Simulations of movements of two liquids in unconfined aquifers

• Main Authors: Lin Lung-Chuan, 林榮川
• Other Authors: Tsay Ting-Kuei
• Format: Others
• Language: zh-TW
• Published: 2001
• Online Access: http://ndltd.ncl.edu.tw/handle/85607633591817750913

博士 === 國立臺灣大學 === 土木工程學研究所 === 89 === The main groundwater bearing strata consist of non-consolidated alluvial layers in many coastal areas of Taiwan. Homogenous anisotropic unconfined aquifers are mainly found in shallow layers. The types of pumping are also mostly of partially penetrating well in the aquifers. When a well is pumping freshwater from an aquifer that consists of two sub-layers (freshwater and saltwater), the interface between freshwater and saltwater will rise due to the drawdown at the free surface of freshwater. The extent of saltwater upconing will affect the pumped freshwater quality if the interface reaches the bottom of the well. Therefore, it is important, particularly in coastal areas, to understand the upconing of saltwater due to freshwater pumping. The governing equation of each layer is Laplace equation that derived from mass conservation in unconfined aquifer. The boundary conditions include free surface boundary, interfacial boundary and impermeable boundary. The free surface and interfacial boundary are nonlinear boundary conditions. Small perturbation method is used to separate many order term of nonlinear boundary. The perturbed parameter, , can be viewed as the ratio of small pressure head changes in freshwater region caused by unsteady flows over freshwater aquifer thickness. The equation of each order is also mostly nonlinear equation. Based on some assumptions, the first order equations are simplified to linear equations. Using integral transform and Laplace transform technique, two-dimensional and three-dimensional axis-symmetric unsteady state analytical solutions for interfacial upconing of two liquids are derived in an unconfined aquifer. To investigate the effects of pumpage, the position of the interface between the two liquids can be determined from the analytical solution. Present analytical solution of an isotropic aquifer is also extended to anisotropic cases. The analytical solution is of a positive infinite integral type. Gauss-quadrature integration is used to carry out numerical integration. In this study, two-dimensional and three-dimensional axis- symmetric sand tanks are built for simulating interfacial upconing due to pumping. First, experiments to determine physical properties of media and to select appropriate liquids are implemented. Base on assumptions of analytical solution, the two liquids are immiscible in the aquifer and hydraulic conductivities of two liquids are the same. A mixed liquid consisted of medial alcohol and industrial alcohol is selected for the bottom layer, and another mixed liquid consisted of isopariffin and heptane for the upper layer. These two mixed liquids satisfy the assumptions of analytical solutions. The electrical conductivity of the mixed liquid of alcohol is higher than that of the mixed liquid of isopariffin. Using the capacity-type wave gauge to measure the height of upconing. The capacity-type wave gauge is always used to measure the change of free-surface water. It is the first time employed to measure the change of groundwater interface. The sensor of wave gauge is modified into a glass tube of 1 cm in diameter. Boring holes are distributed along the wall of the tube to allow free interchanges of liquids. Accurate water level fluctuations are measured after the gauges are calibrated. Some difficulties are experienced to set up instruments and to control of electric power at beginning. Poor results of experiments are observed in two-dimensional cases. Finally, three-dimensional axis-symmetric sand tanks experiments perform very well. Present results of interfacial upconing are verified by comparing analytical solutions and experimental measurements. Very good agreements among these results are observed. The three-dimensional, axis-symmetric unsteady analytical solutions can be used to determine upconing effects of the position and length of a partially penetrating well.