Submit an Article
Become a reviewer
Vol 254
Pages:
210-216
Download volume:
RUS ENG
Research article
Geotechnical Engineering and Engineering Geology

Mathematical model of linear and non-linear proppant concentration increase during hydraulic fracturing – a solution for sequential injection of a number of proppant types

Authors:
Aleksandr V. Kochetkov1
Irik G. Fattakhov2
Vyacheslav V. Mukhametshin3
Lyubov S. Kuleshova4
Shamil G. Mingulov5
About authors
Date submitted:
2021-05-31
Date accepted:
2022-03-24
Date published:
2022-07-13

Abstract

It is known that much of the technology aimed at intensifying fluid inflow by means of hydraulic fracturing involves the use of proppant. In order to transport and position grains in the fracture, a uniform supply of proppant with a given concentration into the fracturing fluid is ensured. The aim of the operation is to eliminate the occurrence of distortions in the injection program of proppant HF. A mathematically accurate linear increase of concentration under given conditions is possible only if the transient concentration is correctly defined. The proposed approach allows to correctly form a proppant HF work program for both linear and non-linear increase in proppant concentration. The scientific novelty of the work lies in application of a new mathematical model for direct calculation of injection program parameters, previously determined by trial and error method. A mathematical model of linear and non-linear increase of proppant concentration during HF was developed. For the first time, an analytical solution is presented that allows direct calculation of parameters of the main HF stages, including transient concentrations for given masses of the various types of proppant. The application of the mathematical model in formation of a treatment plan allows maintaining correct proppant mass distribution by fractions, which facilitates implementation of information and analytical systems, data transfer directly from a work program into databases. It is suggested to improve spreadsheet forms used in production, which would allow applying mathematical model of work program formation at each HF process without additional labour costs. The obtained mathematical model can be used to improve the software applied in the design, modelling and engineering support of HF processes.

Keywords:
HF proppant concentration mathematical model intensification stages of injection with proppant technological control
10.31897/PMI.2022.10
Go to volume 254

