# Elucidating the Role of Interfacial Tension for Hydrological Properties of Two-Phase Flow in Natural Sandstone by an Improved Lattice Boltzmann Method

- 1.1k Downloads
- 25 Citations

## Abstract

We investigated the interfacial tension (IFT) effect on fluid flow characteristics inside micro-scale, porous media by a highly efficient multi-phase lattice Boltzmann method using a graphics processing unit. IFT is one of the most important parameters for carbon capture and storage and enhanced oil recovery. Rock pores of Berea sandstone were reconstructed from micro-CT scanned images, and multi-phase flows were simulated for the digital rock model at extremely high resolution (3.2 \(\upmu \)m). Under different IFT conditions, numerical analyses were carried out first to investigate the variation in relative permeability, and then to clarify evolution of the saturation distribution of injected fluid. We confirmed that the relative permeability decreases with increasing IFT due to growing capillary trapping intensity. It was also observed that with certain pressure gradient \(\Delta P\) two crucial IFT values, \(\sigma _{1}\) and \(\sigma _{2}\), exist, creating three zones in which the displacement process has totally different characteristics. When \(\sigma _{1}< \sigma < \sigma _{2}\), the capillary fingering patterns are observed, while for \(\sigma < \sigma _{1}\) viscous fingering is dominant and most of the passable pore spaces were invaded. When \(\sigma > \sigma _{2}\) the invading fluid failed to break through. The pore-throat-size distribution estimated from these crucial IFT values (\(\sigma _{1 }\)and \(\sigma _{2})\) agrees with that derived from mercury porosimetry measurements of Berea sandstone. This study demonstrates that the proposed numerical method is an efficient tool for investigating hydrological properties from pore structures.

## Keywords

Interfacial tension effect Lattice Boltzmann simulation GPU computing Porous media## Notes

### Acknowledgments

We gratefully acknowledge the support of the I2CNER, which is sponsored by the World Premier International Research Center Initiative (WPI), Ministry of Education, Culture, Sports, Science, and Technology (MEXT), Japan. This work was supported by the grant for Environmental Research Projects facility of The Sumitomo Foundation and partially supported by a grant from the Grant-in-Aid for Challenging Exploratory Research facility of MEXT (No. 24656536).

## Supplementary material

Supplementary material 1 (avi 46979 KB)

