Concentration distribution, effectiveness factor, and reactant exhaustion for catalytic reaction with volume change

Lin, Kan; Lih, Marshall M.

doi:10.1002/aic.690170533

Cited by 16 publications

(7 citation statements)

References 26 publications

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“…Our results for the molecular and Knudsen regimes of transport using the dusty-gas model agree exactly with analytical as well as numerical studies of others (Lin and Lih, 1971; Otani, et al, 1964;Weekman and Gorring, 1965). To our knowledge, however, effectiveness-factor behavior in the transition region has not been previously published.…”

Section: Discussionsupporting

confidence: 86%

“…In agreement with others (Lin and Lih, 1971; Weekman and Gorring, 1965) to be completely dominated by molecular diffusion under constant external pressure, the pressure parameter a for the system conditions should be greater than lo4.…”

Section: Molecular Regimesupporting

confidence: 88%

“…For systems in which mole changes occur and in which the transport of reactants and products is by ordinary molecular diffusion, the effectiveness factor has been shown to be dependent not only on the Thiele modulus but also on a volume-change parameter (Lin and Lih, 1971;Weekman and Gorring, 1965), which contains both the stoichiometric factor describing mole changes and the mole fraction of the reactant on the external surface of the pellet. Exact analytical expressions have been obtained for zero-order reactions with mole changes on the three main geometries (Lin and Lih, 1971).…”

Section: Conclusion and Significancementioning

confidence: 99%

“…Exact analytical expressions have been obtained for zero-order reactions with mole changes on the three main geometries (Lin and Lih, 1971). Higher-order reactions on all three geometries have been treated numerically over wide ranges of values for the two parameters (Weekman and Gorring, 1965); and for large values of the Thiele modulus, asymptotic analytical solutions were obtained.…”

Section: Conclusion and Significancementioning

confidence: 99%

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Reaction with mole changes in porous catalysts in the molecular, transition, and Knudsen regimes

Abed

Rinker

1973

AIChE Journal

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If a reaction with mole changes takes place isothermally in a porous catalyst, intrapellet concentration and pressure gradients can develop and mass transfer will occur by simultaneous diffusion and flow. A very useful equation for describing simuItaneous diffusion and flow in porous media is the one representing the extended dusty-gas model. It was derived by Mason et al. (1967) and independently by Gunn and King (1969). The equation contains three constants Co, C1, and Cz which characterize the porous medium and must be determined experimentally. Abed and Rinker (1973) have derived and solved numerically the equations for intrapellet pressure and composition profiles for a zero-order reaction in a porous catalyst. Since their derivation was based on the extended dusty-gas model, it is valid for all transport regimes, namely, the Knudsen, transition, and the molecular regimes. Otani et al. (1965) have also derived and solved equations for the intrapellet pressure and composition profiles in all transport regimes for a first-order reaction with mole changes. They did this by extending the validity of the simple capillary model to include porous catalysts by applying it in conjunction with the random-pore model.The main purpose of the present paper is to extend the work reported by Abed and Rinker (1973) to a consideration of first-and higher-order reactions. By following their same procedure in deriving the equations for a zero-order reaction, a set of general equations for an nth-order reaction can be obtained. To avoid redundancy, only the final results of the derivation are presented in this paper. THEORYThe case under consideration in this work is an irreversible reaction of nth-order and is given stoichiometrically byThe mole-fraction derivative for species A in dimensionless form is given by A + eB (1) dY where Y K , e, a, are dimensionless parameters; 6 is the dimensionless flux; 5' is the dimensionless pressure; and Q is given by Equation (3) :where W is given byand V is given byThe derivative of the pressure in dimensionless form is given byFinally, the continuity equation for species A in dimensionless form is as follows:The boundary conditions for Equations ( 2 ) , (6), and (7) are given by Equations (8) and (9) atwhere E is the effectiveness factor. RESULTS A N D DISCUSSIONThe numerical integration of Equations (Z), (6), and (7) with the boundary conditions (8) and ( fact for n > 1, there is no main parameter that can be held constant while showing the variation of E with OL as can be done with y M for n = O and Y K for n = 1. Figure 1 also shows that when (Y is small the effectiveness factor is independent of CY; and it reaches an asymptotic value that can be calculated byThe merging of curves in Figure 1 to the limit of E = 1 for Y K L 0.1 is simply a limitation of accuracy in plotting. In the molecular region in which CY is large, the effectiveness factor decreases with increasing CY for constant Y K . 9.ACKNOWLEDGMENT

