«Oilfield engineering»

Physical mechanism and mathematical model of nonlinear filtration of high-viscous oil through rocks with a low permeability coefficient

UDC: 622.276.2
DOI: 10.33285/0207-2351-2022-6(642)-41-46

Authors:

¹ Institute of Oil and Gas Problems of the Russian Academy of Sciences, Moscow, Russia

Keywords: high viscous oil, nonlinear filtration, low permeability, mathematical model, physical model, fractal viscosity theory, colloidal oil particles

Annotation:

When developing high-viscous oil fields (non-Newtonian fluid) in reservoirs with low (≈10–3 μm²) permeability, the task of conducting hydrodynamic calculations is relevant, since in such cases the filtration rate depends nonlinearly on the pressure gradient. To solve this problem, analytical equations obtained empirically are used, in which the dependence of viscosity on the velocity gradient has a power-law form in combination with the presence of an initial shear rate, at which the fluid flow begins. In this article, the fractal viscosity theory of non-Newtonian fluid, describing the dependence of the viscosity of colloidal oil solutions on the shear rate, is applied to filtration. A new physical model is proposed for taking into account the specifics of a colloidal solution flow through the pore space of low-permeable rocks. An equation is proposed that analytically describes the dependence of the filtration rate on pressure gradient. The similarity of the shear stress dependences on the shear rate obtained on rotary viscometers and the dependences of the filtration rate on the pressure gradient obtained experimentally for low permeable rocks during the flow of high-viscous oil is shown. The similar dependencies make it possible to use measurements using rotary viscometers to evaluate filtration parameters in low-permeable reservoirs.

Bibliography:

1. Osnovnye rezul'taty issledovaniy nelineynoy fil'tratsii v nizkopronitsaemykh kollektorakh / A.V. Khanov, I.R. Yakupova, E.S. Tumanova, D.Yu. Bunin // Neftepromyslovoe delo. – 2021. – № 2(626). – S. 25–29. – DOI: 10.33285/0207-2351-2021-2(626)-25-29

2. Nelineynaya fil'tratsiya v nizkopronitsaemykh kollektorakh. Analiz i interpretatsiya rezul'tatov laboratornykh issledovaniy kerna Priobskogo mestorozhdeniya/ V.V. Baykov, R.R. Galeev, A.V. Kolonskikh [i dr.] // Nauch.-tekhn. vestn. OAO "NK "Rosneft'". – 2013. – № 2(31). – S. 8–12

3. Nelineynaya fil'tratsiya v nizkopronitsaemykh kollektorakh. Laboratornye fil'tratsionnye issledovaniya kerna Priobskogo mestorozhdeniya / V.V. Baykov, A.V. Kolonskikh, A.K. Makatrov [i dr.] // Nauch.-tekhn. vestn. OAO "NK "Rosneft'". – 2013. – № 2(31). – S. 4–7.

4. Mikhaylov N.N., Tumanova E.S., Zaytsev M.V. Stepennoy zakon fil'tratsii i ego sledstviya dlya nizkopronitsaemykh kollektorov // Neft. khoz-vo. – 2020. – № 4. – S. 34–37. – DOI: 10.24887/0028-2448-2020-4-34-37

5. Borshchuk O.S., Zhitnikov V.P. Nelineynaya fil'tratsiya v nizkopronitsaemykh kollektorakh. Chislennaya skhema, analiz ustoychivosti i skhodimosti // Nauch.-tekhn. vest. OAO "NK "Rosneft'". – 2013. – № 2(31). – S. 13–16.

6. Shiryaev E.S., Zinov'ev A.M. Vliyanie razrusheniya struktury vysokovyazkoy nefti na effektivnost' protsessa zavodneniya // Neftepromyslovoe delo. – 2022. – № 1(637). – S. 10–14. – DOI: 10.33285/0207-2351-2022-1(637)-10-14

7. Vliyanie obrazovaniya nadmolekulyarnykh struktur na fil'tratsiyu nefti v poristoy srede / V.E. Gal'tsev, I.M. Ametov, E.M. Dzyubenko [i dr.] // Kolloidnyy zhurnal. – 1995. – T. 57, № 5. – S. 660–665.

