Skip to main content
Log in

Pore-Scale Modeling of CO2 Injection Using Density Functional Hydrodynamics

  • Published:
Transport in Porous Media Aims and scope Submit manuscript

Abstract

The pore-scale numerical modeling of CO2 injection into natural rock saturated with oil–water mixture was performed using the density functional hydrodynamics approach. The detailed 3D digital model of the sandstone core sample contained over 7 billion cells, which allowed us to perform analysis of oil displacement efficiency at different scales. Utilization of large-size detailed numerical models make it possible to characterize, both qualitatively and quantitatively, the processes at pore scale to the level of detail not achievable on smaller models. The obtained results indicate large-scale effects even on relatively heterogeneous core indicating possible need for multiscale hierarchical models even in heterogeneous cases. This fact imposes the demand for scalability performance on both the software and hardware used in such simulations, as well as the need for adequate modeling upscaling methods.

Article Highlights

  • The density functional hydrodynamics framework for CO2 flood simulation on pore scale is presented

  • Three-phase density functional hydrodynamics simulation was carried out on a record-size digital rock model of 9000 × 900 × 900 voxels corresponding to a natural sandstone core sample

  • Although the sandstone is homogeneous, the local displacement efficiencies measured on 1.2 mm size windows change from as low as 0.59 to as high as 0.79 indicating large-scale phenomena at work

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6
Fig. 7

References

  • Alhosani, A., Bijeljic, B., Blunt, M.J.: Pore-Scale imaging and analysis of wettability order, trapping and displacement in three-phase flow in porous media with various wettabilities. Transp. Porous Media 140, 59–84 (2021). https://doi.org/10.1007/s11242-021-01595-1

    Article  CAS  Google Scholar 

  • Anderson, D.M., McFadden, G.B., Wheeler, A.A.: Diffuse-interface methods in fluid mechanics. Annu. Rev. Fluid Mech. 30, 139–165 (1998)

    Article  Google Scholar 

  • Andrä, H., Combaret, N., Dvorkin, J., Glatt, E., Han, J., Kabel, M., Keehm, Y., Krzikalla, F., Lee, M., Madonna, C., Marsh, M., Mukerji, T., Saenger, E.H., Sain, R., Saxena, N., Ricker, S., Wiegmann, A., Zhan, X.: Digital rock physics benchmarks—part I: imaging and segmentation. Comput. Geosci. 50, 25–32 (2013)

    Article  Google Scholar 

  • Armstrong, R.T., Berg, S., Dinariev, O., Evseev, N., Klemin, D., Koroteev, D., Safonov, S.: Modeling of pore-scale two-phase phenomena using density functional hydrodynamics. Transp. Porous Media 112, 577–607 (2016)

    Article  Google Scholar 

  • Batalin, O., Vafina, N.: Condensation mechanism of hydrocarbon field formation. Sci. Rep. 7, 10253 (2017). https://doi.org/10.1038/s41598-017-10585-7

    Article  CAS  Google Scholar 

  • Bear, J.: Dynamics of Fluids in Porous Media. American Elsevier Publishing Company, New York (1972)

    Google Scholar 

  • Berg, S., Rücker, M., Ott, H., Georgiadis, A., van der Linde, H., Enzmann, F., Kersten, M., Armstrong, R.T., de With, S., Becker, J., Wiegmann, A.: Connected pathway relative permeability from pore-scale imaging of imbibition. Adv. Water Resour. 90, 24–35 (2016)

    Article  Google Scholar 

  • Berg, C.F., Lopez, O., Berland, H.: Industrial application of digital rock technology. J. Pet. Sci. Eng. 157, 131–147 (2017)

    Article  CAS  Google Scholar 

  • Berg, C.F., Slotte, P.A., Khanamiri, H.H.: Geometrically derived efficiency of slow immiscible displacement in porous media. Phys. Rev. E 102, 033113 (2020)

