Modeling the process of oil displacement by a heat carrier considering the capillary effect

Authors

DOI:

https://doi.org/10.15587/1729-4061.2019.174439

Keywords:

oil production, cracks from hydraulic fracturing, numerical methods of quasiconformal mappings, nonlinear problems

Abstract

The manuscript is aimed at improving the mathematical model of oil production in a heterogeneous environment with the use of a thermal mode of displacement considering the action of capillary effect. We have constructed an algorithm to solve numerically the respective nonlinear boundary value problem on multiphase filtering by introducing the function of quasi-potential  and the respective, conjugated thereto, flow function . In this case, the quasi-potential is represented in the form  thereby having essentially simplified the overall strategy to split the algorithm for solving the original problem.

Owing to the algorithm, which is based on the ideas of methods for quasiconformal mapping and staged registration of parameters, we have carried out calculations of the hydrodynamic grid, velocity fields, temperature, saturation, taking into consideration the impact of a capillary effect and when ignoring it. In particular, the charts of saturation fields demonstrate a difference in the ratio of percentage content of a displacing fluid up to 15 % at temperatures above 80 °C, which explains the effect of capillary forces. Instead, at temperatures from 50 °С to 70 °С the difference is not noticeable, though at 50 °С and below the results of flooding slightly differ (to 5 %) for the worse in terms of the actual representation of the process. In this case, it is believed that the dynamic viscosities of phases change with a change in temperature, the fluid movement is slow and occurs without phase transitions, while functions of relative phase permeabilities and capillary pressure are the known and unambiguous saturation functions.

Numerical calculations of multiphase non-isothermal filtering in the symmetry element at a five-point system of flooding have been presented. In this case, it was found that taking into account the capillary effect makes it possible to not only predict the location of stagnant zones, but also to more accurately estimate the time when a displacing reagent breaks through in an operational well in order to effectively perform respective waterproofing operations.

Author Biographies

Olga Michuta, National University of Water and Environmental Engineering Soborna str., 11, Rivne, Ukraine, 33028

PhD

Department of Applied Mathematics

Alesia Sinchuk, Rivne State University of Humanities Plastova str., 31, Rivne, Ukraine, 33028

PhD

Department of Computer Science and Applied Mathematics

Serhii Yaroshchak, National University of Water and Environmental Engineering Soborna str., 11, Rivne, Ukraine, 33028

