Study on fractal discrete fracture network model of radon migration in fractured medium

doi:10.16265/j.cnki.issn1003-3033.2022.11.0284

Abstract

Abstract:

In order to effectively carry out radon pollution control and radon tracing research, the fractal theory and DFN were combined to establish a model of radon migration in fractured medium. In the model, the distribution of fracture lengths was obtained by a double-power law model. The location of fracture centers was determined by the multiplicative cascade process method. The von Mises-Fisher method and the lognormal distribution method were used to model fracture orientations and fracture apertures, respectively. The model was verified by using a test device, and a natural fractured rock mass was analyzed by the model. The results show that the maximum difference between the radon activity concentrations calculated by the model and the test is less than 4%. The average radon exhalation rate of the fractured rock mass is 0.002 58 Bq/(m²·s), and interconnected fractures in the rock mass constitute the primary channels for radon migration. The maximum radon flux of the dense fractures is about 3 orders of magnitude higher than that at the sparse fractures. The average radon exhalation rate in fractured medium increases linearly with the fractal dimension, decreases linearly with the length index, and shows a nonlinear increase relationship with the convection velocity.

Key words: fractured medium, radon migration, discrete fracture network (DFN), radon exhalation rate, fractal dimension

FENG Shengyang, LI Ce, LIU Yong, KANG Qian. Study on fractal discrete fracture network model of radon migration in fractured medium[J]. China Safety Science Journal, 2022, 32(11): 97-104.

Figures/Tables 14

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Tab.1

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Tab.2

Fig.5

Tab.3

Parameters of DFN

参数	数值	参数	数值
D_f	1.62	b_max/mm	3.6
$β$	1.49	b_min/mm	0.5
α	2.39	$b -$ /mm	1.7
$μ 0$ /(°)	65	h	3
$κ$	2	—

