| 侧向有限越流承压含水层中非完整井非稳定流模型及解析解 |
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| 引用本文： | 冯庆高,蔡兵华,冯晓腊,袁祥.侧向有限越流承压含水层中非完整井非稳定流模型及解析解[J].岩土力学,2021(1):168-176. |
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| 作者姓名： | 冯庆高 蔡兵华 冯晓腊 袁祥 |
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| 作者单位： | ;1.中国地质大学(武汉)工程学院;2.武汉市市政建设集团有限公司 |
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| 基金项目： | 国家自然科学基金项目(No.41702336);武汉市市政建设集团有限公司科研项目(No.wszky201820)。 |
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| 摘 要： | 工程建设中当距离抽水井r=rb处水位基本没有变化或不受抽水影响时,或当此处存在止水帷幕时,含水层系统视为侧向有限延伸,rb为有限半径。为此,构建更加符合工程实际的侧向有限延伸的典型弱透水层-承压水层系统中非完整井非稳定流计算模型,同时考虑井径和井储效应的影响,应用Laplace变换和分离变量法得到了水位降深在拉氏空间下的解析解,并应用拉氏数值逆变换Stehfest法得到真实空间下的水位降深。新建立的解析解可以进一步退化为诸多已有解,并进一步将其与已知解和有限元数值解进行对比,验证了所得解的正确性和可靠性。基于新建解重点分析了侧向边界和井的完整性对承压水层水位降深的影响。结果表明:含水层系统的侧向有限边界仅对抽水后期的水位降深影响明显,含水层系统侧向无限延伸情况下的水位降深要大于情形1(在r=rb处为定水头边界)且明显小于情形2(在r=rb处为不透水边界)下的水位降深,rb越小,两者之间的误差越大;抽水井的完整性对整个抽水期间不同情形下的水位降深均有明显的影响,承压含水层顶板处的水位降深随着抽水井滤管的长度和埋深的增加而减小。
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| 关 键 词： | 非完整井 越流承压含水层 侧向边界 解析解 非稳定流 |
Analytical solutions of transient flow model for a partially penetrating well in a finite leaky confined aquifer system |
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| FENG Qing-gao,CAI Bing-hua,FENG Xiao-la,YUAN Xiang.Analytical solutions of transient flow model for a partially penetrating well in a finite leaky confined aquifer system[J].Rock and Soil Mechanics,2021(1):168-176. |
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| Authors: | FENG Qing-gao CAI Bing-hua FENG Xiao-la YUAN Xiang |
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| Institution: | (Faculty of Engineering,China University of Geosciences,Hubei 430074,China;Wuhan Municipal Construction Group Co.,Ltd.,Hubei 430023,China) |
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| Abstract: | When there is invariant/uninfluenced pumping drawdown and waterproof curtain at a distance r =r_b from the pumping well, the aquifer system is laterally finite in extend(termed finite aquifer) and r_b is termed ‘finite radius’. A practical calculation model of transient flow to a partially penetrating well in a typical aquitard-confined aquifer of finite extent is developed. Also, the model considers the effect of well radius and wellbore storage. The drawdown solution is obtained by the Laplace transform coupled with separation of variables, and inverted into the time-domain solution utilizing the Stehfest method. Moreover, the obtained solutions can reduce to some available solutions and are further validated by comparison with other solutions. Finally, the effect of the lateral boundary and well configuration on pumped aquifer drawdown behaviors are analyzed based on the proposed analytical solution. The results show that the influence of the lateral boundary is obvious during the late pumping time, the drawdown of the finite aquifer system is larger than that for Case 1(constant head boundary at r = rb) and much smaller than that for Case 2(no-flux boundary at r = rb). A smaller finite radius rb results in a larger error between the finite aquifer system(Case 1/Case 2) and the infinite aquifer system. The impact of the well configurations occurs at the whole pumping stage for different cases, and the drawdown at the top of the pumped aquifer becomes smaller with the increase of the length and location of the well screen. |
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| Keywords: | partially penetrating well leaky confined aquifer lateral(radial)boundary analytical solution non-steady flow |
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