Investigating Matrix/Fracture Transfer via a Level Set Method for Drainage and Imbibition
- Maša Prodanovic (The University of Texas at Austin) | Steven L. Bryant (The University of Texas at Austin) | Zuleima T. Karpyn (Pennsylvania State University)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- March 2010
- Document Type
- Journal Paper
- 125 - 136
- 2010. Society of Petroleum Engineers
- 1.8.5 Phase Trapping, 5.5 Reservoir Simulation, 4.3.4 Scale, 1.6.9 Coring, Fishing, 4.3.1 Hydrates, 5.5.3 Scaling Methods, 4.1.2 Separation and Treating, 2.5.2 Fracturing Materials (Fluids, Proppant), 1.2.3 Rock properties, 5.8.6 Naturally Fractured Reservoir, 4.6 Natural Gas, 5.3.2 Multiphase Flow, 5.3.1 Flow in Porous Media, 4.1.5 Processing Equipment, 5.1.8 Seismic Modelling
- drainage; imbibition; rough-wall fractures; matrix/fracture transfer; capillarity; level set method
- 1 in the last 30 days
- 867 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 5.00|
|SPE Non-Member Price:||USD 35.00|
Multiphase flow and transport phenomena within fractures are important because fractures often represent primary flow conduits in otherwise low-permeability rock. Flows within the fracture, between the fracture and the adjacent matrix, and through the pore space within the matrix typically happen on different length and time scales. Capturing these scales experimentally is difficult. It is, therefore, useful to have a computational tool that establishes the exact position and shape of fluid/fluid interfaces in realistic fracture geometries. The level set method (LSM) is such a tool. Our progressive quasistatic (PQS) algorithm based on the level set method finds detailed, pore-level fluid configurations satisfying the Young-Laplace equation at a series of prescribed capillary pressures. The fluid volumes, contact areas, and interface curvatures are readily extracted from the configurations. The method automatically handles topological changes of the fluid volumes as capillary pressure varies. It also accommodates arbitrarily complicated shapes of confining solid surfaces.
Here, we apply the PQS method to analytically defined fracture faces and aperture distributions, to geometries of fractures obtained from high-resolution images of real rocks, and to idealized fractures connected to a porous matrix. We also explicitly model a fracture filled with proppant, using a cooperative rearrangement algorithm to construct the proppant bed and the surrounding matrix. We focus on interface movement between matrix and fracture, and snap-off of nonwetting phase into the fracture during imbibition in particular. The extent to which nonwetting phase is trapped in fracture/enclosed gaps is very sensitive to the direction of the displacement. Simulated drainage curves in matrix differ systematically from drainage curves in fracture and matrix with transfer between them. In a reservoir simulation, the latter might serve as an upscaled drainage curve input for a fractured medium.
|File Size||1 MB||Number of Pages||12|
Behseresht, J., Bryant, S., and Seperhnoori, K. 2007. Infinite-Acting PhysicallyRepresentative Networks for Capillarity-Controlled Displacements. Paper SPE110581 presented at the SPE Annual Technical Conference and Exhibition Anaheim,California, USA, 11-14 November. doi: 10.2118/110581-MS.
Berkowitz, B. 2002. Characterizing flow and transport in fracturedgeological media: A review. Advances in Water Resources 25(8-12): 861-884.
Bertels, S.P., DiCarlo, D.A., and Blunt, M.J. 2001. Measurement of ApertureDistribution, Capillary Pressure, Relative Permeability, and in Situ Saturationin a Rock Fracture using Computed Tomography Scanning. Water Resour.Res. 37 (3): 649-662. doi:10.1029/2000WR900316.
Bruneau, C.-H., Colin,T., Galusinski, C., Tancogne, S., and Vigneaux, P.2007. Simulations of 3D Dynamics of Microdroplets: A Comparison of Rectangularand Cylindrical Channels. In Numerical Mathematics and Advance Applications:Proceedings of ENUMATH 2007, the 7th Annual European Conference on NumericalMathematics and Advanced Applications, Graz, Austria, September 2007, ed.K. Kunisch, G. Of, and O. Steinbach, Part 2, Subpart 9, 449-456. Berlin:Springer.
Chu, K.T. and Prodanovic, M. 2008. Level Set Method Library (LSMLIB), http://ktchu.serendipityresearch.org/software/lsmlib/index.html(accessed 22 October 2009).
Finney, J.L. 1970. RandomPackings and the Structure of Simple Liquids I. The Geometry of Random ClosePacking. Proceedings of the Royal Society of London A 319 (1539): 479. doi:10.1098/rspa.1970.0189.
Gladkikh, M. and Bryant, S. 2005. Prediction of imbibition inunconsolidated granular materials. Journal of Colloid and InterfaceScience 288 (2): 526-539. doi:10.1016/j.jcis.2005.03.029.
Hatiboglu, C.U. and Babadagli, T. 2008. Pore-scale studies ofspontaneous imbibition into oil-saturated porous media. Phys. Rev. E 77 (6): 066311. doi:10.1103/PhysRevE.77.066311.
