◽  
Internal Mass ◽  
Thiele Modulus ◽  
Porous Catalysts ◽  
Diffusion Limitations ◽  
External Diffusion ◽  
Internal Mass Transfer

In this study, criteria for internal mass transfer given in the literature were investigated by considering tortuosity (τ) in the porous catalysts. Uncertainties in τ, which may have values between 2 to 7, have a big impact on the effective diffusivity (Deff) which also affects the Thiele Modulus (Φ). Since effectiveness factor (η) is function of Φ, then the criteria given for limitations are questionable. The value of Deff, and in turn the value of Φ calculated for the τ=2 to 7. At low Φ the effects are very small, but when the Φ increases the effect becomes more pronounced. As a result, when using internal mass transfer limitations, one has to be very careful not to get trapped by the disguised kinetics, results of which may end up with disaster.

scholarly journals Methods—A Potential–Dependent Thiele Modulus to Quantify the Effectiveness of Porous Electrocatalysts

2021 ◽  
Author(s):  
Fikile Brushett ◽  
Charles Tai-Chieh Wan ◽  
Katharine Greco ◽  
Amira Alazmi ◽  
Robert M Darling ◽  
...  
Keyword(s):  
Thiele Modulus
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