Extending CO₂–Oil Relative Permeability Determination Based on Pore-Scale Simulation Using a Phase-Field Approach for Real Porous Media with Nonconstant Fluid Properties

Document Type : Research Paper

Authors

1 Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran

10.22050/ijogst.2025.444342.1704
Abstract
Experimental analysis and numerical simulation of CO₂ injection in oil and gas reservoirs are essential for CO₂ sequestration and enhanced oil recovery applications. However, experimental approaches are often expensive and time-consuming, while numerical methods require input parameters such as two-phase relative permeabilities. In this study, two-phase flow simulations are conducted using a numerical solver based on the phase-field approach under steady-state conditions to determine relative permeability curves. Specifically, flow simulations are performed in realistic porous media, and nonconstant fluid viscosity and density are incorporated, addressing limitations of previous studies. Therefore, the main contribution of this work is the determination of CO₂–oil relative permeabilities in realistic porous media extracted from micro-CT images under conditions of variable fluid viscosity and density. In addition, the influences of wetting properties and hysteresis on relative permeability behavior are investigated.
The numerical results indicate that increased wettability toward the injected fluid enhances displacement efficiency by shifting the intersection point of the relative permeability curves to the right, leading to higher oil recovery, particularly at larger contact angles corresponding to non-wetting conditions and at lower surface tensions. Furthermore, the separation between imbibition and drainage relative permeability curves, representing hysteresis effects, becomes more pronounced as wettability shifts toward larger contact angles. These findings demonstrate the capability of steady-state pore-scale simulations based on the phase-field approach to reliably determine CO₂–oil relative permeability curves when realistic porous media and nonconstant fluid properties are considered.

Highlights

·       Steady-state pore-scale simulations using the phase-field approach are employed to determine CO₂–oil relative permeabilities.

·       Simulations are performed on realistic porous media extracted from micro-CT images.

·       Nonconstant fluid viscosity and density are considered to represent realistic flow conditions.

·       The influence of wetting properties is taken into account.

·       The effects of hysteresis on relative permeability behavior are also investigated.

