Three-Phase Pore-Network Modeling for Reservoirs With Arbitrary Wettability
- Adnan R.S. Al-Dhahli (Heriot-Watt University) | Sebastian Geiger (Heriot-Watt University) | Marinus I.J. van Dijke (Heriot-Watt University)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- December 2012
- Document Type
- Journal Paper
- 285 - 295
- 2012. Society of Petroleum Engineers
- 5.3.1 Flow in Porous Media
- 4 in the last 30 days
- 676 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 10.00|
|SPE Non-Member Price:||USD 30.00|
Oil reservoirs have structural heterogeneities across multiple length scales and, particularly in carbonates, complexly distributed wettabilities. The interplay of structural and wettability heterogeneities is the fundamental control for sweep efficiency and oil recovery. This interplay must be captured in physically robust flow functions, such as relative permeability and capillary pressure functions. Such flow functions then allow us to choose the best improved-oil-recovery (IOR) or enhanced-oil-recovery (EOR) process and forecast oil recovery with adequate precision. Obtaining flow functions for reservoir rocks with varying wettability is a challenging task, especially when three fluid phases coexist. In this work, we use pore-network modeling, a reliable and physically based simulation tool, to predict three-phase flow functions. We have developed a new pore-scale network model for rocks with variable wettability. Unlike other models, this model combines three new and important features. (1) Our network model comprises a novel thermodynamic criterion for the formation and collapse of oil layers. This captures film/layer flow of oil adequately, which affects the oil relative permeability at low oil saturation. We can therefore predict residual oil more accurately. (2) We implemented multiple displacement chains, in which injection of one phase at the inlet triggers a chain of interface displacements throughout the network. This allows us to accurately model the mobilization of disconnected phase clusters that arise during higher-order [water-alternating-gas (WAG)] floods. Again, this feature is key to a better prediction of residual oil saturation (ROS). (3) Our model takes realistic 3D pore networks extracted from pore-space reconstruction methods and X-ray computerizedtomography (CT) images as input. This preserves both topology and pore shape of the rock, providing better estimates of phase conductivities and relative permeability. We have validated our model by use of available experimental data for a range of wettabilities and demonstrated the impact of single vs. multiple displacement on residual oil. We also used a proof-of concept study in which we use flow functions for different wettabilities that have been computed with our model in field-scale reservoir simulations to forecast oil recovery during tertiary gas injection. These results are compared with predictions that used empirical flow functions. Flow functions computed by our network model gave higher oil recovery than corresponding flow functions calculated by empirical models; oil recovery increases with decreasing water-wetness. This shows that the pore-scale physics encapsulated in our new network model leads to the right emergent behavior at the reservoir scale.
|File Size||1 MB||Number of Pages||11|
Al-Dhahli A., van Dijke M.I.J., Geiger S. 2012. Pore-to-Reservoir Modellingof Three-Phase Flow Processes in Mixed-Wet Carbonate Reservoirs. Oralpresentation given at the 13th European Conference on the Mathematics of OilRecovery, Biarritz, France, 10-13 September.
Baker, L.E. 1988. Three-Phase Relative Permeability Correlations. Paper SPE17369 presented at the SPE Enhanced Oil Recovery Symposium, Tulsa, Oklahoma,16-21 April. http://dx.doi.org/10.2118/17369-MS.
Bakke, S., and Øren, P.E. 1997. 3-D Pore-Scale Modelling of Sandstones andFlow Simulations in the Pore Networks. SPE J. 2 (2):136-149. http://dx.doi.org/10.2118/35479-PA.
Bartell, F.E., and Osterhof, H.J. 1927. Determination of the Wettability ofa Solid by a Liquid. Ind. Eng. Chem. 19 (11): 1277-1280. http://dx.doi.org/10.1021/ie50215a026.
Blunt, M.J. 2000. An Empirical Model for Three-Phase Relative Permeability.SPE J. 5 (4): 435-445. http://dx.doi.org/10.2118/67950-PA.
Blunt, M.J. 2001. Flow in Porous Media—Pore-Network Models and MultiphaseFlow. Curr. Opin. Colloid & Interface Sci. 6 (3):197-207. http://dx.doi.org/10.1016/S1359-0294(01)00084-X.
