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Accurate Modelling of Pore-Scale Films and Layers for Three-Phase Flow Processes in Clastic and Carbonate Rocks with Arbitrary Wettability

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Abstract

Three-phase flow is a key process occurring in subsurface reservoirs, for example, during \(\text{ CO }_2\) sequestration and enhanced oil recovery techniques such as water alternating gas (WAG) injection. Predicting three-phase flow processes, for example, the increase in oil recovery during WAG, requires a sound understanding of the fundamental flow physics in water- to oil-wet rocks to derive physically robust flow functions, i.e. relative permeability and capillary pressure. In this study, we use pore-network modelling, a reliable and physically based simulation tool, to predict the flow functions. We have developed a new pore-scale network model for rocks with variable wettability, from water- to oil-wet. It comprises a constrained set of parameters that mimic the wetting state of a reservoir. Unlike other models, it combines three main features: (1) A novel thermodynamic criterion for formation and collapse of oil layers. The new model hence captures wetting film and layer flow of oil adequately, which affects the oil relative permeability at low oil saturation and leads to accurate prediction of residual oil. (2) Multiple displacement chains, where injection of one phase at the inlet triggers a chain of interface displacements throughout the network. This allows for the accurate modelling of the mobilisation of many disconnected phase clusters that arise, in particular, during higher order WAG floods. (3) The model takes realistic 3D pore-networks extracted from pore-space reconstruction methods and CT images as input, preserving both topology and pore shape of the sample. For water-wet systems, we have validated our model with available experimental data from core floods. For oil-wet systems, we validated our network model by comparing 2D network simulations with published data from WAG floods in oil-wet micromodels. This demonstrates the importance of film and layer flow for the continuity of the various phases during subsequent WAG cycles and for the residual oil saturations. A sensitivity analysis has been carried out with the full 3D model to predict three-phase relative permeabilities and residual oil saturations for WAG cycles under various wetting conditions with different flood end-points.

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References

  • Baker, L.E.: Three-phase relative permeability correlations. In: The SPE/DOE Enhanced Oil Recovery Symposium, Tulsa. SPE/ODE 17369 (1988)

  • Bakke, S., Øren, P.E.: 3-d pore-scale modelling of sandstones and flow simulations in the pore networks. SPE J. 2(2), 136–149 (1997)

    Google Scholar 

  • Bartell, F.E., Osterhof, H.J.: Determination of the wettability of a solid by a liquid. Ind. Eng. Chem. 19(11), 1277–1280 (1927)

    Article  Google Scholar 

  • Blunt, M.J.: An empirical model for three-phase relative permeability. SPE J. 5(4), 435–445 (2000)

    Google Scholar 

  • Blunt, Martin J., Bijeljic, Branko, Dong, Hu, Gharbi, Oussama, Iglauer, Stefan, Mostaghimi, Peyman, Paluszny, Adriana, Pentland, Christopher: Pore-scale imaging and modelling. Adv. Water Resour. (0). ISSN 0309–1708. doi:10.1016/j.advwatres.2012.03.003 (2012)

  • Blunt, M.J.: Flow in porous mediapore-network models and multiphase flow. Curr. Opin. Colloid Interface Sci. 6(3), 197–207 (2001)

    Article  Google Scholar 

  • Christensen, J.R., Stenby, E.H., Skauge, A.: Review of WAG field experience. SPE Reserv. Eval. Eng. 4(2), 97–106 (2001)

    Google Scholar 

  • Dong, H., Blunt, M.J.: Pore-network extraction from micro-computerized-tomography images. Phys. Rev. E 80, 036307 (2009)

    Article  Google Scholar 

  • Falta, -R. W., Pruess K., Javandel, I., Witherspoon, P.A.: Numerical modeling of steam injection for the removal of nonaqueous phase liquids from the subsurface: 1. numerical formulation. Water Resour. Res. 28(2), 433–449 (1992a)

  • Falta, -R. W., Pruess K., Javandel, I., Witherspoon, P.A.: Numerical modeling of steam injection for the removal of nonaqueous phase liquids from the subsurface: 2. code validation and application. Water Resour. Res 28(2), 451–465 (1992b)

  • Fatt, I.: The network model of porous media i. Capillary pressure characteristics. Trans. AIME 207(7), 144–159 (1956)

    Google Scholar 

  • Fenwick, D.H., Blunt, M.J.: Pore level modelling of three phase flow in porous media. In: Proceedings of the 8th European Symposium on Improved Oil Recovery, Vienna, (1995)

  • Fenwick, D.H., Blunt, M.J.: Network modeling of three-phase flow in porous media. SPE J. 3(1), 86–96 (1998a)