Keywords

Subjects

Ajayi T., Gomes J.S., and Bera A., A review of CO2 storage in geological formations emphasizing modeling, monitoring and capacity estimation approaches, Petroleum Science, Vol. 16, No. 5, 2019.
AkhlaghiAmiri H. A. and Hamouda A.A., Pore-scale modeling of non-isothermal two-phase flow in 2D porous media: Influences of viscosity, capillarity, wettability, and heterogeneity, International Journal of Multiphase Flow, Vol. 61, 2014.
Alpak F.O., Riviere B., and Frank F., A phase-field method for the direct simulation of two-phase flows in pore-scale media using a non-equilibrium wetting boundary condition, Computational Geosciences, Vol. 20, No. 5, 2016.
Alvarado V., and Manrique E., Enhanced oil recovery: An updated review, Energies, Vol. 3, No. 9. 2010.
Anderson W.G., Wettability literature survey-part 5: the effects of wettability on relative permeability, JPT, Journal of Petroleum Technology, Vol. 39, No. 11, 1987.
Arif M., Barifcani A., and Iglauer S., Solid/ CO2 and solid/water interfacial tensions as a function of pressure, temperature, salinity, and mineral type: Implications for CO2-wettability and CO2 geo-storage, International Journal of Greenhouse Gas Control, Vol. 53, 2016.
Badalassi V.E., Ceniceros H.D., and Banerjee S., Computation of multiphase systems with phase field models, Journal of Computational Physics, Vol. 190, No. 2, 2003.
Basirat F., Yang Z., and Niemi A., Pore-scale modeling of wettability effects on CO2–brine displacement during geological storage, Advances in Water Resources, Vol. 109, 2017.
Blunt M. J. et al., Pore-scale imaging and modeling, Advances in Water Resources, Vol. 51, 2013.
Blunt M.J., Jackson M.D., Piri M., and Valvatne P.H., Detailed physics, predictive capabilities and macroscopic consequences for pore-network models of multiphase flow, Advances in Water Resources, Vol. 25, No. 8–12, 2002.
Bogdanov I., Jardel S., Turki A., and Kamp A., Pore-scale phase field model of two-phase flow in porous medium, Annual COMSOL Conference, Paris, France, 2010.
Cahn J.W., and Hilliard J.E., Free energy of a nonuniform system. I. Interfacial free energy, The Journal of Chemical Physics, Vol. 28, No. 2, 1958.
Chiu P.H., and Lin Y.T., A conservative phase field method for solving incompressible two-phase flows, Journal of Computational Physics, Vol. 230, No. 1, 2011.
Choudhary N., NarayananNair A. K., et al., Bulk and interfacial properties of decane in the presence of carbon dioxide, methane, and their mixture, Scientific Reports, Vol. 9, No. 1, 2019.
Christensen J.R., Stenby E.H., and Skauge A., Review of WAG field experience, SPE Reservoir Evaluation and Engineering, Vol. 4, No. 2, 2001.
Ferrari A., Jimenez-Martinez J., et al., Challenges in modeling unstable two-phase flow experiments in porous micromodels, Water Resources Research, Vol. 51, No. 3, 2015.
Flannery B.P., Deckman H.W., et al., Three-dimensional X-ray microtomography, Science, Vol. 237, No. 4821, 1987.
Ghedan S., Global laboratory experience of CO2-EOR flooding, 2020.
Guo Y. et al., A pore-scale investigation of residual oil distributions and enhanced oil recovery methods, Energies, Vol. 12, No. 19, 2019.
He D., Jiang P., et al., Pore-scale CFD simulation of supercritical carbon dioxide drainage process in porous media saturated with water, Energy Sources, Part A: Recovery, Utilization and Environmental Effects, Vol. 41, No. 15, 2019.
Hemmati-Sarapardeh A., Ghazanfari M.H., Ayatollahi S., and Masihi M., Accurate determination of the CO2 crude oil minimum miscibility pressure of pure and impure CO2 streams: A robust modelling approach, The Canadian Journal of Chemical Engineering, Vol 94, p. 253–261, 2016.
Herring A.L., Harper E.J., Andersson L., et al., Effect of fluid topology on residual nonwetting phase trapping: Implications for geologic CO2 sequestration, Advances in Water Resources, Vol. 62, 2013.
Hirt C.W. and Nichols B.D., Volume of fluid (VOF) method for the dynamics of free boundaries, Journal of Computational Physics, Vol. 39, No. 1, 1981.
