Application of Configuration Mechanics Methods to the Problem of Stimulated Volume Formation

Capa

Citar

Texto integral

Acesso aberto Acesso aberto
Acesso é fechado Acesso está concedido
Acesso é fechado Acesso é pago ou somente para assinantes

Resumo

The zone of activated natural fractures (stimulated volume) in the process of hydraulic fracturing in the continuum approximation is considered as a growing porous body saturated with fluid. Varying the state of the body containing the surface of a strong fracture in the reference and actual configurations and writing the energy conservation law in the form of the principle of possible displacements, conditions for jumps in physical quantities at the fracture front are obtained. A model problem in a one-dimensional formulation is considered, and an estimate of the critical discharge pressure that initiates the process of the stimulated volume formation is made.

Texto integral

Acesso é fechado

Sobre autores

Sh. Mukhamediev

Schmidt Institute of Physics of the Earth of the Russian Academy of Sciences

Email: izvekov_o@inbox.ru
Rússia, Moscow

О. Izvekov

Moscow Institute of Physics and Technology

Autor responsável pela correspondência
Email: izvekov_o@inbox.ru
Rússia, Moscow

Bibliografia

  1. Алексеев А.Д., Ревва В.Н., Рязанцев Н.А. Разрушение горных пород в объемном поле сжимающих напряжений. Киев: Наукова думка. 1989. С. 166.
  2. Извеков О.Я., Кондауров В.И. О рассеянном разрушении пористых материалов с хрупким скелетом // Механика твердого тела. 2010. № 3. С. 182–205.
  3. Извеков О.Я., Кондауров В.И. Модель пористой среды с упругим трещиноватым скелетом // Физика Земли. 2009. № 4. С. 31–42.
  4. Кондауров В. И. Кинетика фазовых переходов 1-го рода в термоупругом материале // Докл. РАН. 2004. Т. 396. № 2. С. 194–198.
  5. Кондауров В.И. Механика и термодинамика насыщенной пористой среды. М.: МФТИ. 2007. 310 с.
  6. Кондауров В.И., Никитин Л.В. О фазовых переходах первого года в нелинейно-упругих средах // Докл. АН СССР. 1982. Т. 262. № 6. С. 1348–1351.
  7. Кондауров В.И., Фортов В.Е. Основы термомеханики конденсированной среды. М.: МФТИ. 2002. C. 336.
  8. Мухамедиев Ш.А. Тензоры энергии-импульса и универсальные условия равновесия сингулярных поверхностей // Изв. АН СССР: Механика твердого тела. 1990. С. 86.
  9. Партон В.З., Морозов Е.М. Механика упругопластического разрушения. URSS. 2008.
  10. Трускиновский Л.М. О тензоре химического потенциала // Геохимия. 1983. № 12. С. 1730–1744.
  11. Фрейдин А.Б. О тензоре химического сродства при химических реакциях в деформируемых материалах //Изв. РАН. Механика твердого тела. 2015. № 3. С. 35–68.
  12. Barati R., Liang J.T. A review of fracturing fluid systems used for hydraulic fracturing of oil and gas wells // J. Applied Polymer Science. 2014. V. 131. № 16.
  13. Baue S., Butz I., Strassburger E., Sauer M., Hiermaier S. Quantification of Crack Volumes in Dynamically Damaged Soda-Lime Glass // Glass Struct. Eng. 2022. P. 1–34.
  14. Chadwick P. Applications of an energy–momentum tensor in non-linear elastostatics // Journal of Elasticity. 1975. Т. 5. № 3–4. P. 249–258.
  15. Cipolla C., Wallace J. Stimulated reservoir volume: A misapplied concept? SPE Hydraulic Fracturing Technology Conference and Exhibition. SPE. 2014. P. SPE-168596-MS.
  16. Cohen C. E. et al. Production Forecast after Hydraulic Fracturing in Naturally Fractured Reservoirs: Coupling a Complex Fracturing Simulator and a Semi-Analytical Production Model. SPE Hydraulic Fracturing Technology Conference and Exhibition. SPE. 2012. P. SPE-152541-MS.
  17. Coussy O. Poromechanics. John Wiley & Sons. 2004.
  18. Eisner L. et al. Beyond the dots in the box: Microseismicity-constrained fracture models for reservoir simulation // The Leading Edge. 2010. V. 29. № 3. P. 326–333.
  19. Eshelby J.D. The elastic energy–momentum tensor //Journal of elasticity. 1975. V. 5. P. 321–335.
  20. Eshelby J.D. The force on an elastic singularity // Philosophical Transactions of the Royal Society of London. Series A // Mathematical and Physical Sciences. 1951. V. 244. № 877. P. 87–112.
  21. Epstein M. The Elements of Continuum Biomechanics. Wiley. 2012. 392 p.
  22. Eyre T.S., van der Baan M. Overview of moment-tensor inversion of microseismic events //The Leading Edge. 2015. V. 34. № 8. P. 882–888.
  23. Freidin A.B., Vilchevskaya E.N., Korolev I.K. Stress-assist chemical reactions front propagation in deformable solids // International Journal of Engineering Science. 2014. V. 83. P. 57–75.
  24. Gale J.F., Elliott S.J., Laubach S.E. Hydraulic fractures in core from stimulated reservoirs: core fracture description of HFTS slant core, Midland Basin, West Texas. In Unconventional Resources Technology Conference, Houston, Texas, 23–25 July 2018 (pp. 1340–1357). Society of Exploration Geophysicists, American Association of Petroleum Geologists, Society of Petroleum Engineers.
  25. Galybin A.N., Mukhamediev S.A. On modelling of fluid-driven fracture branching in jointed rocks. Proceedings of 19th European conference on fracture, fracture mechanics for durability reliability and safety. Kazan, Russia. 2012. P. 26–31.