    Google Scholar 

  • Fenwick, D.H., Blunt, M.J.: Three-dimensional modeling of three phase imbibition and drainage. Adv. Water Resour. 21(2), 121–143 (1998b)

    Article  Google Scholar 

  • Firincioglu, T., Blunt, M.J., Zhou, D.: Three-phase flow and wetability effects in triangular capillaries. Colloids Surf. A 155(2–3), 259–276 (1999)

    Article  Google Scholar 

  • Grate, J.W., Dehoff, K.J., Warner, M.G., Pittman, J.W., Wietsma, T.W., Zhang, C., Oostrom, M.: Correlation of oil–water and air–water contact angles of diverse silanized surfaces and relationship to fluid interfacial tensions. Langmuir 28(18), 7182–7188 (2012)

    Article  Google Scholar 

  • Helland, J.O., Ryazanov, A.V., van Dijke, M.I.J.: Characterization of pore shapes for pore network models. In: Proceedings of the 11th European Conference on the Mathematics of Oil Recovery (ECMOR XI), Bergen, 8 Sept (2008)

  • Holm, R., van Dijke, M.I.J., Geiger, S.: Three-phase flow modelling using pore-scale capillary pressures and relative permeabilities for mixed-wet media at the continuum-scale. Transp. Porous Media 81(3), 423–442 (2010)

    Article  Google Scholar 

  • Hui, M.H., Blunt, M.J.: Pore-scale modeling of three-phase flow and the effects of wettability. In: Proceedings of SPE/DOE Improved Oil Recovery Symposium, Tulsa, 3–5 April (2000). SPE 59309

  • Johnson, R.E., Dettre, R.H.: Wetting of Low Energy Surfaces, Volume 49 of Surfactant Science Series. In: Berg, J.C. (ed.) Wettability. Marcel Dekker Inc., New York (1993)

    Google Scholar 

  • Juanes, R., Patzek, T.W.: Three-phase displacement theory: an improved description of relative permeabilities. SPE J. 9(3), 302–313 (2004)

    Google Scholar 

  • Kalam, M., Negahban, S., Al-Rawahi, A., Al Hosani, I.: Miscible gas injection tests in carbonates and its impact on field development. In: SPE Reservoir Characterisation and Simulation Conference and Exhibition, Abu Dhabi, 9–11 Oct (2011)

  • Lago, M., Araujo, M.: Threshold pressure in capillaries with polygonal cross section. J. Colloid Interface Sci. 243(1), 219–226 (2001). doi:10.1006/jcis.2001.7872

    Article  Google Scholar 

  • Lerdahl, T.R., Øren, P.E., Bakke, S.: A predictive network model for three-phase flow in porous media. In: Improved Oil Recovery Symposium. Tulsa, 3–5 April (2000). SPE 59311

  • Mani, V., Mohanty, K.K.: Effect of the spreading coefficient on three-phase flow in porous media. J. Colloid Interface Sci. 187(1), 45–56 (1997)

    Article  Google Scholar 

  • Mani, V., Mohanty, K.K.: Pore-level network modeling of three-phase capillary pressure and relative permeability curves. SPE J. 3(3), 238–248 (1998)

    Google Scholar 

  • Mayer, R.P., Stowe, R.A.: Mercury porosimetry-breakthrough pressure for penetration between packed spheres. J. Colloid Sci. 20(8), 893–911 (1965)

    Article  Google Scholar 

  • Meakin, P., Tartakovsky, A.M.: Modeling and simulation of pore-scale multiphase fluid flow and reactive transport in fractured and porous media. Rev. Geophys. 47(3), RG3002 (2009)

    Article  Google Scholar 

  • Nardi, C., Lopez, O., Øren, P.E., Held, R., Petersen Jr, E.B.: Pore-scale modelling of three-phase flow: comparative study with experimental reservoir data. In: The International Symposium of the Society of Core Analysts, Noordwijk, 27–30 Sept (2009)

  • Oak, M.J.: Three-phase relative permeability of water-wet berea. In: Proceedings of the SPE/DOE Enhanced Oil Recovery Symposium, Tulsa, 22–25 April (1990). SPE 20183

  • Øren, P.E., Bakke, S.: Reconstruction of berea sandstone and pore-scale modelling of wettability effects. J. Petrol. Sci. Eng. 39(3–4), 177–199 (2003)

    Google Scholar 

  • Øren, P.E., Pinczewski, W.V.: The effect of film-flow on the mobilization of waterflood residual oil by gas flooding. In Proceedings of the 6th European Symposium on Improved Oil Recovery, Stavanger, May (1991)

  • Øren, P.E., Pinczewski, W.V.: Fluid distribution and pore-scale displacement mechanisms in drainage dominated three-phase flow. Transp. Porous Media 20, 105–133 (1995)