Hu  R., Wan J., Kim Y., and Tokunaga  T.K., Wettability effects on supercritical CO2 –brine immiscible displacement during drainage: Pore-scale observation and 3D simulation, International Journal of Greenhouse Gas Control, Vol. 60, p. 129–139, 2017.
Hu H.H., Patankar N.A., and Zhu M.Y., Direct numerical simulations of fluid-solid systems using the arbitrary Lagrangian-Eulerian technique, Journal of Computational Physics, Vol. 169, No. 2, 2001.
Huang W., Moving mesh methods based on moving mesh partial differential equations, Journal of Computational Physics, Vol. 113, No. 2, 1994.
Idowu N.A., and Blunt M. J., Pore-scale modeling of rate effects in waterflooding, Transport in Porous Media, Vol. 83, No. 1, 2010.
Jacqmin D., Calculation of two-phase Navier-Stokes flows using phase-field modeling, Journal of Computational Physics, Vol. 155, No. 1, 1999.
Joekar-Niasar V., Hassanizadeh S.M., and Dahle H.K., Non-equilibrium effects in capillarity and interfacial area in two-phase flow: Dynamic pore-network modeling, Journal of Fluid Mechanics, Vol. 655, 2010.
Kaldi J.G., Gibson-Poole C.M., and Payenberg T.H.D., Geological Input to Selection and Evaluation of CO2 Geosequestration Sites, AAPG Studies in Geology, 2009.
Kumar M., and Fogden A., Patterned wettability of oil and water in porous media, Langmuir, Vol. 26, No. 6, 2010.
Kumar S., Esmaeili S., Sarma H., and Maini B., Can affects
Kumar S., Esmaeili S., Sarma H., and Maini B., Can effects of temperature on two-phase gas/oil-relative permeabilities in porous media be ignored? A critical analysis, Energies, Vol. 13, No. 13. 2020.
Li, X., Xue, J., Wang, Y., Yang, W., Lu, J., Experimental study of oil recovery from pore of different sizes in tight sandstone reservoirs during CO2 flooding. Journal of Petroleum Sciences and Engineering, Vol. 208, 2022.
Liu J. and Song R., Investigation of water and CO2 flooding using pore-scale reconstructed model based on micro-CT images of Berea sandstone core, Progress in Computational Fluid Dynamics, Vol. 15, No. 5, 2015.
Liu J.J., Song R., and Cui M.M., Improvement of predictions of petrophysical transport behavior using three-dimensional finite volume element model with micro-CT images, Journal of Hydrodynamics, Vol. 27, No. 2, 2015.
Lokhorst A., and Wildenborg T., Introduction on CO2 geological storage. Classification of storage options, Oil and Gas Science and Technology, Vol. 60, No. 3, 2005.
Ma Q. et al., Pore-scale simulations of CO2/oil flow behavior in heterogeneous porous media under various conditions, Energies, Vol. 14, No. 3, 2021.
Maaref S., Rokhforouz M. R., and Ayatollahi S., Numerical investigation of two-phase flow in micromodel porous media: Effects of wettability, heterogeneity, and viscosity, Canadian Journal of Chemical Engineering, Vol. 95, No. 6, 2017.
Manrique E.J., Muci V.E., and Gurfinkel M.E., EOR field experiences in carbonate reservoirs in the United States, SPE Reservoir Evaluation and Engineering, Vol. 10, No. 6, 2007.
Meakin P., and Tartakovsky A.M., Modeling and simulation of pore-scale multiphase fluid flow and reactive transport in fractured and porous media, Reviews of Geophysics, Vol. 47, No. 3. 2009.
Olsson E., and Kreiss G., A conservative level set method for two-phase flow, Journal of Computational Physics, Vol. 210, No. 1, p. 225–246, 2005.
Olsson E., Kreiss G., and Zahedi S., A conservative level set method for two-phase flow II, Journal of Computational Physics, Vol. 225, No. 1, 2007.
Ouyang L.B., New correlations for predicting the density and viscosity of supercritical carbon dioxide under conditions expected in carbon capture and sequestration operations, Open Petroleum Engineering Journal, Vol. 4, No. 1, 2011.
 Pereira L.M.C., Chapoy A., Burgass R., and Tohidi B., Measurement and modeling of high-pressure density and interfacial tension of (gas + n-alkane) binary mixtures, Journal of Chemical Thermodynamics, Vol. 97, 2016.
Piri M., and Blunt M.J., Three-dimensional mixed-wet random pore-scale network modeling of two- And three-phase flow in porous media. I. Model description, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 71, No. 2, 2005.
