考虑近井非达西效应的微水试验半解析模型

A semi-analytical model for slug tests considering near-well non-darcy effects

  • 摘要: 微水试验参数反演高度依赖理论模型的物理假设,瞬时激发可显著增大井壁附近水力梯度和渗流速度,诱发Forchheimer 型非线性渗流,使传统线性模型通过降低渗透系数(K)等效补偿近井惯性耗散。为解决这一问题,建立了考虑近井非达西效应的承压含水层微水试验半解析模型,并采用拉普拉斯变换与数值反演方法求解。分析表明:井水位响应对K最敏感,对Forchheimer 系数(β)次之,对贮水系数(S)较弱,且K与β存在明显补偿关系;以1%误差阈值为判据,Cooper-Bredehoeft-Papadopulos(CBP)模型和考虑近井非达西效应的半解析模型对应的临界边界半径分别为8.31 m和10.65 m。室内试验结果表明,随着激发强度增大,实测响应与 CBP 模型的偏离增强,其反演的 K 呈降低趋势,而考虑近井非达西效应的半解析模型反演结果与抽水试验独立参考范围更为一致。研究表明,当非达西惯性作用明显时,考虑近井非达西效应可降低 K 反演偏差。

     

    Abstract: Parameter estimation from slug tests is highly dependent on the physical assumptions underlying the theoretical models used for interpretation. Instantaneous excitation can substantially increase the hydraulic gradient and seepage velocity near the wellbore, thereby inducing Forchheimer-type nonlinear flow. As a result, conventional linear models may implicitly compensate for near-well inertial dissipation by underestimating the permeability coefficient K. To address this issue, a semi-analytical model for slug tests in confined aquifers incorporating near-well non-Darcy effects was developed and solved using the Laplace transform and numerical inversion. The analysis shows that the well water-level response is most sensitive to K, followed by the Forchheimer coefficient \beta , whereas its sensitivity to the storage coefficient S is relatively weak. A pronounced response compensation relationship is also observed between K and β. Using a 1% error threshold as the criterion, the critical boundary radii for the Cooper-Bredehoeft-Papadopulos (CBP) model and the semi-analytical model incorporating near-well non-Darcy effects are 8.31 m and 10.65 m, respectively. Laboratory experiments show that the deviation between measured responses and the CBP model becomes more pronounced with increasing excitation intensity, while the K values estimated by the CBP model decrease. In contrast, the estimates obtained using the semi-analytical model incorporating near-well non-Darcy effects agree better with the independent reference range derived from pumping tests. These findings demonstrate that, when non-Darcy inertial effects are significant, accounting for near-well non-Darcy effects can reduce the bias in K estimation.

     

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