Relative Permeability Calculations from Two-Phase Flow Simulations Directly on Digital Images of Porous Rocks

Transport in Porous Media

Volumn 94, Issue 2, 2012, Pages 487-504

  Ramstad, Thomas ^a   Idowu, Nasiru ^a   Nardi, Cyril ^a   Øren, Pål Eric ^a  

^a Numerical Rocks AS   (Norway)

Author keywords

Lattice Boltzmann simulations; Relative permeability; Sandstone; Steady state; Unsteady state

Indexed keywords

BEREA SANDSTONE; CAPILLARY NUMBERS; DIGITAL IMAGE; DYNAMIC EFFECTS; FLUID CONDITIONS; LATTICE BOLTZMANN SIMULATIONS; MULTI-PHASE FLOW PROPERTIES; NON-WETTING; NON-WETTING FLUIDS; PORE SPACE; POROUS ROCKS; PRESSURE PROFILES; RATE EFFECTS; RELATIVE PERMEABILITY; RELATIVE PERMEABILITY FUNCTIONS; RESIDUAL SATURATION; STEADY STATE DATA; STEADY-STATE; STEADY-STATE FLOWS; SYSTEMATIC STUDY; TRANSIENT DYNAMICS; TRANSIENT EFFECT; UNSTEADY STATE; VERSATILE TOOLS; VISCOUS INSTABILITY; WETTING FLUID; X RAY MICROTOMOGRAPHY;

MULTIPHASE FLOW;

SANDSTONE;

COMPUTER SIMULATION; MULTIPHASE FLOW; PERMEABILITY; POROUS MEDIUM; ROCK MECHANICS; SANDSTONE; STEADY-STATE EQUILIBRIUM; TWO PHASE FLOW; UNSTEADY FLOW;

EID: 84865491918     PISSN: 01693913     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11242-011-9877-8     Document Type: Article

References (44)

