Modelling the properties of gas-water mixtures for forecasting leakage parameters from distribution networks
DOI:
https://doi.org/10.31471/1993-9868-2025-2(44)-70-89Keywords:
compressibility factor; adiabatic index; speed of sound; gas-hydrogen mixture; gas leakage; fundamental equation of state of gas; production and technological costs and losses.Abstract
Simple engineering mathematical models have been developed and validated to determine the key thermodynamic properties that form the basis for improving the accuracy of predicting leakage parameters of hydrogen-natural gas mixtures under the conditions of gas distribution networks. To create a reliable benchmark database for model development, a comprehensive array of values was generated in the PVTsim Nova software package using the fundamental GERG-2008 equation of state. The study encompassed fifty base component compositions of natural gas, reflecting the variability of its quality in the real networks of Ukraine. The modeling was performed for absolute pressures from 0.1 to 1.3 MPa and temperatures from 243.15 to 323.15 K, which fully covers the operating range of distribution networks. The molar content of hydrogen in the gas mixture varied from 0 to 20%. Based on the obtained data, power-law regression equations were developed to calculate the compressibility factor, adiabatic index, and speed of sound as functions of pressure, temperature, the relative density of the mixture with respect to air, and the molar concentration of hydrogen. Validation of the developed models was conducted by comparison with the benchmark data, establishing the high accuracy and adequacy of the proposed equations throughout the entire investigated range. It was determined that for the compressibility factor model, the maximum absolute relative error is 0.44%, and the coefficient of determination is 0.995. For the adiabatic index, the corresponding values are 0.93% and 0.914; for the speed of sound – 1.5% and 0.998. An analysis of the error distribution confirmed the stability of the models and revealed only minor systematic biases for the adiabatic index and speed of sound, which depend on the hydrogen content. The proposed mathematical models have a simple analytical structure and do not require iterative procedures, allowing for their direct implementation into engineering methodologies for the rapid calculation of leakage parameters and production-technological expenditures and losses of gas in distribution networks.
Downloads
References
1. National Renewable Energy Laboratory. (2022). Hydrogen Blending into Natural Gas Pipeline Infrastructure: Review of the State of Technology (Technical Report). Golden. URL: https://www.nrel.gov/docs/fy23osti/81704.pdf
2. European Parliament and Council. (2024, June 13). Regulation (EU) 2024/1789 of the European Parliament and of the Council of 13 June 2024 on the internal markets for renewable and natural gases and for hydrogen. Official Journal of the European Union. L, 2024/1789.
3 GH2 Green Hydrogen Organisation. (2024). Green Hydrogen Vision for Ukraine. URL: https://gh2.org/countries/ukraine Melaina, M. W., Antonia, O., & Penev, M. (2013). Blending Hydrogen into Natural Gas Pipeline Networks: A Review of Key Issues (NREL Technical Report). URL: https://docs.nrel.gov/docs/fy13osti/51995.pdf