Blunt, M.J., Bijeljic, B., Dong, H., et al. 2012. Pore-Scale Imaging andModelling. Adv. Water Resour. (in press; posted 3 April 2012). http://dx.doi.org/10.1016/j.advwatres.2012.03.003.
Christensen, J.R., Stenby, E.H., and Skauge, A. 2001. Review of WAG FieldExperience. SPE Res Eval & Eng 4 (2): 97-106. http://dx.doi.org/10.2118/71203-PA.
Fenwick, D.H., and Blunt, M.J. 1995. Pore Level Modelling of Three PhaseFlow in Porous Media. Oral presentation given at the 8th European Symposium onImproved Oil Recovery, Vienna, Austria, 15 May.
Fenwick, D.H., and Blunt, M.J. 1998. Network Modeling of Three-Phase Flow inPorous Media. SPE J. 3 (1): 86-96. http://dx.doi.org/10.2118/38881-PA.
Firincioglu, T., Blunt, M.J., and Zhou, D. 1999. Three-Phase Flow andWettability Effects in Triangular Capillaries. Colloids & Surf. A:Physicochem. & Eng. Aspects 155 (2-3): 259-276. http://dx.doi.org/10.1016/S0927-7757(99)00039-4.
Holm, R., van Dijke, M., and Geiger, S. 2009. Three-Phase Flow ModellingUsing Pore-Scale Capillary Pressures and Relative Permeabilities for Mixed-WetMedia at the Continuum-Scale. Transport Porous Med 81 (3):423-442. http://dx.doi.org/10.1007/s11242-009-9415-0.
Hui, M.H., and Blunt, M.J. 2000. Effects of Wettability on Three-Phase Flowin Porous Media. J. Phys. Chem. B 104 (16): 3833-3845. http://dx.doi.org/10.1021/jp9933222.
Johnson, R.E., and Dettre, R.H. 1993. Wetting of Low Energy Surfaces. InWettability, ed. J.C. Berg, 1-73, vol. 49, Surfactant Science Series.New York City: Marcel Dekker Inc.
Juanes, R., and Patzek, T.W. (2004). Three-Phase Displacement Theory: AnImproved Description of Relative Permeabilities. SPE J. 9(3): 302-313. http://dx.doi.org/10.2118/88973-PA.
Kalam, M.Z., Negahban, S., Al-Rawahi, A.S., et al. 2011. Miscible GasInjection Tests in Carbonates and Its Impact on Field Development. Paper SPE148374 presented at SPE Reservoir Characterisation and Simulation Conferenceand Exhibition, Abu Dhabi, UAE, 9-11 October. http://dx.doi.org/10.2118/148374-MS.
Kløv, T., Øren, P.E., Stensen, J.A., et al. 2003. Pore-to-Field ScaleModeling of WAG. Paper SPE 84549 presented at the SPE Annual TechnicalConference and Exhibition, Denver, Colorado, 5-8 October. http://dx.doi.org/10.2118/84549-MS.
Lerdahl, T.R., Oren, P.-E., and Bakke, S. 2000. A Predictive Network Modelfor Three-Phase Flow in Porous Media. Paper SPE 59311 presented at SPE/DOESymposium in Improved Oil Recovery, Tulsa, Oklahoma, 3-5 April. http://dx.doi.org/10.2118/59311-MS.
Mayer, R.P., and Stowe, R.A. 1965. Mercury Porosimetry: BreakthroughPressure for Penetration Between Packed Spheres. J. Colloid Sci. 20 (8): 893-911. http://dx.doi.org/10.1016/0095-8522(65)90061-9.
Meakin, P. and Tartakovsky, A.M. 2009. Modeling and Simulation of Pore-ScaleMultiphase Fluid Flow and Reactive Transport in Fractured and Porous Media.Rev. Geophys. 47: RG3002. http://dx.doi.org/10.1029/2008RG000263.
Nardi, C., Lopez, O., Øren, P.E., Held, R., et al. 2009. Pore-Scale Modelingof Three-Phase Flow: Comparative Study with Experimental Reservoir Data. Oralpresentation given at the International Symposium of the Society of CoreAnalysts, Noordwijk, The Netherlands, 27-30 September.
