A Coupled Darcy-Brinkman-NS Simultation Model of Wellbore Effect of an Monitor Well
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摘要: 利用3种不同水流运移方程分别模拟井管附近不同区域的水流运动, 基于流量守恒原理实现不同流态区域边界的耦合, 建立了有代表性的观测井-含水层系统场景; 利用建立的耦合模型模拟了观测井-含水层系统中水头的分布, 基于模型模拟数据分析了观测井井筒存在对含水层局部水头分布及地下水水质采样和环境监测结果的影响; 还分析了地下水三维水流强度、观测井井径以及含水层介质参数等对井筒效应的影响规律: 井筒效应在粘土等渗透系数和比单位贮水系数相对较小的含水层介质中更为明显, 其影响随着三维水流强度及观测井井径的增加而增大; 进行了上述参数的敏感性分析, 指出对于同一参数其在不同区间的敏感性比例不同, 对于不同参数观测井井径的敏感性比例最大, 因此在地下水环境监测的工程实践中减小观测井井径是相对快速且有效提高监测和采样精度的方法.Abstract: In this paper, three different flow equations, namely, Darcy law, Brinkman equation and Navier-Stoke equation, are employed to simulate the water movement with different flow conditions within and around the wellbore in a confined aquifer. Based on the principles of continuity, three different flow equations are coupled. The coupled model is used to simulate the impact of wellbore in aquifer on the head distribution and water movement. Results indicate that the influence of wellbore increases with the strength of three-dimensional flow and wellbore diameter. In addition, being compared with the sandy soil aquifer, wellbore effect is more obvious in clay or similar aquifers with lower permeability and smaller storage coefficient. By conducting parameter sensitivity analysis, it also can be found that the sensitivity ratio differs in different value zones for the same parameter, while for different parameters, wellbore effect is more sensitive to well diameter than other parameters.
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Key words:
- mathematical model /
- wellbore effect /
- monitor well /
- data bias /
- underground water
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图 3 耦合模型解与解析解结果的比较
Fig. 3. Comparison between results of analytical model and coupled mathematical model
图 6 考虑达西流和不考虑达西流模拟结果比较
Fig. 6. Results with and without the consideration of Non-Darcy flow around the wellbore
图 7 不同抽水井滤管长度条件下的降深畸变沿x轴的分布
Fig. 7. Drawdown difference along x axis with different lengths of pump well
图 8 不同观测井内径条件下的降深畸变沿x轴的分布
Fig. 8. Drawdown difference along x axis with different diameters of monitor well
图 9 不同含水层介质条件下的降深畸变沿x轴的分布
Fig. 9. Drawdown difference along x axis with different aquifer media
表 1 含水层和井孔参数
Table 1. Main parameters of aquifer and wells
基本参数 值 含水层参数 介质类型 粗砂 渗透系数(m/d) 30 含水层厚度(m) 50 单位储水量(m-1) 0.000 1 抽水井参数 抽水井内径(m) 0.2 抽水流量(m3/d) 8 640 抽水时间(d) 10.289 抽水井位置 (x, y, z)=(0, 0, 0) 抽水井滤管长度(%) 观测井参数 观测井内径(m) 0.2 观测井位置 (x, y)=(2.18, 0) 观测井类型 完整井 
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表 2 不同组介质的渗流参数取值
Table 2. Hydrological conductivity and Specific storativity of different aquifer media
类型1 类型2 类型3 类型4 含水层介质 细砂 中砂 粗砂 沙砾石 渗透系数(m/d) 7.5 15 30 60 比弹性储水系数(m-1) 7.5e-7 5e-6 1e-5 2e-5
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表 3 不同参数的敏感性比例计算
Table 3. Sensitivity ratio of different parameters
参数 变化区间 区间1 区间2 区间3 区间4 抽水井滤管长度 0.020 0.280 0.480 1.350 观测井井径 4.760 1.140 0.530 / 介质类型 0.003 0.006 0.011 / 注: 区间1、2、3和4对于抽水井滤管长度指1%、10%、25%、50%、75%；对于观测井井径指0.02 m、0.05 m、0.10 m、0.20 m；对于介质类型指介质1、2、3、4.
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