Mathematical Modeling of Reactive Extraction of Solute from Slab Solid Material

https://doi.org/10.22146/ijc.47181

Indah Hartati(1), Hary Sulistyo(2), Wahyudi Budi Sediawan(3*), Muhammad Mufti Azis(4), Moh Fahrurrozi(5)

(1) Department of Chemical Engineering, Faculty of Engineering, Universitas Gadjah Mada, Jl. Grafika No. 2, Yogyakarta 55281, Indonesia Department of Chemical Engineering, Faculty of Engineering, Universitas Wahid Hasyim, Jl. Menoreh Tengah X No. 22, Semarang 50236, Central Java, Indonesia
(2) Department of Chemical Engineering, Faculty of Engineering, Universitas Gadjah Mada, Jl. Grafika No. 2, Yogyakarta 55281, Indonesia
(3) Department of Chemical Engineering, Faculty of Engineering, Universitas Gadjah Mada, Jl. Grafika No. 2, Yogyakarta 55281, Indonesia
(4) Department of Chemical Engineering, Faculty of Engineering, Universitas Gadjah Mada, Jl. Grafika No. 2, Yogyakarta 55281, Indonesia
(5) Department of Chemical Engineering, Faculty of Engineering, Universitas Gadjah Mada, Jl. Grafika No. 2, Yogyakarta 55281, Indonesia
(*) Corresponding Author

Abstract


Reactive extraction is gaining higher attention due its wide application in various solute separation processes. Here, a mathematical model of reactive extraction in slab has been proposed. The model was developed by considering simultaneous processes of active compound intra particle diffusion, second order elemental reaction of solute-active compound, and intra-particle product diffusion. The obtained partial differential equations (PDEs) were solved using Finite Difference Approximation (FDA) method by using realistic parameters. Concentration profile as well as product yield were evaluated as a function of time. As a result, the model proposed here may serve as a basis design for reactive extraction unit. Sensitivity analyses was conducted to inspect the influence of slab thickness, diffusivity and reaction rate constant to the product yield. Eventually, model validation was conducted by comparing the simulation results with analytical solutions for special cases. Validation results showed that the model gave good agreement with the analytical solution.

Keywords


mathematical modeling; reactive extraction; separation; slab; simulation

Full Text:

Full Text PDF


References

[1] Sharma, S., Agarwal, G.K., and Dutta, N.N., 2019, LSER analysis of reactive extraction of Zn and Cu with bis (2-ethylhexyl) phosphate (HDEHP) in six different diluents, Sep. Sci. Technol., 54 (7), 1167–1173.

[2] Zeng, Q., Qin, H., Cheng, H., Chen, L., and Qi, Z., 2019, Development of a reactive extraction process for isobutyl isobutyrate formation intensified by bifunctional ionic liquid, Chem. Eng. Sci. X, 1, 100001.

[3] Pradhan, S., Madankar, C.S., Mohanty, P., and Naik, S.N., 2012, Optimization of reactive extraction of castor seed to produce biodiesel using response surface methodology, Fuel, 97, 848–855.

[4] Santoso, I., Buchari, Amran, M.B., and Sulaeman, A., 2007, The effect of concentration of carrier, pH and time of extraction on separation’s factor of penicillin G-phenyl acetate by reactive extraction, Indones. J. Chem., 7 (2), 185–189.

[5] Tuntiwiwattanapun, N., and Tongcumpou, C., 2018, Sequential extraction and reactive extraction processing of spent coffee grounds: An alternative approach for pretreatment of biodiesel feedstocks and biodiesel production, Ind. Crops Prod., 117, 359–365.

[6] Lu, S., Wang, L., Wang, Y., and Mi, Z., 2011, Kinetic model of gas-liquid-liquid reactive extraction for production of hydrogen peroxide, Chem. Eng. Technol., 34 (5), 823–830.

[7] Chemarin, F., Moussa, M., Chadni, M., Pollet, B., Lieben, P., Allais, F., Trelea, I.C., and Athès, V., 2017, New insights in reactive extraction mechanisms of organic acids: An experimental approach for 3-hydroxypropionic acid extraction with tri-n-octylamine, Sep. Purif. Technol., 179, 523–532.

[8] Lu, X., Zhang, D., He, S., Feng, J., Reda, A.T., Liu, C., Yang, Z., Shi, L., and Li, J., 2017, Reactive extraction of europium(III) and neodymium(III) by carboxylic acid modified calixarene derivatives: Equilibrium, thermodynamics and kinetics, Sep. Purif. Technol., 188, 250–259.

[9] Gorden, J., Zeiner, T., and Brandenbusch, C., 2015, Reactive extraction of cis,cis-muconic acid, Fluid Phase Equilib., 393, 78–84.

[10] Waghmare, M.D., Wasewar, K.L., Sonawane, S.S., and Shende, D.Z., 2013, Reactive extraction of picolinic and nicotinic acid by natural non-toxic solvent, Sep. Purif. Technol., 120, 296–303.

[11] Tang, K., Miao, J., Zhou, T., and Liu, Y., 2011, Equilibrium studies on liquid-liquid reactive extraction of phenylsuccinic acid enantiomers using hydrophilic β-CD derivatives extractants, Chin. J. Chem. Eng., 19 (3), 397–403.

