A study of relative permeability for transient two-phase flow in a low permeability fractal porous medium

Abstract

In this paper, a relative permeability prediction method considering the effects of capillary pressure and threshold pressure gradient in a low permeability fractal porous medium is established and analyzed based on the fractal approximation model that porous medium consist of a bundle of tortuous capillaries. With this method, every parameter has clear physical meaning without empirical constants, and the model's predictions have a good agreement with experimental data. In addition to this, it makes some discussions that how the characteristic parameters (such as tortuosity fractal dimension, pore fractal dimension, ratio of minimum-maximum capillaries diameters and threshold pressure gradient) influence the relative permeability. This study may be conducible to a better understanding of the mechanism for transient two-phase flow in the low permeability fractal porous medium.

Cited as: Li, Z., Duan, Y., Fang, Q., Wei, M. A study of relative permeability for transient two-phase flow in a low permeability fractal porous medium. Advances in Geo-Energy Research, 2018, 2(4): 369-379, doi: 10.26804/ager.2018.04.02

References

Ahmadi, M.A., Zendehboudi, S., Dusseault, M.B., et al. Evolving simple-to-use method to determine water-oil relative permeability in petroleum reservoirs. Petroleum 2016, 2(1): 67-78.

Benzi, R., Succi, S., Vergassola, M. The lattice Boltzmann equation: Theory and applications. Phys. Rep. 1992, 222(3): 145-197.

Bird, R.B. Transport phenomena. Appl. Mech. Rev. 2002, 55(1): R1-R4. Brooks, R.H., Corey, A.T. Properties of porous media affecting fluid flow. J. Irrig. Drain. Div. 1966, 92(2): 61-90.

Brown, H.W. Capillary pressure investigations. J. Pet. Technol. 1951, 3(3): 67-74.

Cai, J. A fractal approach to low velocity non-Darcy flow in a low permeability porous medium. Chin. Phys. B 2014, 23(4): 044701.

Delshad, M., Lenhard, R.J., Oostrom, M., et al. A mixed-wet hysteretic relative permeability and capillary pressure model for reservoir simulations. SPE Reserv. Eval. Eng. 2003, 6(5): 328-334.

Ding, Y.D., Wu, Y.S., Farah, N., et al. Numerical imulation of low permeability unconventional gas reservoirs. Paper SPE 167711 Presented at the SPE/EAGE European Unconventional Conference and Exhibition, Vienna, Austria, 25-27 February, 2014.

Dou, H., Yang, Y. Further understanding on fluid flow through multi-porous media in low-permeability reservoirs. Pet. Explor. Dev. 2012, 39(5): 674-682.

Duan, Y., Lu, T., Wei, M., et al. Buckley-Leverett analysis for transient two-phase flow in fractal porous medium. Comput. Model. Eng. Sci. 2015, 109-110(6): 481-504.

Ge, Y., Li, S., Qu, K. A novel empirical equation for relative permeability in low permeability reservoirs. Chin. J. Chem. Eng. 2014, 22(11-12): 1274-1278.

Huang, S., Yao, Y., Zhang, S., et al. A fractal model for oil transport in tight porous media. Transp. Porous Media 2017, 121(3): 725-739.

Jeannin, L., Bignonnet, F., Agostini, F., et al. Stress effects on the relative permeabilities of tight sandstones. C. R. Geosci. 2018, 350(3): 110-118.

Johnson, E.F., Bossler, D.P., Naumann, V.O. Calculation of relative permeability from Displacement Experiments. Trans. AIME 1959, 216: 370-372.

Katz, A.J., Thompson, A.H. Fractal sandstone pores: Impli-cations for conductivity and pore formation. Phys. Rev. Lett. 1985, 54(12): 1325-1328.

Krohn, C.E., Thompson, A.H. Fractal sandstone pores: Auto-mated measurements using scanning-electron-microscope images. Phys. Rev. B 1986, 33(9): 6366-6374.

Laroche, C., Vizika, O. Two-phase flow properties prediction from small-scale data using pore-network modeling. Transp. Porous Media 2005, 61(1): 77-91.