## References

- 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**(9), 1151–1173 (2008)CrossRefGoogle Scholar - Aidun, C.K., Clausen, J.R.: Lattice-Boltzmann method for complex flows. Annu. Rev. Fluid Mech.
**42**, 439–472 (2010)CrossRefGoogle Scholar - Asar, H., Handy, L.: Influence of interfacial tension on gas/oil relative permeability in a gas-condensate system. SPE Reserv. Eng.
**3**(1), 257–264 (1988)CrossRefGoogle Scholar - Bachu, S., Gunter, W.D., Perkins, E.H.: Aquifer disposal of CO\(_{2}\): hydrodynamic and mineral trapping. Energy Convers. Manag.
**35**(4), 269–279 (1994)CrossRefGoogle Scholar - Badalassi, V.E., Ceniceros, H.D., Banerjee, S.: Computation of multiphase systems with phase field models. J. Comput. Phys.
**190**(2), 371–397 (2003)CrossRefGoogle Scholar - Bailey, P., Myre, J., Walsh, S.D.C., Lilja, D.J., Saar, M.O.: Accelerating lattice Boltzmann fluid flow simulations using graphics processors. In: Proceedings of the 2009 International Conference on Parallel Processing, Vienna, Austria, 2009, pp. 550–557Google Scholar
- Bardon, C., Longeron, D.G.: Influence of very low interfacial tensions on relative permeability. Soc. Pet. Eng. J.
**20**(5), 391–401 (1980)CrossRefGoogle Scholar - Bear, J.: Dyn. Fluids Porous Media. Elsevier Science, New York (1972)Google Scholar
- Boek, E.S., Venturoli, M.: Lattice-Boltzmann studies of fluid flow in porous media with realistic rock geometries. Comput. Math. Appl.
**59**, 2305–2314 (2010)CrossRefGoogle Scholar - Chen, Q., Gingras, M.K., Balcom, B.J.: A magnetic resonance study of pore filling processes during spontaneous imbibition in Berea sandstone. J. Chem. Phys.
**119**(18), 9609–9616 (2003)CrossRefGoogle Scholar - Cuda programming guide 5.0 (2012). http://docs.nvidia.com/cuda/index.html. Accessed 7 Dec 2012
- d’Humieres, D.: Generalized lattice Boltzmann equations. Rarefied gas dynamics: theory and simulations. Prog. Astronaut. Aeronaut.
**159**, 450–458 (1992)Google Scholar - Fulcher Jr, R.A., Ertekin, T., Stahl, C.D.: Effect of capillary number and its constituents on two-phase relative permeability curves. J. Pet. Technol.
**37**(2), 249–260 (1985)CrossRefGoogle Scholar - Ginzburg, I., Verhaeghe, F., d’Humieres, D.: Two-relaxation-time lattice Boltzmann scheme: about parameterization, velocity, pressure and mixed boundary conditions. Commun. Comput. Phys.
**3**, 427–478 (2008)Google Scholar - Goldsmith, H.L., Mason, S.G.: The flow of suspensions thorough tubes: II. Single large bubbles. J. Colloid Interface Sci.
**18**, 237–261 (1963)CrossRefGoogle Scholar - Gunstensen, A., Rothman, D., Zaleski, S., Zanetti, G.: Lattice Boltzmann model of immiscible fluids. Phys. Rev. A
**43**, 4320–4327 (1991)CrossRefGoogle Scholar - Hirt, C.W., Nichols, B.D.: Volume of fluid (VOF) method for the dynamics of free boundaries. J. Comput. Phys.
**39**(1), 201–225 (1981)CrossRefGoogle Scholar - Kandhai, D., Koponen, A., Hoekstra, A.G., Katajam, M., Timonen, J., Sloot, P.M.A.: Lattice-Boltzmann hydrodynamics on parallel systems. Comput. Phys. Commun.
**111**(1–3), 14–26 (1998)CrossRefGoogle Scholar - Kehrwald, D.: Numerical analysis of immiscible lattice BGK. Ph.D. thesis, Universitat Kaiserslautern (2003)Google Scholar
- Kuznik, F., Obrecht, C., Rusaouen, G., Roux, J.J.: LBM based flow simulation using GPU computing processor. Comput. Math. Appl.
**59**(7), 2380–2392 (2010)CrossRefGoogle Scholar - Lallemand, P., Luo, L.: Theory of the lattice Boltzmann method: dispersion, dissipation, isotropy, Galilean invariance, and stability. Phys. Rev. E
**61**, 6546–6562 (2000)CrossRefGoogle Scholar - Latva-Kokko, M., Rothman, D.H.: Static contact angle in lattice Boltzmann models of immiscible fluids. Phys. Rev. E
**72**, 046701 (2005)CrossRefGoogle Scholar - Lenormand, R., Zarcone, C.: Capillary fingering: percolation and fractal dimension. Transp. Porous Media
**4**, 599–612 (1989)CrossRefGoogle Scholar - Metz, B., et al. (eds.): IPCC Special Report, Carbon Dioxide Capture and Storage. Cambridge University Press, Cambridge (2005)Google Scholar
- Michael, K., Golab, A., Shulakova, V., Ennis-King, J., Allinson, G., Sharma, S., Aiken, T.: Geological storage of CO\(_{2}\) in saline aquifers—a review of the experience from existing storage operations. Int. J. Greenh. Gas Control
**4**(4), 659–667 (2010)CrossRefGoogle Scholar - Miller, C.T., Christakos, G., Imhoff, P.T., McBride, J.F., Pedit, J.A., Trangenstein, J.A.: Multiphase flow and transport modeling in heterogeneous porous media: challenges and approaches. Adv. Water Res.
**21**(2), 77–120 (1998)CrossRefGoogle Scholar - Obrecht, C., Kuznik, F., Tourancheau, B., Roux, J.J.: A new approach to the lattice Boltzmann method for graphics processing units. Comput. Math. Appl.
**61**(12), 3628–3638 (2011)CrossRefGoogle Scholar - Øren, P.E., Bakke, S.: Reconstruction of Berea sandstone and pore-scale modelling of wettability effects. J. Pet. Sci. Eng.
**39**(3–4), 177–199 (2003)CrossRefGoogle Scholar - Pan, C., Hilpert, M., Miller, C.T.: Lattice Boltzmann simulation of two-phase flow in porous media. Water Res. Res.
**40**(1) (2004)Google Scholar - Pan, C., Luo, L.S., Miller, C.T.: An evaluation of lattice Boltzmann schemes for porous medium flow simulation. Comput. Fluids
**35**, 898–909 (2006)CrossRefGoogle Scholar - Ramstad, T., Idowu, N., Nardi, C., Øren, P.E.: Relative permeability calculations from two-phase flow simulations directly on digital images of porous rocks. Transp. Porous Media
**94**(2), 487–504 (2012)CrossRefGoogle Scholar - Shan, X., Chen, H.: Lattice Boltzmann model for simulating flows with multiple phases and components. Phys. Rev. E
**47**, 1815–1819 (1993)CrossRefGoogle Scholar - Sussman, M., Almgren, A.S., Bell, J.B., Colella, P., Howell, L.H., Welcome, M.L.: An adaptive level set approach for incompressible two-phase flows. J. Comput. Phys.
**148**(1), 81–124 (1999)CrossRefGoogle Scholar - Swift, M., Orlandini, E., Osborn, W., Yeomans, J.: Lattice Boltzmann simulations of liquid-gas and binary fluid systems. Phys. Rev. E
**54**, 5041–5052 (1996)CrossRefGoogle Scholar - Talash, A.W.: Experimental and calculated relative permeability data for systems containing tension additives. Soc. Pet. Eng. J.
**1976**, 177–188 (1976)Google Scholar - Toelke, J., Krafczyk, M., Schulz, M., Rank, E.: Lattice Boltzmann simulations of binary fluid flow through porous media. Philos. Trans. R. Soci. Lond. A
**360**, 535–545 (2002)CrossRefGoogle Scholar - Toelke, J., Freudiger, S., Krafczyk, M.: An adaptive scheme using hierarchical grids for lattice Boltzmann multi-phase flow simulations. Comput. Fluid
**35**, 820–830 (2006)CrossRefGoogle Scholar - Tölke, J., Krafczyk, M.: TeraFLOP computing on a desktop PC with GPUs for 3D CFD. Int. J. Comput. Fluid Dyn.
**22**(7), 443–456 (2008)CrossRefGoogle Scholar - Tölke, J.: Implementation of a lattice Boltzmann kernel using the compute unified device architecture developed by nVIDIA. Comput. Vis. Sci.
**13**(1), 29–39 (2010)CrossRefGoogle Scholar - Wang, X., Aoki, T.: Multi-GPU performance of incompressible flow computation by lattice Boltzmann method on GPU cluster. Parallel Comput.
**37**(9), 521–535 (2011)Google Scholar - Yang, J., Boek, E.S.: A comparison study of multi-component lattice Boltzmann models for flow in porous media applications. Comput. Math. Appl.
**65**(6), 882–890 (2013)CrossRefGoogle Scholar