Transport in Porous Media

, Volume 94, Issue 1, pp 359–383 | Cite as

Numerical Analysis of Imbibition Front Evolution in Fractured Sandstone under Capillary-Dominated Conditions

Article

Abstract

Fractures serve as primary conduits having a great impact on the migration of injected fluid into fractured permeable media. Appropriate transport properties such as relative permeability and capillary pressure are essential for successful simulation and prediction of multi-phase flow in such systems. However, the lack of a thorough understanding of the dynamics governing immiscible displacement in fractured media, limits our ability to properly represent their macroscopic transport properties. Previous experimental observations of imbibition front evolution in fractured rocks are examined in the present study using an automated history-matching approach to obtain representative relative permeability and capillary pressure curves. Predicted imbibition front evolution under different flow conditions resulted in an excellent agreement with experimental observations. Sensitivity analyses, in combination with direct experimental observation, allowed exploring the competing effects of relative permeability and capillary pressure on the development of saturation distribution and imbibing front evolution in fractured porous media. Results show that residual saturations are most sensitive to matrix relative permeability to oil, while the ratio of oil and water relative permeability, rock heterogeneity, boundary condition, and matrix–fracture capillary pressure contrast, affect displacement shape, speed, and geometry of the imbibing front.

Keywords

Imbibition Computed tomography Fractures Capillarity 

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References

  1. Alajmi, A.F.: The influence of a fracture tip on two-phase flow displacement processes. PhD, The Pennsylvania State University (2003)Google Scholar
  2. Alajmi, A.F., Grader, A.S.: Analysis of fracture–matrix fluid flow interactions using X-ray CT. In: SPE Eastern Meeting, Morgantown, West Virginia, 17–19 Oct 2000Google Scholar
  3. Anderson T.W., Darling D.A.: Asymptotic theory of certain goodness of fit criteria based on stochastic processes. Ann. Math. Stat. 23(2), 193–212 (1952)CrossRefGoogle Scholar
  4. Angeles, R., Torres-Verdín, C., Hadibeik, A., Sepehrnoori, K.: Estimation of capillary pressure and relative permeability from formation-tester measurements using design of experiment and data-weighing inversion: synthetic and field examples. J. Pet. Sci. Eng. (2010). doi: 10.1016/j.petrol.2010.10.006
  5. Archer J.S., Wong S.W.: Use of a reservoir simulator to interpret laboratory waterflood. Data SPE J. 13(6), 5 (1973)Google Scholar
  6. Al-Wadahi, M., Grader, A.S., Ertekin, T.: An investigation of three-phase counter-current flow Using X-ray computerized tomography and neuro-simulation modeling. In: SPE Annual Technical Conference and Exhibition, Dallas, Texas, USA, 1–4 Oct 2000Google Scholar
  7. Babadagli, T.: Injection rate controlled capillary imbibition transfer in fractured systems. In: SPE Annual Technical Conference and Exhibition, New Orleans, LA, USA, 25–28 Sep 1994Google Scholar
  8. Babadagli T.: Efficiency of capillary imbibition dominated displacement of nonwetting phase by wetting phase in fractured porous media. Transp. Porous Media 40(3), 323–344 (2000)CrossRefGoogle Scholar
  9. Basbug B., Karpyn Z.T.: Estimation of fracture–matrix transport properties from saturation profiles using a multivariate automatic history matching method. Pet. Sci. Technol. 29(9), 11 (2011)CrossRefGoogle Scholar
  10. Belayneh M., Geiger S., Matthai S.K.: Numerical simulation of water injection into layered fractured carbonate reservoir analogs. AAPG Bull. 90(10), 1473–1493 (2006). doi: 10.1306/05090605153 CrossRefGoogle Scholar
  11. Bertels S.P., DiCarlo D.A., Blunt M.J.: Measurement of aperture distribution, capillary pressure, relative permeability, and in situ saturation in a rock fracture using computed tomography scanning. Water Resour. Res. 37(3), 649–662 (2001)CrossRefGoogle Scholar