4. Haeseldonckx, D., & D’haeseleer, W. (2007). The use of the natural-gas pipeline infrastructure for hydrogen transport in a sustainable energy system. International Journal of Hydrogen Energy, 32(10–11), 1381–1386. DOI: 10.1016/j.ijhydene.2006.10.018
5. Serediuk, M. D., & Velykyi, S. V. (2022). Analiz metodiv vyznachennia hazodynamichnoi enerhovytratnosti hazovykh merezh naselenykh punktiv [Analysis of methods for determining the gas-dynamic energy consumption of gas networks populated points]. Oil and Gas Power Engineering, (2)38, 51–61. DOI: 10.31471/1993-9868-2022-2(38)-51-61[in Ukrainian]
6. Wang, Z., Sun, J., Liu, Z., & Wang, J. (2024). Numerical Research on Leakage Characteristics of Pure Hydrogen/Hydrogen-Blended Natural Gas in Medium- and Low-Pressure Buried Pipelines. Energies, 17(12), 2951. DOI: 10.3390/en17122951
7. Natsionalna komisiia, shcho zdiisniuie derzhavne rehuliuvannia u sferakh enerhetyky ta komunalnykh posluh. (2020). Pro zatverdzhennia Metodyky vyznachennia rozmiriv normatyvnykh ta vyrobnycho-tekhnolohichnykh vtrat/vytrat pryrodnoho hazu pry zdiisnenni rozpodilu pryrodnoho hazu [On the approval of the Methodology for determining the sizes of normative and production and technological losses/expenditures of natural gas during the distribution of natural gas] Document v2033874-20, valid, current version — Revision on October 9, 2025, on the basis - v1587874-25. URL: https://zakon.rada.gov.ua/laws/show/v2033874-20[in Ukrainian]
8. Nykonorov, O. (2020). Rol hazotransportnoi infrastruktury Ukrainy v rozvytku vodnevoi enerhetyky [The role of gas transport infrastructure of Ukraine in the development of hydrogen energy]. Oil&gas industry of Ukraine, 5(47), 3–8. URL:https://www.ukrenergoexport.com/sites/default/files/2021-02/bulletin_hydrogen_1.pdf [in Ukrainian]
9. Kostohryz, K., Vysochanskyi, I., & Kolesnyk, S. (2020). Pershi vyprobuvannia ukrainskykh hazovykh merezh na vodni [The first tests of Ukrainian gas networks on hydrogen]. Oil&gas industry of Ukraine, 5(47), 24–28. https://www.naftogaz.com/ckeditor_assets/%D0%93%D0%B0%D0%BB%D1%83%D0%B7%D0%B5%D0%B2%D0%B8%D0%B9%20%D0%B6%D1%83%D1%80%D0%BD%D0%B0%D0%BB/Journal-Naftogazova-galuz-05-2020.pdf [in Ukrainian]
10. Kazda, S., & Unihovskyi, L. (2020). Naukove suprovodzhennia eksperymentiv transportuvannia sumishei vodniu ta pryrodnoho hazu rozpodilnymy hazoprovodamy [Scientific support of experiments on the transportation of hydrogen and natural gas mixtures through distribution gas pipelines]. Oil&gas industry of Ukraine, 5(47), 9–14. https://www.naftogaz.com/ckeditor_assets/%D0%93%D0%B0%D0%BB%D1%83%D0%B7%D0%B5%D0%B2%D0%B8%D0%B9%20%D0%B6%D1%83%D1%80%D0%BD%D0%B0%D0%BB/Journal-Naftogazova-galuz-05-2020.pdf [in Ukrainian]
11. Karpash, M. O., Oliinyk, A. P., Raiter, P. M., Yavorskyi, A. V., & Unihovskyi, L. M. (2020). Doslidzhennia hermetychnosti hazorozpodilnykh merezh pry transportuvanni vodniu [Estimation of probabilities of occurrence of factors of negative influence at emergency explosion of hydrogen and hydrogen-gas mixes]. Naftohazova haluz Ukrainy, 6, 24–28. https://www.naftogaz.com/ckeditor_assets/%D0%93%D0%B0%D0%BB%D1%83%D0%B7%D0%B5%D0%B2%D0%B8%D0%B9%20%D0%B6%D1%83%D1%80%D0%BD%D0%B0%D0%BB/Journal-Naftogazova-galuz-05-2020.pdf [in Ukrainian]
12. Serediuk, M. D., & Velykyi, S. V. (2023). Vplyv kontsentratsii vodniu na vlastyvosti hazovodniovykh sumishei ta hazodynamichni protsesy v rozpodilnykh hazovykh merezhakh [Influence of hydrogen concentration on the properties of gas-hydrogen mixtures and gas-dynamic processes in gas distribution networks]. Oil and Gas Power Engineering, 2(40), 25–37. DOI: 10.31471/1993-9868-2023-2(40)-25-37 [in Ukrainian]
