Calculating densities and viscosities of natural gas with a high content of C₂₊ to predict two-phase liquid-gas flow pattern

Abstract

The paper is devoted to the two-phase flow simulation. The gas-condensate mixture flow in a horizontal pipe under high pressure is considered. The influence of the equation of state (EOS) choice for mixture properties modelling on the flow regime calculation results is studied for gas with high content of methane homologues. An analytical overview of the methods to predict the flow pattern is provided. Based on this analysis, two techniques are selected. For these techniques, values of density and viscosity for each phase are required. Density calculation for the gas phase is performed with Van der Waals based EOS. The propriate EOS is selected based on studies of calculation errors for test mixtures. Calculation of liquid phase density is done by means of Patela-Teja and Guo-Du equations, two different models are considered for viscosity estimation. The flow patterns of gas-condensate mixture in a range of temperatures and pressures are calculated and verified via probability map. The results of study allow to recommend the Brusilovsky EOS for calculation of densities for similar gas mixtures and make more rigorous flow regime evaluation. The probability map shows that for the chosen composition and parameters of media the flow pattern is mostly transitional between segregated and annular independent from EOS.

Keywords

Two-phase flow / Flow pattern / Natural gas / Wet gas / High content of C₂₊ / High pressure

Acknowledgements

This research was done by Peter the Great St. Petersburg Polytechnic University and supported under the strategic academic leadership program “Priority 2030” of the Russian Federation (Agreement 075-15-2021-1333 dated 30.09.2021).

References

[1] J.P. Brill, H. Mukherjee, Multiphase flow in wells, SPE Monograph Series 17 (1999) 164. Richardson, Texas.

[2] M.E. Ozbayoglu, C. Omurlu, Modelling of two-phase flow through concentric annuli, Petrol. Sci. Technol. 25 (8) (2007) 1027-1040, https://doi.org/10.1080/10916460600695132.

[3] L. Márquez-Torres, J. Ochoa-Pineda, P. Pico, J.P. Valdés, D. Becerra, A. Pinilla, E. Pereyra, N. Ratkovich, Comparison of 63 different void fraction correlations for different flow patterns, pipe inclinations, and liquid viscosities, SN Appl. Sci. 2 (2020) 1695, https://doi.org/10.1007/s42452-020-03464-w.

[4] R. Nobakht Hassanlouei, H. Firouzfar, N. Kasiri, M.H. Khanof, A simple mathematical model for slug liquid holdup in horizontal pipes, Sci. Iran. 19 (6) (2012) 1653-1660, https://doi.org/10.1016/j.scient.2012.05.010.

[5] A. Arabi, Y. Salhi, Y. Zenati, E.K. Si-Ahmed, J. Legrand, On gas-liquid intermittent flow in a horizontal pipe: influence of sub-regime on slug frequency, Chem. Eng. Sci. 211 (2020), 115251, https://doi.org/10.1016/j.ces.2019.115251.

[6] O. Baker, Simultaneous flow of oil and gas, Oil Gas J. 53 (1954) 185-195.

[7] G.F. Hewitt, D.N. Roberts, Studies of Two-phase Flow Patterns by Simultaneous Flash and XRay Photography, AERE-M 2159, 1969.

[8] Y. Taitel, A.E. Dukler, A model of predicting flow regime transitions in horizontal and near horizontal gas-liquid flow, AIChE J. 22 (1976) 47-55, https://doi.org/10.1002/aic.690220105.

[9] K. Hashizume, Flow pattern, void fraction and pressure drop of refrigerant two-phase flowin a horizontal pipe -I: experimental data, Int. J. Multiphas. Flow 4 (5) (1983) 399-410.

[10] D. Steiner, VDI-Waermeatlas (VDI Heat Atlas), chapter Hbb. Verein Deutscher Ingenieure VDI-Gessellschaft Verfahrenstechnik und Chemieingenieurwessen (GCV), e Dusseldorf, 1993.

[11] N. Petalas, K. Aziz, A mechanistic model for multiphase flow in pipes, J. Can. Pet. Technol. 39 (6) (2000) 43-55, https://doi.org/10.2118/00-06-04.

[12] A.M. Shuard, H.B. Mahmud, A.J. King, Comparison of two-phase pipe flow in OpenFOAM with a mechanistic model, IOP Conf. Ser. Mater. Sci. Eng. 121 (2016), 012018, https://doi.org/10.1088/1757-899X/121/1/012018.

[13] E.W. Jassim, T.A. Newell, Prediction of two-phase pressure drop and void fraction in microchannels using probabilistic flow regime mapping, Int. J. Heat Mass Tran. 49 (15) (2006) 2446-2457, https://doi.org/10.1016/j.ijheatmasstransfer.2006.01.034.

