Examining the Prediction of Vapor-Liquid Equilibria through Comparative Analysis: Deep Learning versus Classical Cubic and Associating Fluid Theory Approaches

Year 2025, Volume: 8 Issue: 1, 11 - 28, 11.03.2025

Muhammad Naveed Khan , Pramod Warrier Babar Zaman Cornelius Peters

https://doi.org/10.58692/jotcsb.1545110

Abstract

Accurate vapor-liquid equilibria (VLE) calculations of carbon dioxide and hydrogen sulfide mixtures are critical to gas processing and the affordable, safe design of flow assurance technologies. Inaccurate VLE predictions can lead to inaccurate gas hydrate phase equilibria predictions and ensuing safety and economic risks. This research paper explores the potential incorporation of Deep Neural Networks (DNNs) to support conventional expert systems within the context of predicting VLE. It facilitates more flexible and data-driven approaches that are required due to the growing intricacy and dynamic character of chemical processes. Moreover, various cubic and non-cubic equation of state (EoS) models (such as SRK, PR, CPA, SAFT, and PC-SAFT) were also examined to compare predicted VLE for various mixtures of CO2 and H2S. Prior to the comparison of DNN-predicted VLE with EOS models, binary interaction parameters were optimized for all EOS with the available experimental phase equilibria measurements. Model accuracies were compared and analyzed for various binary systems containing CO2/H2S + other associative and non-associative components. The absolute average deviation in vapor and liquid phase composition/bubble pressure was calculated and compared for all five-state EOS with DNN predictions. The DNN and equation of states with BIP gave a reliable illustration of the phase behavior of CO2/H2S-containing systems compared to others as indicated by the lower AADP values. By contrasting the applied DNN model with conventional techniques, we explore the promising channel for future research directions and industry applications, as well as an opportunity for innovation and field advancement for modern expert systems.

Keywords

fluid phase equilibria, Equation of state, Deep Learning Network, PC SAT, Cubic Equation of state

