The effect of flow resistance on water saturation profile for transient two-phase flow in fractal porous media

Ting Lu, Zhiping Li, Fengpeng Lai, Ya Meng, Wenli Ma

Abstract view|243|times       PDF download|116|times

Abstract


Due to the rapid development of Micro-Electro-Mechanical System, more and more attention has been paid to the fluid properties of porous media, which is significant for petroleum engineering. However, most of surfaces of pores and capillaries in porous media are rough. On the approximation that porous medium consists of a bundle of tortuous and rough capillaries, a Buckley-Leverett conceptual model with considering flow resistance is developed based on the fractal geometry theory, which is beneficial to predict water saturation profile in porous medium. The proposed Buckley-Leverett solution is a function of fractal structural parameters (such as pore fractal dimension, tortuosity fractal dimension, maximum and minimum diameters of capillaries), fluid properties (such as viscosity, contact angle and interfacial tension) and pore structure parameter (relative roughness) in fractal porous medium. Besides, the relationship between water saturation and distance is presented according to Buckley-Leverett solution. The impaction of flow resistance on water saturation profile is discussed.

Cited as: Lu, T., Li, Z., Lai, F., Meng, Y., Ma, W. The effect of flow resistance on water saturation profifile for transient two-phase flow in fractal porous media. Advances in Geo-Energy Research, 2018, 2(1): 63-71, doi: 10.26804/ager.2018.01.06


Keywords


Fractal, transient two-phase flow, flow resistance, rough surfaces, porous media

Full Text:

PDF

References


Acuna, J.A., Yortsos, Y.C. Application of fractal geometry to the study of networks of fractures and their pressure transient. Water Resour. Res. 1995, 31(3): 527-540.

Bird, R.B. Transport phenomena. Appl. Mech. Rev. 2002, 55(1): R1-R4. Buckley, S.E., Leverett, M.C. Mechanism of fluid displace-ment in sands. Trans. AIME 1942, 146(1): 107-116.

Cai, J.C., Perfect, E., Cheng, C.L., et al. Generalized modeling of spontaneous imbibition based on Hagen-Poiseuille flow in tortuous capillaries with variably shaped apertures. Langmuir 2014, 30(18): 5142-5151.

Chang, J., Yortsos, Y.C. Pressure transient analysis of fractal reservoirs. SPE Reserv. Eng. 1990, 5(1): 31.

Chang, J., Yortsos, Y.C. Effect of capillary heterogeneity in Buckley-Leverett displacement. SPE Reserv. Eng. 1992, 7(2): 3-5.

Chen, Z.X. Some invariant solutions to two-phase fluid displacement problems including capillary effect. SPE Reserv. Eng. 1988, 3(2): 691-700.

Guo, L.X., Jiao, L.C., Wu, Z.S. Electromagnetic scattering from two-dimensional rough surface using the Kirchhoff approximation. Chin. Phys. Lett. 2001, 18(2): 214-216.

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.

Langtangen, H.P., Tveito, A. Instability of Buckley-Leverett flow in a heterogeneous medium. Transp. Porous Media 1992, 9(3): 165-185.

Larsen, L., Kviljo, K., Litlehamar, T. Estimating skin decline and relative permeabilities from clean up effects in well-test data with Buckley-Leverett method. SPE Form. Eval. 1990, 5(4): 5-7.

Lorente, S., Bejan, A. Heterogeneous porous medium as multiscale structures for maximum flow access. J. Appl. Phys. 2006, 100(11): 114909-114916. Majumdar, A., Bhushan, B. Role of fractal geometry in roughness characterization and contact mechanics of surfaces. J. Tribol. 1990, 112(2): 205-216.

Mandelbrot, B.B., Passoja, D.E., Paullay, A.J. Fractal character of fracture surfaces of metals. Nature 1984, 308(5961): 721-722.

Poljacek, S.M., Risovic, D., Furic, K., et al. Comparison of fractal and profilometric methods for surface topography characterization. Appl. Surf. Sci. 2008, 254(11): 3449-3458.

Snyder, R.W., Ramey, Jr.H.J. Application of Buckley-Leverett displacement theory to noncommunicating layered systems. J. Pet. Technol. 1967, 19(11): 3-5.

Spanos, T.J.T., De, L.C.V., Hube, J. An analysis of Buckley-Leverett theory. J. Can. Pet. Technol. 1986, 25(1): 71-75.

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

Warren, T.L., Krajcinovic, D. Random Cantor set models for the elastic-perfectly plastic contact of roughness surfaces. Wear 1996, 196(1-2): 1-15.

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

Wu, J.S., Yu, B.M. A fractal resistance model for flow through porous media. Transp. Porous Media 2007, 71(3): 331-343.

Wu, Y.S., Fakcharoenphol, P., Zhang, R.L., et al. Non-Darcy displacement in linear composite and radial flow porous media. Paper SPE 130343 Presented at the SPE EUROPEC/EAGE Annual conference and exhibition held in Barcelona, Spain, 14-17 June, 2010.

Wu, Y.S., Pruess, K., Chen, Z.X. Buckley-Leverett flow in composite porous media. SPE Adv. Technol. Ser. 1993, 1(2): 36-42.

Xu, P. A discussion on fractal models for transport of porous media. Fractals 2015, 23(3): 1530001.

Xu, P., Qiu, S., Cai, J., et al. A novel analytical solution for gas diffusion in multi-scale fuel cell porous media. J. Power Sources 2017, 362: 73-79.

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

Xu, P., Sasmito, A.P., Yu, B.M., et al. Transport phenomena and properties in treelike networks. Appl. Mech. Rev. 2016, 68(4): 040802.

Yang, S.S. A fractal analysis of flow properties in roughened microchannles. Wuhan, Huazhong University of Science and Technology, 2015. (in Chinese)

Yortsos, Y.C., Fokas, A.S. An analytical solution for linear waterflood including the effects of capillary pressure. SPE J. 1983, 23(1): 115-124.

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

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


Refbacks

  • There are currently no refbacks.


Copyright (c) 2018 The Author(s)

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Copyright ©2018. All Rights Reserved