Tab.3

Fig.6

Fig.7

Fig.8

Fig.9

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Fig.11

References 26

[1]	刘耀炜, 任宏微. 汶川8.0级地震氡观测值震后效应特征初步分析[J]. 地震, 2009, 29(1):121-131.
	LIU Yaowei, REN Hongwei. Preliminary analysis on the characteristics of post-earthquake effect of radon observations in Wenchuan M8.0 earthquake[J]. Earthquake, 2009, 29(1):121-131.
[2]	BASKARAN M. Radon:a tracer for geological, geophysical and geochemical studies[M]. Basel: Springer International Publishing, 2016:1-14.
[3]	NIELSON K, ROGERS V. A mathematical model for radon diffusion in earthen materials[R]. Pacific Northwest Laboratory, 1982.
[4]	ETIOPE G, MARTINELLI G. Migration of carrier and trace gases in the geosphere:an overview[J]. Physics of the Earth and Planetary Interiors, 2002, 129(3/4):185-204. doi: 10.1016/S0031-9201(01)00292-8
[5]	AJAYI K M, SHAHBAZI K, TUKKARAJA P, et al. A discrete model for prediction of radon flux from fractured rocks[J]. Journal of Rock Mechanics and Geotechnical Engineering, 2018, 10(5):879-892. doi: 10.1016/j.jrmge.2018.02.009
[6]	AJAYI K M, SHAHBAZI K, TUKKARAJA P, et al. Estimation of radon diffusivity tensor for fractured rocks in cave mines using a discrete fracture network model[J]. Journal of Environmental Radioactivity, 2019, 196:104-112. doi: S0265-931X(17)30583-0 pmid: 30447553
[7]	ROWBERRY M, MARTÍ X, FRONTERA C, et al. Calculating flux to predict future cave radon concentrations[J]. Journal of Environmental Radioactivity, 2016, 157:16-26. doi: 10.1016/j.jenvrad.2016.02.023 pmid: 26950394
[8]	刘波, 金爱兵, 高永涛, 等. 基于分形几何理论的DFN模型构建方法研究[J]. 岩土力学, 2016, 37(增1):625-630,638.
	LIU Bo, JIN Aibing, GAO Yongtao, et al. Construction method research on DFN model based on fractal geometry theory[J]. Rock and Soil Mechanics, 2016, 37(S1):625-630,638.
[9]	任崇鸿, 李波波, 杨康, 等. 考虑分形效应的煤岩损伤模型及渗透率模型[J]. 中国安全科学学报, 2019, 29(2):63-68.
	REN Chonghong, LI Bobo, YANG Kang, et al. Research on coal damage model and permeability model considering fractal effect[J]. China Safety Science Journal, 2019, 29(2):63-68.
[10]	FENG Shengyang, WU Yurong, LIU Yong, et al. A fractal analysis of radon migration in discrete fracture network model[J]. Chemosphere, 2021, 266:DOI:10.1016/j.chemosphere.2020.129010. doi: 10.1016/j.chemosphere.2020.129010
[11]	FENG Shengyang, WANG Hanqing, CUI Yu, et al. Fractal discrete fracture network model for the analysis of radon migration in fractured media[J]. Computers and Geotechnics, 2020, 128:DOI:10.1016/j.compgeo.2020.103810. doi: 10.1016/j.compgeo.2020.103810
[12]	KIM T H. Fracture characterization and estimation of fracture porosity of naturally fractured reservoirs with no matrix porosity using stochastic fractal models[D]. Texas: Texas A&M University, 2007.
[13]	DAVY P, SORNETTE A, SORNETTE D. Some consequences of a proposed fractal nature of continental faulting[J]. Nature, 1990, 348(6296):56-58. doi: 10.1038/348056a0
[14]	KIM T H, SCHECHTER D S. Estimation of fracture porosity of naturally fractured reservoirs with no matrix porosity using fractal discrete fracture networks[J]. SPE Reservoir Evaluation and Engineering, 2009, 12(2):232-242. doi: 10.2118/110720-PA
[15]	BAGHBANAN A, JING Lanru. Hydraulic properties of fractured rock masses with correlated fracture length and aperture[J]. International Journal of Rock Mechanics and Mining Sciences, 2007, 44(5):704-719.
[16]	ZHANG Liming, QI Ji, ZHANG Kai, et al. Calibrate complex fracture model for subsurface flow based on Bayesian formulation[J]. Petroleum Science, 2019, 16(5):1105-1120. doi: 10.1007/s12182-019-00357-5
[17]	DARCEL C, BOUR O, DAVY P, et al. Connectivity properties of two-dimensional fracture networks with stochastic fractal correlation[J]. Water Resources Research, 2003, 39(10):1-13.
[18]	HARTHONG B, SCHOLTÈS L, DONZÉ F V. Strength characterization of rock masses, using a coupled DEM-DFN model[J]. Geophysical Journal International, 2012, 191(2):467-480. doi: 10.1111/j.1365-246X.2012.05642.x
[19]	MOEIN M J A, VALLEY B, EVANS K F. Scaling of fracture patterns in three deep boreholes and implications for constraining fractal discrete fracture network models[J]. Rock Mechanics and Rock Engineering, 2019, 52(6):1723-1743. doi: 10.1007/s00603-019-1739-7
[20]	ALGHALANDIS Y F, XU Chaoshui, DOWD P A. A general framework for fracture intersection analysis:algorithms and practical applications[C]. Australian Geothermal Energy Conference, 2011:15-20.
[21]	KLIMCZAK C, SCHULTZ R A, PARASHAR R, et al. Cubic law with aperture-length correlation:implications for network scale fluid flow[J]. Hydrogeology Journal, 2010, 18(4):851-862. doi: 10.1007/s10040-009-0572-6
[22]	PARASHAR R, REEVES D M. On iterative techniques for computing flow in large two-dimensional discrete fracture networks[J]. Journal of Computational and Applied Mathematics, 2012, 236(18):4712-4724. doi: 10.1016/j.cam.2012.02.038
[23]	ALGHALANDIS Y F. ADFNE:open source software for discrete fracture network engineering, two and three dimensional applications[J]. Computers & Geosciences, 2017, 102:1-11. doi: 10.1016/j.cageo.2017.02.002
[24]	ROGERS V C, NIELSON K K. Correlations for predicting air permeabilities and ²²²Rn diffusion coefficients of soils[J]. Health Physics, 1991, 61(2):225-230. doi: 10.1097/00004032-199108000-00006
[25]	冯胜洋, 崔宇, 许田贵, 等. 铀尾砂膏体充填材料的流动性能研究[J]. 矿冶工程, 2019, 39(2):8-12.
	FENG Shengyang, CUI Yu, XU Tiangui, et al. Flow properties of uranium tailings as paste backfill[J]. Mining and Metallurgical Engineering, 2019, 39(2):8-12.
[26]	LEE Chenchang, LEE Chenghaw, YEH Hsinfu, et al. Modeling spatial fracture intensity as a control on flow in fractured rock[J]. Environmental Earth Sciences, 2011, 63(6):1199-1211. doi: 10.1007/s12665-010-0794-x

序号	模型计算氡活度浓度/(Bq·m^-3)	试验测得氡活度浓度/(Bq·m^-3)	相对误差/%
试样1	17 598	17 002	3.5
试样2	21 764	21 035	3.4
试样3	22 103	21 255	4.0