{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T03:27:05Z","timestamp":1777087625786,"version":"3.51.4"},"reference-count":53,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2024,1,9]],"date-time":"2024-01-09T00:00:00Z","timestamp":1704758400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Computation"],"abstract":"<jats:p>Flash calculations are essential in reservoir engineering applications, most notably in compositional flow simulation and separation processes, to provide phase distribution factors, known as k-values, at a given pressure and temperature. The calculation output is subsequently used to estimate composition-dependent properties of interest, such as the equilibrium phases\u2019 molar fraction, composition, density, and compressibility. However, when the flash conditions approach criticality, minor inaccuracies in the computed k-values may lead to significant deviation in the dependent properties, which is eventually inherited to the simulator, leading to large errors in the simulation. Although several machine-learning-based regression approaches have emerged to drastically accelerate flash calculations, the criticality issue persists. To address this problem, a novel resampling technique of the ML models\u2019 training data population is proposed, which aims to fine-tune the training dataset distribution and optimally exploit the models\u2019 learning capacity across various flash conditions. The results demonstrate significantly improved accuracy in predicting phase behavior results near criticality, offering valuable contributions not only to the subsurface reservoir engineering industry but also to the broader field of thermodynamics. By understanding and optimizing the model\u2019s training, this research enables more precise predictions and better-informed decision-making processes in domains involving phase separation phenomena. The proposed technique is applicable to every ML-dominated regression problem, where properties dependent on the machine output are of interest rather than the model output itself.<\/jats:p>","DOI":"10.3390\/computation12010010","type":"journal-article","created":{"date-parts":[[2024,1,10]],"date-time":"2024-01-10T05:47:21Z","timestamp":1704865641000},"page":"10","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Enhancement of Machine-Learning-Based Flash Calculations near Criticality Using a Resampling Approach"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0009-0004-0158-5749","authenticated-orcid":false,"given":"Eirini Maria","family":"Kanakaki","sequence":"first","affiliation":[{"name":"School of Mining and Metallurgical Engineering, National Technical University of Athens, 15780 Athens, Greece"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3469-6125","authenticated-orcid":false,"given":"Anna","family":"Samnioti","sequence":"additional","affiliation":[{"name":"School of Mining and Metallurgical Engineering, National Technical University of Athens, 15780 Athens, Greece"}]},{"given":"Vassilis","family":"Gaganis","sequence":"additional","affiliation":[{"name":"School of Mining and Metallurgical Engineering, National Technical University of Athens, 15780 Athens, Greece"},{"name":"Institute of Geoenergy, Foundation for Research and Technology-Hellas, 73100 Chania, Greece"}]}],"member":"1968","published-online":{"date-parts":[[2024,1,9]]},"reference":[{"key":"ref_1","unstructured":"Ahmed, T. (2018). Reservoir Engineering Handbook, Gulf Professional Publishing."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Whitson, C.H., and Brul\u00e9, M.R. (2000). Phase Behavior, Society of Petroleum Engineers Inc.","DOI":"10.2118\/9781555630874"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1016\/j.petrol.2014.03.011","article-title":"An integrated approach for rapid phase behavior calculations in compositional modeling","volume":"118","author":"Gaganis","year":"2014","journal-title":"J. Pet. Sci. Eng."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0378-3812(82)85001-2","article-title":"The isothermal flash problem. Part I. Stability","volume":"9","author":"Michelsen","year":"1982","journal-title":"Fluid Phase Equilibria"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1016\/0378-3812(82)85002-4","article-title":"The isothermal flash problem. Part II. Phase-split calculation","volume":"9","author":"Michelsen","year":"1982","journal-title":"Fluid Phase Equilibria"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Samnioti, A., and Gaganis, V. (2023). Applications of Machine Learning in Subsurface Reservoir Simulation\u2014A Review\u2014Part I. Energies, 16.","DOI":"10.20944\/preprints202307.0630.v1"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Feijoo, G., Lema, J.M., and Moreira, M.T. (2020). Mass Balances for Chemical Engineers, Walter de Gruyter GmbH & Co KG.","DOI":"10.1515\/9783110624304"},{"key":"ref_8","unstructured":"Felder, R.M., Rousseau, R.W., and Bullard, L.G. (2020). Elementary Principles of Chemical Processes, John Wiley & Sons."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Ghasem, N., and Henda, R. (2014). Principles of Chemical Engineering Processes, CRC Press.","DOI":"10.1201\/b17696"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1021\/i200032a029","article-title":"Simplified flash calculations for cubic equations of state","volume":"25","author":"Michelsen","year":"1986","journal-title":"Ind. Eng. Chem. Process Des. Dev."