Pressure Drops in Water-Oil Mixture Flow in Porous Channels

Tyumen State University Herald. Physical and Mathematical Modeling. Oil, Gas, Energy


Release:

2016, Vol. 2. №2

Title: 
Pressure Drops in Water-Oil Mixture Flow in Porous Channels


About the authors:

Aleksandr B. Shabarov, Dr. Sci. (Tech.), Professor, Department of Applied and Technical Physics, Institute of Physics and Technology, University of Tyumen; eLibrary AuthorID, ORCID, ResearcherID, ScopusID, kaf_mms@utmn.ru

Alexander V. Shatalov, Postgraduate Student, Engineer, Department of Multiphase Systems Mechanics, University of Tyumen; sashatl@yandex.ru

Abstract:

The aim of the study is to develop an algorithm for constructing the curves of relative permeabilities (RP) according to the time-efficient laboratory tests of the core material: absolute permeability K0, capillary pressure curves, residual water saturation values SWC = S*, and residual oil saturation 1 – Sor = S*, as well as relative permeability of the core on the water fWS* and oil fPS* in the given bordering points.

To obtain the generalized experimental data about the parameters of interphase interaction, the authors use the RP dependencies on water saturation for the core samples of the characteristic lithological types.

The methodology of calculation of the pressure loss in the flow of oil-water mixture in the pore channels is given with the help of the developed network of the cluster model of a porous medium. The losses on the section of the channel losses are presented as the sum of the three components of the pressure loss: on the viscous friction of the wall of the pore channels; local losses with the changes in the cross-sectional area and the presence of the channel curvature; and the pressure loss in interfacial interactions of the filtering mixture.

Results of pressure loss curves for interfacial interactions for a number of core samples from the fields in Siberia, obtained in the calculation study, are presented.

It has been found that this type of loss in the dimensionless variables can be described as the universal two-parameter “bell” function of water saturation; the values of empirical parameters have been selected.

The obtained data allow to suggest computational and experimental methods for determining the RP, which consists in experimental determination of the parameters K0, S*, S*, fWS*, fPS* and the capillary pressure curves followed by the calculation of the RP dependency on water saturation based on the results of the research outlined in this paper.

References:

