A Dimensionless Capillary Pressure Function for Imbibition Derived From Pore-Scale Modeling in Mixed-Wet-Rock Images
- Yingfang Zhou (International Research Institute of Stavanger (IRIS)) | Johan Helland (International Research Institute of Stavanger (IRIS)) | Dimitrios G. Hatzignatiou (International Research Institute of Stavanger (IRIS))
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- December 2012
- Document Type
- Journal Paper
- 296 - 308
- 2012. Society of Petroleum Engineers
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It has been demonstrated experimentally that Leverett's J-function yields almost unique dimensionless drainage capillary pressure curves in relatively homogeneous rocks at strongly water-wet conditions, whereas for imbibition at mixed-wet conditions, it does not work satisfactorily because the permeability dependency on capillary pressure has been reported to be weak. The purpose of this study is to formulate a new dimensionless capillary pressure function for mixed-wet conditions on the basis of pore-scale modeling, which could overcome these restrictions. We simulate drainage, wettability alteration, and imbibition in 2D rock images by use of a semianalytical pore-scale model that represents the identified pore spaces as cross sections of straight capillary tubes. The fluid configurations occurring during drainage and imbibition in the highly irregular pore spaces are modeled at any capillary pressure and wetting condition by combining the free-energy minimization with an arc meniscus (AM)-determining procedure that identifies the intersections of two circles moving in opposite directions along the pore boundary. Circle rotation at pinned contact lines accounts for mixed-wet conditions. Capillary pressure curves for imbibition are simulated for different mixed-wet conditions in Bentheim sandstone samples, and the results are scaled by a newly proposed improved J-function that accounts for differences in formation wettability induced by different initial water saturations after primary drainage. At the end of primary drainage, oil-wet-pore wall segments are connected by many water-wet corners and constrictions that remain occupied by water. The novel dimensionless capillary pressure expression accounts for these conditions by introducing an effective contact angle that depends on the initial water saturation and is related to the wetting property measured at the core scale by means of a wettability index.
The accuracy of the proposed J-function is tested on 36 imbibition capillary pressure curves for different mixed-wet conditions that are simulated with the semianalytical model in scanning-electron-microscope (SEM) images of Bentheim sandstone. The simulated imbibition capillary pressure curves and the reproduced curves, based on the proposed J-function, are in good agreement for the mixed-wet conditions considered in this study. The detailed behavior is explained by analyzing the fluid displacements occurring in the pore spaces. It is demonstrated that the proposed J-function could be applied to mixed-wet conditions to generate a family of curves describing different wetting states induced by assigning different wetting properties on the solid surfaces or by varying the initial water saturation after primary drainage. The variability of formation wettability and permeability could be described more accurately in reservoir-simulation models by means of the proposed J-function, and hence the opportunity arises for improved evaluation of core-sample laboratory experiments and reservoir performance.
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Ahrenholz, B., Tölke, J., Lehmann, P. et al.2008. Prediction of CapillaryHysteresis in a Porous Material Using Lattice-Boltzmann Methods and Comparisonto Experimental Data and a Morphological Pore Network Model. Adv. WaterResour 31 (9): 1151-1173. http://dx.doi.org/10.1016/j.advwatres.2008.03.009.
Cassie, A.B.D. 1948. Contact Angles. Discuss Faraday Soc 3: 11-16. http://dx.doi.org/10.1039/DF9480300011.
Cassie, A.B.D. and Baxter, S. 1944. Wettability of Porous Surfaces. TransFaraday Soc 40: 546-551. http://dx.doi.org/10.1039/TF9444000546.
El-Khatib, N. 1995. Development of a Modified Capillary Pressure J-Function.Paper SPE 29890 presented at the SPE Middle East Oil Show, Bahrain, 11-14March. http://dx.doi.org/10.2118/29890-MS.
Frette, O.I. and Helland, J.O. 2010. A Semi-Analytical Model for Computationof Capillary Entry Pressures and Fluid Configurations in Uniformly Wet PoreSpaces from 2D Rock Images. Adv Water Resour 33 (8):846-866. http://dx.doi.org/10.1016/j.advwatres.2010.05.002.
Frette, O.I., Virnovsky, G. and Hildebrand-Habel, T. 2009. Modelling theStability of Thin Water Films Using SEM Images. Paper SPE 121250 presented atthe EUROPEC/EAGE Conference and Exhibition, Amsterdam, The Netherlands, 8-11June. http://dx.doi.org/10.2118/121250-MS.
Hamon, G. 2000. Field-Wide Variations of Wettability. Paper SPE 63144presented at the SPE Annual Technical Conference and Exhibition, Dallas, Texas,1-4 October. http://dx.doi.org/10.2118/63144-MS.
Hamon, G. 2004. Revisiting Ekofisk and Eldfisk Wettability. Paper SPE 90014presented at the SPE Annual Technical Conference and Exhibition, Houston,Texas, 26-29 September. http://dx.doi.org/10.2118/90014-MS.
