Diffusion and reaction in a porous catalyst slab: Perturbation solutions

Cardoso, Silvana S. S.; Rodrigues, Alı́rio E.

doi:10.1002/aic.11009

Cited by 9 publications

(10 citation statements)

References 14 publications

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“…For an exothermic reaction the maximum temperature and the minimum concentration occur at The maximum temperature is hence given by In the limit Pe h → 0, i.e. for a highly conductive catalyst material, which is consistent with previously known results for a diffusive and reactive system without convection 19. And, finally, in the limit Pe h → ∞, i.e.…”

Section: Theorysupporting

confidence: 88%

“…The O (1) problem is the same as setting ε = 0 in the original equations, i.e., a diffusive and convective system with no reaction, and has solution The O (ε) problem yields the perturbation functions Thus, the two‐term expansions for c ( x ) and T ( x ) are In the diffusive limit Pe m , Pe h → 0, i.e. when convection becomes negligible compared to diffusion, solutions 21 reduce to previously known perturbation solutions for a system with only diffusion and reaction 19…”

Section: Theorymentioning

confidence: 98%

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Convection, diffusion and reaction in a nonisothermal, porous catalyst slab

Cardoso

Rodrigues

2007

AIChE Journal

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in Wiley InterScience (www.interscience.wiley.com).The problem of simultaneous convection, diffusion and reaction inside a porous catalyst slab is considered. A combination of perturbation and integral mathematical techniques are used to derive approximate analytical solutions for the concentration and temperature profiles, as well as for the maximum temperature and the effectiveness factor, for a first order, nonisothermal reaction. Three regimes of operation are characterized: regime I, in which convection and diffusion are dominant (small Thiele modulus); regime II, in which diffusion and reaction are dominant (large Thiele modulus); and regime III, in which convection and reaction dominate (intermediate Thiele modulus). Our analytical solutions for each of these regimes are validated by comparison with previous results from numerical simulations.

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Section: Theorysupporting

confidence: 88%

Section: Theorymentioning

confidence: 98%

Convection, diffusion and reaction in a nonisothermal, porous catalyst slab

Cardoso

Rodrigues

2007

AIChE Journal

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“…A variação da composição química das paredes dos poros, combinadaà relação entre aárea superficial e o volume do espaço poroso, definem para cada uma dessas amostras diferentes propriedades de catálise [29,30].…”

Section: Próximos Passosunclassified

Processo para produção e caracterização de rochas sintéticas com porosidade controlada para aplicações em Petrofísica por RMN de alto e baixo campo.

Chencarek

Correia

Nascimento

et al. 2018

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Resumo: Neste trabalho apresentamos uma metodologia para a produção de amostras de rochas sintéticas, a partir da sinterização de microesferas de vidro tipo soda-cal, para a realização de um estudo sistemático dos tempos de relaxação em RMN de alto e baixo campo, e aplicações em Petrofísica. Através do controle do intervalo de tamanhos das microesferas, e da calibração do protocolo de tratamento térmico, quatro tipos de amostras de rocha sintética, de mesma mineralogia, foram produzidos com diferentes valores de permeabilidade, em dois padrões de tamanhos utilizados na indústria. Imagens de microscopia eletrônica de varredura e microtomografia computadorizada foram utilizadas para caracterização do nível de sinterização dos grãos e da distribuição do espaço poroso em cada uma das amostras. A caracterização química das amostras foi realizada através da técnica de EDS, para o controle mineralógico. Experimentos de relaxação longitudinal (T 1 ) em RMN de alto campo, e relaxação transversal (T 2 ) em RMN de alto e baixo campo, realizados nas amostras saturadas, mostram correlações entre os valores dos tempos de relaxação (T 1 e T 2 ) e o intervalo de tamanhos do espaço poroso das amostras. Os dados obtidos nas medidas de relaxação de RMN foram ajustados segundo os modelos de relaxação correntes na petrofísica de meios porosos.Palavras chave: RMN, rochas sintéticas, Petrofísica, meios porosos.Abstract: In this paper we present a method for production of synthetic rock samples, by sintering of soda-cal glass microspheres, to perform a systematic study of NMR relaxation times in high and low field, and Petrophysics application. By controlling the size range of the microspheres, and calibration of the thermal treatment protocol, four types of synthetic rock samples, with the same mineralogy, were produced with different values of permeability, in two standard sizes used in industry. Scanning electron microscopy and micro computed tomography images were used to characterize the grain sintering level and the porous space distribution on each sample. The chemical characterization of the samples was performed by EDS technique for mineralogy control. Longitudinal relaxation experiments (T 1 ) in high field NMR, and transverse relaxation (T 2 )

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“…As opposed to the situation of uniform poisoning, wherein after rescaling a new Thiele modulus was defined (see Concentration Profile Section under Uniform Poisoning-Model, Results and Discussion Section), this is not possible for the case of progressive poisoning because a new length scale is introduced in the boundary conditions, as defined in Equation (12).…”

Section: Concentration Profilesmentioning

confidence: 99%

“…In addition, it is assumed that the site that becomes poisoned reverts to complete inactivity. The methodology herein developed for the case study shown can afterwards be extended to other geometries or commercial pellet shapes, [11] to non-isothermal particles where energy equations also have to be accounted for [12] or even to large-pore catalysts where intraparticle convection needs to be considered. [13,14]…”

Section: Introductionmentioning

confidence: 99%

Revisiting the concepts of competition between reaction and diffusion in poisoned catalysts

Madeira

Rodrigues

2012

Can J Chem Eng

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The competition between diffusion and first-order irreversible reaction in poisoned catalysts is revisited. Two cases are considered for isothermal slab catalysts: uniform and shell-progressive (or pore-mouth) poisoning. Analytical concentration profiles are derived, and the implications on catalyst performance are evaluated in different regimes (chemical-or diffusion-controlled) for different levels of poisoning. It was found that depending on the poisoning mechanism, the activity decay can be more or less pronounced. Being of particular concern is the pore-mouth poisoning at high Thiele modulus, conditions under which catalyst performance is drastically affected. The reagent concentration profiles allowed the explanation of the phenomena occurring at the particle scale, in particular the effectiveness factors, observed reaction rates, and poisoning factors' dependence on the Thiele modulus and fraction of the poisoned catalyst; it was found that such relationships are dependent on the mechanism of deactivation.

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Diffusion and reaction in a porous catalyst slab: Perturbation solutions

Cited by 9 publications

References 14 publications

Convection, diffusion and reaction in a nonisothermal, porous catalyst slab

Convection, diffusion and reaction in a nonisothermal, porous catalyst slab

Processo para produção e caracterização de rochas sintéticas com porosidade controlada para aplicações em Petrofísica por RMN de alto e baixo campo.

Revisiting the concepts of competition between reaction and diffusion in poisoned catalysts

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