2411-3336 2541-9404 Записки Горного института Journal of Mining Institute Санкт-Петербургский горный университет императрицы Екатерины ΙΙ Empress Catherine II Saint Petersburg Mining University 10.31897/PMI.2022.59 pmi-15654 https://pmi.spmi.ru/pmi/article/view/15654 Predicting the permeability of the near-bottomhole zone during wave impact Прогнозирование проницаемости призабойной зоны пласта при волновом воздействии Chengzhi Qi Чэнчжи Ци Chengzhi Qi qichengzhi65@163.com 0000-0003-1196-3972 Пекинский университет гражданского строительства и архитектуры (Китай) Beijing University of Civil Engineering and Architecture (China) Guzev Mikhail А. Гузев М. А. Guzev Mikhail А. guzev@iam.dvo.ru 0000-0001-9344-154X Пермский национальный исследовательский политехнический университет (Россия) Perm National Research Polytechnic University (Russia) Poplygin Vladimir V. Поплыгин В. В. Poplygin Vladimir V. poplygin@bk.ru 0000-0003-2142-5246 Пермский национальный исследовательский политехнический университет (Россия) Perm National Research Polytechnic University (Russia) Kunitskikh Artem A. Куницких A. А. Kunitskikh Artem A. artem_kunitskikh@mail.ru 0000-0003-2470-1429 Пермский национальный исследовательский политехнический университет (Россия) Perm National Research Polytechnic University (Russia) 29 12 2022 2022 258 998 1007 10 11 2021 25 05 2022 29 12 2022 © 2022 Ци Чэнчжи, М. А. Гузев, В. В. Поплыгин, A. А. Куницких © 2022 Qi Chengzhi, Mikhail А. Guzev, Vladimir V. Poplygin, Artem A. Kunitskikh 2022 Ци Чэнчжи, М. А. Гузев, В. В. Поплыгин, A. А. Куницких Qi Chengzhi, Mikhail А. Guzev, Vladimir V. Poplygin, Artem A. Kunitskikh Эта статья доступна по лицензии Creative Commons Attribution 4.0 International (CC BY 4.0) This article is licensed under a Creative Commons Attribution 4.0 International License (CC BY 4.0) https://pmi.spmi.ru/pmi/article/view/15654

В результате исследования выявлено, что при выборе метода увеличения нефтеизвлечения необходимо учитывать реологические особенности движения флюидов по пласту, действие капиллярных сил и неоднородность коллекторских свойств продуктивного пласта по мощности и по простиранию. Рассмотрено низкочастотное волновое воздействие, которое применяется для увеличения добычи на месторождениях нефти. При низкочастотном воздействии появляются новые и увеличиваются в размерах существующие трещины в горных породах. Наибольшее увеличение пористости и проницаемости горных пород происходит при частоте воздействия до 10 Гц. В статье исследована динамика амплитуды колебаний при движении волны в насыщенной пористой среде: существенное затухание амплитуды происходит на расстояние до 1 м от оси скважины, с увеличением частоты воздействия от 1 до 10 Гц интенсивность затухания амплитуды снижается. Проведены испытания технологии на скважине в Пермском крае (Россия). Фактическое значение проницаемости оказалось на 50 % больше прогнозной величины. По результатам обработки гидродинамических исследований отмечено, что наибольшее увеличение проницаемости произошло рядом со стволом скважины, а в удалении от оси скважины проницаемость практически не изменилась. Для уточнения математической модели прогноза влияния волнового воздействия на проницаемость горных пород необходимо ввести учет взаимосвязи структуры порового пространства, изменения адгезионного слоя, а также исследовать перенос частиц при вибрации.

The research reveals that during selection of a method to increase oil recovery it is necessary to take into account rheological features of fluid movement through the formation, effect of capillary forces and heterogeneity of reservoir properties of the productive formation in thickness and along the bedding. Low-frequency wave impact, which is used to increase production in oil fields, is considered. At low-frequency impact new fractures appear and existing fractures in rocks increase in size. The greatest increase in porosity and permeability of rocks occurs at an impact frequency up to 10 Hz. Dynamics of oscillation amplitude during wave's movement in saturated porous medium is studied in the paper: essential attenuation of amplitude occurs at distance up to 1 m from borehole axis. With increase of frequency from 1 to 10 Hz the intensity of amplitude's attenuation decreases. The technology was tested on a well in Perm region (Russia). The actual permeability value was 50 % higher than the predicted value. According to the results of hydrodynamic investigations processing, it was noted that the greatest increase of permeability took place near the wellbore, while away from the wellbore axis permeability remained almost unchanged. In order to refine the mathematical model for prediction of wave impact on rock permeability it is necessary to take into account interconnection of pore space structure, change of adhesion layer, as well as to study transfer of particles during vibration.

