Main Article Content

Abdallah Abdallah El Hadj
Salah Hanini
Maamar Laidi


The subject of this work is to propose a new method based on the ANFIS system and PSO algorithm to conceive a model for estimating the solubility of solid drugs in supercritical CO2 (sc-CO2). The high nonlinear process was modeled by the neuro-fuzzy approach (NFS). The PSO algorithm was used for two purposes: replacing the standard backpropagation in training the NFS and optimizing the process. The validation strategy has been carried out using a linear regression analysis of the predicted versus experimental outputs. The ANFIS approach is compared to the ANN in terms of accuracy. Statistical analysis of the predictability of the optimized model trained with a PSO algorithm (ANFIS-PSO) shows a better  agreement with the reference data than the ANN method. Furthermore, the comparison in terms of the AARD deviation (%) between the predicted results, the results predicted by the density-based models, and a set of equations of state demonstrates that the ANFIS-PSO model correlates far better with the solubility of the solid drugs in scCO2. A control strategy was also developed for the first time in the field of phase equilibrium by using the neuro-fuzzy inverse approach (ANFISi) to estimate pure component properties from the solubility data without passing through the GCM methods.

Article Details

How to Cite
Abdallah El Hadj, A., Hanini, S., & Laidi, M. (2022). NEW METHOD BASED ON NEURO-FUZZY SYSTEM AND PSO ALGORITHM FOR ESTIMATING PHASE EQUILIBRIA PROPERTIES: Scientific paper. Chemical Industry & Chemical Engineering Quarterly, 28(2), 141–150.


J.C. Rojas-Thomas, M. Mora, S. Santos, Neural Comput. Appl.31 (2019) 2311–2327.

S.K. Ashan, M.A. Behnajady, N. Ziaeifar, Neural Comput. Appl. 29 (2018) 969–979.

M. Khayet, C. Cojocaru, Desalination 308 (2013) 102–110.

B. Gülçin, G. Sezin, Energy 123 (2017) 149-163.

M. Laidi, S. Hanini, Rezrazi A, M.R. Yaiche, A. Abdallah el Hadj, F. Chellali, Theor. Appl. Climatol. 128 (2017) 439-451.

A. Abdallah El Hadj, C. Si-Moussa, S. Hanini, M. Laidi, Chem. Ind. Chem. Eng. Q. 19 (2013) 449-460.

M. Velibor, Chem. Ind. Chem. Eng. Q. 26 (2020)309−319.

Y. Jewajinda, P. Chongstitvatana, Neural Comput. Appl. 22 (2013)1609–1626.

R. Fuller, H.J. Zimmermann, in Proceedings of 2nd International Workshop on Current Issues in Fuzzy Technologies, University of Trento, Trento, May 28-30 (1993) 45-54.

A. Abdallah El Hadj, M. Laidi, C. Simoussa, S. Hanini, Neural Comput Appl. 28 (2017) 87–99.

J.W. Chen, F.N. Tsai, Fluid Phase. Equilib. 107 (1995) 189–200.

F.E. Wubbolts, O.S.L. Bruinsma, G.M. Van Rosmalen, J. Supercrit. Fluids 32 (2004) 79–87.

M. Shammsipur, F. Reza, Y. Yamini, A.R. Ghiasvand, J. Supercrit. Fluids 23 (2002) 225–231.

S. David, L.A. Estévez, J.C. Pulido, J.E. Garcia, M. Carmen, J. Chem. Eng. Data 50 (2005) 1234–1241.

M.D. Gordillo, M.A. Blanco, A. Molero, E. Martinez de la Ossa, J. Supercrit. Fluids 15 (1999) 183–190.

J.S.R. Jang, IEEE Trans. Syst. Man. Cybern. 23 (1993) 665–685.

A.R. Fallahpour, A.R. Moghassem, J. Eng. Fibers Fabr. 8 (2013) 6–18.

R. Kamali, A.R. Binesh, Microfluid. Nanofluid. 14 (2013) 575–581.

R.Babuska, Neuro-Fuzzy Methods for Modeling, In Recent Advances in Intelligent Paradigms and Applications, A. Abraham, L.C. Jain, J. Kacprzyk, Springer-Verlag, Heidelberg (2002), pp 161-186.

P. Coimbra, C.M. Duarte, H.C. de Sousa, Fluid Phase Equilib. 239 (2006) 188-199.

O. Pfohl, S. Petkov, G. Brunner, High-pressure fluid-phase equilibria containing supercritical fluids, In 8th International Conference on properties and Phase Equilibria for Product and Process Design, Noordwijkerhout, Netherlands, April 26-May (1998).

Y. Nannoolal, J. Rarey, D. Ramjugernath, Fluid Phase Equilib. 269 (2008) 117-133.

J. Marrero, R. Gani, Fluid Phase Equilib. (183-184) (2001) 183-208.

G.D. Garson, Interpreting Neural Network Connections weights, Al Expert: Miller Freeman, Inc. San Francisco (1991), p. 46.

G. Sodeifian, S.A. Sajadian, F. Razmimanesh, Fluid Phase Equilib. 25 (2017) 149-159.

P.C. Larissa, M.C. Acosta, C. Turner, J. Supercrit. Fluids 130 (2017) 381-388.

K. Tamura, R.S. Alwi, Dyes Pigm. 113 (2015) 351–356.

R.S. Alwi, T. Tanaka, K. Tamura, J. Chem. Thermodyn. 74 (2014) 119–125.

P. Coimbra, M.H. Gil, C.M.M. Duarte, B.M Heron, H.C. de Sousa, Fluid Phase Equilib. 238 (2005) 120–128.

A. Mehdi, M. Mehrdad, Z. Fatemeh, Chin. J. Chem. Eng. 22 (2014) 549–558.

G.R. Bitencourt, F.A. Cabral, A. Meirelles, J. Chem. Thermodyn. 103 (2016) 285–291.

C. Chun-Ta, L. Chen-An, T. Muoi, Y.P. Chen, J. CO2 Util. 18 (2017) 173–180.

Y. Khayyat, S.M. Kashkouli, F. Esmaeilzadeh, Fluid Phase Equilib. 399 (2015) 98–104.

M. Ota, M. Sato, Y. Sato, L.S.J. Richard, H. Inomata, J. Supercrit. Fluids 128 (2017) 166–172.

J.P. Paulaa, I.M.O. Sousab, M. Foglioc, F. Cabral, J. Supercrit. Fluids 112 (2016) 89–94.

A.G. Reveco-Chilla, A.L. Cabrera, J.C. de la Fuente, F.C. Zacconi, J.M. del Valle, L.M. Valenzuela, Fluid Phase Equilib.42 (2016) 84-92.

G. Sodeifian, S. Sajadian, N.S. Ardestani, J. Supercrit. Fluids128 (2017) 102-111.

F.C. Zacconi, O.N. Nuñez, A.L. Cabrera, L.M. Valenzuela, J.M. del Valle, J.C. de la Fuente, J. Chem. Thermodyn. 103 (2016) 325-332.

E. Potrich, F.A.P. Voll, V.F. Cabral, L. Cardozo Filho, Chem. Ind. Chem. Eng. Q. 25 (2019) 153−162.

Most read articles by the same author(s)