13. Ghafri, S. A., Alkhaldi, M., & Charif, A. (2015). New Correlation for Hydrogen-Natural Gas Mixture Compressibility Factor. In Mechanics, Simulation and Control, 761, 667–674. Springer. DOI: 10.1007/978-3-319-17527-0_79
14. Lozano-Martín, D., et al. (2018). Accurate experimental (p, ρ, T) data of natural gas mixtures for the assessment of reference equations of state when dealing with hydrogen-enriched natural gas. International Journal of Hydrogen Energy, 43(49), 22356–22374. DOI: 10.1016/j.ijhydene.2018.10.057
16. Al-Malah, A., et al. (2024). Experimental ($rho$, P, T) data of $text{H}_2 + text{CH}_4$ mixtures at temperatures from 278 to 398 K and pressures up to 56 MPa. International Journal of Hydrogen Energy, 65, 719–731. DOI: 10.1016/j.ijhydene.2024.04.220
17. Cecchini, M., et al. (2021). Impact of hydrogen injection on thermophysical properties and measurement reliability in natural gas networks. E3S Web of Conferences, 312, 01004. DOI: 10.1051/e3sconf/202131201004
18. Derzhstandart Ukrainy. (2022). DSTU EN ISO 20765-2:2022 (EN ISO 20765-2:2018, IDT; ISO 20765-2:2015, IDT). Pryrodnyi haz. Obchysliuvannia termodynamichnykh vlastyvostei. Chastyna 2. Odnofazni vlastyvosti (haz, ridyna ta shchilnyi plyn) dlia rozshyrenykh diapazoniv zastosuvannia [Natural gas. Calculation of thermodynamic properties. Part 2. Single-phase properties (gas, liquid and dense fluid) for extended application ranges]. DP «UkrNDNTs». https://online.budstandart.com/ua/catalog/doc-page.html?id_doc=116893 [in Ukrainian]
19. Kunz, O., & Wagner, W. (2012). GERG-2008: A New Equation of State for Natural Gas and Other Mixtures. Journal of Chemical & Engineering Data, 57(11), 3032–3091. DOI: 10.1021/je300655b
20. Calsep: official web-site. (n.d.). Retrieved October 22, 2025, from https://www.calsep.com
21. Natsionalna komisiia, shcho zdiisniuie derzhavne rehuliuvannia u sferakh enerhetyky ta komunalnykh posluh. (2015). Kodeks hazotransportnoi systemy [Gas Transmission System Code] (Postanova № 2493). URL: https://zakon.rada.gov.ua/laws/show/z1378-15 [in Ukrainian]
22. Natsionalna komisiia, shcho zdiisniuie derzhavne rehuliuvannia u sferakh enerhetyky ta komunalnykh posluh. (2015). Kodeks hazorozpodilnykh system [Gas Distribution Systems Code] (Postanova № 2494). URL: https://zakon.rada.gov.ua/laws/show/z1379-15 [in Ukrainian]
23. Derzhstandart Ukrainy. (2020). DSTU EN ISO 6976:2020 (EN ISO 6976:2016, IDT; ISO 6976:2016, IDT). Pryrodnyi haz. Obchyslennia teploty zhoriannia, hustyny, vidnosnoi hustyny ta chysla Vobbe na osnovi komponentnoho skladu [Natural gas. Calculation of calorific value, density, relative density and Wobbe index from compositional analysis]. DP «UkrNDNTs». [in Ukrainian]
24. International Organization for Standardization. (2012). ISO/TR 29922:2012. Natural gas – Supporting information on the calculation of physical properties according to ISO 6976. Geneva. URL: https://www.iso.org/standard/45233.html
25. Nocedal, J., & Wright, S. J. (2006). Numerical Optimization (2nd ed.). Springer.
26. Beck, A. (2024). Introduction to Nonlinear Optimization: Theory, Algorithms, and Applications with Python and MATLAB (2nd ed.). SIAM. DOI: 10.1137/1.9781611977797
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Oil and Gas Power Engineering
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
.png)
1.png){kind=logo}