 Ключевые слова проницаемость горная порода волновое воздействие частота колебаний амплитуда колебаний повышение нефтеотдачи дилатационно-волновое воздействие продуктивный пласт Keywords permeability rock wave impact oscillation frequency oscillation amplitude enhanced oil recovery dilatation-wave impact reservoir LeiZhang, XufengWang, JiyaoWang, ZhanbiaoYang. Mechanical characteristics and pore evolution of red sandstone under ultrasonic high-frequency vibration // AIP Advances. 2021. Vol. 11. Iss. 51. № 055202. DOI: 10.1063/5.0051640 Lei Zhang, Xufeng Wang, Jiyao Wang, Zhanbiao Yang. Mechanical characteristics and pore evolution of red sandstone under ultrasonic high-frequency vibration. AIP Advances. 2021. Vol. 11. Iss. 51. N 055202. DOI: 10.1063/5.0051640 Cardoni A., Harkness P., Lucas M. Ultrasonic rock sampling using longitudinal-torsional vibrations //Ultrasonics. 2010. Vol. 50. Iss. 4-5. P. 447-452. DOI: 10.1016/j.ultras.2009.09.036 Cardoni A., Harkness P., Lucas M. Ultrasonic rock sampling using longitudinal-torsional vibrations. Ultrasonics. 2010. Vol. 50. Iss. 4-5, p. 447-452. DOI: 10.1016/j.ultras.2009.09.036 Fernando P.K.S.C., Meng Zhang, Pei Z. Rotary ultrasonic machining of rocks: An experimental investigation // Advances in Mechanical Engineering. 2018. Vol. 10. Iss. 3. DOI: 10.1177/1687814018763178 Fernando P.K.S.C., Meng Zhang, Pei Z. Rotary ultrasonic machining of rocks: An experimental investigation. Advances in Mechanical Engineering. 2018. Vol. 10. Iss. 3. DOI: 10.1177/1687814018763178 Wiercigroch M., Wojewoda J., Krivtsov A.M. Dynamics of ultrasonic percussive drilling of hard rocks // Journal of Sound and Vibration. 2005. Vol. 280. Iss. 3-5. P. 739-757. DOI: 10.1016/j.jsv.2003.12.045 Wiercigroch M., Wojewoda J., Krivtsov A.M. Dynamics of ultrasonic percussive drilling of hard rocks. Journal of Sound and Vibration. 2005. Vol. 280. Iss. 3-5, p. 739-757. DOI: 10.1016/j.jsv.2003.12.045 Ning Li, Ping Zhang, Yunsheng Chen, Swoboda G. Fatigue properties of cracked, saturated and frozen sandstone samples under cyclic loading // International Journal of Rock Mechanics and Mining Sciences. 2003. Vol. 40. Iss. 1. P. 145-150. DOI: 10.1016/S1365-1609(02)00111-9 Ning Li, Ping Zhang, Yunsheng Chen, Swoboda G. Fatigue properties of cracked, saturated and frozen sandstone samples under cyclic loading. International Journal of Rock Mechanics and Mining Sciences. 2003. Vol. 40. Iss. 1, p. 145-150. DOI: 10.1016/S1365-1609(02)00111-9 Fernando P.K.S.C., Pei Z.J., Meng Zhang. Mechanistic cutting force model for rotary ultrasonic machining of rocks // International Journal of Advanced Manufacturing Technology. 2020. Vol. 109. Iss. 1-2. P. 109-128. DOI: 10.1007/s00170-020-05624-z Fernando P.K.S.C., Pei Z.J., Meng Zhang. Mechanistic cutting force model for rotary ultrasonic machining of rocks. International Journal of Advanced Manufacturing Technology. 2020. Vol. 109. Iss. 1-2, p. 109-128. DOI: 10.1007/s00170-020-05624-z Da-jun Zhao, Peng Yuan. Research on the Influence Rule of Ultrasonic Vibration Time on Granite Damage // Journal of Mining Science. 2018. Vol. 54. Iss. 5. P. 751-762. DOI: 10.1134/S1062739118054856 Da-jun Zhao, Peng Yuan. Research on the Influence Rule of Ultrasonic Vibration Time on Granite Damage. Journal of Mining Science. 2018. Vol. 54. Iss. 5, p. 751-762. DOI: 10.1134/S1062739118054856 Kozhevnikov E.V., Turbakov M.S., Riabokon E.P., Poplygin V.V. Effect of Effective Pressure on the Permeability of Rocks Based on Well Testing Results // Energies. 