    Article  CAS  Google Scholar 

  • Blunt, M.J., Bijeljic, B., Dong, H., Gharbi, O., Iglauer, S., Mostaghimi, P., Paluszny, A., Pentland, C.: Pore-scale imaging and modelling. Adv. Water Resour. 51, 197–216 (2013)

    Article  Google Scholar 

  • Bultreys, T., Boever, W.D., Cnudde, V.: Imaging and image-based fluid transport modeling at the pore scale in geological materials: a practical introduction to the current state-of-the-art. Earth Sci. Rev. 155, 93–128 (2016)

    Article  Google Scholar 

  • Cârcoanӑ, A.: Applied Enhanced Oil Recovery. Prentice Hall, Englewood Cliffs (1992)

    Google Scholar 

  • Coles, M.E., Hazlett, R.D., Spanne, P., Muegge, E.L., Furr, M.J.: Characterization of reservoir core using computed microtomography. SPE 2, 295–542 (1996)

    Google Scholar 

  • Debarre, D., Gahlot, P., Grillet, C., Plaisant, M.: Carbon Capture, Utilization and Storage. Kearney Energy Transition Institute, New York (2021)

    Google Scholar 

  • Demianov, A., Dinariev, O., Evseev, N.: Density functional modeling in multiphase compositional hydrodynamics. Can. J. Chem. Eng. 89, 206–226 (2011)

    Article  CAS  Google Scholar 

  • Demianov, A., Dinariev, O., Evseev, N.: Introduction to the Density Functional Method in Hydrodynamics. Fizmatlit, Moscow (2014)

    Google Scholar 

  • Dinariev, O.: A hydrodynamic description of a multicomponent multiphase mixture in narrow pores and thin layers. J. Appl. Math. Mech. 59, 745–752 (1995)

    Article  Google Scholar 

  • Dinariev, O.: Thermal effects in the description of a multicomponent mixture using the density functional method. J. Appl. Math. Mech. 62, 397–405 (1998)

    Article  Google Scholar 

  • Dinariev, O., Evseev, N.: Multiphase flow modeling with density functional method. Comput. Geosci. 20, 835–856 (2016)

    Article  Google Scholar 

  • Dinariev, O., Evseev, N.: Application of digital rock analysis for evaluation of gas-condensate transport, SPE-206587-MS (2021)

  • Dinariev, O., Evseev, N., Klemin, D.: Density functional hydrodynamics in multiscale pore systems: chemical potential drive. In: The 33th International Symposium of the Society of Core Analysts, Pau, France, 26–30 August, 2019, SCA2019-0009, E3S Web of Conferences, vol. 146, pp. 01001 (2020)

  • Dinariev, O., Evseev, N., Klemin, D.: The problem of stability of gas-condensate mixture at pore-scale: the study by density functional hydrodynamics. In: SCA-2021, E3S Web of Conferences, vol 366, pp. 01005 (2023). https://doi.org/10.1051/e3sconf/202336601005

  • Du, F., Nojabaei, B.: Estimating diffusion coefficients of shale oil, gas, and condensate with nano-confinement effect. J. Petrol. Sci. Eng. 193, 107362 (2020)

    Article  CAS  Google Scholar 

  • Dunsmuir, J.H. Ferguson, S.R., D’Amico, K.L., Stokes, J.P.: X-ray Microtomography: A New Tool for the Characterization of Porous Media, SPE-22860 (1991)

  • England, W.A., Mackenzie, A.S., Mann, D.M., Quigley, T.M.: The movement and entrapment of petroleum fluids in the subsurface. J. Geol. Soc. Lond. 144, 327–347 (1987)

    Article  CAS  Google Scholar 

  • Espinoza, D.N., Santamarina, J.C.: Water-CO2-mineral systems: Interfacial tension, contact angle, and diffusion—Implications to CO2 geological storage. Water Resour. Res. 46, W07537 (2010). https://doi.org/10.1029/2009WR008634