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Section: Discussionsupporting

confidence: 86%

Section: Molecular Regimesupporting

confidence: 88%

Section: Conclusion and Significancementioning

confidence: 99%

Section: Conclusion and Significancementioning

confidence: 99%

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Reaction with mole changes in porous catalysts in the molecular, transition, and Knudsen regimes

Abed

Rinker

1973

AIChE Journal

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“…Most of the works deal with the zeroth-order reaction (Wheeler, 1951;Weekman and Gorring, 1965;Lin and Lih, 1971 …”

Section: Critical Thiele Modulusmentioning

confidence: 99%

The dead zone in a catalyst particle for fractional‐order reactions

Garcı́a-Ochoa

Salvador

1988

AIChE Journal

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Simulataneous heat and mass transfer with and without reactant exhaustion in catalyst particles for reaction with volume change

Lih

Lin

1973

AIChE Journal

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Asymptotic analytic expressions for the concentration and temperature profiles as well as effectiveness factor inside porous, thin-disk shaped catalyst particles have been developed for zeroth-order exothermic reaction with reactant-to-product volume change. The individual and combinative effects of volume-change, Thiele and thermal Thiele moduli, and of the dimensionless activation energy are discussed. As expected, the expressions revert to those for the corresponding isothermal and constant-volume cases. Errors arising from the approximation were calculated and found to be quite acceptable. MARSHALL SCOPEThe general objective of the authors' recent works has been to study the influence of volume or mole change on the mass transfer efficiency inside catalyst particles. In this paper, the heat transfer effect is and the system studied is a zeroth-order exothermic reaction which frequently occurs in industrial practice such as the hydrogenation and dehydrogenation of cyc!ic hydrocarbons. characteristic of zeroth-order reactions in exhibiting the reactant-exhaustion phenomenon which makes the interaction of heat and mass transfer highly interesting. HOWever, because of mathematical complications, the simplifying approximation of moderate temperature rise has been made. However, analysis shows that the general applicability of the result is not seriously affected. ~h~ present study is also confined to thin-disk geometry.This reaction was chosen also because of the unique The heat and transfer the film surrounding the catalyst particle is treated as a separate problem and thus not included here. CONCLUSIONS AND SIGNIFICANCEWe have developed analytic solutions for the concentration and temperature profiles as well as for the effectiveness factor for zeroth-order reaction occurring in porous, thin-disk type catalyst particles with reactant-toproduct volume change. Although an approximation was made, the error introduced is small enough to render the results useful in a large number of reaction systems, including such catalytic reactions as hydrogenation and dehydrogenation of cyclic hydrocarbons wherein the strong hydrocarbon adsorption allows the rate to be approximated by zeroth-order behavior.The results show that the effectiveness factor decreases it increases with increasing combination of the thermal Thiele modulus and dimensionless activation energy. However, the temperature profile inside the pellet does depend on the latter two factors separately. The study also confirms that when a reactant is exhausted before reaching the center of the pellet a flat temperature profile is maintained in this no-reaction central layer and the level of this temperature is a function of the thermal Thiele modulus (dimensionless heat generation-to-mass diffusion ratio) but not of the dimensionless activation energy. These dependencies and behaviors can be qualitatively applied to cylindrical and spherical particles as r re1. --with increasing volume-change modulus (expansion) while well.In a recent series of papers (Lih and Lin...

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Concentration distribution, effectiveness factor, and reactant exhaustion for catalytic reaction with volume change

Cited by 16 publications

References 26 publications

Reaction with mole changes in porous catalysts in the molecular, transition, and Knudsen regimes

Reaction with mole changes in porous catalysts in the molecular, transition, and Knudsen regimes

The dead zone in a catalyst particle for fractional‐order reactions

Simulataneous heat and mass transfer with and without reactant exhaustion in catalyst particles for reaction with volume change

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