考虑毛细饱水带的非承压含水层中仿Theis井流模型及解析解  

Modified Theis Well Model and Its Analytical Solution in Unconfined Aquifers Considering Capillary Saturated Zone

作　　者：晋浩颖 程大伟[1,2] 詹红兵 杨胜科[1,2] 张晓斐 张琳 Jin Haoying;Cheng Dawei;Zhan Hongbing;Yang Shengke;Zhang Xiaofei;Zhang Lin(School of Water and Environment,Chang’an University,Xi’an 710064,China;Key Laboratory of Subsurface Hydrology and Ecological Effects in Arid Region(Chang’an University),Ministry of Education,Xi’an 710064,China;Department of Geology and Geophysics,Texas A&M University,College Station,TX 77843-3115,USA;Xi’an Qujiang Meibei Lake Investment and Construction Co.,Ltd.,Xi’an 710300,China)

机构地区：[1]长安大学水利与环境学院,西安710064 [2]旱区地下水文与生态效应教育部重点实验室(长安大学),西安710064 [3]德克萨斯农工大学地理与地球物理系,美国德克萨斯卡城TX77843-3115 [4]西安曲江渼陂湖投资建设有限公司,西安710300

出　　处：《吉林大学学报(地球科学版)》2025年第2期563-574,共12页Journal of Jilin University:Earth Science Edition

基　　金：国家重点研发计划项目(2020YFC1808304);国家自然科学基金项目(41602237)。

摘　　要：受制于经典饱和渗流理论中自由面定位在潜水面处的局限性,非承压含水层中仿Theis井流模型存在理论基础不坚实、参数物理意义不明确等问题。为克服上述局限性,首先将自由面由潜水面移动到进气值面,以定位在进气值面处的Boussinesq方程为控制方程,修正仿Theis井流模型,并推导模型的解析解;之后,构建参数反演模型,以校准模型参数,并通过分别将修正模型计算的降深和经典模型计算的理论降深与实测降深进行对比,检验修正模型的合理性;然后,利用参数敏感性分析探讨修正模型下进气值面高程的变化特征;最后,讨论进气值面处铅直方向渗流分速度的计算方法和变化特征。结果表明:修正模型计算的降深曲线与实测降深曲线基本吻合;进气值面高程随与井中心的距离、给水度增大而增大,随抽水流量增大而减小。在抽水早期,进气值面高程随渗透系数的增大而减小,在抽水后期则相反。基于进气值面处水量均衡关系(基于线性或非线性方程,采用完整解或近似解)及进气值面处渗流连续性方程(基于线性方程,采用完整解)等5种情况,推导的铅直方向渗流分速度的解析表达计算结果基本吻合,曲线趋势一致,表现为随抽水时间的延长呈非线性增长。Due to the limitation of setting the upper boundary at the free surface located at the water table,the Theis well model in unconfined aquifers has some problems such as unsound theoretical basis and unreasonable physical meaning of parameters.To overcome these issues,firstly,the well model is revised by moving the free surface from the water table to the air entry plane,and takes the Boussinesq equation located at the air entry plane as the governing equation,and derives the analytical solution of the model;Then,a parameter inversion model is constructed to calibrate the model parameters.By comparing the revised model drawdown and the theoretical drawdown of the classical model with the measured drawdown,it verifies the rationality of the well revised model proposed in this paper.Then,the variation characteristics of the air entry plane elevation under the modified well model are discussed by using parameter sensitivity analysis.Finally,the computational method and variation characteristics of seepage velocity in the vertical direction of the air entry plane are discussed.It is found that the drawdown curve obtained by the revised model coincides with the measured drawdown curve;The air entry plane elevation increases with increasing distance from the center of the well and the specific yield and decreases with increasing pumping flow rate.In the early stage of pumping,the air entry plane elevation decreases with increasing hydraulic conductivity,but the opposite is true in the late stage of pumping.The calculation results of the analytical expressions of the seepage velocity in the vertical direction based on the water balance relation at the air entry plane(based on the linearized or non-linearized equation,using complete solutionor approximate solution)and based on continuity equation of seepage flow at the air entry plane(based on the linearized equation,using complete solution)under five conditions are basically consisent,and the trends of the curve are consistent with each other,showing a nonlinear increase

关 键 词：进气值面 井流模型 完整井 BOUSSINESQ方程 解析解 参数反演模型 

分 类 号：P641.2[天文地球—地质矿产勘探]