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Direct Calculation of Permeability by High-Accurate Finite Difference and Numerical Integration Methods

Part of:Flows in porous media; filtration; seepage

Published online by Cambridge University Press:  21 July 2016

Yi Wang and
Shuyu Sun
Yi Wang*
Affiliation:
National Engineering Laboratory for Pipeline Safety/MOE Key Laboratory of Petroleum Engineering/Beijing Key Laboratory of Urban Oil and Gas Distribution Technology, China University of Petroleum-Beijing, Beijing 102249, China
Shuyu Sun*
Affiliation:
Computational Transport Phenomena Laboratory, Division of Physical Science and Engineering, King Abdullah University of Science and Technology, Thuwal 23955-6900, Saudi Arabia
*
*Corresponding author. Email addresses:yiwang1031@gmail.com (Y. Wang), shuyu.sun@kaust.edu.sa (S. Sun)
*Corresponding author. Email addresses:yiwang1031@gmail.com (Y. Wang), shuyu.sun@kaust.edu.sa (S. Sun)

Abstract

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Velocity of fluid flow in underground porous media is 6~12 orders of magnitudes lower than that in pipelines. If numerical errors are not carefully controlled in this kind of simulations, high distortion of the final results may occur [1–4]. To fit the high accuracy demands of fluid flow simulations in porous media, traditional finite difference methods and numerical integration methods are discussed and corresponding high-accurate methods are developed. When applied to the direct calculation of full-tensor permeability for underground flow, the high-accurate finite difference method is confirmed to have numerical error as low as 10–5% while the high-accurate numerical integration method has numerical error around 0%. Thus, the approach combining the high-accurate finite difference and numerical integration methods is a reliable way to efficiently determine the characteristics of general full-tensor permeability such as maximum and minimum permeability components, principal direction and anisotropic ratio.

Keywords

Finite difference methodnumerical integration methodhigh accuracyfull tensor permeabilitystokes

MSC classification

Secondary:76S05: Flows in porous media; filtration; seepage

Information

Type
Research Article
Information
Communications in Computational Physics , Volume 20 , Issue 2 , August 2016, pp. 405 - 440
Copyright
Copyright © Global-Science Press 2016 