2021. Vol. 14. Iss. 8. № 2306. DOI: 10.3390/en14082306 Kozhevnikov E.V., Turbakov M.S., Riabokon E.P., Poplygin V.V. Effect of Effective Pressure on the Permeability of Rocks Based on Well Testing Results. Energies. 2021. Vol. 14. Iss. 8. N 2306. DOI: 10.3390/en14082306 Kozhevnikov E., Riabokon E., Turbakov M.A. Model of Reservoir Permeability Evolution during Oil Production // Energies. 2021. Vol. 14. Iss. 9. № 2695. DOI: 10.3390/en14092695 Kozhevnikov E., Riabokon E., Turbakov M.A. Model of Reservoir Permeability Evolution during Oil Production. Energies. 2021. Vol. 14. Iss. 9. N 2695. DOI: 10.3390/en14092695 Momeni A.A., Karakus M., Khanlari G.R., Heidari M. Effects of cyclic loading on the mechanical properties of a granite // International Journal of Rock Mechanics & Mining Sciences. 2015. Vol. 77. P. 89-96. DOI: 10.1016/j.ijrmms.2015.03.029 Momeni A.A., Karakus M., Khanlari G.R., Heidari M. Effects of cyclic loading on the mechanical properties of a granite. International Journal of Rock Mechanics & Mining Sciences. 2015. Vol. 77, p. 89-96. DOI: 10.1016/j.ijrmms.2015.03.029 Yi Liu, Feng Dai, Lu Dong et al. Experimental Investigation on the Fatigue Mechanical Properties of Intermittently Jointed Rock Models Under Cyclic Uniaxial Compression with Different Loading Parameters // Rock Mechanics and Rock Engineering. 2018. Vol. 51. Iss. 1. P. 47-68. DOI: 10.1007/s00603-017-1327-7 Yi Liu, Feng Dai, Lu Dong et al. Experimental Investigation on the Fatigue Mechanical Properties of Intermittently Jointed Rock Models Under Cyclic Uniaxial Compression with Different Loading Parameters. Rock Mechanics and Rock Engineering. 2018. Vol. 51. Iss. 1, p. 47-68. DOI: 10.1007/s00603-017-1327-7 Bagde M.N., Petroš V. Fatigue properties of intact sandstone samples subjected to dynamic uniaxial cyclical loading // International Journal of Rock Mechanics and Mining Sciences. 2005. Vol. 42. Iss. 2. P. 237-250. DOI: 10.1016/j.ijrmms.2004.08.008 Bagde M.N., Petroš V. Fatigue properties of intact sandstone samples subjected to dynamic uniaxial cyclical loading. International Journal of Rock Mechanics and Mining Sciences. 2005. Vol. 42. Iss. 2, p. 237-250. DOI: 10.1016/j.ijrmms.2004.08.008 Lin-jian Ma, Xin-yu Liu, Ming-yang Wang et al. Experimental investigation of the mechanical properties of rock salt under triaxial cyclic loading // International Journal of Rock Mechanics and Mining Sciences. 2013. Vol. 62. P. 34-41. DOI: 10.1016/j.ijrmms.2013.04.003 Lin-jian Ma, Xin-yu Liu, Ming-yang Wang et al. Experimental investigation of the mechanical properties of rock salt under triaxial cyclic loading. International Journal of Rock Mechanics and Mining Sciences. 2013. Vol. 62, p. 34-41. DOI: 10.1016/j.ijrmms.2013.04.003 Mingming He, Ning Li, Yunsheng Chen, Caihui Zhu. Strength and Fatigue Properties of Sandstone under Dynamic Cyclic Loading // Shock and Vibration. 2016. Vol. 2016. № 9458582. DOI: 10.1155/2016/9458582 Mingming He, Ning Li, Yunsheng Chen, Caihui Zhu. Strength and Fatigue Properties of Sandstone under Dynamic Cyclic Loading. Shock and Vibration. 2016. Vol. 2016. N 9458582. DOI: 10.1155/2016/9458582 Xiao X., Pan Y., Lu X., Yang X. Mechanism of methane permeability enhance through ultrasonic irradiating on low permeable coal seam // Chinese Journal of Geophysics. 2013. Vol. 56. P. 1726-1733. DOI: 10.6038/cjg20130530 Xiao X., Pan Y., Lu X., Yang X. Mechanism of methane permeability enhance through ultrasonic irradiating on low permeable coal seam. Chinese Journal of Geophysics. 