承压含水层中非完整井附近“非达西-达西” 两区渗流模型近似解析解
Approximate Analytical Solutions for Two-Region Non-Darcian Flow to a Partially Penetrating Well

抽水井附近由于流速过快往往发生非达西流,而远离抽水井随着流速下降又变为达西流.为了描述这些特征,建立了承 压含水层中非完整井附近“非达西-达西”两区渗流模型,即距离抽水井较近的区域由于流速较快假设发生非达西渗流,并利 用Izbash公式刻画,而距离抽水井较远由于流速较慢假设仍然满足达西定律,含水层中垂向流速较小也利用达西定律描述.通 过线性化近似方法结合Laplace变换和有限Fourier余弦变换对模型进行了求解,分析探讨了该两区模型下水位降深曲线特 征.结果表明:抽水初期,非达西渗流区域水位降深与全非达西渗流模型结果吻合,而抽水后期两区模型非达西渗流区域的水 位降深与全达西模型水位降深基本一致,但大于全非达西渗流模型的水位降深;抽水初期,两区模型中达西渗流区域的水位 降深比全达西渗流模型结果大,但比全非达西渗流模型结果小;对不同时间的水位降深随井距变化曲线分析发现非达西渗流 区域水位降深随Izbash公式中的幂指数n 增大而减小,而在达西渗流区域水位降深基本不受n 值的影响.研究成果对非完整 井抽水试验参数反演具有重要理论意义.
Non-Darcian f1ow islikely to occur in the region near a pumping we11 because of high ve1ocities, while f1ow becomes Darcian again in the region far away from the pumping we11 as the ve1ocity decreases. To describe these characteristics, a two- region non-Darcian f1ow mode1 toward a partia11y penetrating we11 is deve1oped in this study. The f1ow in the region near the pumping we11 is assumed to be non-Darcian which can be described by the Izbash equation. The f1ow in the region far away from the pumping we11 was assumed to be Darcian as we11 as the vertica1 f1ow due to the1ow ve1ocities. Alinearization procedure as- sociated with the Laplace transform and finite cosine transform is used to work out such two-region non-Darcian f1ow mode1. The characteristics of the drawdowns under such f1ow conditions are examined. It is concluded that: (1) the drawdown in the non-Darcian f1ow region is the same as that of the fu11y non-Darcian f1ow mode1 at early times, and it is the same at that of the fu11y Darcian f1ow mode1 andlarger than that of the fu11y non-Darcian f1ow mode1 atlate times. (2) the drawdown in the Darcian f1ow region islarger than that of the fu11y Darcian f1ow mode1 and sma11er than that of the fu11 non-Darcian f1ow mode1 at early times; (3) the drawdown-distance behavior indicates that the drawdown in the non-Darcian f1ow region increases as the power index n in the Izbash equation increases, while the value of n has alittle effect on the drawdown in the Darcian f1ow region. The results of this study wi11 be of great theoretica1 significance for the aquifer parameters estimation with the pumping test data in a partia11y penetrating we11