References

  1. Дмитриевский А.Н. Ресурсно-инновационная стратегия развития экономики России // Нефтяное хозяйство. 2017. № 5. С. 6-7.
  2. Якупов Р.Ф., Мухаметшин В.Ш., Хакимзянов И.Н., Трофимов В.Е. Оптимизация выработки запасов из водонефтяных зон горизонта D3ps Шкаповского нефтяного месторождения с помощью горизонтальных скважин // Георесурсы. 2019. Т. 21. № 3. С. 55-61. DOI: 10.18599/grs.2019.3.55-61
  3. Сергеев В.В., Беленкова Н.Г., Зейгман Ю.В., Мухаметшин В.Ш. Физические свойства эмульсионных систем с содержанием наночастиц SiO2 // Нанотехнологии в строительстве. 2017. Т. 9. № 6. C. 37-64. DOI: 10.15828/2075-8545-2017-9-6-37-64
  4. Галкин В.И., Колтырин А.Н. Исследование и анализ методов определения эффективности применения технологии пропантного гидроразрыва пласта // Известия Томского политехнического университета. Инжиниринг георесурсов. 2019. Т. 330. № 11. С. 50-58. DOI: 10.18799/24131830/2019/11/2347
  5. ChizhovA.P., AndreevV.E., ChibisovA.V. etal. Hydraulically perfect modes of injection of grouting mixtures when isolating absorbing formations // International Conference on Extraction, Transport, Storage and Processing of Hydrocarbons & Materials (ETSaP), 24-25 August 2020, Tyumen, Russian Federation. IOP Conference Series: Materials Science and Engineering, 2020. Vol. 952. № 012040. P. 1-7. DOI: 10.1088/1757-899X/952/1/012040
  6. Mukhametshin V.V., Kuleshova L.S. Using the method of canonical discriminant functions for a qualitative assessment of the response degree of producing wells to water injection during the development of carbonate deposits // MEACS 2020 – International Conference on Mechanical Engineering, Automation and Control Systems, 17th September 2020, Novosibirsk, Russian Federation. IOP Conference Series: Materials Science and Engineering, 2021. Vol. 1064. № 012069. P. 1-9. DOI: 10.1088/1757-899X/1064/1/012069
  7. Mukhametshin V.G., Dubinskiy G.S., Andreev V.E. et al. Geological, technological and technical justification for choosing a design solution for drilling wells under different geological conditions // MEACS 2020 – International Conference on Mechanical Engineering, Automation and Control Systems, 17th September 2020, Novosibirsk, Russian Federation. IOP Conference Series:
  8. Materials Science and Engineering, 2021. Vol. 1064. № 012061. P. 1-9. DOI: 10.1088/1757-899X/1064/1/012061
  9. Tyncherov K.T., Mukhametshin V.Sh., Khuzina L.B. Method to control and correct telemtry well information in the basis of residue number system // Journal of Fundamental and Applied Sciences. 2017. Vol. 9. № 2S. P. 1370-1374. DOI: 10.4314/jfas.v9i2s.848
  10. Zeigman Yu.V., Mukhametshin V.V., Kuleshova L.S. Differential impact on wellbore zone based on hydrochloric-acid simulation // International Conference on Extraction, Transport, Storage and Processing of Hydrocarbons & Materials (ETSaP), 24-25 August 2020, Tyumen, Russian Federation. IOP Conference Series: Materials Science and Engineering. 2020. Vol. 952. № 012069. DOI: 10.1088/1757-899X/952/1/012069
  11. Мухаметшин В.Ш. Зейгман Ю.В., Андреев А.В. Экспресс-оценка потенциала добывных возможностей залежей для определения эффективности применения нанотехнологий и необходимости стимулирования ввода их в разработку // Нанотехнологии в строительстве. 2017. Т. 9. № 3. С. 20-34. DOI: 10.15828/2075-8545-2017-9-3-20-34
  12. Nur Wijaya, Sheng J.J. Comparative study of well soaking timing (pre vs. post flowback) for water blockage removal from matrix-fracture interface // Petroleum. 2020. Vol. 6. Iss. 3. P. 286-292. DOI: 10.1016/j.petlm.2019.11.001
  13. Ruimin Feng, Shengnan Chen, Steven Bryant, Jun Liu. Stress-dependent permeability measurement techniques for unconventional gas reservoirs: Review, evaluation, and application // Fuel. 2019. Vol. №115987. DOI: 10.1016/j.fuel.2019.115987