2013. Vol. 56, p. 1726-1733. DOI: 10.6038/cjg20130530 Yin Songyu, Zhao Dajun, Zhai Guobing. Investigation into the characteristics of rock damage caused by ultrasonic vibration // International Journal of Rock Mechanics and Mining Sciences. 2016. Vol. 84. P. 159-164. DOI: 10.1016/j.ijrmms.2015.12.020 Yin Songyu, Zhao Dajun, Zhai Guobing. Investigation into the characteristics of rock damage caused by ultrasonic vibration. International Journal of Rock Mechanics and Mining Sciences. 2016. Vol. 84, p. 159-164. DOI: 10.1016/j.ijrmms.2015.12.020 Dajun Zhao, Shulei Zhang, Meiyan Wang. Microcrack Growth Properties of Granite under Ultrasonic High-Frequency Excitation // Advances in Civil Engineering. 2019. № 3069029. DOI: 10.1155/2019/3069029 Dajun Zhao, Shulei Zhang, Meiyan Wang. Microcrack Growth Properties of Granite under Ultrasonic High-Frequency Excitation. Advances in Civil Engineering. 2019. N 3069029. DOI: 10.1155/2019/3069029 Guzev M.A., Kozhevnikov E.V., Turbakov M.S. et al. Experimental Investigation of the Change of Elastic Moduli of Clastic Rocks under Nonlinear Loading // International Journal of Engineering. 2021. Vol. 34. Iss. 3. P. 750-755. DOI: 10.5829/ije.2021.34.03c.21 Guzev M.A., Kozhevnikov E.V., Turbakov M.S. et al. Experimental Investigation of the Change of Elastic Moduli of Clastic Rocks under Nonlinear Loading. International Journal of Engineering. 2021. Vol. 34. Iss. 3, p. 750-755. DOI: 10.5829/ije.2021.34.03c.21 Guzev M., Kozhevnikov E., Turbakov M. et al. Experimental Studies of the Influence of Dynamic Loading on the Elastic Properties of Sandstone // Energies. 2020. Vol. 13. Iss. 23. № 6195. DOI: 10.3390/en13236195 Guzev M., Kozhevnikov E., Turbakov M. et al. Experimental Studies of the Influence of Dynamic Loading on the Elastic Properties of Sandstone. Energies. 2020. Vol. 13. Iss. 23. N 6195. DOI: 10.3390/en13236195 Guzev M., Riabokon E., Turbakov M. et al. Modelling of the Dynamic Young’s Modulus of a Sedimentary Rock Subjected to Nonstationary Loading // Energies. 2020. Vol. 13. Iss. 23. № 6461. DOI: 10.3390/en13236461 Guzev M., Riabokon E., Turbakov M. et al. Modelling of the Dynamic Young’s Modulus of a Sedimentary Rock Subjected to Nonstationary Loading. Energies. 2020. Vol. 13. Iss. 23. N 6461. DOI: 10.3390/en13236461 Marfin E., Gavrilov A., Abdrashitov A., Kadyirov A. Pressure build-up test under elastic-wave action on the reservoir // CMMASS 21st International Conference, 24-31 May 2019, Crimea, Russian Federation. Computational Mechanics and Modern Applied Software Systems. 2019. Vol. 2181. № 020018. P. 020018-1-020018-7. DOI: 10.1063/1.5135678 Marfin E., Gavrilov A., Abdrashitov A., Kadyirov A. Pressure build-up test under elastic-wave action on the reservoir. CMMASS 21st International Conference, 24-31 May 2019, Crimea, Russian Federation. Computational Mechanics and Modern Applied Software Systems. 2019. Vol. 2181. N 020018, p. 020018-1-020018-7. DOI: 10.1063/1.5135678 Xiaodong Han, Liming Zheng, Cunliang Chen, Hongfu Shi. Velocity and attenuation of elastic wave in a developed layer with the initial inner percolation in the pores // Journal of Petroleum Exploration and Production Technology. 2018. Vol. 8. DOI: 10.1007/s13202-018-0468-x Xiaodong Han, Liming Zheng, Cunliang Chen, Hongfu Shi. Velocity and attenuation of elastic wave in a developed layer with the initial inner percolation in the pores. Journal of Petroleum Exploration and Production Technology. 