Hamon, G. and Pellerin, F.M. 1997. Evidencing Capillary Pressure andRelative Permeability Trends for Reservoir Simulation. Paper SPE 38898presented at the SPE Annual Technical Conference and Exhibition, San Antonio,Texas, 5-8 October. http://dx.doi.org/10.2118/38898-MS.
Helland, J.O. and Frette O.I. 2010. Computation of Fluid Configurations andCapillary Pressures in Mixed-Wet 2D Pore Spaces from Rock Images.Proceedings of the XVIII International Conference on Water Resources,21-24 June 2010, Barcelona, Spain.
Helland, J.O. and Skjæveland, S.M. 2006. Physically-Based Capillary PressureCorrelation for Mixed-Wet Reservoirs from a Bundle-of-Tubes Model. SPEJ. 11 (2): 171-180. http://dx.doi.org/10.2118/89428-PA.
Helland, J.O., Jettestuen, E., Hatzignatiou, D.G. et al. 2011.Three-Dimensional Level Set Modelling of Capillary-Controlled Displacements inDigital Porous Media. Abstract H54C-07 presented at 2011 American GeophysicalUnion Fall Meeting, San Francisco, California, 5-9 December.
Jadhunandan, P.P. and Morrow, N.R. 1995. Effect of Wettability on WaterfloodRecovery for Crude-Oil/Brine/Rock Systems. SPE Res Eng 10(1): 40-46. http://dx.doi.org/10.2118/22597-PA.
Jerauld, G.R. and Rathmell, J.J. 1997. Wettability and Relative Permeabilityof Prudhoe Bay: A Case Study in Mixed-Wet Reservoirs. SPE Res Eng 12 (1): 58-65. http://dx.doi.org/10.2118/28576-PA.
Kovscek, A.R., Wong, H., and Radke, C.J. 1993. A Pore-Level Scenario for theDevelopment of Mixed Wettability in Oil Reservoirs, AIChE J 39(6): 1072-1085. http://dx.doi.org/10.1002/aic.690390616.
Lago, M. and Araujo, M. 2001. Threshold Pressure in Capillaries withPolygonal Cross Section. J Colloid Interf Sci 243 (1):219-226. http://dx.doi.org/10.1006/jcis.2001.7872.
Leverett, M.C. 1941. Capillary Behavior in Porous Solids. Trans AIME 142 (1): 152-169. http://dx.doi.org/10.2118/941152-G.
Long, J., Hyder, M.N., Huang, R.Y.M. et al. 2005. Thermodynamic Modelling ofContact Angles on Rough, Heterogeneous Surfaces. Adv Colloid Interf Sci118: 173-190. http://dx.doi.org/10.1016/j.cis.2005.07.004.
Ma, S., Mason, G., and Morrow, N.R. 1996. Effect of Contact Angle n Drainageand Imbibition in Regular Polygonal Tubes. Colloids Surf A Physicochem &Eng Asp 117: 273-291. http://dx.doi.org/10.1016/0927-7757(96)03702-8.
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.
Porter, M.L., Wildenschild, D., Grant, G. et al. 2010. Measurement andPrediction of the Relationship Between Capillary Pressure, Saturation andInterfacial Area in a NAPL-Water-Glass Bead System. Water Resour Res 46: W08512. http://dx.doi.org/10.1029/2009WR007786.
Prodanovic, M., Bryant, S.L. and Karpyn, Z.T. 2010. InvestigatingMatrix/Fracture Transfer Via a Level Set Method for Drainage and Imbibition.SPE J 15 (1): 125-136. http://dx.doi.org/10.2118/116110-PA.
Ramstad, T., Øren, P.-E. and Bakke, S. 2010. Simulation of Two-Phase Flow inReservoir Rocks Using a Lattice Boltzmann Method. SPE J 15(4): 917-927. http://dx.doi.org/10.2118/124617-PA.
Ryazanov, A.V., van Dijke, M.I.J., and Sorbie, K.S. 2009. Two-PhasePore-Network Modelling: Existence of Oil Layers During Water Invasion. TransPorous Media 80 (1): 79-99. http://dx.doi.org/10.1007/s11242-009-9345-x.
Silin, D., Tomutsa, L., Benson, S.M. et al. 2011. Microtomography andPore-Scale Modeling of Two-Phase Fluid Distribution. Trans Porous Media 86 (2): 495-515. http://dx.doi.org/10.1007/s11242-010-9636-2.
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 InterfSci 293 (2): 455-463. http://dx.doi.org/10.1016/j.jcis.2005.06.059.
Zhou, Y., Helland, J.O., and Hatzignatiou, D.G. 2011. A Model for Imbibitionin Pore Spaces from 2D Rock Images. In Proceedings of theInternational Conference on Flows and Mechanics in Natural Porous Media fromPore to Field Scale, Rueil-Malmaison, France, 16-18 November.Rueil-Malmaison, France: IFP Energies Nouvelles.