Artificial Neural Network (FFBP-ANN) Based Grey Relational Analysis for Modeling Dyestuff Solubility in Supercritical CO2 with Ethanol as the Co-Solvent

Document Type : Research Article


Department of Biotechnology, M S. Ramaiah Institute of Technology.


The research on dye solubility modeling in supercritical carbon dioxide is gaining prominence over the past few decades. A simple and ubiquitous model that is capable of accurately predicting the solubility in supercritical carbon dioxide would be invaluable for industrial and research applications. In this study, we present such a model for predicting dye solubility in supercritical carbon dioxide with ethanol as the co-solvent for a qualitatively diverse sample of eight dyes. A feed forward back propagation - artificial neural network model based on Levenberg-Marquardt algorithm was constructed with seven input parameters for solubility prediction, the network architecture was optimized to be [7-7-1] with mean absolute error, mean square error, root mean square error and Nash-Sutcliffe coefficient to be 0.026, 0.0016, 0.04 and 0.9588 respectively. Further, Pearson-product moment correlation analysis was performed to assess the relative importance of the parameters considered in the ANN model. A total of twelve prevalent semiempirical equations were also studied to analyze their efficiency in correlating to the solubility of the prepared sample. Mendez-Teja model was found to be relatively efficient with root mean square error and mean absolute error to be 0.094 and 0.0088 respectively. Furthermore, Grey relational analysis was performed and the optimum regime of temperature and pressure were identified with dye solubility as the higher the better performance characteristic. Finally, the dye specific crossover ranges were identified by analysis of isotherms and a strategy for class specific selective dye extraction using supercritical CO2 extraction process is proposed.


