Solid-Liquid Countercurrent Extractors

Plachco, Florencio P.; Krasuk, J. H.

doi:10.1021/i260035a010

Cited by 11 publications

(4 citation statements)

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“…Using draft lower than 0.5 leads to inefficient extraction, while draft higher than 2.0 leads to over dilution (Placho and Krasuk, 1970) (b) Peclet number: In completely mixed system, Peclet number is zero; while in plug flow process, the value approaches infinite (Mclenberg and Hartland, 1975). Using draft lower than 0.5 leads to inefficient extraction, while draft higher than 2.0 leads to over dilution (Placho and Krasuk, 1970) (b) Peclet number: In completely mixed system, Peclet number is zero; while in plug flow process, the value approaches infinite (Mclenberg and Hartland, 1975).…”

Section: Simulation Results: Steady-state Conditionmentioning

confidence: 99%

“…There have been many types of extractors invented for various processing tasks. Various models to explain the kinetics of extraction in this type of extractor have been developed for different cases with considerable success (Munro & Amunsen, 1950;Placho & Krasuk, 1970;Mecklenberg & Hartland, 1975;Osterberg & Sorensen, 1981;Siripatana, 1986;Schwartzberg, 1987;Gunasekaran et al, 1989;Lee and Schwartzberg, 1990;Simeonov et al, 2003). al., 2001;UPASI, 2006;Simeonov et al, 2004;and Jones, 2007).…”

Section: Introductionmentioning

confidence: 99%

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Mathematical Simulation of Solid-Liquid Diffusion in Continuous Countercurrent Extraction Process, Part I - Modeling Development

Rittirut¹,

Thongurai²,

Siripatana³

2010

International Journal of Chemical Reactor Engineering

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This work extends the development of backmixing-diffusion model by further removal of some assumptions from the previous works. The model covers for steady and unsteady state conditions in continuous countercurrent extraction and will be available for simulation purpose for reversing continuous countercurrent extractor (RCCE) in a more realistic ways, especially in beverage juice production. Solution of the modeling was carried out by numerical method, namely, an implicit finite difference. For the unsteady state condition, the Crank-Nicholson method was selected for calculation due to its stability; for the steady state one, the selected numerical method was center-difference formula with second order of magnitude of error, cooperated with Richardson's extrapolation. Matrix inversions were done by Gauss Jordan method. Considerable verification was made by assuring the accuracy and stability of numerical method for both steady and unsteady state conditions in a practical range. It was found that the solution obtained from the developed model with aforementioned numerical method compared well with the well-established analytical solution whenever they are available. Generally, the numerical solutions gave high accuracy for the steady state condition, while still being acceptable for practical purpose. * x =average solute concentration in solid phase at equilibrium condition (kg/m 3 ) * y = solute concentration in liquid phase at equilibrium condition (kg/m 3 )According to material balance equation for the differential volume, we obtain:-(solute flow rate at inlet)-(solute flow rate at outlet)-(rate of solute transferred to liquid phase) = (rate of solute accumuled in the volume)

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Section: Simulation Results: Steady-state Conditionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Mathematical Simulation of Solid-Liquid Diffusion in Continuous Countercurrent Extraction Process, Part I - Modeling Development

Rittirut¹,

Thongurai²,

Siripatana³

2010

International Journal of Chemical Reactor Engineering

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“…It is well known that the products of biological origin have variable diffusivities and therefore give rise to nonlinear problems, the solution of which, often numerical, is highly specific. According to Plachco and Krasuk (1970), there are cases when it is possible, considering adequate diffusivity, to treat these problems as linear; the results obtained compare favorably with the experimental values. This must be considered as a first approximation to the solution of the problem.…”

Section: Introductionmentioning

confidence: 54%

“…It should be noted that wif appears in the demensionless terms defined by (7). This value is unknown a priori, but as shown by Munro and Amundson (1950), Kitaev et al (1967), Plachco and Krasuk (1970), and Plachco and Lago (1972), in countercurrent arrangements, it is possible to solve for it with an overall mass balance.…”

Section: Modelmentioning

confidence: 99%

Solid-Liquid Extraction in Countercurrent Cascade with Retention of Liquid by the Solid Spherical Geometry Constant Diffusivity

Plachco¹,

Lago²

1976

Ind. Eng. Chem. Proc. Des. Dev.

