ISSN 1000-3665 CN 11-2202/P
    陈崇希, 唐仲华. Theis不稳定潜水井流模型的改进——具入渗补给[J]. 水文地质工程地质, 2021, 48(6): 1-12. DOI: 10.16030/j.cnki.issn.1000-3665.202104057
    引用本文: 陈崇希, 唐仲华. Theis不稳定潜水井流模型的改进——具入渗补给[J]. 水文地质工程地质, 2021, 48(6): 1-12. DOI: 10.16030/j.cnki.issn.1000-3665.202104057
    CHEN Chongxi, TANG Zhonghua. Improvement of the Theis unsteady well flow model with infiltration recharge in a phreatic aquifer[J]. Hydrogeology & Engineering Geology, 2021, 48(6): 1-12. DOI: 10.16030/j.cnki.issn.1000-3665.202104057
    Citation: CHEN Chongxi, TANG Zhonghua. Improvement of the Theis unsteady well flow model with infiltration recharge in a phreatic aquifer[J]. Hydrogeology & Engineering Geology, 2021, 48(6): 1-12. DOI: 10.16030/j.cnki.issn.1000-3665.202104057

    Theis不稳定潜水井流模型的改进——具入渗补给

    Improvement of the Theis unsteady well flow model with infiltration recharge in a phreatic aquifer

    • 摘要: 地下水的补排主要包括垂向的地面入渗补给、蒸发排泄(蒸发可视为入渗的负值)及侧向的地表水补给、排泄。水文地质学最基本的问题之一——地下水可持续开釆量的评价准则,涉及补给的增量与排泄的减量,因此地下水开采的预测模型必须包含上述两类的补给、排泄因素,否则不能满足要求。然而,经典的Theis不稳定井流模型,即使在傍河抽水,也只有侧边界的补给、排泄作用,而不涉及上边界的地面入渗补给。这样一来,这个解析模型基本上不能够用于预测,而只能在旱季用于井流试验求取含水系统的参数。为此,文章的目标是发展具地面入渗补给的Theis不稳定潜水井流模型。对于潜水流问题,不能再用承压水流的以水头为应变量的方程来建立,应采用第二类线性化方法的势函数来建立潜水流问题。对于既有降雨入渗补给,又有抽水井作用的复杂的水文地质问题所概化数学模型的求解,采取的方法是把它分解成若干个简单的子模型问题求解,然后将其合成为原来复杂数学模型的解。基于质量守恒原理,假定渗流服从Darcy定律并满足Dupuit徦定建立了水流基本微分方程。然后对于两平行河流及一河流平行一隔水边界形成的两类条形区域,具地面均匀稳定入渗补给的井流问题,获得通用水位方程和几类常见的特定条件水位方程及其流量方程。此外,提出并采用“边界对边界的反映法”用以求解一河流平行一隔水边界条形区域的同一问题,减少了许多推导过程。最后,作为上述理论成果的初步应用,也是一个重要的应用,即在河水水质不能满足要求的河流附近,设有一口抽水井,计算该抽水井在不汲取河水的前提下的临界流量方程,获得具重要意义的结构简洁的关系式。该方程也可以用于滨海区的抽水井,在不发生海水入侵前提下的临界抽水流量计算。给出了上述条件不稳定井流过程某时刻的地下水流网图,其流网与文献中常见的傍河井流的流网相比,具显明的特征。

       

      Abstract: The recharge and discharge of groundwater are mainly vertical surface infiltration recharge, evaporation discharge (evaporation can be shown as negative value of infiltration) and lateral surface water recharge and discharge. One of the most basic problems in hydrogeology is the evaluation criteria of sustainable exploitation of groundwater, which involves the increment of recharge and the decrease of discharge. Therefore, the prediction model of groundwater exploitation must include the above two kinds of recharge and discharge factors, otherwise the evaluation of groundwater cannot meet the requirements. However, the classic Theis unsteady well flow model (1935) only involves the recharge and discharge of the side boundary, and does not considers the surface infiltration recharge of the upper boundary, even when groundwater is pumped near the river. In this way, the analytical model cannot be basically used for prediction, and can only be used for well flow test to obtain the aquifer parameters in dry season. Therefore, the goal of this paper is to develop the Theis unsteady well flow model with surface infiltration recharge. For the problem of phreatic flow, the equation of groundwater flow cannot be established by using head as the dependent variable in a confined aquifer. We use the potential function of the second linearization method to establish groundwater flow equation in the phreatic aquifer. For the solution of the generalized mathematical model of the complex hydrogeological problem with rainfall infiltration and a pumping well, we adopt the method of decomposing it into several simple sub-models and synthesizing them into the solution of the original complex mathematical model. Based on the principle of mass conservation and assuming that the seepage obeys the Darcy’s law and satisfies the Dupuit's assumptions, the differential equation of groundwater flow is established. Then, for the well flow problem with uniform and stable infiltration recharge in two parallel rivers and two kinds of strip regions formed by a river parallel to an impermeable boundary, the general equation of groundwater flow and several kinds of water table equations under specific conditions and their flux equations are obtained. In addition, the “boundary to boundary reflection method” is proposed and applied to solve the same problem in a strip of region between a river boundary in parallel to an impermeable boundary, which reduces many derivation processes. Finally, as a preliminary application of the above theoretical results, it is also an important application, that is, there is a pumping well near the river whose water quality cannot meet the requirements, and the critical flux equation of the pumping well is calculated on the premise of not absorbing the river water. The important and concise relation equation is obtained. The equation can also be used to calculate the critical pumping rate of pumping wells in coastal areas without seawater intrusion. In this paper, the groundwater flow network diagram at a certain time in the process of unstable well flow under the above conditions is given. Compared with the flow network of well flow near the river, which is commonly seen in the literature, the flow network has obvious characteristics.

       

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