Main Subjects

[1] H. Kamali, H.S. Ghaziaskar, Pressurized hot water  extraction of benzoic acid and phthalic anhydride from petrochemical wastes using a modified supercritical fluid extractor and a central composite design for optimization, J. Supercrit. Fluids. 54 (2010) 16–21. doi:10.1016/j.supflu.2010.04.002.
[2] A. Natolino, C. Da Porto, Supercritical carbon dioxide extraction of pomegranate (Punica granatum L.)seed oil: Kinetic modelling and solubility evaluation, J. Supercrit. Fluids. 151 (2019) 30–39. doi:10.1016/j.supflu.2019.05.002.
[3] J. Yan, L.J. Zheng, B. Du, Y.F. Qian, F. Ye, Dye solubility in supercritical carbon dioxide fluid, Therm. Sci. 19 (2015) 1311–1315. doi:10.2298/TSCI1504311Y.
[4] K.C. Pitchaiah, K. Sujatha, J. Deepitha, S. Ghosh, N. Sivaraman, Recovery of uranium and plutonium from pyrochemical salt matrix using supercritical fluid extraction, J. Supercrit. Fluids. 147 (2019) 194–204. doi:10.1016/j.supflu.2018.10.015.
[5] F.P. Lucien, N.R. Foster, Solubilities of solid mixtures in supercritical carbon dioxide: A review, J. Supercrit. Fluids. 17 (2000) 111–134. doi:10.1016/S0896-8446(99)00048-0.
[6] F. Gharagheizi, A. Eslamimanesh, A.H. Mohammadi, D. Richon, Representation/Prediction of solubilities of pure compounds in water using artificial neural network-group contribution method, J. Chem. Eng. Data. 56 (2011) 720–726. doi:10.1021/je101061t.
[8] J. Schmidhuber, Deep Learning in neural networks: An overview, Neural Networks. 61 (2015) 85–117. doi:10.1016/j.neunet.2014.09.003.
[9] S. Foorginezhad, M.Z.-D.A. WATER,  undefined 2019, Preparation of low-cost ceramic membranes using Persian natural clay and their application for dye clarification, Deswater.Com. (n.d.). (accessed March 7, 2020).
[10] G.S. Shankarling, K.J. Jarag, Laser dyes, Resonance. 15 (2010) 804–818. doi:10.1007/s12045-010-0090-9.
[11] U.N. Yadav, G.S. Shankarling, Synergistic effect of ultrasound and deep eutectic solvent choline chloride-urea as versatile catalyst for rapid synthesis of β-functionalized ketonic derivatives, J. Mol. Liq. 195 (2014) 188–193. doi:10.1016/j.molliq.2014.02.016.
[12] R. Tabaraki, T. Khayamian, A.A. Ensafi, Wavelet neural network modeling in QSPR for prediction of solubility of 25 anthraquinone dyes at different temperatures and pressures in supercritical carbon dioxide, J. Mol. Graph. Model. 25 (2006) 46–54. doi:10.1016/j.jmgm.2005.10.012.
[13] R. Tabaraki, T. Khayamian, A.A. Ensafi, Solubility prediction of 21 azo dyes in supercritical carbon dioxide using wavelet neural network, Dye. Pigment. 73 (2007) 230–238. doi:10.1016/j.dyepig.2005.12.003.
[14] A. Khazaiepoul, M. Soleimani, S. Salahi, Solubility prediction of disperse dyes in supercritical carbon dioxide and ethanol as co-solvent using neural network, Chinese J. Chem. Eng. 24 (2016) 491–498. doi:10.1016/j.cjche.2015.11.027.
[15] K. Mishima, K. Matsuyama, H. Ishikawa, K.I. Hayashi, S. Maeda, Measurement and correlation of solubilities of azo dyes and anthraquinone in supercritical carbon dioxide, Fluid Phase Equilib. 194–197 (2002) 895–904. doi:10.1016/S0378-3812(01)00720-8.
[16] K. Tamura, T. Shinoda, Binary and ternary solubilities of disperse dyes and their blend in supercritical carbon dioxide, Fluid Phase Equilib. 219 (2004) 25–32. doi:10.1016/j.fluid.2004.01.009.
[17] A. Ferri, M. Banchero, L. Manna, S. Sicardi, An experimental technique for measuring high solubilities of dyes in supercritical carbon dioxide, J. Supercrit. Fluids. 30 (2004) 41–49. doi:10.1016/S0896-8446(03)00114-1.
[18] C.L. Cui, W. Shi, J.J. Long, Solubility and data correlation of a reactive disperse dye in a quaternary system of supercritical carbon dioxide with mixed cosolvents, J. Taiwan Inst. Chem. Eng. 91 (2018) 213–223. doi:10.1016/j.jtice.2018.06.028.
[19]         T. Funazukuri, T. Yamasaki, M. Taguchi, C.Y. Kong, Measurement of binary diffusion coefficient and solubility estimation for dyes in supercritical carbon dioxide by CIR method, Fluid Phase Equilib. 420 (2016) 7–13. doi:10.1016/j.fluid.2016.01.010.
[20]         E. Bach, E. Cleve, J. Schuttken, E. Schollmeyer, J.W. Rucker, Correlation of solubility data of azo disperse dyes with the dye uptake of poly(ethylene terephthalate) fibres in supercritical carbon dioxide, Color. Technol. 117 (2001) 13–18. doi:10.1111/j.1478-4408.2001.tb00329.x.
[21]         D. Julong, Introduction to Grey System Theory, J. Grey Syst. 1 (1989) 1–24.
[22]         P. Ertl, B. Rohde, P. Selzer, Fast calculation of molecular polar surface area as a sum of fragment-based contributions and its application to the prediction of drug transport properties, J. Med. Chem. 43 (2000) 3714–3717. doi:10.1021/jm000942e.
[23]         E.W. Lemmon, M.O. McLinden,  and D.G. Friend, NIST Chemistry WebBook, NIST Standard Reference Database, 2017. doi:10.18434/T4D303.
[24]         J. Fasihi, Y. Yamini, F. Nourmohammadian, N. Bahramifar, Investigations on the solubilities of some disperse azo dyes in supercritical carbon dioxide, Dye. Pigment. 63 (2004) 161–168. doi:10.1016/j.dyepig.2004.01.007.
[25]         M. Banchero, A. Ferri, L. Manna, S. Sicardi, Solubility of disperse dyes in supercritical carbon dioxide and ethanol, Fluid Phase Equilib. 243 (2006) 107–114. doi:10.1016/j.fluid.2006.02.010.
[26]         H. Do Sung, J.J. Shim, Solubility of C. I. Disperse Red 60 and C. I. Disperse Blue 60 in supercritical carbon dioxide, J. Chem. Eng. Data. 44 (1999) 985–989. doi:10.1021/je990018t.