    Article  CAS  Google Scholar 

  • Golparvar, A., Zhou, Y., Wu, K., Ma, J., Yu, Zh.: A comprehensive review of pore scale modeling methodologies for multiphase flow in porous media. Adv Geo Energy Res 2(4), 418–440 (2018)

    Article  Google Scholar 

  • Hirt, C.W., Nichols, B.D.: Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys. 39(1), 201–225 (1981)

    Article  Google Scholar 

  • Hounsfield, G.N.: A method of and apparatus for examination of a body by radiation such as X- or gamma-radiation. British Patent No.1283915, London (1972)

  • Joekar-Niasar, V., van Dijke, M.I.J., Hassanizadeh, S.M.: Pore-scale modeling of multiphase flow and transport: achievements and perspectives. Transp. Porous Med. 94, 461–464 (2012)

    Article  Google Scholar 

  • Kamashev, A., Amanbek, Y.: Reservoir simulation of CO2 storage using compositional flow model for geological formations in Frio field and Precaspian basin. Energies 14(23), 8023 (2021)

    Article  CAS  Google Scholar 

  • Ketcham, R.A., Carlson, W.D.: Acquisition, optimization and interpretation of X-ray computed tomographic imagery: applications to the geosciences. Comput. Geosci. 27(4), 381–400 (2001)

    Article  CAS  Google Scholar 

  • Kim, J.: Phase-field models for multi-component fluid flows. Commun. Comput. Phys. 12(3), 613–661 (2012)

    Article  Google Scholar 

  • Klemin, D., Serebryanskaya, A., Savelev, O., Melnikov, S.: Digital Rock Technology Accelerates Carbonate Rock Laboratory Analysis. SPE-198610 (2019)

  • Kornilov, A., Safonov, I., Yakimchuk, I.: A review of watershed implementations for segmentation of volumetric images. J. Imaging 8(5), 127 (2022)

    Article  Google Scholar 

  • Koroteev, D., Dinariev, O., Evseev, N., Klemin, D., Nadeev, A., Safonov, S., Gurpinar, O., Berg, S., Van Kruijsdijk, C., Hathan, L., de Jong, H.: Direct hydrodynamic simulation of multiphase flow in porous rock. Petrophysics. 55, 294–303 (2014)

    Google Scholar 

  • Lake, L.W., Johns, R., Rossen, B.: Fundamentals of Enhanced Oil Recovery, SPE (2014). ISBN 9781613994078

  • Latil, M., Bardon, C., Burger, G., Sourieau, P.: Enhanced Oil Recovery. Editions Technip (1980)

  • Linstrom, P.J., Mallard, W.G., Eds.: NIST Chemistry WebBook, NIST Standard Reference Database Number 69, National Institute of Standards and Technology, Gaithersburg MD, 20899, https://doi.org/10.18434/T4D303 (retrieved January 18, 2024)

  • Liu, T., Wang, M.: Critical REV size of multiphase flow in porous media for upscaling by pore-scale modeling. Transp. Porous Media 144, 111–132 (2022)

    Article  CAS  Google Scholar 

  • Lyons, W.C., Plisga, G.J.: Standard Handbook of Petroleum and Natural Gas Engineering, 2nd edn. Elsevier Inc., Burlington (2005)

    Google Scholar 

  • Mavar, K.N., Gaurina-Međimurec, N., Hrnčević, L.: Significance of enhanced oil recovery in carbon dioxide emission reduction. Sustainability 13, 1800 (2021). https://doi.org/10.3390/su13041800

    Article  CAS  Google Scholar 

  • McPhee, C., Reed J., Zubizarreta, I.: Core analysis: a best practice guide. In: Developments in petroleum science volume 64. Elsevier B.V., Amsterdam, Netherlands (2015)