},{"key":"ref_11","unstructured":"Lewis, G.N., and Randall, M. (1963). Thermodynamics, Krishna Prakashan Media."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"19","DOI":"10.2118\/952327-G","article-title":"Procedure for use of electronic digital computers in calculating flash vaporization hydrocarbon equilibrium","volume":"4","author":"Rachford","year":"1952","journal-title":"J. Pet. Technol."},{"key":"ref_13","first-page":"141","article-title":"K-value program for crude oil components at high pressures based on PVT laboratory data and genetic programming","volume":"24","author":"Fattah","year":"2012","journal-title":"J. King Saud Univ. Eng. Sci."},{"key":"ref_14","unstructured":"Ahmed, T. (2013). Equations of State and PVT Analysis, Elsevier."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"77","DOI":"10.2516\/ogst\/2019049","article-title":"Application of near critical behavior of equilibrium ratios to phase equilibrium calculations","volume":"74","author":"Nichita","year":"2019","journal-title":"Oil Gas Sci. Technol. Rev. D\u2019ifp Energ. Nouv."},{"key":"ref_16","unstructured":"Press, W.H. (2007). Numerical Recipes 3rd Edition: The Art of Scientific Computing, Cambridge University Press."},{"key":"ref_17","unstructured":"Lindfield, G., and Penny, J. (2018). Numerical Methods: Using MATLAB, Academic Press."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1016\/j.fluid.2015.07.035","article-title":"Phase equilibrium calculations with quasi-Newton methods","volume":"406","author":"Nichita","year":"2015","journal-title":"Fluid Phase Equilibria"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Kelley, C.T. (1999). Iterative Methods for Optimization, Society for Industrial and Applied Mathematics.","DOI":"10.1137\/1.9781611970920"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"926","DOI":"10.1002\/aic.690330606","article-title":"The isothermal flash problem: New methods for phase split calculations","volume":"33","author":"Ammar","year":"1987","journal-title":"AIChE J."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1381","DOI":"10.1002\/aic.690310817","article-title":"Thermodynamically consistent quasi-Newton formulae","volume":"31","author":"Lucia","year":"1985","journal-title":"AIChE J."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2847","DOI":"10.1016\/0009-2509(87)87051-3","article-title":"Customized minimization techniques for phase equilibrium computations in reservoir simulation","volume":"42","author":"Trangenstein","year":"1987","journal-title":"Chem. Eng. Sci."},{"key":"ref_23","unstructured":"Wilson, G.M. (1969, January 4\u20137). A modified Redlich-Kwong equation of state, application to general physical data calculations. Proceedings of the 65th National AIChE Meeting, Cleveland, OH, USA."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1193","DOI":"10.2118\/7903-PA","article-title":"A set of equations for computing equilibrium ratios of a crude oil\/natural gas system at pressures below 1000 psia","volume":"31","author":"Standing","year":"1979","journal-title":"J. Pet. Technol."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2118\/219-G","article-title":"Equilibrium constants for a gas-condensate system","volume":"5","author":"Hoffman","year":"1953","journal-title":"J. Pet. Technol."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Whitson, C.H., and Torp, S.B. (1981, January 5\u22127). Evaluating constant volume depletion data. Proceedings of the SPE 56th Annual Fall Technical Conference, San Antonio, TX, USA.","DOI":"10.2118\/10067-MS"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1072","DOI":"10.1021\/ie50333a022","article-title":"Vaporization equilibrium constants in a crude oil\u2013natural gas system","volume":"29","author":"Katz","year":"1937","journal-title":"Ind. Eng. Chem."},{"key":"ref_28","first-page":"131","article-title":"Simplified nomographic presentation hydrocarbon vapor-liquid equilibria","volume":"33","author":"Winn","year":"1954","journal-title":"Chem. Eng. Prog. Symp. Ser."},{"key":"ref_29","unstructured":"Campbell, J.M., Maddox, R.N., Lilly, L.L., and Hubbard, R.A. (1976). Gas Conditioning and Processing, Campbell Petroleum Series."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"1233","DOI":"10.2118\/558-PA","article-title":"A compositional material balance for combination drive reservoirs with gas and water injection","volume":"15","author":"Lohrenz","year":"1963","journal-title":"J. Pet. Technol."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.fluid.2011.10.021","article-title":"Non-iterative phase stability calculations for process simulation using discriminating functions","volume":"314","author":"Gaganis","year":"2012","journal-title":"Fluid Phase Equilibria"},{"key":"ref_32","unstructured":"Gaganis, V., and Varotsis, N. (2012). SPE Europec\/EAGE Annual Conference, OnePetro."},{"key":"ref_33","unstructured":"Gaganis, V., and Varotsis, N. (2014, January 6\u20139). Rapid multiphase stability calculations in process simulation. Proceedings of the 27th European Symposium on Applied Thermodynamics, Eindhoven, The Netherlands."