Research on the scale effects of solute transport in a bended karst conduit
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摘要:
岩溶管道溶质运移的尺度效应研究对穿透曲线的正确解译非常重要，但目前针对单一弯曲管道中溶质运移尺度效应的研究仍比较缺乏。文章将岩溶管道和溶潭分别概化为透明软管和水箱，基于前期建立的水箱-管道系统（简称“管道系统”），在水箱下游设置不同长度的弯曲管道，通过示踪试验研究管道运移尺度对穿透曲线的影响，并采用暂时存储模型模拟试验曲线。结果表明：（1）随着水箱下游管道长度的增加，峰值质量浓度逐渐缓慢降低，穿透曲线上升段斜率无明显变化，穿透曲线拖尾逐渐缩短，表明运移管道长度增加对溶质运移的影响大于下游管道弯曲；（2）穿透曲线偏度系数、后段溶质羽穿透时间和溶质羽穿透时间与管道系统长度呈良好的负线性相关关系（R2>0.96）；（3）当对称和不对称水箱管道系统长度分别增加至154.5 m和164.3 m时，偏度系数接近0，穿透曲线分布接近对称；（4）弥散系数、存储区截面积和交换系数与管道系统长度呈良好的负线性相关关系，当对称和不对称水箱管道系统长度分别增加至159.9 m和178.1 m时，存储区截面积接近0，水箱导致的溶质运移滞后效应基本消失。研究结果对野外岩溶管道穿透曲线的解译具有一定指示作用。
Abstract:Research on the scale effect of solute transport in karst conduits is very important for the correct interpretation of breakthrough curves (BTCs), but the scale effect of solute transport in a bended conduit has not been examined. In this paper, a karst conduit and a pool developed within the conduit are generalized into the transparent hose and cubic pool, respectively. Based on the previously established pool-pipe system, the bended pipes with different lengths are arranged downstream of the pool, and the tracer experiments are conducted to study the effect of the transport scale on the BTCs in conduits. We use the transient storage model to simulate the experimental curves. The results show that with the increasing pipe length downstream the pool, the peak concentration gradually decreases slowly, the rising slope of the BTCs does not change significantly, and the BTC tails gradually shorten, indicating that the longer transport distance exerts a larger effect on solute transport than the conduit bend. The coefficient of skewness (CSK), breakthrough time of posterior solute plume (tre) and breakthrough time of solute plume (td) are well negatively correlated with the length of the pipe system (R2>0.96). When the length of the pipe system with the symmetrical or asymmetrical pool increases to 154.5 m and 164.3 m, respectively, the CSK is close to zero, and the BTC is nearly symmetrical. The dispersion coefficient (D), cross-sectional area of the storage zones (As) and exchange coefficient (α) have a good negative correlation with the length of the pipe system. When the length of the pipe system with the symmetrical or asymmetrical pool increases to 159.9 m and 178.1 m, respectively, the As is close to zero. Then, the solute retention caused by the pool basically disappears. The results have certain indications for the interpretation of the BTCs in field karst conduits.
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Key words:
- karst conduit /
- bend /
- solute transport /
- scale effect /
- tracer experiment
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表 1 穿透曲线特征参数
Table 1. Characteristic parameters of breakthrough curve
特征参数 参数分类 计算方法 Cp 最大示踪剂浓度 
Rt 示踪剂回收率 
tm 水力参数 
v 水力参数 
σt2 水力参数 
CSK 水力参数 
tre 水力参数 
t0.5Cp 水力参数 
td 水力参数 
注：C（t）为在任意t时刻的质量浓度；Q（t）为t时刻的流量；M为示踪剂注入质量。 
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表 2 不同管道系统长度的穿透曲线特征参数
Table 2. Characteristic parameters of breakthrough curve of the pipe system with different lengths
水箱结构 L/m v/（m·s−1） tm/min σt2/min2 CSK tre/s t0.5Cp/s td/s Rt/% SP15 72.25 0.447 2.7004 0.15768 0.1472 175 12 187 91.97 83.00 0.450 3.0745 0.15320 0.1274 164 12 178 91.92 93.75 0.458 3.4124 0.14015 0.1097 148 13 161 92.50 104.50 0.467 3.7317 0.10996 0.0889 125 13 137 89.27 ASP15 72.25 0.446 2.7016 0.052305 0.0847 89 20 105 94.99 83.00 0.452 3.0594 0.048710 0.0722 82 21 98 96.88 93.75 0.457 3.4227 0.045040 0.0620 74 21 90 91.83 104.50 0.461 3.7739 0.044096 0.0557 63 21 79 92.36
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表 3 不同管道系统长度的模型参数
Table 3. Model parameters of the pipe system with different lengths
水箱结构 L/m D/（m2·s−1） A/m2 As/m2 α/s−1 Vs/m3 DaI SP15 72.25 1.48×10−2 4.98×10−4 4.37×10−5 5.04×10−3 3.16×10−3 13.2 83.00 1.33×10−2 5.00×10−4 3.89×10−5 4.26×10−3 3.23×10−3 12.6 93.75 1.27×10−2 4.97×10−4 3.42×10−5 3.76×10−3 3.21×10−3 12.4 104.50 1.18×10−2 4.96×10−4 2.72×10−5 3.32×10−3 2.84×10−3 13.5 ASP15 72.25 1.87×10−2 5.09×10−4 3.54×10−5 1.04×10−2 2.56×10−3 34.7 83.00 1.63×10−2 5.06×10−4 3.18×10−5 1.02×10−2 2.64×10−3 37.3 93.75 1.57×10−2 5.08×10−4 2.67×10−5 8.44×10−2 2.50×10−3 36.5 104.50 1.34×10−2 5.04×10−4 2.52×10−5 8.42×10−2 2.63×10−3 38.0
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