A numerical simulation of seepage structure surface and its feasibility

Abstract

According to Cubic law and incompressible fluid law of mass conservation, the seepage character of the fracture surface was simulated with the simulation method of fractal theory and random Brown function. Furthermore, the permeability coefficient of the single fracture was obtained. In order to test the stability of the method, 500 simulations were conducted on each different fractal dimension. The simulated permeability coefficient was analyzed in probability density distribution and probability cumulative distribution statistics. Statistics showed that the discrete degree of the permeability coefficient increases with the increase of the fractal dimension. And the calculation result has better stability when the fractal dimension value is relatively small. According to the Bayes theory, the characteristic index of the permeability coefficient on fractal dimension P(D_fj|R_i) is established. The index, P(D_fj|R_i), shows that when the simulated permeability coefficient is relatively large, it can clearly represent the fractal dimension of the structure surface, the probability is 82%. The calculated results of the characteristic index verify the feasibility of the method.

Keywords

fractal theory / numerical simulation / representative elementary volume (REV) / random brown function / permeability coefficient / fractal dimension

References

[1] PruessK, TsangY W. On two-phase relative permeability and capillary pressure of rough-walled rock fractures [J]. Water Resources, 1990, 26(9): 1915-1926

[2] SnowD T. Anisotropic permeability of fractured media [J]. Water Resources Research, 1969, 5(6): 1273-1289

[3] WangM, WangM, KulatilakeP, UmJ, NarvaizJ. Estimation of REV size and three-dimensional hydraulic conductivity tensor for a fractured rock mass through a single well packer test and discrete fracture fluid flow modeling [J]. International Journal of Rock Mechanics and Mining Sciences, 2002, 39(7): 887-904

[4] ChenS H, FengX. Numerical estimation of REV and permeability tensor for fractured rock masses by composite element method [J]. Int J Numer Anal Meth Geomech, 2008, 32: 1459-77

[5] FourarM, BoriesS. Experimental study of air-water two-phase flow through a fracture (narrow channel) [J]. Int J Multiphase Flow, 1995, 21(4): 621-637

[6] LeeH B. Wettability-dependent DNAPL migration in a rough-walled fracture [J]. Journal of Contaminant Hydrology, 2010, 113: 44-55

[7] HuY-j, QianR, SuB-yu. A numedcal simulation method to dermine unsaturated hydraulic parameters of fracture [J]. Chinese Journal of Geotedmical Engineering, 2001, 23(3): 284-288

[8] ZhuD-z, GuoH-qingThe fractured rock mass hydraulics basis [M], 2007BeijingScience Publishing Company78-80

[9] WangK, TangY-jun. Study on seepage characteristics of seepage structure surface based on fractal theory [J]. Journal of Water Resources and Architectural Engineering, 2005, 3(2): 37-41

[10] DeveliK. Quantification of natural fracture surfaces using fractal geometry [J]. Mathematical Geology, 1998, 30(8): 971-998

[11] KwicklisE M, HealyR W. Numerical investigation of steady liquid water flow in a variable saturated fracture network [J]. Water Resour Res, 1993, 21(12): 4091-4102

[12] HuY-j, LuoL-hong. The conditions of Local Cubic law established of rock fracture [C]. Sixth National Rock Mechanics and Engineering Academic Conference, Beijing, 2000357-359

[13] LeeY H, LeeY H, CarrJ R, BarrD J, HaasC J. The fractal dimension as a measure of the roughness of rock discontinuity profiles [J]. Int J Rock Mech Min Sci, 1990, 27(6): 453-464

[14] BrownS R, ScholzC H. Broad bandwidth study of topography of natural rock surfaces [J]. J Geophys Res, 1985, 90B14: 12575-12582

[15] ChenS H. Composite element method for the seepage analysis of rock masses containing fractures and drainage holes [J]. Int J Rock Mech Min Sci, 2010, 47(4): 762-770

[16] OdaM. Permeability tensor for discontinuous rock masses [J]. Geotechnique, 1985, 35(4): 483-495

[17] OdaM. Numerical experiments on permeability tensor and its application to jointed granite at Stripa Mine Sweden [J]. J Geophy Res, 1987, 92B8: 8037-8048

[18] CacasM C, LedouxB, MarsilyG D, TillieB, BarbreauA, DurandE, et al. . Modeling fracture flow with a stochastic discrete fracture network: Calibration and validation, 1. The flow model [J]. Water Resour Res, 1990, 26(3): 479-489

[19] AnderssonJ, DverstorpB. Conditional simulation of fluid flow in three-dimensional networks of discrete fractures [J]. Water Resour Res, 1987, 23(10): 1876-1886