  12. Bogdanov I.I., Mourzenko V.V., Thovert J.-F., Adler P.M.: Two-phase flow through fractured porous media. Phys. Rev. E 68(2), 1–24 (2003)CrossRefGoogle Scholar
  13. Bourbiaux B.J., Kalaydjian F.J.: Experimental study of cocurrent and countercurrent flows in natural porous media. SPE Reserv. Eng. 5(3), 361–368 (1990)Google Scholar
  14. Brooks R.H., Corey A.T.: Hydraulic properties of porous media: hydrology papers. Colorado State University, Fort Collins (1964)Google Scholar
  15. Chavent, G., Cohen, G., Espy, M.: Determination of relative permeability and capillary pressure by automatic adjustment method. In: SPE Annual Technical Conference and Exhibition, Dallas, Texas, USA, 21–24 Sep 1980Google Scholar
  16. Chen, S., Li, G., Peres, A., Reynolds, A.C.: A well test for in-situ determination of relative permeability curves. In: SPE Annual Technical Conference and Exhibition, Dallas, Texas, USA, 9–12 Oct 2005Google Scholar
  17. De la Porte, J.J., Kossack, C.A., Zimmerman, R.W.: The effect of fracture relative permeabilities and capillary pressures on the numerical simulation of naturally fractured reservoirs. Paper presented at the SPE annual technical conference and exhibition, Dallas, Texas, USA, 9–12 Oct 2005Google Scholar
  18. Donato G., Lu H.Y., Tavassoli Z., Blunt M.J.: Multirate-transfer dual-porosity modeling of gravity drainage and imbibition. SPE J. 12(1), 77–88 (2007)Google Scholar
  19. El-Khatib, N.: Development of a modified capillary pressure J-function In: Middle East Oil Show, Bahrain, 11–14 March 1995Google Scholar
  20. Ertekin, T., Abou-Kassem, J.H., King, G.R.: Basic applied reservoir simulation. SPE Textbook Series, vol. 7. Society of Petroleum Engineers Publications Department, Dallas (2001)Google Scholar
  21. Ewing R.P., Berkowitz B.: A generalized growth model for simulating initial migration of dense non-aqueous phase liquids. Water Resour. Res. 34(4), 611–622 (1998)CrossRefGoogle Scholar
  22. Firoozabadi A., Hauge J.: Capillary-pressure in fractured porous-media. J. Pet. Technol. 42(6), 784–791 (1990)Google Scholar
  23. Firoozabadi, A., Markeset, T.: An experimental study of capillary and gravity crossflow fractured porous media. In: SPE Annual Technical Conference and Exhibition, Washington, DC, 4–7 Oct 1992Google Scholar
  24. Hatiboglu C.U., Babadagli T.: Oil recovery by counter-current spontaneous imbibition: Effects of matrix shape factor, gravity, IFT, oil viscosity, wettability, and rock type. J. Pet. Sci. and Eng 59(1-2), 106–122 (2007)CrossRefGoogle Scholar
  25. Heaviside, J., Black, C.J.J., Berry, J.F.: Fundamentals of relative permeability: experimental and theoretical considerations In: SPE Annual Technical Conference and Exhibition, San Francisco, California, USA, 5–8 Oct 1983Google Scholar
  26. Hoteit H., Firoozabadi A.: An efficient numerical model for incompressible two-phase flow in fractured media. Adv. Water Resour. 31(6), 891–905 (2008). doi: 10.1016/j.advwatres.2008.02.004 CrossRefGoogle Scholar
  27. Hughes R.G., Blunt M.J.: Pore scale modeling of rate effects in imbibition. Transp. Porous Media 40(3), 295–322 (2000)CrossRefGoogle Scholar
  28. IMEX: Three-Phase Black Oil Simulator, User’s Guide. Computer Modeling Group (CMG), Calgary (2009)Google Scholar
  29. Karimi-Fard M., Durlofsky L.J., Aziz K.: An efficient discrete-fracture model applicable for general-purpose reservoir simulators. SPE J. 9(2), 227–236 (2004)Google Scholar
  30. Karpyn Z.T., Alajmi A., Radaelli F., Halleck P.M., Grader A.S.: X-ray CT and hydraulic evidence for a relationship between fracture conductivity and adjacent matrix porosity. Eng. Geol. 103(3–4), 139–145 (2009). doi: 10.1016/j.enggeo.2008.06.017 CrossRefGoogle Scholar
  31. Kruger W.D.: Determining areal permeability distribution by calculations. J. Pet. Technol. 13(7), 6 (1961)Google Scholar
  32. Lee, C.H., Karpyn, Z.T.: Experimental investigation of rate effects on two-phase flow through fractured rocks using X-ray computed tomography. Paper presented at the 3rd international workshop on X-ray CT for geomaterials, New Orleans, Louisiana, USA, 1–3 MarchGoogle Scholar
  33. Lenormand R., Touboul E., Zarcone C.: Numerical-nodels and experiments on immiscible displacements in porous-media. J. Fluid Mech. 189, 165–187 (1988)CrossRefGoogle Scholar
