Hydrogeological Parameter Estimations for Slug Test in Sloping Confined Aquifer
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摘要: 为了准确的推估出倾斜承压含水层的水文地质参数，有必要考虑倾角对于参数推估的影响.通过建立倾斜承压含水层微水试验的数学模型，利用理论和现场试验数据分析方法，得出倾角对导水系数等水文地质参数推估的影响.结果表明：低渗透条件下，倾角越大非振荡水位恢复速度越快；高渗透条件下，倾角越大振荡水位振幅越大.储水系数越大倾角上限越小，倾角影响越明显，而倾角上限对于导水系数的变化不敏感.根据该结论建立了无因次储水系数和倾角界限之间的经验方程，用于预测倾角是否会影响水文地质参数的推估.当实测倾角大于倾角上限时，倾角影响不可以被忽略，忽略倾角会导致导水系数估值偏高，储水系数估值偏低.Abstract: It is necessary to take into account the dip angle effects on accurate estimation of hydrogeological parameters in the sloping confined aquifer. To explore how the dip angle influences the test response, a new slug test model is developed in this study by using theoretical and filed data analysis. For test well, it is found that when the aquifer hydraulic conductivity is relatively low, a larger dip angle causes a faster recovery of the non-oscillatory test response; when the aquifer hydraulic conductivity is relatively high, a larger dip angle causes an increase of amplitude of the oscillatory test response. The dip angle effect is more pronounced for a larger storage coefficient, being less sensitive to the change of transmissivity. An empirical relationship is developed for the limiting dip angle as a function of the dimensionless storage coefficient. The function can be used to predict whether the estimate of hydrogeological parameters would be influenced by the dip angle. The effect can be neglected if the dip angle is less than the upper limit. However, it cannot be neglected if the dip angle is larger than the upper limit, otherwise, it can result in an overestimate of transmissivity and an underestimate of the storage coefficient.
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Key words:
- slug test /
- dip angle /
- field data analysis /
- hydrogeology /
- ground water
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图 1 倾角为α的倾斜承压含水层中双封塞微水试验概念模型和仪器设备示意
Fig. 1. Schematics of a double-packer slug test in a fracture of a dip angle α
图 3 高、低渗透条件下倾角α对测试井内水位变化w(τ)的影响
Fig. 3. Influence of α on the test response for low-K and high-K conditions
图 4 高、低渗透条件下倾角上限α*随σ值的减小而增大，当σ保持不变时，α*基本不受ϕ值变化影响
Fig. 4. The limiting angle α*increases as σ decreases, while remains relatively insensitive to ϕ for the same σ for low-K and high-K conditions
图 6 倾角为47°的裂隙含水层微水试验现地数据分析
Fig. 6. Analysis of the slug test data in the fracture of a dip angle equal to 47°
图 7 模型结果对T值变化±30%的敏感性
Fig. 7. Sensitive of the model solution to a ±30% change of transmissivity
表 1 符号说明
Table 1. Nomenclature
符号 定义 量纲 b 含水层垂向厚度 [L] g 重力加速度 [L/T2] H(t) 测试井内水位 [L] H0 初始水位位移 [L] h(x, y, t) 承压含水层水头 [L] hw(t) 井边含水层水头的圆周平均值 [L] K 渗透系数 [L/T] K0(x) 0级第二类修正贝赛尔函数 K1(x) 1级第二类修正贝赛尔函数 l 与倾斜含水层平行方向的距离 [L] Le 测试井有效井长 [L] P(x, y, t) 承压含水层压力水头 [L] r 径向距离 [L] rc 连接管半径 [L] rw 测试井半径 [L] S 储水系数 [-] s 拉普拉斯转换变量 [-] T 导水系数 [L2/T] t 试验时间 [T] w(τ) =H(t)/H0, 无因次测试井内水位 [-] Z(x, y) 承压含水层位置水头 [L] α 含水层倾角 [-] α* 倾角上限 [-] β 振荡的阻尼系数 [T-1] β* =βrc2/2T，无因次β [-] ηp(τ) =P(r, t)/H0，含水层无因次压力水头 [-] ηw(τ) =hw(t)/H0, 无因次hw(t) [-] θ =tan-1(y/x') [-] λ(θ) (cos2θcos2α+sin2θ)0.5 [-] ρ =r/rw，无因次径向距离 [-] σ =2rw2S/rc2，无因次储水系数 [-] τ =t/(rc2/2T)，无因次时间 [-] υ =S/T [T/L2] ϕ =2T(Le/g)0.5/rc2，无因次导水系数 [-] ω 振荡的频率 [T-1] ω* =ωrc2/2T，无因次ω [-] 
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