[27]         P. Muthukumaran, R.B. Gupta, H. Do Sung, J.J. Shim, H.K. Bae, Dye solubility in supercritical carbon dioxide. Effect of hydrogen bonding with cosolvents, Korean J. Chem. Eng. 16 (1999) 111–117. doi:10.1007/BF02699013.
[28]         C.C. Tsai, H. mu Lin, M.J. Lee, Solubility of disperse yellow 54 in supercritical carbon dioxide with or without cosolvent, Fluid Phase Equilib. 260 (2007) 287–294. doi:10.1016/j.fluid.2007.07.070.
[29]         B. Pavlić, L. Pezo, B. Marić, L.P. Tukuljac, Z. Zeković, M.B. Solarov, N. Teslić, Supercritical fluid extraction of raspberry seed oil: Experiments and modelling, J. Supercrit. Fluids. 157 (2020). doi:10.1016/j.supflu.2019.104687.
[30]         M.M. Mukaka, Statistics Corner: A guide to appropriate use of Correlation coefficient in medical research, Malawi Med. J. 24 (2012) 69–71. doi:10.1016/j.cmpb.2016.01.020.
[31]         J. Chrastil, Solubility of solids and liquids in supercritical gases, J. Phys. Chem. 86 (1982) 3016–3021. doi:10.1021/j100212a041.
[32]         S.K. Kumar, K.P. Johnston, Modelling the solubility of solids in supercritical fluids with density as the independent variable, J. Supercrit. Fluids. 1 (1988) 15–22. doi:10.1016/0896-8446(88)90005-8.
[33]         A. Jouyban, A. Fathi-Azarbayjani, M. KhoubnasabjafariC, W.E. Acree Jrd, Mathematical representation of the density of liquid mixtures at various temperatures using Jouyban-Acree model, 2005. (accessed March 6, 2020).
[34]         J. Mendez-Santiago, A.S. Teja, Solubility of solids in supercritical fluids: Consistency of data and a new model for cosolvent systems, Ind. Eng. Chem. Res. 39 (2000) 4767–4771. doi:10.1021/ie000339u.
[35]         C. Garlapati, G. Madras, New empirical expressions to correlate solubilities of solids in supercritical carbon dioxide, Thermochim. Acta. 500 (2010) 123–127. doi:10.1016/j.tca.2009.12.004.
[36]         S. Jafari Nejad, H. Abolghasemi, M.A. Moosavian, M.G. Maragheh, Prediction of solute solubility in supercritical carbon dioxide: A novel semi-empirical model, Chem. Eng. Res. Des. 88 (2010) 893–898. doi:10.1016/j.cherd.2009.12.006.
[37]         K. Keshmiri, A. Vatanara, Y. Yamini, Development and evaluation of a new semi-empirical model for correlation of drug solubility in supercritical CO2, Fluid Phase Equilib. 363 (2014) 18–26. doi:10.1016/j.fluid.2013.11.013.
[38]         M. Asgarpour Khansary, F. Amiri, A. Hosseini, A. Hallaji Sani, H. Shahbeig, Representing solute solubility in supercritical carbon dioxide: A novel empirical model, Chem. Eng. Res. Des. 93 (2015) 355–365. doi:10.1016/j.cherd.2014.05.004.
[39]         X.Q. Bian, Q. Zhang, Z.M. Du, J. Chen, J.N. Jaubert, A five-parameter empirical model for correlating the solubility of solid compounds in supercritical carbon dioxide, Fluid Phase Equilib. 411 (2016) 74–80. doi:10.1016/j.fluid.2015.12.017.
[40]         G. Sodeifian, S.M. Hazaveie, S.A. Sajadian, N. Saadati Ardestani, Determination of the Solubility of the Repaglinide Drug in Supercritical Carbon Dioxide: Experimental Data and Thermodynamic Modeling, J. Chem. Eng. Data. (2019). doi:10.1021/acs.jced.9b00550.
[41]         D.L. Sparks, L.A. Estévez, R. Hernandez, K. Barlow, T. French, Solubility of nonanoic (pelargonic) acid in supercritical carbon dioxide, J. Chem. Eng. Data. 53 (2008) 407–410. doi:10.1021/je700465u.
[42]         S. Dharmalingam, R. Subramanian, K. Somasundara Vinoth, B. Anandavel, Optimization of tribological properties in aluminum hybrid metal matrix composites using gray-taguchi method, J. Mater. Eng. Perform. 20 (2011) 1457–1466. doi:10.1007/s11665-010-9800-4.
[43]         F. Gharagheizi, A. Eslamimanesh, A.H. Mohammadi, D. Richon, Artificial neural network modeling of solubilities of 21 commonly used industrial solid compounds in supercritical carbon dioxide, Ind. Eng. Chem. Res. 50 (2011) 221–226. doi:10.1021/ie101545g.
[44]         A. Aminian, Estimating the solubility of different solutes in supercritical CO2 covering a wide range of operating conditions by using neural network models, J. Supercrit. Fluids. 125 (2017) 79–87. doi:10.1016/j.supflu.2017.02.007.
[45] S.K. Jha, G. Madras, Neural network modeling of adsorption equilibria of mixtures in supercritical fluids, Ind. Eng. Chem. Res. 44 (2005) 7038–7041. doi:10.1021/ie049010p.
[46] J.J. Montaño, A. Palmer, Numeric sensitivity analysis applied to feedforward neural networks, Neural Comput. Appl. 12 (2003) 119–125. doi:10.1007/s00521-003-0377-9.
[47] G.D. Garson, Interpreting neural-network connection weights, (1991).
[48] B. Suryawanshi, B. Mohanty, Application of an artificial neural network model for the supercritical fluid extraction of seed oil from Argemone mexicana (L.) seeds, Ind. Crops Prod. 123 (2018) 64–74. doi:10.1016/j.indcrop.2018.06.057.
[49] N.R. Foster, G.S. Gurdial, J.S.L. Yun, K.K. Liong, K.D. Tilly, S.S.T. Ting, H. Singh, J.H. Lee, Significance of the Crossover Pressure in Solid-Supercritical Fluid Phase Equilibria, (1991) 1955–1964.
[50] K. Ongkasin, M. Sauceau, Y. Masmoudi, J. Fages, E. Badens, Solubility of cefuroxime axetil in supercritical CO2: Measurement and modeling, J. Supercrit. Fluids. 152 (2019) 104498. doi:10.1016/j.supflu.2019.03.010.
[51] G. Madras, C. Kulkarni, J. Modak, Modeling the solubilities of fatty acids in supercritical carbon dioxide, Fluid Phase Equilib. 209 (2003) 207–213. doi:10.1016/S0378-3812(03)00148-1.
[52] F. Esmaeilzadeh, I. Goodarznia, Supercritical  Extraction of Phenanthrene in the Crossover Region, (2005) 49–51