2018. Vol. 8. DOI: 10.1007/s13202-018-0468-x Liming Zheng, Hao Wang. Numerical study on the variation of single phase flow in three-dimensional layer under low-frequency artificial vibration of seismic production technique // Energy Sources. Part A: Recovery, Utilization, and Environmental Effects, 2020. DOI: 10.1080/15567036.2020.1840668 Liming Zheng, Hao Wang. Numerical study on the variation of single phase flow in three-dimensional layer under low-frequency artificial vibration of seismic production technique. Energy Sources. Part A: Recovery, Utilization, and Environmental Effects, 2020. DOI: 10.1080/15567036.2020.1840668 Louhenapessy S.C., Ariadji T. The effect of type waves on vibroseismic implementation of changes properties of rock, oil viscosity, oil compound composition, and enhanced oil recovery // Petroleum Research. 2020. Vol. 5. Iss. 4. P. 304-314. DOI: 10.1016/j.ptlrs.2020.05.001 Louhenapessy S.C., Ariadji T. The effect of type waves on vibroseismic implementation of changes properties of rock, oil viscosity, oil compound composition, and enhanced oil recovery. Petroleum Research. 2020. Vol. 5. Iss. 4. p. 304-314. DOI: 10.1016/j.ptlrs.2020.05.001 Ariadji T. Effect of Vibration on Rock and Fluid Properties: On Seeking the Vibroseismic Technology Mechanisms // SPE Asia Pacific Oil and Gas Conference and Exhibition, 5-7 April 2005, Jakarta, Indonesia. Society of Petroleum Engineers, 2005. P. 161-168. DOI: 10.2118/93112-ms Ariadji T. Effect of Vibration on Rock and Fluid Properties: On Seeking the Vibroseismic Technology Mechanisms. SPE Asia Pacific Oil and Gas Conference and Exhibition, 5-7 April 2005, Jakarta, Indonesia. Society of Petroleum Engineers, 2005, p. 161-168. DOI: 10.2118/93112-ms Liming Zheng, Chaoxiang Pu, Li Y.-J. et al. Biot's consolidation with variables for influence of low-frequency vibration stimulation on radial flow in low-permeability developed reservoir // Chinese Journal of Geotechnical Engineering. 2017. Vol. 39. Iss. 4. P. 752-758. DOI: 10.11779/CJGE201704022 Liming Zheng, Chaoxiang Pu, Li Y.-J. et al. Biot's consolidation with variables for influence of low-frequency vibration stimulation on radial flow in low-permeability developed reservoir. Chinese Journal of Geotechnical Engineering. 2017. Vol. 39. Iss. 4, p. 752-758. DOI: 10.11779/CJGE201704022 Liming Zheng, Pu C., Jiaxiang Xu et al. Modified model of porosity variation in seepage fluid-saturated porous media under elastic wave // Journal of Petroleum Exploration and Production Technology. 2016. Vol. 6. Iss. 4. P. 569-575. DOI: 10.1007/s13202-015-0217-3 Liming Zheng, Pu C., Jiaxiang Xu et al. Modified model of porosity variation in seepage fluid-saturated porous media under elastic wave. Journal of Petroleum Exploration and Production Technology. 2016. Vol. 6. Iss. 4, p. 569-575. DOI: 10.1007/s13202-015-0217-3 Li S.Q., Yan T., Li W., Bi F.Q. Modeling of vibration response of rock by harmonic impact // Journal of Natural Gas Science and Engineering. 2015. Vol. 23. P. 90-96. DOI: 10.1016/j.jngse.2015.01.025 Li S.Q., Yan T., Li W., Bi F.Q. Modeling of vibration response of rock by harmonic impact. Journal of Natural Gas Science and Engineering. 2015. Vol. 23, p. 90-96. DOI: 10.1016/j.jngse.2015.01.025 Shedid S.A. An ultrasonic irradiation technique for treatment of asphaltene deposition // Journal of Petroleum Science and Engineering. 