    Article  Google Scholar 

  • Øren, P.E., Billiotte, J., Pinczewski, W.V.: Mobilization of waterflood residual oil by gas injection for water-wet conditions. SPE Forma. Eval. 7(1), 70–78 (1992)

    Google Scholar 

  • Øren, P.E., Billiotte, J., Pinczewski, W.V.: Pore-scale network modelling of waterflood residual oil recovery by immiscible gas flooding. In: Proceedings of the SPE/DOE Symposium in Improved Oil Recovery, Tulsa, 17–20 April (1994). SPE 27814

  • Øren, P.E., Bakke, S., Arntzen, O.J.: Extending predictive capabilities to network models. SPE J. 3(4), 324–336 (1998)

    Google Scholar 

  • Patzek, T.: Verification of a complete pore network simulator of drainage and imbibition. SPE J. 6(2), 144–156 (2001)

    Google Scholar 

  • Pereira, G.G., Pinczewski, W.V., Chan, D.Y.C., Paterson, L., Øren, P.E.: Pore-scale network model for drainage-dominated three-phase flow in porous media. Transp. Porous Media 24, 167–201 (1996)

    Article  Google Scholar 

  • Jr. Petersen, E.B., Lohne, A., Vatne, K.O., Helland, J.O., Virnovsky, G., Øren, P.E.: Relative Permeabilities for Two- and Three Phase Flow Processes Relevant to the Depressurization of the Statfjord Field. 29 Oct–2 Nov (2008)

  • Piri, M., Blunt, M.J.: Three-dimensional mixed-wet random pore-scale network modeling of two- and three-phase flow in porous media. i. Model description. Phys. Rev. E 71(2), 026301 (2005a)

    Article  Google Scholar 

  • Piri, M., Blunt, M.J.: Three-dimensional mixed-wet random pore-scale network modeling of two- and three-phase flow in porous media. ii. Results. Phys. Rev. E 71(2), 026302 (200b)

    Article  Google Scholar 

  • Princen, H.M.: Capillary phenomena in assemblies of parallel cylinders : I. Capillary rise between two cylinders. J. Colloid Interface Sci. 30(1), 69–75 (1969a)

    Article  Google Scholar 

  • Princen, H.M.: Capillary phenomena in assemblies of parallel cylinders : II. Capillary rise in systems with more than two cylinders. J. Colloid Interface Sci. 30(3), 359–371 (1969b)

    Article  Google Scholar 

  • Princen, H.M.: Capillary phenomena in assemblies of parallel cylinders : III. Liquid columns between horizontal parallel cylinders. J. Colloid Interface Sci. 34(2), 171–184 (1970)

    Article  Google Scholar 

  • Qi, R., LaForce, T., Blunt, M.: Design of carbon dioxide storage in oil fields. In: SPE Annual Technical Conference and Exhibition, Denver, 21–24 Sept (2008)

  • Qi, R., LaForce, T.C., Blunt, M.J.: A three-phase four-component streamline-based simulator to study carbon dioxide storage. Comput. Geosci. 13(4), 493–509 (2009)

    Article  Google Scholar 

  • Ryazanov, A.V., van Dijke, M.I.J., Sorbie, K.S.: Two-phase pore-network modelling: existence of oil layers during water invasion. Transp. Porous Media 80(1), 79–99 (2009)

    Article  Google Scholar 

  • Ryazanov, A.V., van Dijke, M.I.J., Sorbie, K.S.: Pore-network prediction of residual oil saturation based on oil layer drainage in mixed-wet systems. In: SPE Improved Oil Recovery Symposium, Tulsa, 24–28 April (2010). SPE 129919

  • Sohrabi, M., Henderson, G.D., Tehrani, D.H., Danesh, A.: Visualisation of oil recovery by water alternating gas ( WAG) injection using high pressure micromodels—water-wet system. In: SPE Annual Technical Conference and Exhibition, Dallas, 1–4 Oct (2000). SPE 63000

  • Sohrabi, M., Tehrani, D.H., Danesh, A., Henderson, G.D.: Visualisation of oil recovery by water alternating gas ( WAG) injection using high pressure micromodels—oil-wet and mixed-wet systems. In: SPE Annual Technical Conference and Exhibition, New Orleans, 30 Sept–3 Oct (2001). SPE 71494

  • Sohrabi, M., Tehrani, D.H., Danesh, A., Henderson, G.D.: Visualization of oil recovery by water-alternating-gas injection using high-pressure micromodels. SPE J. 9(3), 290–301 (2004)

    Google Scholar 

  • Stone, H.L.: Probability model for estimating three-phase relative permeability. J. Petrol. Technol. 22(2), 214–218 (1970)