  1. Al-Gharbi M. S. 2004. “Dynamic Pore-Scale Modelling of Two-Phase Flow”. PhD thesis. University of London and the Diploma of Imperial College.
  2. Altunin A. Ye., Sokolov S. V., Stepanov S. V., Cheremisin N. A., Shabarov A. B. 2013. “Raschetnyy metod polucheniya OFP na osnove resheniya obobshchennykh uravneniy Bernulli dlya sistemy porovykh kanalov” [Calculation Method for Producing RP (Relative Permeability) Based on the Decision of the Generalized Bernoulli Equation for the Pore Channels of the System]. Neftepromyslovoe delo, no 8, pp. 40–46.
  3. Atabekov G. I. 1978. Teoreticheskie osnovy elektrotekhniki [Theoretical Foundations of Electrical Engineering]. In 3 vols. Vol. I. Lineynye elektricheskie tsepi: uchebnik dlya vuzov [Linear Circuits: Students’ Textbook]. 5th edition, revised, p. 158. Moscow: Energiya.
  4. Avraam D. G., Payatakes A. C. 1995. “Generalized Relative Permeability Coefficients during Steady-State Two-Phase Flow in Porous Media, and Correlation with the Flow Mechanisms”. Transport in Porous Media, vol. 20, pp. 135–168. DOI: 10.1007/BF00616928
  5. Basniev K. S., Kochina I. N., Maksimov V. M. 1993. Podzemnaya gidromekhanika: Uchebnik dlya vuzov [Underground Fluid Mechanics: Students’ Textbook]. Moscow: Nedra.
  6. Brooks R. H., Corey A. T. 1964. “Hydraulic Properties of Porous Media”. Hydrology Papers, no 3. Colorado State U., Fort Collins, Colorado.
  7. Burdine N. T. 1953. “Relative Permeability Calculations from Pore Size Distribution Data”. Journal of Petroleum Technology, March, vol. 5, no 3, pp. 71–78. DOI: 10.2118/225-G
  8. Burdine N. T., Gournay L. S., Reichertz P. P. 1950. “Pore Size Distribution of Petroleum Reservoir Rocks”. Journal of Petroleum Technology, July, vol. 2, no 7, pp. 195–204. DOI: 10.2118/950195-G
  9. Corey A. T. 1954. “The Interrelation between Gas and Oil Relative Permeabilities”. Producers Monthly, November 19, pp. 38–41.
  10. Demyanov A. Yu., Dinariev O. Yu., Yevseev N. V. 2009. Osnovy metoda funktsionala plotnosti v gidrodinamike [Foundations of the Density Functional Theory Method in Hydrodynamics]. Moscow: FIZMATLIT.
  11. Doroginitskaya L. M., Yenikeev B. N., Yefimov V. A., Isaev G. D., Kostenevich K. A., Malshakov A. V., Ratnikov I. B., Semenov V. V., Sokova K. I., Fedortsov I. V., Shnurman I. G. 2010. Aktualnye voprosy petrofiziki slozhno postroennykh kollektorov [Topical Petrophysics Issues of Complex Collectors]. Edited by I. G. Shnurman. Krasnodar: Prosveshchenie-Yug.
  12. Ehrlich R., F. E. Crane 1969. “A Model for Two-Phase Flow in Consolidated Materials”. Society of Petroleum Engineers Journal, June, vol. 2, no 2, pp. 221–231. DOI: 10.2118/2231-PA
  13. Fatt I. 1956. “The Network Model of Porous Media, I. Capillary Pressure Characteristics”. Petroleum Transactions, AIME, vol. 207, pp. 144–159.
  14. Fatt I. 1956. “The Network Model of Porous Media, II. Dynamic Properties of a Single Size Tube Network”. Petroleum Transactions, AIME, vol. 207, pp. 160–181.
  15. Fatt I., Dykstra H. 1951. “Relative Permeability Studies”. Journal of Petroleum Technology, September, vol. 3, no 9, pp. 249–256. DOI: 10.2118/951249-G
  16. Gates J. I., Lietz W. T. 1950. “Relative Permeabilities of California Cores by the Capillary — Pressure Method”. Paper Presented at the Drilling and Production Practice Conference (New York, January1). API-50-285.
  17. Jamin M. J. 1860. “Mémoire sur l’équilibre et le movement des liquids dans les corps poreux”. Comptes rendus hebdomadaires des séances de l'Académie des sciences, no 50, pp. 172-176.
  18. Kalitkin N. N. 1978. Chislennye metody. Uchebnoe posobie dlya studentov vuzov [Numerical Methods: Students’ Textbook]. Edited by Ye. V. Shikin. Moscow: Nauka.
  19. Langaas K., Papatzacos P. 2001. “Numerical Investigations of the Steady State Relative Permeability of a Simplified Porous Medium”. Transport in Porous Media, November, vol. 45, no 2, pp. 241–266. DOI: 10.1023/A:1012002002804
  20. Malshakov A. V., Yefimov V. A. 1991. “Pronitsaemost i perkolyatsionnye svoystva porovogo prostranstva osadochnykh gornykh porod”. Inzhenerno-fizicheskiy zhurnal, vol. 61, no 4, pp. 635–640.