[14] R. Amaya-Gómez, J. López, H. Pineda, D. Urbano-Caguasango, J. Pinilla, Probabilistic approach of a flow pattern map for horizontal, vertical, and inclined pipes, Oil & Gas Science and TechnologyeRevue d’IFP Energies nouvelles 74 (67) (2019) 1-13.

[15] Shell Company, Manual: Gas/liquid Separators-type Selection and Design Rules, 2007.

[16] O.V. Klapchuk, G.E. Odisharia, A.T. Shatalov, YuV. Babayanz, Instructions for the Hydraulic Calculation of Field Pipelines for Gas-Liquid Mixtures, Gazprom VNIIGAZ LLC, 1980, p. 22 (in Russian).

[17] Flow regime map for two-phase flow. Excel calculations. Free chemical and petroleum engineering spreadsheets. http://excelcalculations.blogspot.com/2012/02/flow-regime-map.html. (Accessed 13 March 2022).

[18] J. Clerk-Maxwell, O ver de continuiteit van den gas-en vloeistofiocstand Academisch proefschrift, Nature 10 (1874) 477-480, https://doi.org/10.1038/010477a0.

[19] D.Y. Peng, D.B. Robinson, A new two-constant equation of state, Ind. Eng. Chem. Fund. 1 (15) (1976) 59-64, https://doi.org/10.1021/i160057a011.

[20] G. Soave, Equilibrium constants from a modified Redlich-Kwong equation of state, Chem. Eng. Sci. 27 (6) (1972) 1197-1203, https://doi.org/10.1016/0009-2509(72)80096-4.

[21] N.C. Patel, A.S. Teja, A new cubic equation of state for fluids and fluid mixtures, Chem. Eng. Sci. 37 (3) (1982) 463-473, https://doi.org/10.1016/0009-2509(82)80099-7.

[22] A.I. Brusilovsky, Mathematical simulation of phase behavior of natural multicomponent systems at high pressures with an equation of state, SPE Reservoir Eng. 7 (1992) 117-122, https://doi.org/10.2118/20180-PA, 01.

[23] L. Lee, M.H. Gonzalez, B.E. Eakin, The viscosity of natural gases, J. Petrol. Technol. 18 (8) (1966) 997-1000, https://doi.org/10.2118/1340-PA.

[24] C.R. Wilke, A viscosity equation for gas mixtures, J. Chem. Phys. 18 (4) (1950) 517-519, https://doi.org/10.1063/1.1747673.

[25] F. Herning, L. Zipperer, Calculation of the viscosity of technical gas mixtures from the viscosity of the individual gases, Gas u. Wasserfach 79 (1936) 69.

[26] D.E. Dean, L.I. Stiel, The viscosity of nonpolar gas mixtures at moderate and high pressures, AIChE J. 11 (3) (1965) 526-532, https://doi.org/10.1002/aic.690110330.

[27] R.C. Reid, J.M. Prausnitz,The Properities of Gases and Liquids, 4th ed., McGraw-Hill, NewYork, 1989 https://doi.org/10.1036/0070116822.

[28] A.R. Salehpour, K. Nasrifar, Predicting the liquid density of gas condensates and LNG mixtures from equations of state, J. Algorithms and Computation 42 ( 2) (2013) 257-268, https://doi.org/10.22059/jac.2013.7751.

[29] T.M. Guo, L. Du, A three-parameter cubic equation of state for reservoir fluids, Fluid Phase Equil. 52 (1989) 47-57, https://doi.org/10.1016/0378-3812(89)80310-3.

[30] S. Arrehenius, K. Meddelanden Från, Vetenskapsakademiens nobelinstitut, Nobel Inst. 2 (1913) 25.

[31] J. Kendall, K.P. Monroe,The viscosity of liquids. II. The viscosity-composition curve for ideal liquid mixtures, J. Am. Chem. Soc. 39 (9) (1917) 1787e1802, https://doi.org/10.1021/ja02254a001.

[32] R.L. McAllister, The viscosity of liquid mixtures, AIChE J. 6 (3) (1960) 427-431, https://doi.org/10.1002/aic.690060316.

[33] D. Ramachandran, N.G. Devi, N. V.N.B.S. Rao,Correlative and predictive models of viscosity study on Propiophenone with isomeric xylenes binary mixtures at T=(303.15 to 318.15) K, Kor. J. Chem. Eng. 35 (2018) 1919-1931, https://doi.org/10.1007/s11814-018-0104-y.