  • Núñez-López, V., Moskal, E.: Potential of CO2-EOR for near-term decarbonization. Front. Clim. 1, 1–14 (2019). https://doi.org/10.3389/fclim.2019.00005

    Article  Google Scholar 

  • Oh, W., Lindquist, W.B.: Image thresholding by indicator kriging. IEEE Trans. Pattern Anal. Mach. Intell. 21(7), 590–602 (1999)

    Article  Google Scholar 

  • Peskin, C.S.: The immersed boundary method. Acta Numer. 11, 479–517 (2002)

    Article  Google Scholar 

  • Saraf, S., Bera, A.: A review on pore-scale modeling and CT scan technique to characterize the trapped carbon dioxide in impermeable reservoir rocks during sequestration. Renew. Sustain. Energy Rev. 144, 110986 (2021)

    Article  CAS  Google Scholar 

  • Saxena, N., Hofmann, R., Alpak, F.O., Berg, S., Dietderich, J., Agarwal, U., Tandon, K., Hunter, S., Freeman, J., Wilson, O.B.: References and benchmarks for pore-scale flow simulated using micro-CT images of porous media and digital rocks. Adv. Water Resour. 109, 211–235 (2017)

    Article  Google Scholar 

  • Schlüter, S., Berg, S., Rücker, M., Armstrong, R.T., Vogel, H.-J., Hilfer, R., Wildenschild, D.: Pore-scale displacement mechanisms as a source of hysteresis for two-phase flow in porous media. Water Resour. Res. 52, 2194–2205 (2016)

    Article  Google Scholar 

  • Sedov, L.I.: Mechanics of Continuous Media, vol. 1. World Scientific, Singapore (1997)

    Google Scholar 

  • Seyyedi, M., Sohrabi, M.: Oil reservoir on a chip: pore-scale study of multiphase flow during near-miscible CO2 EOR and storage. Transp. Porous Media 134, 331–349 (2020). https://doi.org/10.1007/s11242-020-01448-3

    Article  CAS  Google Scholar 

  • Shah, S.M., Crawshaw, J.P., Gray, F., Yang, J., Boek, E.S.: Convex hull approach for determining rock representative elementary volume for multiple petrophysical parameters using pore-scale imaging and Lattice-Boltzmann modelling. Adv. Water Resour. 104, 65–75 (2017)

    Article  Google Scholar 

  • Shandrygin, A., Shelepov, V., Ramazanov, R., Andrianov, N., Klemin, D., Nadeev, A., Safonov, S., Yakimchuk, I.: Mechanism of Oil Displacement During Polymer Flooding in Porous Media with Micro-Inhomogeneities. SPE-182037-RU (2016)

  • Stauffer, D.: Scaling theory of percolation clusters. Phys. Rep. (rev. Sect. Phys. Lett.) 54, 1–74 (1979)

    Google Scholar 

  • Tinet, A.-J., Corlay, Q., Collon, P., Golfier, F., Kalo, K.: Comparison of various 3D pore space reconstruction methods and implications on transport properties of nanoporous rocks. Adv. Water Resour. 141, 103615 (2020)

    Article  Google Scholar 

  • Tomasi, C., Manduchi, R.: Bilateral filtering for gray and color images. In: Proceedings of the IEEE International Conference on Computer Vision, Bombay, India, pp. 839–846 (1998)

  • Tryggvason, G., Bunner, B., Esmaeeli, A., Juric, D., Al-Rawahi, N., Tauber, W., Han, J., Nas, S., Jan, Y.J.: A front-tracking method for the computations of multiphase flow. J. Comput. Phys. 169(2), 708–759 (2001)

    Article  CAS  Google Scholar 

  • Wang, Zh., Hou, J.: Measurement of CO2 diffusion coefficients in both bulk liquids and carven filling porous media of fractured-vuggy carbonate reservoirs at 50 MPa and 393 K. RSC Adv. 11, 19712 (2021)