  21. Øren P. E., Bakke S., Rueslåtten H. G. 2006. “Digital Core Laboratory Rock and Flow Properties Derived from Computer Generated Rocks”. Paper Presented at the SCA2006-21 (Norway, Trondheim, November 12–16).
  22. Payatakes A. C., Dias M. M. 1984. “Immiscible Microdisplacement and Ganglion Dynamics in Porous Media”. Reviews in Chemical Engineering, vol. 2, pp. 85–174. DOI: 10.1515/REVCE.1984.2.2.85
  23. Payatakes A. C., Ng K. M., Flumerfelt R. W. 1980. “Oil Ganglion Dynamics during Immiscible Displacement: Model Formulation”. American Institute of Chemical Engineers Journal, vol. 26, no 3, pp. 430–443. DOI: 10.1002/aic.690260315
  24. Piri M. 2003. “Pore-Scale Modeling of Three-Phase Flow”. PhD thesis. University of London and the Diploma of Imperial College December.
  25. Purcell W. R. 1949. “Capillary Pressures — Their Measurement Using Mercury and the Calculation of Permeability Therefrom”. Journal of Petroleum Technology, February, vol. 1, no 2, pp. 39–48. DOI: 10.2118/949039-G
  26. Raeini A. Q. 2013. “Modelling Multiphase Flow through Micro-CT Images of the Pore Space”. PhD thesis. Supervised by Dr Branko Bijeljic and Prof. Martin Blunt. Imperial College London.
  27. Shabarov A. B. 2013. Gidrogazodinamika: uchebnoe posobie [Fluid Dynamics: Textbook]. 2nd edition, reworked, p. 156. Tyumen: Tyumen State University.
  28. Shabarov A. B., Saranchin N. V., Chistyakova N. F., Shirshova A. V., Puldas L. A., Stupnikov A. A., Vetrov I. M., Shatalov A. V., Bembel G. S., Vakulin A. A., Varyukhin S. Ye., Berdyugin S. V., Medvedev D. N., Molchanov D. A., Vorobyov V. V. 2011. The Final Report on “Chislennoe issledovanie protsessa vytesneniya v masshtabakh kerna dlya polucheniya soglasovannykh krivykh kapillyarnogo davleniya i otnositelnykh fazovykh pronitsaemostey” [Numerical Investigation of the Process of Repression Across the Core for Consistent Curve of Capillary Pressure and Relative Permeability] (Framework Agreement of Tyumen Oil Research Center—Tyumen State University of June 16, 2011)] Tyumen Oil Research Center–Tyumen State University.
  29. Shabarov A. B., Shatalov A. V. 2016. “Geometricheskaya model porovogo prostranstva dlya rascheta filtratsii nefti i vody” [Geometric Model of the Pore Space to Calculate Oil and Water Filtration]. In: Proceedings of the 9th seminar-school of young scientists “Teplofizika, teplotekhnika, gidrogazodinamika. Innovatsionnye tekhnologii” under the supervision of honored RF science representative professor Shabarov A. B. (Tyumen, May 25-27, 2016), pp. 25–36. Tyumen: Tyumen State University.
  30. Stepanov S. V. Shabarov A. B., Bembel G. S., Shatalov A. V. 2015. “Issledovanie dinamicheskikh fazovykh pronitsaemostey na osnove chislennogo modelirovaniya dvukhfaznogo techeniya v porovykh kanalakh” [Investigation of Dynamic Permeability, Based on Numerical Simulation of Two-Phase Flow in Porous Channels]. In: Akhmetov D. Yu., Gerasimov A. N., Khaydarov Sh. M. (comps). 2015. XI Vserossiyskiy syezd po fundamentalnym problemam teoreticheskoy i prikladnoy mekhaniki: sbornik dokladov (Kazan, 20–24 avgusta 2015 g.). Edited by D. A. Gubaydullin, A. M. Yelizarov, Ye. K. Lipachev. Pp. 3600–3601. Kazan: Kazan University. 
  31. USSR Industrial Standard 39-235-89 of July 1, 1989. “Neft. Metod opredeleniya fazovykh pronitsaemostey v laboratornykh usloviyakh pri sovmestnoy statsionarnoy fil'tratsii” [Oil. The Method for Permeability Determining under the Laboratory Conditions in the Joint Stationary Filtration].
  32. Valavanides M. S. 2015. “ImproDeProF Project: Recent Advances and New Challenges in the Development of the DeProF Tentative Theory for Steady-State Two-Phase Flow in Porous Media”. Paper Presented at the International Conference “Science in Technology” SCinTE 2015 (Greece, Athens, November 5-7).
  33. Valavanides M. S., Payatakes A. C. 2001. “True-to-Mechanism Model of Steady-State Two-Phase Flow in Porous Media, Using Decomposition into Prototype Flows”. Advanced Water Resources, vol. 24, pp. 385–407. DOI: 10.1016/S0309-1708(00)00063-4
  34. Valvatne P. H. 2004. “Predictive Pore-Scale Modelling of Multiphase Flow”. PhD diss. Imperial college of London.