  14. Муслимов Р.Х. Новая стратегия освоения нефтяных месторождений в современной России – оптимизация добычи и максимизация КИН // Нефть. Газ. Новации. 2016. № 4. С. 8-17.
  15. Cheng Jing, Xiaowei Dong, Wenhao Cuid et al. Artificial neural network–based time-domain interwell tracer testing for ultralow-permeability fractured reservoirs // Journal of Petroleum Science and Engineering. 2020. Vol. 195. № 107558. DOI: 10.1016/j.petrol.2020.107558
  16. Economides J.M., Nolte K.I. Reservoir stimulation. Chichester: John Wiley and Sons, 2000. 856p.
  17. Галкин В.И., Колтырин А.Н. Исследование вероятностных моделей для прогнозирования эффективности технологии пропантного гидравлического разрыва пласта // Записки Горного института. 2020. Т. 246. С. 179-190. DOI: 10.31897/PMI.2020.6.7
  18. Prashanth Siddhamshetty, Shaowen Mao, Kan Wu, Joseph Sang-Il Kwon. Multi-Size Proppant Pumping Schedule of Hydraulic Fracturing: Application to a MP-PIC Model of Unconventional Reservoir for Enhanced Gas Production // Processes. 2020. Vol. 8. Iss. 5. № 570. DOI: 10.3390/pr8050570
  19. Nurgaliev R.Z., Kozikhin R.A., Fattakhov I.G. et al. Prospects for the use of new technologies in assessing the impact of geological and technological risks // IPDME 2019 – International Workshop on Innovations and Prospects of Development of Mining Machinery and Electrical Engineering, 24-27 April 2019, Saint-Petersburg Mining University, Saint-Petersburg, Russian Federation. IOP Conference Series: Earth and Environmental Science, 2019. Vol. 378. № 012117. DOI: 10.1088/1755-1315/378/1/012117
  20. ШляпкинА.С., ТатосовА.В. Формирование трещины гидроразрыва пласта высоковязким гелем // Геология, геофизика и разработка нефтяных и газовых месторождений. 2020. № 9 (345). С. 109-112. DOI: 10.30713/2413-5011-2020-9(345)-109-112
  21. Nolte K.G. Determination of proppant and fluid schedules from fracturing-pressure decline // SPE Prod. Eng. 1986. Vol. 1. Iss. 4. P. 255-265. DOI: 10.2118/13278-PA
  22. Seeyub Yang, Prashanth Siddhamshetty, Joseph Sang-Il Kwon. Optimal pumping schedule design to achieve a uniform proppant concentration level in hydraulic fracturing // Computers & Chemical Engineering. 2017. Vol. 101. P. 138-147. DOI: 10.1016/j.compchemeng.2017.02.035
  23. Yakupov R.F., Mukhametshin V.Sh., Tyncherov K.T. Filtration model of oil coning in a bottom water-drive reservoir // Periodico Tche Quimica. 2018. Vol.15. Iss. 30. P. 725-733.
  24. Галкин В.И., Пономарева И.Н., Черепанов С.С. и др. Новый подход к оценке результатов гидравлического разрыва пласта (на примере бобриковской залежи Шершневского месторождения // Известия Томского политехнического университета. Инжиниринг георесурсов. 2020. Т. 331. № 4. С. 107-114. DOI: 10.18799/24131830/2020/4/2598
  25. Fokker P.A, Borello E.S., Verga F., Viberti D. Harmonic pulse testing for well performance monitoring // Journal of Petroleum Science and Engineering. 2018. Vol. 162. P. 446-459. DOI: 10.1016/j.petrol.2017.12.053
  26. Humoodi A., Hamoudi M., Sarbast R. Implementation of Hydraulic Fracturing Operation for a Reservoir in KRG // UKH Journal of Science and Engineering. 2019. Vol.3. № 2. P. 10-21. DOI: 10.25079/ukhjse.v3n2y2019
  27. Булгакова Г.Т., Шарифуллин А.Р., Ситдиков М.Р. Математическое моделирование тепломассопереноса в вертикальной трещине гидроразрыва пласта при закачке и очистке // Вестник Тюменского государственного университета. Физико-математическое моделирование. Нефть, газ, энергетика. 2020. Т. 6. № 2 (22). С. 41-62. DOI: 10.21684/2411-7978-2020-6-2-41-62
  28. Нургалиев Р.З., Козихин Р.А., Фаттахов И.Г., Кулешова Л.С. Перспективы применения новых технологий при оценке влияния геолого-технологических рисков // Горный журнал. 2019. № 4 (2261). С. 36-40. DOI: 10.17580/gzh.2019.04.08