    Google Scholar 

  • Stone, H.L.: Estimation of three-phase relative permeability and residual oil data. J. Can. Petrol. Technol. 12(4), 53–61 (1973)

    Google Scholar 

  • Suicmez, V., Piri, M., Blunt, M.J.: Pore-scale simulation of water alternate gas injection. Transp. Porous Media 66, 259–286 (2007)

    Article  Google Scholar 

  • Suicmez, V.S., Piri, M., Blunt, M.J.: Pore-scale modeling of three-phase WAG injection: Prediction of relative permeabilities and trapping for different displacement cycles. In: SPE/DOE Symposium on Improved Oil Recovery, Tulsa, 22–26 April (2006). SPE 95594

  • Svirsky, D.S., van Dijke, M.I.J., Sorbie, K.S.: Prediction of three-phase relative permeabilities using a pore-scale network model anchored to two-phase data. SPE Reserv. Eval. Eng. 10(5), (2007)

  • Valvatne, P.H., Blunt, M.J.: Predictive pore-scale modeling of two-phase flow in mixed wet media. Water Resour. Res. 40(7), W07406 (2004)

    Article  Google Scholar 

  • van Dijke, M., Lorentzen, M., Sohrabi, M., Sorbie, K.: Pore-scale simulation of wag floods in mixed-wet micromodels. SPE J. 15(1), 238–247 (2010)

    Google Scholar 

  • van Dijke, M.I.J., Sorbie, K.S.: The relation between interfacial tensions and wettability in three-phase systems: consequences for pore occupancy and relative permeability. J. Petrol. Sci. Eng. 33(1), 39–48 (2002)

    Article  Google Scholar 

  • van Dijke, M.I.J., Sorbie, K.S.: Three-phase capillary entry conditions in pores of noncircular cross-section. J. Colloid Interface Sci. 260(2), 385–397 (2003)

    Article  Google Scholar 

  • van Dijke, M.I.J., Sorbie, K.S., McDougall, S.R.: Saturation-dependencies of three-phase relative permeabilities in mixed-wet and fractionally wet systems. Adv. Water Resour. 24(3), 365–384 (2001)

    Article  Google Scholar 

  • van Dijke, M.I.J., Lago, M., Sorbie, K.S., Araujo, M.: Free energy balance for three fluid phases in a capillary of arbitrarily shaped cross-section: capillary entry pressures and layers of the intermediate-wetting phase. J. Colloid Interface Sci. 277(1), 184–201 (2004a)

    Article  Google Scholar 

  • van Dijke, M.I.J., Sorbie, K.S., Sohrabi, M., Danesh, A.: Three-phase flow WAG processes in mixed-wet porous media: pore-scale network simulations and comparison with water-wet micromodel experiment. SPE J. 9(1), 57–66 (2004b)

    Google Scholar 

  • van Dijke, M.I.J., Sorbie, K.S., Sohrabi, M., Danesh, A.: Simulation of WAG floods in an oil-wet micromodel using a 2-D pore-scale network model. J. Petrol. Sci. Eng. 52(1–4), 71–86 (2006)

    Article  Google Scholar 

  • van Dijke, M.I.J., Piri, M., Helland, J.O., Sorbie, K.S., Blunt, M.J., Skjæveland, S.M.: Criteria for three-fluid configurations including layers in a pore with nonuniform wettability. Water Resour. Res. 43(12), W12S05 (2007)

    Google Scholar 

  • van Dijke, M.I.J., Juri, J.E., Sorbie, K.S.: Shortest path algorithm for pore-scale simulation of water-alternating-gas injection. In: Proceedings of the 11th European Conference on the Mathematics of Oil Recovery (ECMOR XI), Bergen, Sept (2008)

  • Zhou, D.G., Blunt, M.J.: Effect of spreading coefficient on the distribution of light non-aqueous phase liquid in the subsurface. J. Contam. Hydrol. 25(1–2), 1–19 (1997)

    Article  Google Scholar 

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Acknowledgments

The authors are thankful to the Petroleum Development Oman (PDO) for providing a PhD scholarship for Adnan Al-Dhahli. S. Geiger is grateful to the CMG Reservoir Simulation Foundation for financial support. The authors thank Kejian Wu for supplying carbonate network B.

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Correspondence to Adnan Al-Dhahli.

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Al-Dhahli, A., van Dijke, M.I.J. & Geiger, S. Accurate Modelling of Pore-Scale Films and Layers for Three-Phase Flow Processes in Clastic and Carbonate Rocks with Arbitrary Wettability. Transp Porous Med 98, 259–286 (2013). https://doi.org/10.1007/s11242-013-0144-z

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