An improved version of the rate equation for molecular diffusion in a dispersed phase

Jury, Stanley H.

doi:10.1002/aic.690130617

Cited by 29 publications

(6 citation statements)

References 2 publications

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“…The leading term of the approximation is of the LDF form, with a coefficient of K=15 (Glueckauf, 1955). Frequency analysis of the diffusion equation (Jury, 1967) confirms these results at slow modulation. Recently, Kim (1989) has extended the formal derivation to obtain a masstransfer law based on second-order truncation, which extends the region of validity to moderate rates of mass transfer.…”

Section: Introductionsupporting

confidence: 71%

Memory‐integral mass‐transfer models for adsorption process simulation

Harriott

1993

AIChE Journal

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The memory integral based on convolution of the unit step response to loading a clean pellet with concentration history at the pellet surface is proposed for computations of mass transfer in adsorption process simulation. Although rate laws are widely used to describe diffusion and sorption in pellets for slow ( Glueckauf, 1955) and moderate (Kim, 1989) rates of mass transfer, these models fail to describe mass transfer at short contact times because the concentration history experienced by the pellet is not accounted for. To facilitate memory integral computations, approximations to the unit step response to loading a clean pellet are derived based on a single moving finite element and by asymptotic matching in time. Numerical evaluation of the memory integral is demonstrated on simple cycles which show the merits of this approach.

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Section: Introductionsupporting

confidence: 71%

Memory‐integral mass‐transfer models for adsorption process simulation

Harriott

1993

AIChE Journal

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“…A number of authors have approximated diffusion in solids obeying Fick's law by a kinetic expression similar to that of the film model. One version of such kinetic model may be expressed in terms of the solid phase concentration difference (Glueckauf, 1955; Jury, 1967; Hsieh, 1974), given by…”

Section: €-+U-and + P : = Omentioning

confidence: 99%

Optimal design of multistage adsorption‐bed systems

1979

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The operation of two arrangements of multistage adsorption beds, parallel and series, was analyzed, and the optimal design problem of minimizing the capital and operating costs of the multistage adsorption bed systems was formulated. Solution of the optimization problem was obtained by using the Fibonacci search scheme. For the purpose of the study, data on the adsorption of liquid on activated carbon were taken from the literature for both single solute and multisolute adsorption systems and was used to derive the expressions for adsorption rate and the equilibrium relationship. Details of the performance of the optimally designed multistage adsorption bed systems are presented in terms of the physical and design parameters.

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“…Equilibrium coefficients were obtained from Perry's Chemical Engineers' Handbook for 8% cross-linked divinyl benzene cationexchange resin (Levan and Carta, 2008). Mass transfer coefficients for regeneration and for the softening cycle were initially estimated by the relationships described by Jury (1967) and Kataoka et al (1973), respectively. Mass transfer coefficients were then adjusted to fit the experimental data.…”

Section: Resultsmentioning

confidence: 99%

Brine Reuse in Ion‐Exchange Softening: Salt Discharge, Hardness Leakage, and Capacity Tradeoffs

Flodman

Dvorak

2012

Water Environment Research

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Ion-exchange water softening results in the discharge of excess sodium chloride to the aquatic environment during the regeneration cycle. In order to reduce sodium chloride use and subsequent discharge from ion-exchange processes, either brine reclaim operations can be implemented or salt application during regeneration can be reduced. Both result in tradeoffs related to loss of bed volumes treated per cycle and increased hardness leakage. An experimentally validated model was used to compare concurrent water softening operations at various salt application quantities with and without the direct reuse of waste brine for treated tap water of typical midwestern water quality. Both approaches were able to reduce salt use and subsequent discharge. Reducing salt use and discharge by lowering the salt application rate during regeneration consequently increased hardness leakage and decreased treatment capacity. Single or two tank brine recycling systems are capable of reducing salt use and discharge without increasing hardness leakage, although treatment capacity is reduced. Water Environ. Res., 84, 535 (2012).

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An improved version of the rate equation for molecular diffusion in a dispersed phase

Cited by 29 publications

References 2 publications

Memory‐integral mass‐transfer models for adsorption process simulation

Memory‐integral mass‐transfer models for adsorption process simulation

Optimal design of multistage adsorption‐bed systems

Brine Reuse in Ion‐Exchange Softening: Salt Discharge, Hardness Leakage, and Capacity Tradeoffs

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