Oak, M.J. 1990. Three-Phase Relative Permeability of Water-Wet Berea. PaperSPE 20183 presented at the SPE/DOE Seventh Symposium on Enhanced Oil Recovery,Tulsa, Oklahoma, 22-25 April. http://dx.doi.org/10.2118/20183-MS.
Oak, M.J., Baker, L.E., Thomas, D.C., et al. 1990. Three-Phase RelativePermeability of Berea Sandstone. J. Pet Technol 42 (8):1054-1061. http://dx.doi.org/10.2118/17370-PA.
Øren, P.E., and Bakke, S. 2003. Reconstruction of Berea Sandstone andPore-Scale Modelling of Wettability Effects. J. Pet. Sci. Eng. 39 (3-4): 177-199. http://dx.doi.org/10.1016/S0920-4105(03)00062-7.
Øren, P.E., Bakke, S., and Arntzen, O.J. 1998. Extending PredictiveCapabilities to Network Models. SPE J. 3 (4): 324-336. http://dx.doi.org/10.2118/52052-PA.
Øren, P.E., and Pinczewski, W.V. 1995. Fluid Distribution and Pore-ScaleDisplacement Mechanisms in Drainage Dominated Three-Phase Flow. TransportPorous Med 20 (1-2):105-133. http://dx.doi.org/10.1007/BF00616927.
Patzek, T.W. 2001. Verification of a Complete Pore Network Simulator ofDrainage and Imbibition. SPE J. 6 (2): 144-156. http://dx.doi.org/10.2118/71310-PA.
Piri, M., and Blunt, M.J. 2005a. Three-Dimensional Mixed-Wet RandomPore-Scale Network Modeling of Two- and Three-Phase Flow in Porous Media. I.Model Description. Phys. Rev. E 71 (2): 026301. http://dx.doi.org/10.1103/PhysRevE.71.026301.
Piri, M., and Blunt, M.J. 2005b. Three-Dimensional Mixed-Wet RandomPore-Scale Network Modeling of Two- and Three-Phase Flow in Porous Media. II.Results. Phys. Rev. E 71 (2): 026302. http://dx.doi.org/10.1103/PhysRevE.71.026302.
Princen, H.M. 1969a. Capillary Phenomena in Assemblies of ParallelCylinders: I. Capillary Rise Between Two Cylinders. J. Colloid &Interface Sci. 30 (1): 69-75. http://dx.doi.org/10.1016/0021-9797(69)90379-8.
Princen, H.M. 1969b. Capillary Phenomena in Assemblies of ParallelCylinders: II. Capillary Rise in Systems with More Than Two Cylinders. J.Colloid & Interface Sci. 30 (3): 359-371. http://dx.doi.org/10.1016/0021-9797(69)90403-2.
Princen, H.M. 1970. Capillary Phenomena in Assemblies of Parallel Cylinders:III. Liquid Columns Between Horizontal Parallel Cylinders. J. Colloid &Interface Sci. 34 (2): 171-184. http://dx.doi.org/10.1016/0021-9797(70)90167-0.
Ryazanov, A., van Dijke, M., and Sorbie, K. 2009. Two-Phase Pore-NetworkModelling: Existence of Oil Layers During Water Invasion. Transport PorousMed 80 (1): 79-99. http://dx.doi.org/10.1007/s11242-009-9345-x.
Ryazanov, A.V., van Dijke, M.I.J., and Sorbie, K.S. 2010. Pore-NetworkPrediction of Residual Oil Saturation Based on Oil Layer Drainage in Mixed-WetSystems. Paper SPE 129919 presented at the SPE/DOE Symposium in Improved OilRecovery, Tulsa, Oklahoma, 24-28 April. http://dx.doi.org/10.2118/129919-MS.
Sohrabi, M., Henderson, G.D., Tehrani, D.H., et al. 2000. Visualisation ofOil Recovery by Water Alternating Gas (WAG) Injection Using High PressureMicromodels - Water-Wet System. Paper SPE 63000 presented at the SPE AnnualTechnical Conference and Exhibition, Dallas, Texas, 1-4 October. http://dx.doi.org/10.2118/63000-MS.