Project Number

This manuscript was not supported by any research project

References

• Abadi, M., Agarwal, A., Barham, P., Brevdo, E., Chen, Z., Citro, C.,…Devin, M. (2016). Tensorflow: Large-scale machine learning on heterogeneous distributed systems. arXiv preprint arXiv:1603.04467.
• Azari, A., Atashrouz, S., & Mirshekar, H. (2013). Prediction the vapor-liquid equilibria of CO2-containing binary refrigerant mixtures using artificial neural networks. International Scholarly Research Notices, 2013.
• Carranza-Abaid, A., Svendsen, H. F., & Jakobsen, J. P. (2023). Thermodynamically consistent vapor-liquid equilibrium modelling with artificial neural networks. Fluid Phase Equilibria, 564, 113597.
• Chapman, W. G., Gubbins, K. E., Jackson, G., & Radosz, M. (1989). SAFT: equation-of-state solution model for associating fluids. Fluid Phase Equilibria, 52, 31-38.
• Chapman, W. G., Gubbins, K. E., Jackson, G., & Radosz, M. (1990). New reference equation of state for associating liquids. Industrial & Engineering Chemistry Research, 29(8), 1709-1721.
• da Silva, V. M., do Carmo, R. P., Fleming, F. P., Daridon, J.-L., Pauly, J., & Tavares, F. (2018). High pressure phase equilibria of carbon dioxide+ n-alkanes mixtures: Experimental data and modeling. Fluid Phase Equilibria, 463, 114-120.
• Dahl, S., & Michelsen, M. L. (1990). High‐pressure vapor‐liquid equilibrium with a UNIFAC‐based equation of state. AIChE journal, 36(12), 1829-1836.
• Del-Mazo-Alvarado, O., & Bonilla-Petriciolet, A. (2022). Assessment of the simultaneous regression of liquid-liquid and vapor-liquid equilibria data of binary systems using NRTL and artificial neural networks. Fluid Phase Equilibria, 561, 113537.
• Diamantonis, N. I., Boulougouris, G. C., Mansoor, E., Tsangaris, D. M., & Economou, I. G. (2013). Evaluation of cubic, SAFT, and PC-SAFT equations of state for the vapor–liquid equilibrium modeling of CO2 mixtures with other gases. Industrial & Engineering Chemistry Research, 52(10), 3933-3942.
• Espanani, R., Miller, A., & Jacoby, W. (2016). Prediction of vapor–liquid equilibria for mixtures of low boiling point compounds using Wong–Sandler mixing rule and EOS/GE model. Chemical Engineering Science, 152, 343-350.
• Eze, P. C., & Masuku, C. M. (2018). Vapour–liquid equilibrium prediction for synthesis gas conversion using artificial neural networks. South African journal of chemical engineering, 26(1), 80-85.
• Faúndez, C. A., & Valderrama, J. O. (2013). Modeling associating hydrocarbon+ alcohol mixtures using the Peng-Robinson equation of state and the Wong-Sandler mixing rules. Comptes Rendus Chimie, 16(2), 135-143.
• Ghosh, P. (1999). Prediction of vapor‐liquid equilibria using peng‐robinson and soave‐redlich‐kwong equations of state. Chemical Engineering & Technology: Industrial Chemistry‐Plant Equipment‐Process Engineering‐Biotechnology, 22(5), 379-399.
• Gross, J., & Sadowski, G. (2001). Perturbed-chain SAFT: An equation of state based on a perturbation theory for chain molecules. Industrial & Engineering Chemistry Research, 40(4), 1244-1260.
• Han, X., Zhang, L., Zhou, K., & Wang, X. (2019). ProGAN: Protein solubility generative adversarial nets for data augmentation in DNN framework. Computers & chemical engineering, 131, 106533.
• Han, Y., Du, Z., Geng, Z., Fan, J., & Wang, Y. (2023). Novel long short-term memory neural network considering virtual data generation for production prediction and energy structure optimization of ethylene production processes. Chemical Engineering Science, 267, 118372.
• Hanin, B. (2019). Universal function approximation by deep neural nets with bounded width and relu activations. Mathematics, 7(10), 992.
• Hornik, K. (1991). Approximation capabilities of multilayer feedforward networks. Neural networks, 4(2), 251-257.
• Huang, S. H., & Radosz, M. (1990). Equation of state for small, large, polydisperse, and associating molecules. Industrial & Engineering Chemistry Research, 29(11), 2284-2294.
• Huang, S. H., & Radosz, M. (1991). Equation of state for small, large, polydisperse, and associating molecules: extension to fluid mixtures. Industrial & Engineering Chemistry Research, 30(8), 1994-2005.
• Irie, & Miyake. (1988). Capabilities of three-layered perceptrons. IEEE 1988 international conference on neural networks,
• Jhaveri, B. S., & Youngren, G. K. (1988). Three-parameter modification of the Peng-Robinson equation of state to improve volumetric predictions. SPE reservoir engineering, 3(03), 1033-1040.
• Kalra, H., Kubota, H., Robinson, D. B., & Ng, H.-J. (1978). Equilibrium phase properties of the carbon dioxide-n-heptane system. Journal of chemical and Engineering Data, 23(4), 317-321.
• Kamari, E., Hajizadeh, A. A., & Kamali, M. R. (2020). Experimental investigation and estimation of light hydrocarbons gas-liquid equilibrium ratio in gas condensate reservoirs through artificial neural networks. Iranian Journal of Chemistry and Chemical Engineering (IJCCE), 39(6), 163-172.
• Khan, M. N., Warrier, P., Peters, C. J., & Koh, C. A. (2016). Review of vapor-liquid equilibria of gas hydrate formers and phase equilibria of hydrates. Journal of Natural Gas Science and Engineering, 35, 1388-1404.
• Laugier, S., & Richon, D. (1995). Vapor-liquid equilibria for hydrogen sulfide+ hexane,+ cyclohexane,+ benzene,+ pentadecane, and+(hexane+ pentadecane). Journal of chemical and Engineering Data, 40(1), 153-159.
• Lee, M.-T., & Lin, S.-T. (2007). Prediction of mixture vapor–liquid equilibrium from the combined use of Peng–Robinson equation of state and COSMO-SAC activity coefficient model through the Wong–Sandler mixing rule. Fluid Phase Equilibria, 254(1-2), 28-34.
• Li, H. (2008). Thermodynamic properties of CO2 mixtures and their applications in advanced power cycles with CO2 capture processes KTH].