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The analytical solution and the method of calculation are presented for a cascade of N perfectly mixed batch extractors operating countercurrently. The solid is assumed to have spherical geometry and to retain solvent on its surface when passing from one extractor to the next. The results obtained, assuming constant diffusivity and a linear adsorption isotherm, are presented in dimensionless plots for direct use in design; N varies from 2 through 10. * * ***** * * aThe asterisks indicate that under these conditions the desired extraction cannot be obtained even at Fq

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Counter‐current solid liquid extraction in a cascade of batch extractors

Plachco¹,

Lago²

1972

Can J Chem Eng

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An analytical solution and method of calculation is presented for a cascade of N perfectly mixed batch extractors operating counter-currently, for spherical solid particles, with parameters which may vary for each extractor.The results for the case of constant and equal parameters along the complete cascade are presented in dimensionless plots; N varies from 1 through 10.The practical interest of these diagrams lies in their use in design and/or in foreseeing the behavior of a cascade when its parameters undergo variations.A sample calculation is included.ounter-current solid-liquid extraction in a cascade C of batch extractors, perfectly mixed and with finite volume, is widely used because of its mechanical simplicity, good efficiency and flexibility. However, a rigorous analytical treatment of this arrangement is not to be found in the literature. Thorough bibliographical reviews of solid-liquid extraction and current design methods appear elsewhere".*'. This industrial set-up is used in the extraction of oils from oilbearing seeds, of sugar from beets, of tannin quebracho, of different soluble substances from fish, etc.In this work an analytical treatment and a method of calculation is presented which takes into consideration parameters which vary in a discrete way for each extractor. This might be important in systems which show shrinking or swelling of the solid or variations of diffusivity, the constant of the adsorption isotherm, apparent density of the solution, etc. and when a certain average for each extractor. can be assumed.It is well known that the products of biological origin present variable diffusivities and therefore constitute non-linear problems, the solution of which is often numerical and highly specific. If an adequate value of the diffusivity is taken for each extractor it is possible to obtain which agree fairly well with experimental determinations. This must be considered as a first approximation to the solution of the problem. In this present work the following assumptions are made for extractor i: 1. The diffusivity is constant. 2. The adsorption isotherm is linear. 3. The resistance to mass transfer in the film is 4. The apparent density of the solvent PI,, remains 5. The dimensions of the so'lid are constant. 6. The mixing is perfect. 7. The solid has a given size and geometry. The assumptions 2 and 3 have been ascertained negligible. constant. On prksente une solution analytigue et une methode de calcul dans le cas d'une cascade de n extracteurs pour particules solides et sphkriques parfaitement mklangh, lesqueh fouctionnent B contre-courant; les param&res peuvent varier pour chaque extracteur. (31 prksente, sous forme de diagrammes sans dimensions, les rksultats dans le cas de paramares constants et &gaux sur la cascade entiere; la valeur de n varie de 1 h 10. L'intkret pratique des dits diagrammes se trouve dans leur emploi pour un projet de conception ou pour la prkliction du comportement d'une cascade, lorsque ses paramktres subissent des variations. On prksente un calcul comme...

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Solid-Liquid Countercurrent Extractors

Cited by 11 publications

References 3 publications

Mathematical Simulation of Solid-Liquid Diffusion in Continuous Countercurrent Extraction Process, Part I - Modeling Development

Mathematical Simulation of Solid-Liquid Diffusion in Continuous Countercurrent Extraction Process, Part I - Modeling Development

Solid-Liquid Extraction in Countercurrent Cascade with Retention of Liquid by the Solid Spherical Geometry Constant Diffusivity

Counter‐current solid liquid extraction in a cascade of batch extractors

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