Derivation of Shrinking Core Model for Finite Cylinder.

Moon, Jeremy; Sahajwalla, Veena

doi:10.2355/isijinternational.41.1

Cited by 7 publications

(5 citation statements)

References 4 publications

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“…In the present case, solid carbon and gaseous oxygen serve as reactants forming carbon dioxide (by neglecting solid ash as the reaction product) Unlike for continuous models, according to the SCM, the position of the reaction site is determined by a geometrical relationship with the reaction extent X ∈ [0,1] of the solid reactant B in the particle (here for cylinder shape) where r core is the radius of the shrinking core and R is the outer radius of the reacting specimen. The combination of the flat plate and infinite cylinder solutions to form a finite cylinder is briefly described by Moon et al After simplifications discussed above, two simultaneous resistances within the overall reaction proceeding are identified: the product layer diffusion and the limited chemical reactivity. The combination is conducted in the form of a serial connection The reaction rate is further given by where d N B /d t is the molar flow rate of reactant B, carbon herein, and c Ag and c Ag eq.…”

Section: Reaction Modelmentioning

confidence: 99%

“…The combination of the flat plate and infinite cylinder solutions to form a finite cylinder is briefly described by Moon et al After simplifications discussed above, two simultaneous resistances within the overall reaction proceeding are identified: the product layer diffusion and the limited chemical reactivity. The combination is conducted in the form of a serial connection The reaction rate is further given by where d N B /d t is the molar flow rate of reactant B, carbon herein, and c Ag and c Ag eq. are the concentrations of the gaseous reactant (O 2 ) in the bulk gas flow and the equilibrium concentration at the reaction site in the particle, respectively.…”

Section: Reaction Modelmentioning

confidence: 99%

“…where r core is the radius of the shrinking core and R is the outer radius of the reacting specimen. The combination of the flat plate and infinite cylinder solutions to form a finite cylinder is briefly described by Moon et al 14 After simplifications discussed above, two simultaneous resistances within the overall reaction proceeding are identified: the product layer diffusion and the limited chemical reactivity. The combination is conducted in the form of a serial connection…”

Section: ■ Reaction Modelmentioning

confidence: 99%

“…The SCM has been utilized by many researchers for various applications such as reduction of iron oxides, , oxidation reactions, ,, dissociation of methane hydrate in porous media, CO 2 removal and capture, , or calcination . Sadrnezhaad et al investigated the oxidation mechanism of carbon in refractory bricks composed of magnesia, graphite, and phenolic resin by means of the SCM.…”

Section: Introductionmentioning

confidence: 99%

“…For the derivation of the SCM for cylindrical forms, a basic concept was taken from the valuable work of Moon et al 14 and applied to the experimental data to evaluate the model parameters: effective diffusion coefficient D e (mass transfer) and reaction rate constant k c (chemical kinetics). The temperature dependency of the parameters was described by means of the Arrhenius equation.…”

Section: ■ Introductionmentioning

confidence: 99%

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An Unreacted Shrinking Core Model Serves for Predicting Combustion Rates of Organic Additives in Clay Bricks

et al. 2020

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The present study investigates the suitability and restrictions of the unreacted shrinking core model to describe the combustion of a fixed organic substance in a clay matrix, as found in the firing process of clay bricks. The model was applied to the experimental data of isothermal measurements and validated by the model prediction of nonisothermal experiments, which were examined by combustion of mixed clay containing several organic additives in a fluidized bed combustor. Besides reactivity measurements, the shrinking core proceeding was also indicated by apparent separated phases within partially reacted clay specimens. The reaction site moves from the surface toward the inner site dividing a reacting solid into two distinct zones with different organic carbon concentrations, which was confirmed by separated analyses. Mass transfer and reactivity parameters of the model were found to be both exponentially related to temperature (Arrhenius law). The apparent chemical activation energies were determined to be 39.8−59.3 kJ/mol and, therefore, relatively small compared to literature data derived from the experimental procedure with low heating rates, but similar to values of experimental data associated with fast warming rates similar to the present investigation. The determined chemical pre-exponential factors seemed to reflect the specific surface of the organic substance incorporated in the clay matrix. The porosity of the clay samples was investigated by means of mercury intrusion porosimetry and found to be dependent on the amount of added organic substance. The porosity of the pure clay sample was 36.4%, while moderately higher values were found for mixed samples (41.0−44.2%). The effective diffusion coefficients appeared to be directly related to the portion of the total porosity generated by the organic additives. The diffusion coefficients found were around 0.002− 0.02 cm 2 /s for a temperature range of 350−650 °C, which is in the same order of magnitude as reported in comparable studies. The presented model provides an important item for the simulation of the firing process of ceramic goods in oxidizing atmospheres and explains mass transfer mechanisms evolving inside ceramic material blended with organic substances under heat exposure.

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Section: Reaction Modelmentioning

confidence: 99%

Section: Reaction Modelmentioning

confidence: 99%

Section: ■ Reaction Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: ■ Introductionmentioning

confidence: 99%

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An Unreacted Shrinking Core Model Serves for Predicting Combustion Rates of Organic Additives in Clay Bricks

et al. 2020

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Design of Disperse Solids by Chemical Reactions

2014

Industrial Product Design of Solids and Liquids

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Product design of Disperse Raw Materials by Chemical Reactions

Rähse¹,

Dicoi²

2010

Chemie Ingenieur Technik

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Product design of Disperse Raw Materials by Chemical ReactionsDuring the recovery and processing of materials from natural resources reactions between ground raw materials and fluid media take place. Starting materials are mineral and fossil substances, e.g., ore and coal, and renewable resources. In the physical model the particles shrink during the reaction. The design of the formed particles depends on the deposit, type and quantity of impurities, on further pre-treatments and the disperse properties of raw materials. Molten materials can be purified, doped and shaped. Otherwise, particles formed from powders, granular or fibrous materials show a completely different chemistry after the reaction, but largely kept size and shape of the starting material. Others disperse properties such as bulk density, density and flow properties, are changing by the reaction. For additional product design (cleaning, shaping) downstream processes are required. Keywords

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Derivation of Shrinking Core Model for Finite Cylinder.

Cited by 7 publications

References 4 publications

An Unreacted Shrinking Core Model Serves for Predicting Combustion Rates of Organic Additives in Clay Bricks

An Unreacted Shrinking Core Model Serves for Predicting Combustion Rates of Organic Additives in Clay Bricks

Design of Disperse Solids by Chemical Reactions

Product design of Disperse Raw Materials by Chemical Reactions

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