[12] Chemarin, F., Moussa, M., Allais, F., Athès, V., and Trelea, I.C., 2017, Mechanistic modeling and equilibrium prediction of the reactive extraction of organic acids with amines: A comparative study of two complexation-solvation models using 3-hydroxypropionic acid, Sep. Purif. Technol., 189, 475–487.

[13] Blaga, A.C., and Malutan, T., 2012, Selective separation of vitamin C by reactive extraction, J. Chem. Eng. Data, 57 (2), 431–435.

[14] Salmi, T., Wärn, J., Mikkola, J.P., and Rönnholm, M., 2005, Modelling and simulation of porous, reactive particles in liquids: Delignification of wood, Comput. Aided Chem. Eng., 20, 325–330.

[15] Bludworth, J., and Knopf, F.C., 1993, Reactive extraction of lignin from wood using supercritical ammonia-water mixtures, J. Supercrit. Fluids, 6 (4), 249–254.

[16] Constant, S., Basset, C., Dumas, C., Di Renzo, F., Robitzer, M., Barakat, A., and Quignard, F., 2015, Reactive organosolv lignin extraction from wheat straw: Influence of Lewis acid catalysts on structural and chemical properties of lignins, Ind. Crops Prod., 65, 180–189.

[17] Sulaiman, S., Aziz, A.R.A., and Aroua, M.K., 2013, Reactive extraction of solid coconut waste to produce biodiesel, J. Taiwan Inst. Chem. Eng., 44 (2), 233–238.

[18] Thakre, N., Datta, D., Prajapati, A.K., Chaudhari, P.K., and Pal, D., 2017, Reactive extraction of citric acid using different extractants: Equilibrium, kinetics and modeling, Chem. Biochem. Eng. Q., 31 (4), 437–446.

[19] Eda, S., Borra, A., Parthasarathy, R., Bankupalli, S., Bhargava, S., and Thella, P.K., 2018, Recovery of levulinic acid by reactive extraction using tri-n-octylamine in methyl isobutyl ketone: Equilibrium and thermodynamic studies and optimization using Taguchi multivariate approach, Sep. Purif. Technol., 197, 314–324.

[20] Bora, M.M., Ghosh, A.C., Dutta, N.N., and Mathur, R.K., 1997, Reactive extraction or 6-aminopenicillanic acid with aliquat-336: Equilibrium and kinetics, Can. J. Chem. Eng., 75 (3), 520–526.

[21] Zhao, X., Wu, R., and Liu, D., 2018, Evaluation of the mass transfer effects on delignification kinetics of atmospheric acetic acid fractionation of sugarcane bagasse with a shrinking-layer model, Bioresour. Technol., 261, 52–61.

[22] Hajiha, H., and Sain, M., 2015, “The use of sugarcane bagasse fibres as reinforcements in composites” in Biofiber Reinforcements in Composite Materials, Eds. Faruk, O., and Sain, M., Woodhead Publishing Company, Cambridge, 525–549.

[23] Hemmasi, A.H., Samariha, A., Tabei, A., Nemati, M., and Khakifirooz, A., 2011, Study of morphological and chemical composition of fibers from Iranian sugarcane bagasse, Am. Eurasian J. Agric. Environ. Sci., 11 (4), 478–481.

[24] Gil, M., Teruel, E., and Arauzo, I., 2014, Analysis of standard sieving method for milled biomass through image processing. Effects of particle shape and size for poplar and corn stover, Fuel, 116, 328–340.

[25] Pirogov, B.Y., and Zelinskii, A.G., 2009, Mass transport and effective diffusion coefficient in the reduction of hydrogen ions from aqueous sulfuric acid solutions: Numerical modeling, Russ. J. Electrochem., 45 (3), 336–344.

[26] Li, W., You, L., Schaffler, M.B., and Wang, L., 2009, The dependency of solute diffusion on molecular weight and shape in intact bone, Bone, 45 (5), 1017–1023.

[27] Tolbert, A., Akinosho, H., Khunsupat, R., Naskar, A.K., and Ragauskas, A.J., 2014, Characterization and analysis of the molecular weight of lignin for biorefining studies, Biofuels, Bioprod. Biorefin., 8 (6), 836–856.

[28] Pianosi, F., Beven, K., Freer, J., Hall, J.W., Rougier, J., Stephenson, D.B., and Wagener, T., 2016, Sensitivity analysis of environmental models: A systematic review with practical workflow, Environ. Modell. Software, 79, 214–232.

[29] Nan, H.S., Dias, M.M., Lopes, J.C.B., and Rodrigues, A.E., 1996, Diffusion, convection and reaction in catalyst particles: Analogy between slab and cylinder geometries, Chem. Eng. J., 61 (2), 113–122.

[30] Fogler, H.S., 2016, Elements of Chemical Reaction Engineering, 5th Ed., Prentice Hall, New Jersey.

[31] Crank, J., 1975, The Mathematics of Diffusion, 2nd Ed., Clarendon Press, Oxford.

[32] Cussler, E.L., 2009, Diffusion: Mass Transfer in Fluid Systems, 3rd Ed., Cambridge University Press, Cambridge.



DOI: https://doi.org/10.22146/ijc.47181

Article Metrics

Abstract views : 328 | views : 355


Copyright (c) 2019 Indonesian Journal of Chemistry

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

 


Indonesian Journal of Chemistry (ISSN 1411-9420 / 2460-1578) - Chemistry Department, Universitas Gadjah Mada, Indonesia.

Web
Analytics View The Statistics of Indones. J. Chem.