Sohrabi, M., Tehrani, D.H., Danesh, A., et al. 2001. Visualisation of OilRecovery by Water Alternating Gas (WAG) Injection Using High PressureMicromodels - Oil-Wet and Mixed-Wet Systems. Paper SPE 71494 presented at theSPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 30September-3 October. http://dx.doi.org/10.2118/71494-MS.
Stone, H.L. 1970. Probability Model for Estimating Three-Phase RelativePermeability. J. Pet. Tech. 22 (2): 214-218. http://dx.doi.org/10.2118/2116-PA.
Stone, H.L. 1973. Estimation of Three-Phase Relative Permeability andResidual Oil Data. J. Cdn. Pet. Tech. 12 (4): 53-61. http://dx.doi.org/10.2118/73-04-06.
Suicmez, V.S., Piri, M., and Blunt, M.J. 2006. Pore-Scale Modeling ofThree-Phase WAG Injection: Prediction of Relative Permeabilities and Trappingfor Different Displacement Cycles. Paper SPE 95594 presented at the SPE/DOESymposium on Improved Oil Recovery, Tulsa, Oklahoma, 22-26 April. http://dx.doi.org/10.2118/95594-MS.
Svirsky, D.S., Dijke, M.I.J., and Sorbie, K.S. 2007. Prediction ofThree-Phase Relative Permeabilities Using a Pore-Scale Network Model Anchoredto Two-Phase Data. SPE Res Eval & Eng 10 (5): 527-538.http://dx.doi.org/10.2118/89992-PA.
Valvatne, P.H., and Blunt, M.J. 2004. Predictive Pore-Scale Modeling ofTwo-Phase Flow in Mixed Wet Media. Water Resour. Res. 40(7): W07406. http://dx.doi.org/10.1029/2003WR002627.
van Dijke, M.I.J., Juri, J.E., and Sorbie, K.S. 2008. Shortest PathAlgorithm for Pore-Scale Simulation of Water-Alternating-Gas Injection. Oralpresentation given at the 11th European Conference on the Mathematics of OilRecovery, Bergen, Norway, 8 September.
van Dijke, M.I.J., Lago, M., Sorbie, K.S., et al. 2004. Free Energy Balancefor 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. http://dx.doi.org/10.1016/j.jcis.2004.05.021.
van Dijke, M.I.J., McDougall, S.R., and Sorbie, K.S. 2001. Three-PhaseCapillary Pressure and Relative Permeability Relationships in Mixed-WetSystems. Transport Porous Med 44 (1): 1-32. http://dx.doi.org/10.1023/A:1010773606657 .
van Dijke, M.I.J., Piri, M., Helland, J.O., et al. 2007. Criteria forThree-Fluid Configurations Including Layers in a Pore with NonuniformWettability. Water Resour. Res. 43 (12): W12S05. http://dx.doi.org/10.1029/2006WR005761.
van Dijke, M.I.J., and Sorbie, K.S. 2002. Pore-Scale Network Model forThree-Phase Flow in Mixed-Wet Porous Media. Phys. Rev. E 66(4): 046302. http://dx.doi.org/10.1103/PhysRevE.66.046302.
van Dijke, M.I.J., and Sorbie, K.S. 2006. Existence of Fluid Layers in theCorners of a Capillary with Non-Uniform Wettability. J. Colloid &Interface Sci. 293 (2): 455-463. http://dx.doi.org/10.1016/j.jcis.2005.06.059.
van Dijke, M.I.J., Sorbie, K.S., Sohrabi, M., et al. 2002. Three-Phase Flowin WAG Processes in Mixed-Wet Porous Media: Pore-Scale Network Simulations andComparison with Micromodel Experiments. Paper SPE 75192 presented at theSPE/DOE Tenth Symposium on Improved Oil Recovery, Tulsa, Oklahoma, 13-17 April.http://dx.doi.org/10.2118/75192-MS.
Zhou, D.G., and Blunt, M. 1997. Effect of Spreading Coefficient on theDistribution of Light Non-Aqueous Phase Liquid in the Subsurface. J. Contam.Hydrol. 25 (1-2): 1-19. http://dx.doi.org/10.1016/S0169-7722(96)00025-3.