A computational model for predicting and correlating the behavior of fixed‐bed reactors: I. Derivation of model for nonreactive systems

Deans, H.A.; Lapidus, Leon

doi:10.1002/aic.690060428

Cited by 158 publications

(61 citation statements)

References 5 publications

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“…are shown as smoothed data in Figure 12. The point values of mass diffusivity [Or ( T " ) ] were calculated from the concentration, velocity and temperature data using Equation (10). An analysis of the data and computational scheme (see Appendix) showed that the calculation of D, (r') should be performed only for…”

Section: Concentration and Mass Diffusivity Resultsmentioning

confidence: 99%

“…These results demonstrate that the numerical procedure has the greatest deviation at the center of the bed and near the edges. This is expected since the denominator of Equation (10) approaches zero in these regions.…”

Section: Appendix: Error Analysismentioning

confidence: 89%

“…Equation ( 6 ) where the pn are the roots of Equation ( A 3 ) was used to generate concentration profiles for various values of 01 = D~, D . This data was then analyzed by the numerical scheme that was devised for the evaluation of Equation (10) and the resulting values of D,(r*) compared with the theoretical value that had been used to generate the data. The entire process was repeated twice with random error of 0 to 10% and 0 to 20% being added to the concentration values.…”

Section: Appendix: Error Analysismentioning

confidence: 99%

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Thermal and material transport in nonisothermal packed beds

Schertz

Bischoff

1969

AIChE Journal

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T e x a sThe turbulent transport of mass, energy, and momentum was studied in a 4 in. diameter cylindrical column packed with 0.3 in. diameter stoneware spheres. Helium was used as a tracer material, with air as the mainstream fluid. The concentration of tracer present, the temperature, and the velocity of the gas were measured a t several axial and radial increments.These data were analyzed numerically to obtain the radial component of the effective thermal conductivity and the radial component of the mass-dispersion coefficient as functions of radial position. Experimental conditions covered isothermal determinations a t room temperature and nonisothermal determinations in which a temperature gradient was established in the radial direction. Significant differences were found between the isothermal and strong13 nonisothermal results, primarily for the velocity profiles and thermal conductivities. Correlations were developed for the local values of the parameters.Heat and mass transfer in packed beds is important in many ways in the chemical industry. Some examples of the use of packed beds are catalytic reactors, chromatographic reactors, ion exchange columns, and contacting towers. The objective of this study was to obtain correlations of the point values of eddy thermal conductivity and mass dispersion coefficients in a nonisothermal system in terms of the physical properties of the packed bed and the fluid flowing through it.Considerable data has been reported in the literature concerning the prediction of temperatures and concentrations in packed bed reactors (1 through 9). Much of the effort has utilized the procedure of writing differential mass and energy balances on the reactor, assuming that the packed bed could be treated as a continuum, although alternate methods have also been used (I 0, 11 ) . The resulting differential equations were then simplified by various assumptions to yield equations that could be solved analytically. Results from computations of this type have been useful tools, but have not been completely successful in predicting the performance of actual reactors (1 ) . The next level of sophistication was to solve the partial differential equations by numerical methods using high speed computers. This allowed Richardson and Fahien ( 1 2 ) , for example, to use varying values for the bed properties in calculations of reactor behavior. However, they found that various assumptions utilizing mean value correlations for varying local values gave poor comparison with measured reactor data.Ideally, one would like the values of the mass and heat transfer dispersion coefficients to be as representative of the real case as possible. In other words, if these parameters are dependent upon temperature level, concentration, position, velocity, etc., knowledge of this dependence is desired so that the most accurate values may be used in design calculations. Yagi and Kunii ( 1 3 ) measured effective values of thermal conductivity, and also used values reported by other investigators (1 4 through 19) t...