  29. Siddhamshetty P., Yang S., Kwon J.S. Modeling of hydraulic fracturing and designing of online pumping schedules to achieve uniform proppant concentration in conventional oil reservoirs // Computers & Chemical Engineering. 2018. Vol.114. P. 306-317. DOI: 10.1016/j.compchemeng.2017.10.032
  30. Масооми Р., Долгов С.В. Сравнение разных сценариев для жидкостей ГРП (гели на водной основе и пены) с помощью численного моделирования // Булатовские чтения. 2017. Т. 2. С. 150-155.
  31. Geertsma J., Haafkens R. Comparison of the theories for predicting width and extent of vertical hydraulically induced fractures // Journal of Energy Resource Technology. 1979. Vol. 101. Iss. 1. P. 8-19. DOI: 10.1115/1.3446866
  32. Keshavarz A., Yang Y., Badalyan A. et al. Laboratory-based Mathematical Modelling of Graded Proppant Injection in CBM Reservoirs // International Journal of Coal Geology. 2014. Vol. 136. P. 1-16. DOI: 10.1016/j.coal.2014.10.005
  33. Jiaxiang Xu, Yunhong Ding, Lifeng Yang et al. Effect of proppant deformation and embedment on fracture conductivity after fracturing fluid loss // Journal of Natural Gas Science and Engineering. 2019. Vol.71. № 102986. DOI: 10.1016/j.jngse.2019.102986
  34. Bahtizin R.N., Nurgaliev R.Z., Fattakhov I.G. et al. On the question of the efficiency analysis of the bottom-hole area stimulation method // International Journal of Mechanical Engineering and Technology. 2018. Vol. 9. Iss. 6. P. 1035-1044.
  35. Dali Guo, Yunxiang Zhao, Zixi Guo, Xianhui Cui, Bo Huang. Theoretical and Experimental Determination of Proppant Crushing Rate and Fracture Conductivity // Journal of Energy Resources Technology. 2020. Vol.142. Iss. 10. № 103005. DOI: 10.1115/1.4047079
  36. Нургалиев О.Т., Волченко Ю.А. Радиоизотопный метод и измерительный комплекс РИКП-01 для экспрессного определения концентрации проппанта в рабочих смесях, применяемых при гидравлическом разрыве нефтегазосодержащих пластов // Автоматизация, телемеханизация и связь в нефтяной промышленности. 2016. № 8. С. 24-28.
Access statistics
Abstract Views
1058
Full-Text Views
174
Cited
Scopus:
2
Crossref:
1
Cited By
1. Application of resonance functions in estimating the parameters of interwell zones. Journal of Mining Institute. 2022, Vol. 257, P. 755-763. DOI: 10.31897/PMI.2022.85 [Scopus] (cited: 1)
2. Adsorbed residual oil saturation and phase permeability relationship in productive formations of Western Siberias. SOCAR Proceedings. 2022, P. 38-44. DOI: 10.5510/OGP20220300706 [Scopus]
Article Menu
Mathematical model of linear and non-linear proppant concentration increase during hydraulic fracturing – a solution for sequential injection of a number of proppant types

Similar articles

Prediction of the stress-strain state and stability of the front of tunnel face at the intersection of disturbed zones of the soil mass
2022 Anatoly G. Protosenya, Alexander V. Alekseev, Pavel E. Verbilo
Tensor compaction of porous rocks: theory and experimental verification
2022 Ivan A. Panteleev, Vladimir Lyakhovsky, Virginiya A. Mubassarova, Vladimir I. Karev, Nikolaj I. Shevtsov, Eyal Shalev
Mullite production: phase transformations of kaolinite, thermodynamics of the process
2022 Olga B. Kotova, Vladimir A. Ustyugov, Shiyong Sun, Alexey V. Ponaryadov
Experimental study on the effect of rock pressure on sandstone permeability
2022 Dmitry G. Petrakov, Grigory M. Penkov, Anatoly B. Zolotukhin
The Upper Kotlin clays of the Saint Petersburg region as a foundation and medium for unique facilities: an engineering-geological and geotechnical analysis
2022 Regina E. Dashko, Georgiy A. Lokhmatikov
Remote sensing techniques in the study of structural and geotectonic features of Iturup Island (the Kuril Islands)
2022 Irina V. Talovina, Nikita S. Krikun, Yurii Yu. Yurchenko, Aleksei S. Ageev