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Approximate Solution for Solute Transport during Spherical-Flow Push-Pull Tests

机译：球流推挽试验中溶质运移的近似解决方案

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摘要

An approximate analytical solution to the advection-dispersion equation was derived to describe solute transport during spherical-flow conditions in single-well push-pull tests. The spherical-flow case may be applicable to aquifer tests conducted in packed intervals or partially penetrating wells. Using results of two-dimensional numerical simulations, we briefly illustrate the applicability of the derived spherical-flow solution and provide a comparison with its cylindrical-flow counterpart. Good agreement between simulated extraction-phase breakthrough curves and the spherical-flow solution was found when the length of the injection/extraction region was small compared to both aquifer thickness and maximum solute frontal position at the end of the injection phase. On the other hand, discrepancies between simulated breakthrough curves and the spherical-flow solution increased with increasing anisotropy in hydraulic conductivities. Several inherent limitations embedded in its derivation such as assumptions of isotropy and homogeneity warrant the cautious use of the spherical-flow solution.
机译：推导了对流扩散方程的近似解析解，以描述单井推挽试验中球形流动条件下的溶质运移。球形流情况可能适用于以填充间隔或部分穿透井进行的含水层测试。使用二维数值模拟的结果，我们简要说明了导出的球面流解决方案的适用性，并提供了与其圆柱流对应项的比较。当注入/提取区域的长度比含水层厚度和注入阶段结束时的最大溶质前沿位置小时，模拟的萃取阶段穿透曲线与球流解之间的一致性很好。另一方面，随着水力传导率各向异性的增加，模拟的突破曲线与球面流解决方案之间的差异也随之增加。推导中存在的一些固有局限性，例如各向同性和均质性的假设，都需要谨慎使用球流解决方案。

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