  26. Galybin A.N., Mukhamediev S.A. Fracture development on a weak interface ahead of a fluid-driven crack // Engineering Fracture Mechanics. 2014. V.129. P. 90–101.
  27. Goda I., Ganghoffer J.-F. Maurice G. Combined bone internal and external remodeling based on Eshelby stress // International Journal of Solids and Structures. 2016. V. 94–95. Р. 138–157.
  28. Grady D. Physics of Shock and Impact, V. 2. Materials and shock response. IOP Publishing. 2017.
  29. Griffith A.A. The Phenomena of Rupture and Flow in Solids // Phil. Trans. Roy. Soc. 1921. V. 221. P. 163–198.
  30. Gu H. et al. Hydraulic fracture crossing natural fracture at nonorthogonal angles: a criterion and its validation //SPE Production & Operations. 2012. V. 27. № 01. P. 20–26.
  31. Kanamori H. The energy release in great earthquakes //Journal of geophysical research. 1977. V. 82. № 20. P. 2981–2987.
  32. Kanel G.I., Razorenov S.V., Savinykh A.S., Rajendran A., Chen Z. A Study of the Failure Wave Phenomenon in Glasses Compressed at Different Levels // J. Appl. Phys. 2005. V. 98. № 11.
  33. Kishore K., Mohanty A.G., Ming Gu. Improvement of Fracturing for Gas Shales // Report for RPSEA (Research Partnership to Secure Energy for America). 2012.
  34. Lemaitre J. A Course on Damage Mechanics. Springer-Verlag Berlin Heidelberg. 1996. P. 228.
  35. Li L., Lee S.H. Efficient field-scale simulation of black oil in a naturally fractured reservoir through discrete fracture networks and homogenized media //SPE Reservoir evaluation & engineering. 2008. V. 11. № 04. P. 750–758
  36. Liu X., Jin Y., Lin B. Classification and evaluation for stimulated reservoir volume (SRV) estimation models using microseismic events based on three typical grid structures //Journal of Petroleum Science and Engineering. 2022. V. 211. P. 110169.
  37. Maugin G.A. Sixty years of configurational mechanics (1950–2010) //Mechanics Research Communications. 2013. V. 50. P. 39–49.
  38. Maugin G.A. Configurational forces: thermomechanics, physics, mathematics, and numerics. CRC Press. 2016.
  39. Moinfar A. et al. Development of an efficient embedded discrete fracture model for 3D compositional reservoir simulation in fractured reservoirs //SPE Journal. 2014. V. 19. № 02. С. 289–303.
  40. Mukhamediev S.A., Galybin A.N., Morozov Y.A. The geometry of a dyke swarm as a result of dyke interaction with each other and with external stresses //Doklady Earth Sciences. Pleiades Publishing. 2017. V. 473. P. 406–410.
  41. Murakami S. Continuum Damage Mechanics. Springer Netherlands. 2012. P. 402.
  42. Norris J.Q., Turcotte D.L., Rundle J.B. A damage model for fracking //International Journal of Damage Mechanics. 2015. V. 24. № 8. P. 1227–1238.
  43. Olson J.E. Predicting fracture swarms—The influence of subcritical crack growth and the crack-tip process zone on joint spacing in rock // Geological Society, London, Special Publications. 2004. V. 231. № 1. P. 73–88.
  44. Palisch T.T.T., Vincent M.C.C., Handren P.J.J. Slickwater fracturing: food for thought // SPE Production & Operations. 2010. V. 25. № 03. P. 327–344.
  45. Raterman K.T., Farrell H.E., Mora O.S., Janssen A.L., Gomez G.A., Busetti S., McEwen J., Friehauf K., Rutherford J., Reid R., Jin G., Roy B., Warren M. Sampling a Stimulated Rock Volume: An Eagle Ford Example // SPEReserv. Eval. Eng. V. 21. P. 0927–0941.
  46. Renshaw C.E., Pollard D.D. An experimentally verified criterion for propagation across unbounded frictional interfaces in brittle, linear elastic materials. International journal of rock mechanics and mining sciences & geomechanics abstracts. Pergamon. 1995. V. 32. 3. P. 237–249.
  47. Sharipova L.L., Maugin G.A., Freidin A.B. Modeling the influence of mechanical factors on the growth plate. In Proc. 2nd International Conference on Recent advances in nonlinear mechanics (Kuala-Lumpur, Malaysia), ed. Jee-Hou Ho, M.Woercigroch and Ko-Choong Woo. 2008. 102–103. Kuala-Lumpur, Malaysia: University Press.
  48. Snow D.T. Rock fracture spacings, openings, and porosities // J. Soil Mech. Found. Div. 1968. V. 94. № 1. P. 73–92.
  49. Truesdell C., Noll W. The non-linear field theories of mechanics. Springer Berlin Heidelberg. 2004. P. 579.
  50. Umar I.A. et al. An outlook into recent advances on estimation of effective stimulated reservoir volume //Journal of Natural Gas Science and Engineering. 2021. V. 88. P. 103822.
  51. Warpinski N.R., Mayerhofer M.J., Vincent M.C., Cipolla C.L., Lolon E.P. Stimulating unconventional reservoirs: maximizing network growth while optimizing fracture conductivity // J. Canadian Petroleum Technology. 2009. V. 48. № 10. P. 39–51.
  52. Weng X., Kresse O., Cohen C., Wu R., Gu H. Modeling of hydraulic-fracture-network propagation in a naturally fractured formation // SPE Production & Operations. 2011. V. 26. № 4. 368–380.
  53. Wu Y.S., Li J., Ding D., Wang C., Di Y.A. Generalized Framework Model for the Simulation of Gas Production in Unconventional Gas Reservoirs //SPE Journal. 2014. V. 19. № 5. P. 845–857.
  54. Wu R., Kresse O., Weng X., Cohen C.E., Gu H. Modeling of interaction of hydraulic fractures in complex fracture networks. SPE Hydraulic Fracturing Technology Conference and Exhibition. SPE. 2012. P. SPE-152052-MS.