Popinet S., and Zaleski S., A front-tracking algorithm for accurate representation of surface tension, International Journal for Numerical Methods in Fluids, Vol. 30, No. 6, 1999.
Raeini A.Q., Blunt M.J., and Bijeljic B., Modelling two-phase flow in porous media at the pore scale using the volume-of-fluid method, Journal of Computational Physics, Vol. 231, No. 17, 2012.
Rokhforouz M.R., and AkhlaghiAmiri H.A., Effects of grain size and shape distribution on pore-scale numerical simulation of two-phase flow in a heterogeneous porous medium, Advances in Water Resources, Vol. 124, 2019.
Saraf S., and Bera A., A review on pore-scale modeling and CT scan technique to characterize the trapped carbon dioxide in impermeable reservoir rocks during sequestration, Renewable and Sustainable Energy Reviews, Vol. 144., 2021.
Sethian J.A., and Smereka P., Level set methods for fluid interfaces, Annual Review of Fluid Mechanics, Vol. 35, 2003.
Shi, Y., Tang, G., Non-Newtonian rheology property for two-phase flow on fingering phenomenon in porous media using the lattice Boltzmann method. Journal of Non-Newtonian Fluid Mechanics, Vol. 229, p. 86–95, 2016.
Song R., Tang Y., et al., Pore-scale numerical simulation of CO2–Oil two-phase flow: a multiple-parameter analysis based on phase-field method, Energies, Vol. 16, 2023.
Spiteri E.J., Juanes R., Blunt M.J. and  Orr F.M., Relative permeability hysteresis: trapping models and application to geological CO2 sequestration, Paper presented at the SPE Annual Technical Conference and Exhibition, Dallas, Texas, October 2005. (SPE-96448-MS)
Srivastava R.K., Huang S.S., and Dong M., Laboratory investigation of Weyburn CO2 miscible flooding, Journal of Canadian Petroleum Technology, Vol. 39, No. 2, 2000.
Sun D.L., and Tao W.Q., A coupled volume-of-fluid and level set (VOSET) method for computing incompressible two-phase flows, International Journal of Heat and Mass Transfer, Vol. 53, No. 4, 2010.
Sussman M., A level set approach for computing solutions to incompressible two-phase flow, Journal of Computational Physics, Vol. 114, No. 1, 1994.
Sussman M., and Puckett E.G., A coupled level set and volume-of-fluid method for computing 3D and axisymmetric incompressible two-phase flows, Journal of Computational Physics, Vol. 162, No. 2, 2000.
Teklu T.W., Alameri W., Graves R.M., Kazemi H., and Al-Sumaiti A.M., Low-salinity water-alternating- CO2 EOR, Journal of Petroleum Science and Engineering, Vol. 142, 2016.
Tryggvason G., et al., A front-tracking method for the computations of multiphase flow, Journal of Computational Physics, Vol. 169, No. 2, 2001.
van der Waals J.D., The thermodynamic theory of capillarity under the hypothesis of a continuous variation of density, Journal of Statistical Physics, Vol. 20, No. 2, 1979.
Wildenschild D., Vaz C.M.P., et al., Using X-ray computed tomography in hydrology: Systems, resolutions, and limitations, Journal of Hydrology, Vol. 267, No. 3–4, 2002.
Xu R., Luo S., and Jiang P., Pore-scale numerical simulation of supercritical CO2 injecting into porous media containing water, Energy Procedia, Vol. 4, p.  4418–4424, 2011.
Yue P., Zhou C., et al., Phase-field simulations of interfacial dynamics in viscoelastic fluids using finite elements with adaptive meshing, Journal of Computational Physics, Vol. 219, No. 1, 2006.
Yue, P.T., Feng, J.J., Liu, C., and Shen, J., A diffuse-interface method for simulating two-phase flows of complex fluids, Journal of Fluid Mechanics, 515, 293–317, 2004.
Zacharoudiou I., Boek E. S., and Crawshaw J., The impact of drainage displacement patterns and Haines jumps on CO2 storage efficiency, Scientific Reports, Vol. 8, No. 1, 2018.
Zhang, C., Oostrom, M., Grate, J., Liquid CO2 displacement of water in a dual-permeability pore network micromodel. Environmental Sciences Technology Vol. 45, p. 7581–7588, 2011.
Zhu G., Yao J., Li A., et al., Pore-scale investigation of carbon dioxide-enhanced oil recovery, Energy and Fuels, Vol. 31, No. 5, 2017.

  • Receive Date 17 February 2024
  • Revise Date 05 April 2025
  • Accept Date 29 April 2025