Abstract Natural hydrogeological settings may delineate wedge-shaped aquifers that are sandwiched between streams, lakes or sea water bodies along arbitrary-oriented boundary lines. This is the case in multiple river basins, river deltas, alluvial fans, and coastal promontories and heterogeneity patterns are likely to arise because of sedimentation zoning. The aim of present study is to provide a steady-state analytical solution describing the nature of well extraction in heterogeneous wedge-shaped aquifers formed by intersection of arbitrary-oriented streams. This laterally bounded aquifer comprises two zones of constant but differing transmissivity (hydraulic conductivity) which are hydraulically connected through a common interface. First, the method of Green's function constructs a closed-form expression for the spatial distribution of dual-zone potential. Next, the stream function is derived from the integration of Cauchy-Riemann equations which in turn completes an analytical representation of the flow net. The stream depletion rates are shown to be explicitly linked to the stream function. This leads to simple expressions for the stream depletion rates, demonstrating that the lateral recharge from adjacent streams varies linearly with the angular position of pumping well without any dependency on the aquifer heterogeneity. The present solution encompasses a number of existing solutions for homogeneous aquifer system as subsets. Flow nets are generated for hypothetical test cases whereby stagnation points are identified semi-analytically. The present formulation ensures preservation of water balance for a capture zone subject to regional flow. Sensitivity analysis is conducted to address how drawdown at a certain observation point responds to a heterogeneity perturbation. Wider wedges appear more sensitive to variation of heterogeneity. The formulation is extended to account for rainfall-induced recharge over a dual-zone unconfined aquifer. In each case, the computed head profiles agree well with numerical counterparts from finite element method.

中文翻译：

---

双区非均质楔形含水层在稳态抽水和区域流下的响应

摘要 自然水文地质环境可能描绘出沿任意方向边界线夹在溪流、湖泊或海水体之间的楔形含水层。多个河流流域、河流三角洲、冲积扇和沿海海角都是这种情况，并且由于沉积分区可能会出现异质性模式。本研究的目的是提供一种稳态分析解决方案，描述由任意方向的河流相交形成的非均质楔形含水层中井提取的性质。这个横向有界的含水层包括两个具有恒定但不同的透射率（水力传导率）的区域，它们通过一个公共界面水力连接。一、Green'的方法 s 函数为双区势的空间分布构造了一个闭式表达式。接下来，流函数是从柯西-黎曼方程的积分导出的，后者又完成了流网的解析表示。流消耗率显示为明确链接到流函数。这导致了河流枯竭率的简单表达式，表明相邻河流的横向补给随抽水井的角度位置线性变化，而不依赖于含水层的非均质性。本解决方案包括作为子集的均质含水层系统的许多现有解决方案。为假设的测试用例生成流网，从而以半分析的方式识别停滞点。本配方确保受区域流影响的捕集区保持水平衡。进行敏感性分析以解决某个观察点的回撤如何响应异质性扰动。更宽的楔形似乎对异质性的变化更敏感。该公式扩展到考虑降雨引起的双区无承压含水层补给。在每种情况下，计算的头部轮廓与有限元方法的数值对应物非常吻合。该公式扩展到考虑降雨引起的双区无承压含水层补给。在每种情况下，计算的头部轮廓与有限元方法的数值对应物非常吻合。该公式扩展到考虑降雨引起的双区无承压含水层补给。在每种情况下，计算的头部轮廓与有限元方法的数值对应物非常吻合。