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Section: Concentration and Mass Diffusivity Resultsmentioning

confidence: 99%

Section: Appendix: Error Analysismentioning

confidence: 89%

Section: Appendix: Error Analysismentioning

confidence: 99%

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Thermal and material transport in nonisothermal packed beds

Schertz

Bischoff

1969

AIChE Journal

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“…There have been a few dynamic model calculations leaving in all the accumulation time-derivative terms: cell models- Batke et al [1957], Deans and Lapidus (1960), C, = 0.7, McGuire and Lapidus (196S), C, = 0.5; plug flow models- Feick and Quon (1970), C, = 0.5, Waede Hansen et al (1971), C, = 0.02, and Stewart and SIdrensen (1972), C, = 0.0002. Liu and Amundson (1963) neglected the accumulation terms for the fluid mass balance and fluid and particle energy balance.…”

Section: Review Of Literaturementioning

confidence: 99%

Transient modeling of a catalytic converter to reduce nitric oxide in automobile exhaust

Ferguson

Finlayson

1974

AIChE Journal

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Mathematical models m e developed to study the catalytic reduction of nitric oxide contained in $utomobile exhaust in which the temperature, flow rate, and concentrations of various species vary widely with time. The quasi-static approximatio$ is compared to the fully dynamic model. In the quasi-static model all prQcesses are steady state except for the solid temperature and inlet condiGons. Suggestions are given for deciding a priori if the quasi-static model is appropriate. Suggestions are also given for integrating the quasi-sta6c equations in order to minimize errors compared to the dynamic model. The exhaust gas from an automobile contains nitric oxide which must be reduced to nitrogen in order to meet Federal pollution standards. The problem is compIicated because the temperaturg, flow rate, and concentrations of different species vary in time over wide ranges. We develop transient ma*ematical models for a catalytic muffler applicable to this situation. The mathematical model is then used to examine the performance of three different catalysts.The inIet conditions correspond to those encountered when an automobile is operated in the Federal Test Procedure. The automobili: begins cold, and as it operates the catalyst bed graduglly warms up. The one feature of interest is to compare aatalysts having different properties so that they warm up at different rates. Furthermore, as the automobile changes driving modes the exhaust properties (or their time rates of change) may change discontinuously.The mathematical npodels employ a mixing-cell model for the packed bed aqd consider the reduction of nitric oxide with two catalyFic reactions. The reaction rate of nitric oxide with carb+ monoxide is closely coupled with the reaction rate of qitric oxide with hydrogen because nitric oxide is reacted essentially completely inside the catalyst. Thus one new feature of this model is the inability to construct pl@ts of effectiveness factor vs. Thiele modulus a priori, due )to the coupling of the two reaction rates. Rather, the problem of diffusion and reaction inside the catalyst pellet must be solved at each time for each mixing cell, and the orthogonal collocation method is used to do this efficiently.Three models are developed. The main model employs the quasi-static approximation which recognizes that the time response of the system is governed by the thermal response of the packing. All other processes are assumed to occur so fast that they are essentially steady state. A dynamic model is also used to test the conditions under which the quasi-static model is inappropriate. In the dynamic model all processes are allowed to be transient. Due to the wide difference in time constants for the system, the dynamic model leads to stiff ordinary differential equations, which necessitate small integration time steps. The comparison of the two models is interesting because the quasi-static model is frequently used but seldom tested. An even simpler model results when, in the quasistatic model, the reaction rate expression is assu...

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“…This is also depicted in Figure 2. A similar analysis has been applied to a reactor system by Deans and Lapidus (6).…”

Section: Formulation Of the Problemmentioning

confidence: 98%

Adsorption dynamics of nonisothermal systems with nonlinear isotherms

Ahn

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A computational model for predicting and correlating the behavior of fixed‐bed reactors: I. Derivation of model for nonreactive systems

Cited by 158 publications

References 5 publications

Thermal and material transport in nonisothermal packed beds

Thermal and material transport in nonisothermal packed beds

Transient modeling of a catalytic converter to reduce nitric oxide in automobile exhaust

Adsorption dynamics of nonisothermal systems with nonlinear isotherms

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