Lu, T., Duan, Y., Fang, Q., et al. Analysis of fractional flow for transient two-phase flow in fractal porous medium. Fractals 2016, 24(1): 1650013.

Mandelbrot, B.B. The fractal geometry of nature. New York, USA, WH Freeman, 1982.

Mo, S., He, S., Lei, G., et al. Effect of the drawdown pressure on the relative permeability in tight gas: A theoretical and experimental study. J. Nat. Gas Sci. Eng. 2015, 24: 264-271.

Ofagbohunmi, S., Chalaturnyk, R.J., Leung, J.Y.W. Coupling of Stress-Dependent relative permeability and reservoir simulation. Paper SPE 154083 Presented at the SPE Improved Oil Recovery Symposium, Tulsa, Oklahoma, USA, 14-18 April, 2012.

Prada, A., Civan, F. Modification of Darcy’s law for the threshold pressure gradient. J. Pet. Sci. Eng. 1999, 22(4): 237-240.

Standnes, D.C., Evje, S,, Andersen P.Ø. A novel relative permeability model based on mixture theory approach accounting for solid-fluid and fluid-fluid interactions. Transp. Porous Media 2017, 119(3): 707-738.

Tan, X., Li, X., Liu, J., et al. Analysis of permeability for transient two-phase flow in fractal porous media. J. Appl. Phys. 2014, 115(11): 113502.

Tan, X., Li, X., Liu, J., et al. Study of the effects of stress sensitivity on the permeability and porosity of fractal porous media. Phys. Lett. A 2015, 379(39): 2458-2465.

Thomas, L.K., Katz, D.L., Tek, M.R. Threshold pressure phenomena in porous media. Soc. Petrol. Eng. J. 1968, 8(2): 174-184.

Tian, X., Cheng, L., Yan, Y., et al. An improved solution to estimate relative permeability in tight oil reservoirs. J. Pet. Explor. Prod. Technol. 2014, 5(3): 305-314.

Verma, A.K., Pruess, K., Tsang, C.F., et al. A study of two-phase concurrent flow of steam and water in an unconsolidated porous medium. Paper Presented at the 23rd ASME/AICHE National Heat Transfer Conference, Denver, 4-7 August, 1985.

Welge, H.J. A simplified method for computing oil recovery by gas or water drive. J. Pet. Technol. 1952, 4(4): 91-98.

Wheatcraft, S.W., Tyler, S.W. An explanation of scaledepen-dent dispersivity in heterogeneous aquifers using concepts of fractal geometry. Water Resour. Res. 1988, 24(4): 566-578.

Xu, P., Qiu, S., Yu, B., et al. Prediction of relative permeability in unsaturated porous media with a fractal approach. Int. J. Heat Mass Transf. 2013, 64: 829-837.

Xu, Y., Wu, F. A new method for the analysis of relative permeability in porous media. Chin. Phys. Lett. 2002, 19(12): 1835-1837.

Yu, B., Cheng, P. A fractal permeability model for bi-dispersed porous media. Int. J. Heat Mass Transf. 2002, 45(14): 2983-2993.

Yu, B., Li, J. Some fractal characters of porous media. Fractals 2001, 9(3): 365-372.

Yu, B., Liu, W. Fractal analysis of permeabilities for porous media. Aiche J. 2004, 50(1): 46-57.

Yun, M., Yu, B., Cai, J. A fractal model for the starting pressure gradient for Bingham fluids in porous media. Int. J. Heat Mass Transf. 2008, 51(5-6): 1402-1408.

Zhang, B., Liu, X. Effects of fractal trajectory on gas diffusion in porous media. Aiche J. 2003, 49(12): 3037-3047.

Zhang, T., Li, X., Li, J., et al. A fractal model for gas-water relative permeability in inorganic shale with nanoscale pores. Transp. Porous Media 2018, 122(2): 305-331.

Zhang, Y., Osamu, N., Hyuck, P., et al. Relative permeability of CO2 in a low-permeability rock: Implications for CO2 flow behavior in reservoirs with tight interlayers. Energy Procedia 2017, 114: 4822-4831.