A General Semi-analytical Solution to Characterize the Hydraulic Head Distribution for Constant-head, Constant-flux, or Slug tests in Various Aquifers
|關鍵字:||半解析解;定水頭試驗;定流量試驗;微水試驗;受壓含水層;自由含水層;滲漏受壓含水層;部分貫穿井;Semi-analytical solution;Constant-head test;Constant-flux test;Slug test;Confined aquifer;Unconfined aquifer;Leaky confined aquifer;Partial penetration well|
This study develops a general mathematical model for analyzing the hydraulic head distribution in confined, unconfined or leaky confined aquifers with a finite radius and partial penetration well during different types of aquifer tests (i.e., constant-head test, constant-flux test, and slug test). The semi-analytical solution is derived using the methods of Laplace transform and separation of variables, and the time-domain results are obtained by Stehfest method. The conservation of mass flux across the well screen is applied to describe the groundwater flow in these three aquifer tests. The pumping rate is maintained constant in the constant-flux test. In the slug test, a small volume of water is quickly added or removed from the well. In a constant-head test is performed to keep a constant well water level. A general upper boundary condition of the model is applied for three types of aquifers. For a confined aquifer, the top boundary of the aquifer is impermeable; for an unconfined aquifer, the free surface equation is used; for leaky confined aquifer, an equation describing the leakage rate from the aquitard is applied. The proposed solution agrees well with the solutions for confined and unconfined aquifers presented in previous studies. The result predicted from the present solution demonstrates that the well water level is underestimated when neglecting the delayed gravity response for slug test at a fully or partially penetrating well conducted in unconfined aquifers. For the constant head test at a partially penetrating well in the leaky confined aquifer, the hydraulic head decreases with the distance of observation well, the leakance and the vertical hydraulic conductivity of aquitard, and increases with decreasing the penetration ratio. Furthermore, the drawdown decreases with increasing the distance of observation well, the penetration ratio, the leakance and the vertical hydraulic conductivity of aquitard during the constant flux test.