8. Galtsev V.E., Ametov I.M., Grinberg O.Y. Asphaltene association in crude oil as studied by ENDOR // Fuel. – 1995. – Vol. 74, No. 5. – P. 670–673. – DOI: doi.org/10.1016/0016-2361(94)00009-G

9. Shishkin Issledovanie termoreologicheskikh svoystv vysokovyazkoy nefti mestorozhdeniy Permskogo kraya na ustanovke WAXFLOW LOOP / P.Yu. Ilyushin, K.A. Vyatkin, A.V. Kozlov, N.A. Shishkin // Neftepromyslovoe delo. – 2022. – № 1(637). – S. 49–54. – DOI: 10.33285/0207-2351-2022-1(637)-49-54

10. Suleymanov B.A. Osobennosti fil'tratsii geterogennykh sistem. – M.–Izhevsk: Institut komp'yuternykh issledovaniy, 2006. – 356 s.

11. Barnes H.A. A Handbook of Non-Newtonian Fluid Mechanics. – Institute of Non-Newtonian Fluid Mechanics University of Wales, 2000. – 201 p.

12. Lesin V.I., Koksharov Yu.A., Khomutov G.B. Viscosity of liquid suspensions with fractal aggregates: Magnetic nanoparticles in petroleum colloidal structures // Colloids and Surfaces A: Physicochem. Eng. Aspects. – 2011. – Vol. 392. – P. 88–94.

13. Lesin V.I. Matematicheskaya model' vyazkosti tyazheloy nefti, soderzhashchey primesi kolloidnykh nanochastits oksidov metallov // Elektronnyy nauch. zhurnal Neftegazovoe delo. – 2019. – № 2. – C. 200–216. – DOI: 10.17122/ogbus-2019-2- 199-216

14. Bossis G., Grasselli Y., Volkova O. Capillary flow of a suspension in the presence of discontinuous shear thickening // Rheologica Acta. – 2022. – Vol. 61. – P. 1–12. – doi.org.10.1007/s00397-021-01305-0

15. Lesin V.I. Fizicheskiy mekhanizm vozniknoveniya "anomal'noy vyazkosti", oslozhnyayushchiy dobychu i transportirovku nefti // Elektronnyy nauch. zhurnal Neftegazovoe delo. – 2020. – № 5. – P. 74–92. – DOI: 10.17122/ogbus-2020-5-74-92

16. Roldugin V.I. Svoystva fraktal'nykh sistem // Uspekhi khimii. – 2003. – T. 72, № 11. – C. 1027–1054.

17. Lesin V.I., Alekseeva Yu.V. Issledovanie rezhimov vozdeystviya sdvigovymi napryazheniyami s tsel'yu snizheniya vyazkosti nefti // Ekspozitsiya. Neft'. Gaz. – 2020. – № 2. – S. 56–60. – DOI: 10/24411/2076-6785-2020-10080

18. Lesin V.I., Lesin S.V. Vliyanie kolebaniy davleniya na vyazkost' nefti, soderzhashchey kolloidnye chastitsy // Aktual'nye problemy nefti i gaza. – 2019. – Vyp. 1(24). – DOI: 29222/ipng.2078-5712.2019-24.art11

19. Tao R., Tang H. Reducing viscosity of paraffin based crude oil with electric field for oil production and transportation // Fuel. – 2014. – Vol. 118. – P. 69–72.

20. Loskutova Yu.V., Yudina N.V. Vliyanie postoyannogo magnitnogo polya na reologicheskie svoystva vysokoparafinistykh neftey // Kolloidnyy zhurnal. – 2003. – T. 65, № 4. – S. 510–515.