1. Ahrenholz B., Tölke J., Lehmann P., Peters A., Kaestner A., Krafczyk M., Durner W.: Prediction of capillary hysteresis in a porous material using lattice-Boltzmann methods and comparison to experimental data and a morphological pore network model. Adv. Water Resour. 31, 1151-1173 (2008).
2. Arns C. H., Knackstedt M. A., Pinczewski V., Garboczi E. J.: Computation of linear elastic properties from microtomographic images: methodology and agreement between theory and experiments. Geophysics 67, 1396-1405 (2002).
3. Avraam D. G., Payatakes A. C.: Flow mechanisms, relative permeability, and coupling effects in steady-state two-phase flow through porous media. The case of strong wettability. Ind. Eng. Chem. Res. 38, 778-786 (1999).
4. Badalassi V., Ceniceros H., Banerjee S.: Computation of multiphase systems with phase field models. J. Comput. Phys. 190, 371-397 (2003).
5. Bardon C., Longeron D. G.: Influence of very low interfacial tensions on relative permeability. SPE J. 20, 391-401 (1980).
6. Bhatnagar P. L., Gross E. P., Krook M.: A model for collision processes in gases. 1. Small amplitude processes in charges and neutral one-component systems. Phys. Rev. 94, 511-525 (1954).
7. Craig F. F.: The Reservoir Engineering Aspects of Waterflooding. Society of Petroleum Engineers of AIME, New York (1971).
8. d'Humières D., Ginzburg I., Krafczyk M., Lallemand P., Li-Shi L.: Multiple-relaxation-time lattice Boltzmann models in three dimensions. Philos. Trans. R. Soc. Lond. A 360, 437-451 (2002).
9. Dullien F. A. L.: Porous Media: Fluid Transport and Pore Structure. 2nd edn. Academic Press, New York (1992).
10. Eleri, O. O., Graue, A., Skauge, A.: Steady-state and unsteady-state two-phase relative permeability hysteresis and measurements of three-phase relative permeabilities using imaging techniques. Paper SPE 30764, presented at the annual SPE conference and exhibition, Dallas, TX, USA (1995).
11. Gunstensen A. K., Rothman D. H., Zaleski S., Zanetti G.: Lattice Boltzmann model of immiscible fluids. Phys. Rev. A 43, 4320-4327 (1991).
12. Honarpour M., Koederitz L., Harvey A. H.: Relative Permeabilities for Petroleum Reservoirs. CRC Press, Boca Raton (1986).
13. Idowu N. A., Blunt M. J.: Pore-Scale modelling of rate effects in waterflooding. Transp. Porous Med. 83, 151-169 (2010).
14. Inamuro T., Ogata T., Tajima S., Konishi N.: A lattice Boltzmann method for incompressible two-phase flow with large density differences. J. Comput. Phys. 155, 96-127 (2004).
15. Jiang Z., Wu K., Couples G., van Dijke M. I. J., Sorbie K. S., Ma J.: Efficient extraction of networks from three-dimensional porous media. Water Resour. Res. 43, W12S03 (2007).
16. Jin, G., Patzek, T. W., Silin, D. B.: Direct prediction of the absolute permeability of unconsolidated and consolidated reservoir rocks. Paper SPE 90084, presented at the annual SPE conference and exhibition, Houston, TX, 26-29 September 2004.
17. Joekar-Niasar V., Hassanizadeh S. M.: Specific interfacial area: the missing state variable in two-phase flow equations?. Water Resour. Res. 47, W05513 (2011).
18. Johnson E. F., Bossler D. D., Naumann V. O.: Calculation of relative permeability from displacement experiments. Trans. AIME 216, 370 (1959).
19. Knackstedt, M. A., Arns, C. H., Limaye, A., Sakellariou, A., Senden, T. J., Sheppard, A. P., Sok, R. M., Pinczewski, W. V.: Digital Core Laboratory: properties of reservoir core derived from 3D images. SPE paper 87009, Kuala Lumpur, Malaysia (2004).
20. Lallemand P., Luo L. A.: Theory of the lattice Boltzmann method: dispersion, isotropy, Galilean invariance and stability. Phys. Rev. E 61, 6546 (2000).
21. Latva-Kokko M., Rothmann D. H.: Diffusion properties of gradient-based lattice Boltzmann models of immiscible fluids. Phys. Rev. E 71, 056702 (2005).
22. Lindquist W. B., Lee S. M., Coker D., Jones K., Spanne P.: Medial axis analysis of void structure in three-dimensional tomographic images of porous media. J. Geophys. Res. 101, 8297 (1996).
23. Marle C. M.: Multiphase Flow in Porous Media. Editions Technip, Paris (1981).
24. Martys N., Chen H.: Simulation of multicomponent fluids in complex three-dimensional geometries by the lattice-Boltzmann method. Phys. Rev. E 53, 743-750 (1996).
25. Mohanty K. K., Miller A. E.: Factors influencing unsteady relative permeability of a mixed-wet reservoir rock. SPE Form. Eval. 6, 349-358 (1991).
26. Oak, M. J., Baker, L. E., Thomas, D. C.: Three-phase relative permeability of Berea sandstone. JPT August 1990, 1054 (1990).
27. Øren P. E., Bakke S.: Process based reconstruction of sandstones and prediction of transport properties. Transp. Porous Media 46, 311-314 (2002).
28. Øren P. E., Bakke S.: Reconstruction of Berea sandstone and pore scale modeling of wettability effects. J. Pet. Sci. Eng. 39, 177-199 (2003).
29. Øren P. E., Bakke S., Arntzen O. J.: Extending Predictive Capabilities to Network Models. SPE J. 3, 324-336 (1998).
30. Øren, P. E., Bakke, S., Rueslåtten, H. G.: Digital core laboratory: rock and flow properties derived from computer generated rocks. In: Proceedings of International Symposium of the Society of Core Analysts, Trondheim, Norway (2006).
31. Pan C., Hilpert M., Miller C. T.: Lattice-Boltzmann simulation of two-phase flow in porous media. Water Resour. Res. 40, W01501 (2004).
32. Pan C., Luo L.-S., Miller C. T.: An evaluation of lattice Boltzmann schemes for porous medium flow simulations. Comput. fluids 35, 898-909 (2006).
33. Ramstad T., Hansen A.: Cluster evolution in steady-state two-phase flow in porous media. Phys. Rev. E 73, 026306 (2006).
34. Ramstad T., Øren P.-E., Bakke S.: Simulation of two phase flow in reservoir rocks using a lattice Boltzmann method. SPE J. 15(4), 917-927 (2010).
35. Rothmann D. H., Zaleski S.: Lattice-Gas Cellular Automata. Cambridge University Press, Cambridge (1997).
36. Schaap M. G., Porter M. L., Christensen B., Wildenschild D.: Comparison of pressure-saturation characteristics derived from computed tomography and lattice Boltzmann simulations. Water Resour. Res. 43, W12S06 (2007).
37. Shan X., Chen H.: Lattice Boltzmann model for simulating flows with multiple phases and components. Phys. Rev. E 47, 1815-1819 (1993).
38. Succi S.: The Lattice Boltzmann Equation. Clarendon Press, Oxford (2001).
39. Succi S., Foti E., Higuera F.: Three dimensional flows in complex geometries with the lattice Boltzmann method. Europhys. Lett. 10, 433 (1989).
40. Sukop M. C., Thorne D. T.: Lattice Boltzmann Modeling. An Introduction for Geoscientists and Engineers. Springer, Berlin (2006).
41. Sussman M., Smereka P., Osher S.: A level set approach for computing solutions to incompressible two-phase flows. J. Comput. Phys. 114, 146-159 (1994).
42. Swift M. R., Osborn W. R., Yoemans J. M.: Lattice Boltzmann simulations of non-ideal fluids. Phys. Rev. Lett. 75, 830 (1995).
43. Tryggvason G., Sussman M., Hussaini M. Y.: Immersed boundary methods for fluid interfaces. In: Prosperetti, A., Tryggvasson, G. (eds) Computational Methods for Multiphase Flow, pp. 37-78. Cambridge University Press, Cambridge (2007).
44. Valvatne P. H., Blunt M.: Predictive pore-scale modeling of two-phase flow in mixed wet media. Water Resour. Res. 40, 1-21 (2004).