Arquivos suplementares

Arquivos suplementares
Ação
1. JATS XML
Baixar
2. Fig. 1. Volume of fractured rock saturated with fluid: (a) - regular natural fracturing; (b) - chaotic fracturing.

Baixar (327KB)
Metadados
3. Fig. 2. Reference (material) configurations of the fluid, κF, and skeleton, κS, and their small perturbations dκF and dκS due to material addition.

Baixar (200KB)
Metadados
4. Fig. 3. Variation of the state of the material volume of a two-phase medium modelling the studied array of fractured saturated rock: (a) - actual configuration of c volume; (b) - variation of χ due to the action of external forces; (c) - variation of χ due to the build-up of skeleton and fluid masses; (d) - varied configuration; 1 - fluid; 2 - fluid volume added during variation; 3 - skeleton; 4 - skeleton volume added during variation.

Baixar (394KB)
Metadados
5. Fig. 4. Variation of the state of the material volume of the medium in the one-dimensional case: 1 - position of the fracture front before variation; 1′ - position of the old front after variation; 2 - new position of the fracture front after variation.

Baixar (222KB)
Metadados
6. Fig. 5. Composite body in the actual configuration.

Baixar (165KB)
Metadados
7. Fig. 6. Formulation of the one-dimensional problem.

Baixar (107KB)
Metadados

Declaração de direitos autorais © Russian academy of sciences, 2025