  34. Li, G.: History dependent modeling of countercurrent flow in porous media. PhD, The Pennsylvania State University (2003)Google Scholar
  35. Li K.: A new method for calculating two-phase relative permeability from resistivity data in porous media. Transp. Porous Media 74(1), 21–33 (2008). doi: 10.1007/s11242-007-9178-4 CrossRefGoogle Scholar
  36. Li, K., Horne, R.N.: Correlation between resistivity index, capillary pressure and relative permeability. In: Proceedings of the World Geothermal Congress 2010, Bali, Indonesia, 25–29 April 2010Google Scholar
  37. Matthai S.K., Mezentsev A., Belayneh M.: Finite element-node-centered finite-volume two-phase-flow experiments with fractured rock represented by unstructured hybrid-element meshes. SPE Reserv. Eval. Eng. 10(6), 740–756 (2007)Google Scholar
  38. Melean Y., Broseta D., Blossey R.: Imbibition fronts in porous media: effects of initial wetting fluid saturation and flow rate. J. Pet. Sci. Eng. 39(3–4), 327–336 (2003). doi: 10.1016/S0920-4105(03)00072-X CrossRefGoogle Scholar
  39. Mohamad Ibrahim, M.N., Koederitz, L.F.: Two-phase steady-state and unsteady-state relative permeability prediction models. In: SPE Middle East Oil Show, Bahrain, 17–20 March 2001Google Scholar
  40. Mowla A., Firoozabadi A., Borhani Haghighi A., Sahraian A.: Megadose clonazepam dependence: a case report. J. Clin. Psychopharmacol. 27(5), 542–543 (2007). doi: 10.1097/JCP.0b013e3181506e4e CrossRefGoogle Scholar
  41. Or D.: Scaling of capillary, gravity and viscous forces affecting flow morphology in unsaturated porous media. Adv. Water Resour. 31(9), 1129–1136 (2008). doi: 10.1016/j.advwatres.2007.10.004 CrossRefGoogle Scholar
  42. Prodanovic, M., Bryant, S.L., Karpyn, Z.T.: Investigating matrix–fracture transfer via a level set method for drainage and imbibition. In: SPE Annual Technical Conference and Exhibition, Denver, Colorado, 21–24 Sep 2008Google Scholar
  43. Rangel-German E.R., Kovscek A.R.: Experimental and analytical study of multidimensional imbibition in fractured porous media. J. Pet. Sci. Eng. 36(1–2), 45–60 (2002)CrossRefGoogle Scholar
  44. Rangel-German E.R., Kovscek A.R.: Time-dependent matrix–fracture shape factors for partially and completely immersed fractures. J. Pet. Sci. Eng. 54(3–4), 149–163 (2006). doi: 10.1016/j.petrol.2006.08.004 CrossRefGoogle Scholar
  45. Rangel-German E.R., Akin S., Castanier L.: Multiphase-flow properties of fractured porous media. J. Pet. Sci. Eng. 51(3–4), 197–213 (2006). doi: 10.1016/j.petrol.2005.12.010 CrossRefGoogle Scholar
  46. Reichenberger V., Jakobs H., Bastian P., Helmig R.: A mixed-dimensional finite volume method for two-phase flow in fractured porous media. Adv. Water Resour. 29(7), 1020–1036 (2006)CrossRefGoogle Scholar
  47. Slough K.J., Sudicky E.A., Forsyth P.A.: Numerical simulation of multiphase flow and phase partitioning in discretely fractured geologic media. J. Contam. Hydrol. 40(2), 107–136 (1999)CrossRefGoogle Scholar
  48. Tavassoli Z., Zimmerman R.W., Blunt M.J.: Analysis of counter-current imbibition with gravity in weakly water-wet systems. J. Pet. Sci. Eng. 48(1–2), 94–104 (2005). doi: 10.1016/j.petrol.2005.04.003 CrossRefGoogle Scholar
  49. Tavassoli Z., Zimmerman R.W., Blunt M.J.: Analytic analysis for oil recovery during counter-current imbibition in strongly water-wet systems. Transp. Porous Media 58(1–2), 173–189 (2005). doi: 10.1007/s11242-004-5474-4 CrossRefGoogle Scholar
  50. Timur, A.: An investigation of permeability, porosity, and residual water saturation relationship for sandstone reservoirs. Paper presented at the SPWLA 9th annual logging symposium, 23–26 JuneGoogle Scholar
  51. Trivedi J.J., Babadagli T.: Experimental and numerical modeling of the mass transfer between rock matrix and fracture. Chem. Eng. J. 146(2), 194–204 (2009). doi: 10.1016/j.cej.2008.05.032 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.John and Willie Leone Family Department of Energy and Mineral Engineering, EMS Energy InstituteThe Pennsylvania State UniversityUniversity ParkUSA
  2. 2.CPC CorporationTaipei CityTaiwan

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