References

[1] Qiao, Z. and Sun, S. (2014), Two-phase fluid simulation using a diffuse interface model with Peng-Robinson equation of state, SIAM J. Sci. Comput., 36(4), B708-B728.Google Scholar
[2] Dong, H., Qiao, Z., Sun, S., and Tang, T. (2014), Adaptive moving grid methods for two-phase flow in porous media, J. Comput. Appl. Math., 265, 139–150.CrossRefGoogle Scholar
[3] Kou, J. and Sun, S. (2015), Numerical methods for a multi-component two-phase interface model with geometric mean influence parameters, SIAM J. Sci. Comput., 37(4), B543-B569.Google Scholar
[4] Kou, J. and Sun, S. (2016), Unconditionally stable methods for simulating multi-component two-phase interface models with Peng-Robinson equation of state and various boundary conditions, J. Comput. Appl. Math., 291, 158–182.CrossRefGoogle Scholar
[5] Darcy, H. (1856), Les Fontaines Publiques de la Vill de Dijon. Dalmont, Paris.Google Scholar
[6] Moortgat, J., Sun, S., and Firoozabadi, A. (2011), Compositional modeling of three-phase flow with gravity using higher-order finite element methods, Water Resour. Res., 47, W05511.CrossRefGoogle Scholar
[7] Sun, S. and Liu, J. (2009), A locally conservative finite element method based on piecewise constant enrichment of the continuous Galerkin method, SIAM J. Sci. Comput., 31(4), 2528–2548.Google Scholar
[8] Sun, S. and Wheeler, M. F. (2006a), Analysis of discontinuous Galerkin methods for multicomponent reactive transport problems, Comput. Math. Appl., 52(5), 637–650.Google Scholar
[9] Sun, S. and Wheeler, M. F. (2006b), A dynamic, adaptive, locally conservative and nonconforming solution strategy for transport phenomena in chemical engineering, Chem. Eng. Commun., 193(12), 1527–1545.Google Scholar
[10] Sun, S. and Wheeler, M. F. (2007), Discontinuous Galerkin methods for simulating bioreactive transport of viruses in porous media, Adv. Water Resour., 30(6-7), 1696–1710.Google Scholar
[11] Hwang, W.R. and Advani, S.G. (2010), Numerical simulations of Stokes-Brinkman equations for permeability prediction of dual scale fibrous porousmedia. Phys. Fluids, 22, 113101-1-14.CrossRefGoogle Scholar
[12] Jensen, J.L. and Heriot-Watt, U. (1990), A model for small-scale permeability measurement with applications to reservoir characterization, paper presented at SPE/DOE Enhanced Oil Recovery Symposium, Society of Petroleum Engineers, Inc., Tulsa, Oklahoma.Google Scholar
[13] Wang, T.J., Wu, C.H., and Lee, L.J. (1994), In-plane permeability measurement and analysis in liquid composite molding, Polym. Compos., 15(4), 278–288.Google Scholar
[14] Ferland, P., Guittard, D., and Trochu, F. (1996), Concurrent methods for permeability measurement in resin transfer molding, Polym. Compos., 17(1), 149–158.CrossRefGoogle Scholar
[15] Gauvin, R., Trochu, F., Lemenn, Y., and Diallo, L. (1996), Permeability measurement and flow simulation through fiber reinforcement, Polym. Compos., 17(1), 34–42.CrossRefGoogle Scholar
[16] Luo, Y., Verpoest, I., Hoes, K., Vanheule, M., Sol, H., and Cardon, A. (2001), Permeability measurement of textile reinforcements with several test fluids, Composites Part A, 32(10), 1497–1504.Google Scholar
[17] Fwa, T.F., Tan, S.A., Chuai, C.T., and Guwe, Y.K. (2001), Expedient permeability measurement for porous pavement surface. Int. J. Pavement Eng., 2(4), 259–270.CrossRefGoogle Scholar
[18] Arbter, R., Beraud, J.M., Binetruy, C., Bizet, L., Brard, J., Comas-Cardona, S., Demaria, C., Endruweit, A., Ermanni, P., Gommer, F., Hasanovic, S., Henrat, P., Klunker, F., Laine, B., Lavanchy, S., Lomov, S.V., Long, A., Michaud, V., Morren, G., Ruiz, E., Sol, H., Trochu, F., Verleye, B., Wietgrefe, M., Wu, W., and Ziegmann, G. (2011), Experimental determination of the permeability of textiles: A benchmark exercise, Composites Part A, 42(9), 1157–1168.Google Scholar
[19] Weitzenbock, J.R., Shenoi, R.A., and Wilson, P.A. (1998), Measurement of principal permeability with the channel flow experiment, Polym. Compos., 20(2), 321–335.Google Scholar
[20] Weitzenbock, J.R., Shenoi, R.A., and Wilson, P.A. (1999a), Radial flow permeability measurement. Part A: Theory, Composites Part A, 30(6), 781–796.CrossRefGoogle Scholar
[21] Weitzenbock, J.R., Shenoi, R.A., and Wilson, P.A. (1999b), Radial flow permeability measurement. Part B: Application, Composites Part A, 30(6), 797–813.Google Scholar
[22] Padmavathi, B.S., Amaranath, T., and Nigam, S.D. (1993), Stokes flow past a porous sphere using Bringkman's model, Z. angew. Math. Phys., 44(5), 929–939.Google Scholar
[23] Ngo, N.D., and Tamma, K.K. (2001), Microscale permeability predictions of porous fibrous media, Int. J. Heat Mass Transf., 44(16), 3135–3145.CrossRefGoogle Scholar
[24] Al-Hadhrami, A.K., Elliott, L., and Ingham, D.B. (2003), A new model for viscous dissipation in porous media across a range of permeability values, Transp. Porous Media, 53(1), 117–122.Google Scholar
[25] Ghaddar, C.K. (1995), On the permeability of unidirectional fibrous media: A parallel computational approach, Phys. Fluids, 7(11), 2563–2586.Google Scholar
[26] Wang, C.Y. (1996), Stokes flow through an array of rectangular fibers, Int. J. Multiph. Flow, 22(1), 185–194.Google Scholar
[27] Arbogast, T., and Lehr, H.L. (2006), Homogenization of a Darcy-Stokes system modeling vuggy porous media, Comput. Geosci., 10(3), 291–302.Google Scholar
[28] Lemaitre, R., and Adler, P.M. (1990), Fractal porous media IV: Three-dimensional Stokes flow through random media and rectangular fractals, Transp. Porous Media, 5(4), 325–340.Google Scholar
[29] Bosl, W.J. (1998), A study of porosity and permeability using a lattice Boltzmann simulation, Geophys. Res. Lett., 25(9), 1475–1478.Google Scholar
[30] Manwart, C., Aaltosalmi, U., Koponen, A., Hilfer, R., and Timonen, J. (2002), Lattice-Boltzmann and finite-difference simulations for the permeability for three-dimensional porous media, Phys. Rev. E, 66(1), 016702-1-11.Google Scholar
[31] Li, X.Y. and Logan, B.E. (2001), Permeability of fractal aggregates, Wat. Res., 35(14), 3373–3380.Google Scholar
[32] Zaman, Z. and Payman, J. (2010), On hydraulic permeability of random packs of monodisperse spheres: Direct flow simulations versus correlations, Physica A, 389, 205–214.Google Scholar
[33] Wang, Y., Sun, S., and Yu, B. (2013), On full-tensor permeabilities of porous media from numerical solutions of the Navier-Stokes equation, Advances in Mechanical Engineering, 137086, 1-11.Google Scholar
[34] Wang, Y. (2011), Essential consistency of pressure Poisson equation method and projection method on staggered grid, Appl. Math. Mech., 32, 789–794.Google Scholar