• Li, H., & Yan, J. (2009). Evaluating cubic equations of state for calculation of vapor–liquid equilibrium of CO2 and CO2-mixtures for CO2 capture and storage processes. Applied Energy, 86(6), 826-836.
• Li, J., Cheng, J.-h., Shi, J.-y., & Huang, F. (2012). Brief introduction of back propagation (BP) neural network algorithm and its improvement. Advances in Computer Science and Information Engineering: Volume 2,
• Lopez-Echeverry, J. S., Reif-Acherman, S., & Araujo-Lopez, E. (2017). Peng-Robinson equation of state: 40 years through cubics. Fluid phase equilibria, 447, 39-71.
• Mahfooz, S., Alhasani, A., & Hassan, A. (2023). SDG-11.6. 2 Indicator and Predictions of PM2. 5 using LSTM Neural Network. 2023 1st International Conference on Advanced Innovations in Smart Cities (ICAISC),
• Mahfooz, S., Ali, I., & Khan, M. N. (2022). Improving stock trend prediction using LSTM neural network trained on a complex trading strategy. International Journal for Research in Applied Science and Engineering Technology, 10(7), 4361-4371.
• Martín, Á., Bermejo, M. D., Mato, F. A., & Cocero, M. J. (2011). Teaching advanced equations of state in applied thermodynamics courses using open source programs. Education for Chemical Engineers, 6(4), e114-e121.
• Mathias, P. M., & Copeman, T. W. (1983). Extension of the Peng-Robinson equation of state to complex mixtures: Evaluation of the various forms of the local composition concept. Fluid phase equilibria, 13, 91-108.
• Nasrifar, K., & Tafazzol, A. H. (2010). Vapor− liquid equilibria of acid gas− aqueous ethanolamine solutions using the PC-SAFT equation of state. Industrial & Engineering Chemistry Research, 49(16), 7620-7630.
• Ng, H.-J., Kalra, H., Robinson, D. B., & Kubota, H. (1980). Equilibrium phase properties of the toluene-hydrogen sulfide and heptane-hydrogen sulfide binary systems. Journal of chemical and Engineering Data, 25(1), 51-55.
• Nguyen, V. D., Tan, R. R., Brondial, Y., & Fuchino, T. (2007). Prediction of vapor–liquid equilibrium data for ternary systems using artificial neural networks. Fluid Phase Equilibria, 254(1-2), 188-197.
• Peng, D.-Y., & Robinson, D. B. (1976). A new two-constant equation of state. Industrial & Engineering Chemistry Fundamentals, 15(1), 59-64.
• Redlich, O., & Kwong, J. (1949). On the thermodynamics of solutions. V. An equation of state. Fugacities of gaseous solutions. Chemical Reviews, 44(1), 233-244.
• Roosta, A., Hekayati, J., & Javanmardi, J. (2019). Application of artificial neural networks and genetic programming in vapor–liquid equilibrium of C 1 to C 7 alkane binary mixtures. Neural Computing and Applications, 31, 1165-1172.
• Sharma, R., Singhal, D., Ghosh, R., & Dwivedi, A. (1999). Potential applications of artificial neural networks to thermodynamics: vapor–liquid equilibrium predictions. Computers & chemical engineering, 23(3), 385-390.
• Soave, G. (1972). Equilibrium constants from a modified Redlich-Kwong equation of state. Chemical Engineering Science, 27(6), 1197-1203.
• Stamataki, S., & Magoulas, K. (2000). Prediction of phase equilibria and volumetric behavior of fluids with high concentration of hydrogen sulfide. Oil & Gas Science and Technology, 55(5), 511-522.
• Tato, A., & Nkambou, R. (2018). Improving adam optimizer.
• Théveneau, P., Coquelet, C., & Richon, D. (2006). Vapour–liquid equilibrium data for the hydrogen sulphide+ n-heptane system at temperatures from 293.25 to 373.22 K and pressures up to about 6.9 MPa. Fluid phase equilibria, 249(1-2), 179-186.
• Twu, C. H., Sim, W. D., & Tassone, V. (2002a). An extension of CEOS/AE zero-pressure mixing rules for an optimum two-parameter cubic equation of state. Industrial & Engineering Chemistry Research, 41(5), 931-937.
• Twu, C. H., Sim, W. D., & Tassone, V. (2002b). Getting a handle on advanced cubic equations of state. Chemical engineering progress, 98(11), 58-65.
• Tzirakis, F., Karakatsani, E., & Kontogeorgis, G. M. (2016). Evaluation of the cubic-plus-association equation of state for ternary, quaternary, and multicomponent systems in the presence of monoethylene glycol. Industrial & Engineering Chemistry Research, 55(43), 11371-11382.
• Vaferi, B., Lashkarbolooki, M., Esmaeili, H., & Shariati, A. (2018). Toward artificial intelligence-based modeling of vapor liquid equilibria of carbon dioxide and refrigerant binary systems. Journal of the Serbian Chemical Society, 83(2), 199-211.
• Wertheim, M. S. (1984). Fluids with highly directional attractive forces. I. Statistical thermodynamics. Journal of statistical physics, 35(1-2), 19-34.
• Wong, D. S., & Sandler, S. I. (1984). Calculation of vapor-liquid-liquid equilibrium with cubic equations of state and a corresponding states principle. Industrial & engineering chemistry fundamentals, 23(3), 348-354.
• Wu, Y., Kowitz, C., Sun, S., & Salama, A. (2015). Speeding up the flash calculations in two-phase compositional flow simulations–The application of sparse grids. Journal of Computational Physics, 285, 88-99.
• Young, A. F., Magalhães, G. D., Pessoa, F. L., & Ahón, V. R. (2018). Vapor-liquid equilibrium of binary systems with EoS/GE models at low pressure: Revisiting the Heidemann-Kokal Mixing Rule. Fluid Phase Equilibria, 466, 89-102.
• Zarenezhad, B., & Aminian, A. (2011). Predicting the vapor-liquid equilibrium of carbon dioxide+ alkanol systems by using an artificial neural network. Korean Journal of Chemical Engineering, 28, 1286-1292.
• Zhang, K., & Zhang, H. (2022). Predicting solute descriptors for organic chemicals by a deep neural network (DNN) using basic chemical structures and a surrogate metric. Environmental Science & Technology, 56(3), 2054-2064.
• Zhong, S., Zhang, K., Wang, D., & Zhang, H. (2021). Shedding light on “Black Box” machine learning models for predicting the reactivity of HO radicals toward organic compounds. Chemical Engineering Journal, 405, 126627.