Hubei Key Laboratory of Yangtze Catchment Environmental Aquatic Science, School of Environmental studies, China University of Geosciences, Wuhan, 430074, Hubei, China.
Department of Civil Engineering, Baze University, Abuja, Nigeria.
Ground Water. 2022 Nov;60(6):792-800. doi: 10.1111/gwat.13198. Epub 2022 Apr 22.
During aquifer pumping tests in the field, the attenuation process of the pumping rate is generally monitored, and the aquifer may be slanted, especially in riverbank terraces, piedmont plain and other similar terrains. The combination of these two factors (attenuation process and aquifer slope) has not received enough academic attention, therefore, a two-dimensional groundwater flow model is developed for an exponentially decreasing variable rate pumping well in a sloping aquifer in this study. The new semi-analytical solution (based on a linearized free-surface boundary) is obtained using the Laplace transform and finite Fourier cosine transform. Meanwhile, to depict the linearized boundary precisely with the first-order free surface equation, a numerical model that considers the decline of the water table is also developed. Results show that under the effect of the variable rate, the time-drawdown curve presents a downward trend at intermediate times. Additionally, the error caused by the linearization of the free-surface equation on the analytical model is found to be acceptable except when the sloping angle is larger than π/6. Furthermore, since this study extends the work of Huang et al. (2014), who considered a constant pumping rate, the new solution was found better to interpret real pumping test data reported by Antonio and Pacheco (2002), and the laboratory experiment results. Overall, the new solution proves to be useful for parameter inversion accurately as the average pumping rate tended to underestimate hydraulic parameters when fitting short-term pumping data.
在现场含水层抽水试验中，通常会监测抽水速率的衰减过程，而含水层可能是倾斜的，特别是在河漫滩、山前平原和其他类似地形中。这两个因素（衰减过程和含水层坡度）的组合没有得到足够的学术关注，因此，本研究针对倾斜含水层中呈指数递减的变量抽水率，开发了一个二维地下水流动模型。使用拉普拉斯变换和有限傅里叶余弦变换，获得了新的半解析解（基于线性化自由表面边界）。同时，为了用一阶自由表面方程精确描述线性化边界，还开发了一个考虑地下水位下降的数值模型。结果表明，在变量速率的影响下，时间降落曲线在中间时间呈现下降趋势。此外，发现解析模型中自由表面方程线性化引起的误差是可以接受的，除非倾斜角大于π/6。此外，由于本研究扩展了 Huang 等人（2014 年）的工作，他们考虑了恒定的抽水率，因此新的解被发现更适合解释 Antonio 和 Pacheco（2002 年）报告的实际抽水试验数据和实验室实验结果。总体而言，新的解被证明在参数反演方面非常有用，因为当拟合短期抽水数据时，平均抽水率往往会低估水力参数。