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1016\/j.compchemeng.2017.09.006","article-title":"Rapid phase stability calculations in fluid flow simulation using simple discriminating functions","volume":"108","author":"Gaganis","year":"2018","journal-title":"Comput. Chem. Eng."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1016\/j.fluid.2018.02.004","article-title":"A fast algorithm for calculating isothermal phase behavior using machine learning","volume":"465","author":"Kashinath","year":"2018","journal-title":"Fluid Phase Equilibria"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"113207","DOI":"10.1016\/j.cma.2020.113207","article-title":"A self-adaptive deep learning algorithm for accelerating multi-component flash calculation","volume":"369","author":"Zhang","year":"2020","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"12312","DOI":"10.1021\/acs.iecr.9b00527","article-title":"Acceleration of the NVT flash calculation for multicomponent mixtures using deep neural network models","volume":"58","author":"Li","year":"2019","journal-title":"Ind. Eng. Chem. Res."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1016\/j.fluid.2019.02.023","article-title":"Solving vapor-liquid flash problems using artificial neural networks","volume":"490","author":"Poort","year":"2019","journal-title":"Fluid Phase Equilibria"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/j.fluid.2019.01.002","article-title":"Artificial neural network assisted two-phase flash calculations in isothermal and thermal compositional simulations","volume":"486","author":"Wang","year":"2019","journal-title":"Fluid Phase Equilibria"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s10596-021-10107-5","article-title":"Acceleration of thermodynamic computations in fluid flow applications","volume":"26","author":"Sheth","year":"2022","journal-title":"Comput. Geosci."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"107886","DOI":"10.1016\/j.petrol.2020.107886","article-title":"Accelerating flash calculations in unconventional reservoirs considering capillary pressure using an optimized deep learning algorithm","volume":"195","author":"Zhang","year":"2020","journal-title":"J. Pet. Sci. Eng."},{"key":"ref_42","unstructured":"Hernandez Mejia, J.L. (2019). Application of Artificial Neural Networks for Rapid Flash Calculations. [Master\u2019s Thesis, University of Texas]."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1016\/j.fuel.2019.05.023","article-title":"Accelerating and stabilizing the vapor-liquid equilibrium (VLE) calculation in compositional simulation of unconventional reservoirs using deep learning based flash calculation","volume":"253","author":"Wang","year":"2019","journal-title":"Fuel"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/j.fluid.2006.02.013","article-title":"Artificial neural networks for the solution of the phase stability problem","volume":"245","author":"Schmitz","year":"2006","journal-title":"Fluid Phase Equilibria"},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"153","DOI":"10.3390\/cleantechnol4010011","article-title":"Application of machine learning to accelerate gas condensate reservoir simulation","volume":"4","author":"Samnioti","year":"2022","journal-title":"Clean Technol."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"1001","DOI":"10.3390\/cleantechnol4040062","article-title":"Acid gas re-injection system design using machine learning","volume":"4","author":"Anastasiadou","year":"2022","journal-title":"Clean Technol."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/0378-3812(89)80072-X","article-title":"The negative flash","volume":"53","author":"Whitson","year":"1989","journal-title":"Fluid Phase Equilibria"},{"key":"ref_48","unstructured":"Robinson, D.B., and Peng, D.Y. (1978). The Characterization of the Heptanes and Heavier Fractions, Gas Processors Association Report."},{"key":"ref_49","unstructured":"Danesh, A. (1998). PVT and Phase Behaviour of Petroleum Reservoir Fluids, Elsevier."},{"key":"ref_50","doi-asserted-by":"crossref","unstructured":"Pedersen, K.S., Christensen, P.L., Shaikh, J.A., and Christensen, P.L. (2006). Phase Behavior of Petroleum Reservoir Fluids, CRC Press.","DOI":"10.1201\/9781420018257"},{"key":"ref_51","unstructured":"Bahadori, A. (2016). Fluid Phase Behavior for Conventional and Unconventional Oil and Gas Reservoirs, Gulf Professional Publishing."},{"key":"ref_52","doi-asserted-by":"crossref","unstructured":"Tewari, R.D., Dandekar, A.Y., and Ortiz, J.M. (2018). Petroleum Fluid Phase behavior: Characterization, Processes, and Applications, CRC Press.","DOI":"10.1201\/9781315228808"},{"key":"ref_53","unstructured":"Dake, L.P. (1983). Fundamentals of Reservoir Engineering, Elsevier."}],"container-title":["Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2079-3197\/12\/1\/10\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T13:43:18Z","timestamp":1760103798000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2079-3197\/12\/1\/10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1,9]]},"references-count":53,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,1]]}},"alternative-id":["computation12010010"],"URL":"https:\/\/doi.org\/10.3390\/computation12010010","relation":{},"ISSN":["2079-3197"],"issn-type":[{"value":"2079-3197","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,1,9]]}}}