    Article  CAS  Google Scholar 

  • Wang, Y.D., Meyer, Q., Tang, K., McClure, J.E., White, R.T., Kelly, S.T., Crawford, M.M., Iacoviello, F., Brett, D.J.L., Shearing, P.R., Mostaghimi, P., Zhao, C., Armstrong, R.T.: Large-scale physically accurate modelling of real proton exchange membrane fuel cell with deep learning. Nat. Commun. 14, 745 (2023). https://doi.org/10.1038/s41467-023-35973-8

    Article  CAS  Google Scholar 

  • Wellington, S.L., Vinegar, H.J.: X-ray computerized tomography. J. Petrol. Technol. 39, 885–898 (1987)

    Article  Google Scholar 

  • White, M.D., McPherson, B.J., Grigg, R.B., Ampomah, W., Appold, M.S.: Numerical simulation of carbon dioxide injection in the western section of the farnsworth unit. Energy Procedia 63, 7891–7912 (2014)

    Article  CAS  Google Scholar 

  • Yakimchuk, I., Evseev, N., Korobkov, D., Varfolomeev, I., Dinariev, O., Khan, V., Orlov, D., Muravleva, E., Belozerov, B., Krutko, V., Kondratev, A.: Permeability and porosity study of achimov formation using digital core analysis. Soc. Pet. Eng. (2019). https://doi.org/10.2118/196928-MS

    Article  Google Scholar 

  • Yakimchuk, I., Evseev, N., Korobkov, D., Dinariev, O., Ridzel, O., Khan, V., Semkov, V., Zhonin, A., Kravets, D.: Digital Core Analysis—Innovative Approach for EOR Agent Screening at Pore-Scale for Achimov Rocks. SPE-202015-MS (2020a)

  • Yakimchuk, I., Evseev, N., Korobkov, D., Ridzel, O., Pletneva, V., Yaryshev, M., Ilyasov, I., Glushchenko, N., Orlov, A.: Study of Polymer Flooding at Pore Scale by Digital Core Analysis for East-Messoyakhskoe Oil Field. SPE-202013-MS (2020b)

  • Yang, Z., Liu, X., Hua, Z., Ling, Y., Li, M., Lin, M., Dong, Z.: Interfacial tension of CO2 and crude oils under high pressure and temperature. Colloids Surf. A Physicochem. Eng. Aspects 482, 611–616 (2015)

    Article  CAS  Google Scholar 

  • Yang, Y., Stenby, E.H., Shapiro, A.A., Yan, W.: Diffusion coefficients in systems related to reservoir fluids: available data and evaluation of correlations. Processes 10(8), 1554 (2022)

    Article  CAS  Google Scholar 

  • Yang, Y., Wang, J., Wang, J., Li, Y., Sun, H., Zhang, L., et al.: Pore-scale modeling of coupled CO2 flow and dissolution in 3D porous media for geological carbon storage. Water Resour. Res. 59, e2023WR035402 (2023). https://doi.org/10.1029/2023WR035402

    Article  CAS  Google Scholar 

  • Zacharov, I., Arslanov, R., Gunin, M., Stefonishin, D., Bykov, A., Pavlov, S., Panarin, O., Maliutin, A., Rykovanov, S., Fedorov, M.: “Zhores”—Petaflops supercomputer for data-driven modeling, machine learning and artificial intelligence installed in Skolkovo Institute of Science and Technology. Open Eng. 9(1), 512–520 (2019)

    Article  Google Scholar 

Download references

Funding

This work was funded by LLC TCS.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Nikolay Evseev.

Ethics declarations

Conflict of interest

The authors report no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dinariev, O., Evseev, N., Sidorenkov, A. et al. Pore-Scale Modeling of CO2 Injection Using Density Functional Hydrodynamics. Transp Porous Med 151, 753–771 (2024). https://doi.org/10.1007/s11242-024-02064-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11242-024-02064-1

Keywords

Navigation