Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-10T17:06:17.176Z Has data issue: false hasContentIssue false
  • English
  • Français

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)
Get access

Abstract

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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