Hughes, R.G. and Blunt, M.J. 2001. Pore-scale Modeling of MultiphaseFlow in Fractures and Matrix/Fracture Transfer. SPE J. 6 (2): 126-136. SPE-71297-PA.doi: 10.2118/71297-PA.
Karpyn, Z.T. and Piri, M. 2007. Prediction of fluidoccupancy in fractures using network modeling and X-ray microtomography. I:Data conditioning and model description. Phy. Rev. E 76(1): 016315. doi: 10.1103/PhysRevE.76.016315.
Karpyn, Z.T., Grader, A.S., and Halleck, P.M. 2007. Visualization of fluidoccupancy in a rough fracture using micro-tomography. Journal of Colloidand Interface Science 307 (1): 181-187.doi:10.1016/j.jcis.2006.10.082.
Lake, L.W. 1989. Enhanced Oil Recovery. Englewood Cliffs, New Jersey:Prentice Hall.
Lee, T.C., Kashyap, R.L., and Chu, C.N. 1994. Building Skeleton Models via3-D Medial Surface Axis Thinning Algorithms. CVGIP-GMIP 56(6): 462-478.
Lindquist, W.B. 2008. 3DMA-Rock: A Software Package for Automated Analysisof Rock Pore Structure in 3-D Computed Microtomography Images, http://www.ams.sunysb.edu/~lindquis/3dma/3dma_rock/3dma_rock.html(accessed 22 October 2009).
Martys, N.S. and Chen, H.D. 1996. Simulation of multicomponentfluids in complex three-dimensional geometries by the lattice Boltzmannmethod. Phy. Rev. E 53 (1): 743-750.doi:10.1103/PhysRevE.53.743.
Narr, W., Schechter, D.W., and Thompson, L.B. 2006. Naturally FracturedReservoir Characterization. Richardson, Texas: SPE.
Neuweiler, I., Sorensen, I., and Kinzelbach, W. 2004. Experimental andtheoretical investigations of drainage in horizontal rough-walled fractureswith different correlation structures. Advances in Water Resources 27 (12): 1217-1231. doi:10.1016/j.advwatres.2004.07.005.
Olson, J.E., Laubach, S.E., and Lander, R.H. 2007. Combining diagenesis andmechanics to quantify fracture aperture distributions and fracture patternpermeability. In Fractured Reservoirs, No. 270, 101-116. London: SpecialPublication, Geological Society of London.
Osher, S. and Fedkiw, R. 2003. Level Set Methods and Dynamic ImplicitSurfaces. New York: Springer-Verlag.
Piri, M. and Karpyn, Z.T. 2007. Prediction of fluidoccupancy in fractures using network modeling and X-ray microtomography. II:Results. Phy. Rev. E 76 (1): 016316. doi:10.1103/PhysRevE.76.016316.
Prodanovic, M. 2009. Level Set Method based Progressive Quasi-Static(LSMPQS) software, http://users.ices.utexas.edu/~masha/lsmpqs/index.html(accessed 22 October 2009).
Prodanovic, M. and Bryant S.L. 2006. A level set method fordetermining critical curvatures for drainage and imbibition. Journal ofColloid and Interface Science 304 (2): 442-458.doi:10.1016/j.jcis.2006.08.048.
Prodanovic, M. and Bryant, S.L. 2007. Physics-Driven Interface Modelingfor Drainage and Imbibition in Fractures. Paper SPE 110448 presented at theSPE Annual Technical Conference and Exhibition, Anaheim, California, USA, 11-14November. doi: 10.2118/110448-MS.
Prodanovic, M. and Bryant, S.L. 2008. Resolving Meniscus Movement WithinRough Confining Surfaces Via the Level Set Method. In Focus on WaterResource Research, ed. E. Heikkinen, 237-262. Hauppage, New York: NovaScience Publishers.
Prodanovic, M. and Bryant, S.L. 2009. Physics-DrivenInterface Modeling for Drainage and Imbibition in Fractures. SPE J. 14 (3): 532-542. SPE-110448-PA. doi: 10.2118/110448-PA.
Schaap, M.G., Porter, M.L., Christensen, B.S.B., and Wildenschild, D. 2007.Comparison ofpressure-saturation characteristics derived from computed tomography andlattice Boltzmann simulations. Water Resour. Res. 43(12): W12S06. doi:10.1029/2006WR005730.
Sethian, J.A. 1999. Level Set Methods and Fast Marching Methods: EvolvingInterfaces in Computational Geometry, Fluid Mechanics, Computer Vision, andMaterials Science, second edition. Cambridge, UK: Cambridge UniversityPress.
Sukop, M.C. and Thorne, D.T. Jr. 2006. Lattice Boltzmann Modeling: AnIntroduction for Geoscientists and Engineers. Heidelberg, Germany:Springer-Verlag.
Thane, C.G. 2006. Geometry and Topology of Model Sediments and TheirInfluence on Sediment Properties. MS thesis, University of Texas at Austin,Austin, Texas.