PhD

Department of Applied Mathematics

References

  1. Fazlyev, R. T. (2008). Ploshchadnoe zavodnenie neftyanyh mestorozhdeniy. Moscow: Izhevsk, IKI, NITS RHD, 256.
  2. Chekalyuk, E. B. (1965). Termodinamika neftyanogo plasta. Moscow: Nedra, 238.
  3. Astaf'ev, V. I., Fedorchenko, G. D. (2007). Modelirovanie fil'tratsii zhidkosti pri nalichii treshchiny gidravlicheskogo razryva plasta. Vestnik Samarskogo gosudarstvennogo tehnicheskogo universiteta. Seriya: Fiziko-matematicheskie nauki, 2 (15), 128–132.
  4. Jahandideh, A., Jafarpour, B. (2016). Optimization of hydraulic fracturing design under spatially variable shale fracability. Journal of Petroleum Science and Engineering, 138, 174–188. doi: https://doi.org/10.1016/j.petrol.2015.11.032
  5. Bomba, A. Ya., Sinchuk, A. M., Yaroschak, S. V. (2015). The complex analysis methods for modeling the oil displacement process by the heat transfer fluid taking into account the hydraulic fracturing effect. System Research & Information Technologies, 1, 130–140.
  6. Bomba, A., Sinchuk, A. (2016). Modeling of impact of hydraulic fractures on the process of fluid displacement from low-permeability sedimentary rocks. Eastern-European Journal of Enterprise Technologies, 4 (8 (82)), 49–55. doi: https://doi.org/10.15587/1729-4061.2016.73368
  7. Miehe, C., Mauthe, S. (2016). Phase field modeling of fracture in multi-physics problems. Part III. Crack driving forces in hydro-poro-elasticity and hydraulic fracturing of fluid-saturated porous media. Computer Methods in Applied Mechanics and Engineering, 304, 619–655. doi: https://doi.org/10.1016/j.cma.2015.09.021
  8. Wang, H. (2015). Numerical modeling of non-planar hydraulic fracture propagation in brittle and ductile rocks using XFEM with cohesive zone method. Journal of Petroleum Science and Engineering, 135, 127–140. doi: https://doi.org/10.1016/j.petrol.2015.08.010
  9. Abdollahipour, A., Fatehi Marji, M., Yarahmadi Bafghi, A., Gholamnejad, J. (2015). Simulating the propagation of hydraulic fractures from a circular wellbore using the Displacement Discontinuity Method. International Journal of Rock Mechanics and Mining Sciences, 80, 281–291. doi: https://doi.org/10.1016/j.ijrmms.2015.10.004
  10. Salama, A. (2018). Modeling of flux decline behavior during the filtration of oily-water systems using porous membranes: Effect of pinning of nonpermeating oil droplets. Separation and Purification Technology, 207, 240–254. doi: https://doi.org/10.1016/j.seppur.2018.06.043
  11. Miah, M. I., Elhaj, M. A., Ahmed, S., Hossain, M. E. (2018). Modeling of temperature distribution and oil displacement during thermal recovery in porous media: A critical review. Fuel, 226, 423–440. doi: https://doi.org/10.1016/j.fuel.2018.04.018
  12. Wójcik, W. (2016). Fractional flow formulation for three-phase non-isothermal flow in porous media. PRZEGLĄD ELEKTROTECHNICZNY, 1 (7), 26–33. doi: https://doi.org/10.15199/48.2016.07.04
  13. Nojabaei, B., Siripatrachai, N., Johns, R. T., Ertekin, T. (2016). Effect of large gas-oil capillary pressure on production: A compositionally-extended black oil formulation. Journal of Petroleum Science and Engineering, 147, 317–329. doi: https://doi.org/10.1016/j.petrol.2016.05.048
  14. Telegin, I. G., Bocharov, O. B. (2019). A change in oil viscosity during crude oil production influence on the solutions of counter-current capillary. Oil and Gas Studies, 6, 71–78. doi: https://doi.org/10.31660/0445-0108-2018-6-71-78
  15. Ber, Ya., Zaslavski, D. (1971). Fiziko-matematicheskie osnovy fil'tratsii vody. Moscow: Mir, 452.
  16. Dahi Taleghani, А. (2009). Analysis of hydraulic fracture propagation in fractured reservoirs: an improved model for the interaction between induced and natural fractures. University of Texas at Austin, 216.
  17. Zhang, S., Yin, S. (2014). Determination of in situ stresses and elastic parameters from hydraulic fracturing tests by geomechanics modeling and soft computing. Journal of Petroleum Science and Engineering, 124, 484–492. doi: https://doi.org/10.1016/j.petrol.2014.09.002
  18. Bomba, А. Y., Yaroshchak, S. V. (2012). Complex approach to modeling of two-phase filtration processes under control conditions. Journal of Mathematical Sciences, 184 (1), 56–68. doi: https://doi.org/10.1007/s10958-012-0852-x
  19. Bomba, A. Ya., Sinchuk, A. M. (2013). Kompleksnyi analiz povedinky systemy «sverdlovyny-trishchyny-plast» v elementakh ploshchadnoho zavodnennia. Visnyk NTU «KhPI». Seriya: Matematychne modeliuvannia v tekhnitsi ta tekhnolohiiakh, 54 (1027), 4–15.
  20. Salimzadeh, S., Khalili, N. (2015). A three-phase XFEM model for hydraulic fracturing with cohesive crack propagation. Computers and Geotechnics, 69, 82–92. doi: https://doi.org/10.1016/j.compgeo.2015.05.001
  21. Bomba, A. Ya., Sinchuk, A. M., Yaroshchak, S. V. (2016). Modeliuvannia filtratsiynykh protsesiv u naftohazovykh plastakh chyslovymy metodamy kvazikonformnykh vidobrazhen. Rivne: TzOV «Assol», 238.

Downloads

Published

2019-07-30

How to Cite

Michuta, O., Sinchuk, A., & Yaroshchak, S. (2019). Modeling the process of oil displacement by a heat carrier considering the capillary effect. Eastern-European Journal of Enterprise Technologies, 4(5 (100), 49–55. https://doi.org/10.15587/1729-4061.2019.174439

Issue

Vol. 4 No. 5 (100) (2019): Applied physics

Section

Applied physics

License

Copyright (c) 2019 Olga Michuta, Alesia Sinchuk, Serhii Yaroshchak

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

The consolidation and conditions for the transfer of copyright (identification of authorship) is carried out in the License Agreement. In particular, the authors reserve the right to the authorship of their manuscript and transfer the first publication of this work to the journal under the terms of the Creative Commons CC BY license. At the same time, they have the right to conclude on their own additional agreements concerning the non-exclusive distribution of the work in the form in which it was published by this journal, but provided that the link to the first publication of the article in this journal is preserved.

A license agreement is a document in which the author warrants that he/she owns all copyright for the work (manuscript, article, etc.).
The authors, signing the License Agreement with TECHNOLOGY CENTER PC, have all rights to the further use of their work, provided that they link to our edition in which the work was published.
According to the terms of the License Agreement, the Publisher TECHNOLOGY CENTER PC does not take away your copyrights and receives permission from the authors to use and dissemination of the publication through the world's scientific resources (own electronic resources, scientometric databases, repositories, libraries, etc.).
In the absence of a signed License Agreement or in the absence of this agreement of identifiers allowing to identify the identity of the author, the editors have no right to work with the manuscript.
It is important to remember that there is another type of agreement between authors and publishers – when copyright is transferred from the authors to the publisher. In this case, the authors lose ownership of their work and may not use it in any way.