2004. Vol. 42. Iss. 1. P. 57-70. DOI: 10.1016/j.petrol.2003.11.001 Shedid S.A. An ultrasonic irradiation technique for treatment of asphaltene deposition. Journal of Petroleum Science and Engineering. 2004. Vol. 42. Iss. 1, p. 57-70. DOI: 10.1016/j.petrol.2003.11.001 Abaa K., Ityokumbul M.T., Adewumi M. Effect of Acoustic Stimulationon Aqueous Phase Trappingin Low-Permeability Sandstones // Journal of Energy Resources Technology, Transactions of the ASME. 2017. Vol. 139. Iss. 61. № 062905. DOI: 10.1115/1.4037156 Abaa K., Ityokumbul M.T., Adewumi M. Effect of Acoustic Stimulationon Aqueous Phase Trapping in Low-Permeability Sandstones. Journal of Energy Resources Technology, Transactions of the ASME. 2017. Vol. 139. Iss. 61. N 062905. DOI: 10.1115/1.4037156 Chun Huh. Improved Oil Recovery by Seismic Vibration: A Preliminary Assessment of Possible Mechanisms // SPE 1st International Oil Conference and Exhibition in Mexico, 31 August – 2 September 2006, Cancun, Mexico. Society of Petroleum Engineers, 2006. P. 358-373. DOI: 10.2118/103870-ms Chun Huh. Improved Oil Recovery by Seismic Vibration: A Preliminary Assessment of Possible Mechanisms. SPE 1st International Oil Conference and Exhibition in Mexico, 31 August – 2 September, 2006, Cancun, Mexico. Society of Petroleum Engineers, 2006, p. 358-373. DOI: 10.2118/103870-ms Fasfiev B.R., Marfin E.A., Khusnullina A.А. The Change in the Temperature Dependence of the Viscosity of Oil Under Ultrasonic Action // European Association of Geoscientists & Engineers 20th Conference on Oil and Gas Geological Exploration and Development – Geomodel 2018, 10-14 September 2018, Gelendzhik, Russian Federation. 2018. P. 1-5. DOI: 10.3997/2214-4609.201802359 Fasfiev B.R., Marfin E.A., Khusnullina A.А. The Change in the Temperature Dependence of the Viscosity of Oil under Ultrasonic Action. European Association of Geoscientists & Engineers 20th Conference on Oil and Gas Geological Exploration and Development – Geomodel 2018, 10-14 September 2018, Gelendzhik, Russian Federation. 2018, p. 1-5. DOI: 10.3997/2214-4609.201802359 Mardegalyamov M.M., Marfin E.A., Vetoshko R.A. Change in Permeability of a Porous Medium at Ultrasonic Action // EAGE 8th International conference and exhibition – Innovations in Geosciences-Time for Breakthrough, 9-12 April 2018, Saint Petersburg, Russian Federation. European Association of Geoscientists & Engineers, 2018. P. 1-5. DOI: 10.3997/2214-4609.201800258 Mardegalyamov M.M., Marfin E.A., Vetoshko R.A. Change in Permeability of a Porous Medium at Ultrasonic Action. EAGE 8th International conference and exhibition – Innovations in Geosciences-Time for Breakthrough, 9-12 April 2018, Saint Petersburg, Russian Federation. European Association of Geoscientists & Engineers, 2018, p 1-5. DOI: 10.3997/2214-4609.201800258 Elkhoury J.E., Niemeijer A.R., Brodsky E.E., Marone C. Laboratory observations of permeability enhancement by fluid pressure oscillation of in situ fractured // Journal of Geophysical Research. 2011. Vol.116. P. 2-16. DOI: 10.1029/2010JB007759 Elkhoury J.E., Niemeijer A.R., Brodsky E.E., Marone C. Laboratory observations of permeability enhancement by fluid pressure oscillation of in situ fractured. Journal of Geophysical Research. 2011. Vol. 116, p. 2-16. DOI: 10.1029/2010JB007759 Жуковский Н.Е. О гидравлическом ударе в водопроводных трубах. М.-Л.: Государственное изд-во технико-теоретической литературы, 1949. 105с. Zhukovskii N.E. About hydroshock in water pipes. Moscow-Leningrad: Gosudarstvennoe izd-vo tekhniko-teoreticheskoi literatury, 1949, p. 105 (in Russian).