Numerical Modeling of Seepage into Underground Openings in a Heterogeneous Continuum: A Sensitivity Study of Media Parameters
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摘要: 影响任何一个地下废物处置场所长期行为的一个重要因素是进入地下废物贮置洞室内的渗流量的大小.预测地下洞室中的渗流量是困难的, 特别是当地下废物贮置洞室位于非均质非饱和带中.三维数值模型用于研究地下非均质中非饱和流动及流入地下洞室中的渗流量.讨论了非均质模型与均质模型的比较以及数值剖分尺度对计算结果的影响.进入洞室中的渗漏率随着引入系统中入渗量的增加而增大.选用4个参数来衡量渗流场的非均质程度: (1) 介质的平均渗透率K0; (2) VanGenuchten参数α; (3) 渗透率空间分布相关尺度; (4) 渗透率空间分布变化的标准差σ.根据一个随机实现的渗透率分布, 通过改变平均渗透率来研究其对流入洞室中渗透量的影响.对一个固定的入渗率而言, 流入洞室中的渗漏率将随着VanGenuchten参数α的减小而减小.模拟结果表明流入洞室的渗漏率与介质的平均渗透率相关, 即随平均渗透率的增大, 流入洞室的渗漏率亦增大.流入洞室的渗漏率还高度依赖于非均质渗透率场的空间分布相关长度与标准差.一个大的相关长度或高的标准差均能导致流入洞室的渗漏率增大.Abstract: The amount of water seeping into the waste emplacement underground openings is an important issue for the long-term performance of any underground waste repository. Seepage controls the corrosion rates of waste packages, the waste mobilization rates and transport rates of contaminant leaving the underground openings. Predicting the seepage rate is difficult under any circumstances, and is particularly complicated for repository sites located in unsaturated, heterogeneous media. In this study, a 3-D numerical model is used to study unsaturated flow and seepage through a heterogeneous medium into the underground openings with strongly variable parameters and boundary conditions. The model has been compared with homogeneous model. The seepage rate into the underground openings increases with an increase in percolation flux introduced into the system. Four parameters, (1) fracture continuum permeability, (2) Van Genuchten parameter α, (3) spatial correlation length and (4) standard deviation σ, are chosen to measure permeability-field heterogeneity. Based on a stochastically realized permeability distribution, the authors scale the mean permeability to study its effect on seepage into underground openings. For a chosen percolation flux, the seepage rate into the underground openings was reduced as the Van Genuchten parameter α decreased. Simulation results show that the seepage into the underground openings is sensitive to the mean permeability, with seepage rate decreasing as the mean permeability increased. Simulation results indicate that the seepage is also very sensitive to the correlation length and standard deviation of the heterogeneous field. Either a high correlation value or a high standard deviation σ value increases seepage into the underground openings for a substantially heterogeneous continuum.
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Key words:
- underground openings /
- heterogeneous medium /
- unsaturated zone /
- seepage rate /
- sensitivity study /
- waste disposal.
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图 2 三维非均质渗流场中水平剖面(a) 和垂向剖面(b) 上水饱和度分布(入渗量为500 mm/a, 参数见表 1)
Fig. 2. Saturation profiles on horizontal planes (a) and vertical planes (b) in a 3-D heterogeneous field for basecase properties and a percolation flux of 500 mm/year
图 3 渗漏率与入渗量、网格大小的关系曲线
a.渗漏率与入渗量关系曲线; b. 3种剖分方案条件下3种随机实现的非均质模型中渗漏率与入渗量关系曲线; c.在50 mm/a和500 mm/a 2种入渗量(Qp) 条件下, 3种随机实现的非均质模型中渗漏率与网格大小的关系曲线
Fig. 3. Seepage percentage as a function of percolation flux and grid size
图 4 基础方案条件下3种随机实现的非均质模型中渗漏率与入渗量(a)、介质平均渗透率(b) 的关系曲线; c.渗漏率和Van Genuchten参数1/α的关系曲线(b, c的入渗量为213 mm/a, 参数见表 1)
Fig. 4. Seepage percentage as a function of percolation flux (a), mean permeability (b) for three realizations in the heterogeneous model with the basecase properties, and seepage percentage as a function of Van Genuchten parameter 1/α from 200 to 800 Pa with a percolation flux of 213 mm/year (c)
图 5 2种渗透率的自然对数标准差条件下水饱和度分布(入渗量为213 mm/a, 参数见表 1)
Fig. 5. Saturation profiles for the standard deviation σ of ln k=1.66 (a) and 1.0 (b) with basecase properties and a percolation flux of 213 mm/year
图 6 a.3种随机实现的非均质模型中渗漏率与渗透率空间变化的自然对数标准差(σ) 关系曲线; b.5种随机实现随机模拟结果的平均渗漏率与渗透率空间分布的相关长度(λ) 关系曲线
Fig. 6. Seepage percentage as a function of the standard deviation σ (in natural log) of permeability for three realizations of the heterogeneous model for a percolation flux of 73.2 mm/year (a); Mean seepage percentage over five realizations as a function of correlation length for the basecase with a percolation flux of 213 mm/year (b)
图 7 2种渗透率空间分布相关长度1 m (a) 与4 m (b) 条件下的非均匀渗透率空间分布
Fig. 7. Heterogeneous permeability fields for the correlation length 1 m (a) and 4 m (b)
图 8 2种渗透率空间分布相关长度1 m (a) 与4 m (b) 条件下水饱和度的空间分布(入渗量为213 mm/a)
Fig. 8. Saturation profiles for the correlation length of 1 m (a) and 4 m (b) with basecase properties and a percolation flux of 213 mm/year
表 1 基础方案中的参数组
Table 1. Basecase parameters set used for fracture continuum in drift scale modeling
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