The Variable Conductivity Interface – Expanded Usefulness for the Image Well Technique

The image well (IW) technique has long been used to simulate either no-flow or constant head boundaries near a pumping well (PW) in a confined, saturated aquifer; and is described in virtually every introductory hydrogeology text book. However, because the technique is a result of the properties of superposition, it is possible to use it to simulate pumping near an interface with a lower hydraulic conductivity (K) if the storage coefficient (S) is constant. MODFLOW was utilized to simulate K ratios in multiples of 1000, 300, 100, 30, 10, 5 and 2:1 in a scenario where the pumping well (1 l/s) is located 100m from the interface in a 10-meter-thick aquifer with K of 0.0001 m/s. K across the interface was adjusted downward per the multiples given above. S was constant at 0.001. Comparison of drawdown in simulated observation wells (OW) in MODFLOW and with variable image-well pumping rates using the analytical Theis solution made it possible to develop a regression for generating a pumping-ratio coefficient. As the ratio of pumping rate to drawdown for a given K ratio is a linear function in each OW, generation of an IW rate matching drawdown in each MODFLOW scenario is trivial. A series of at least three pumping rates at the IW was employed which results in a first order regression with an r² of 1.00. A curve fit of this IW/PW ratio versus the K ratio from MODFLOW yields the fifth order equation y = -2.44x⁵ + 8.45x⁴ - 11.59x³ + 8.74x² - 4.32x + 1.17. This equation enables the correct IW pumping ratio to be calculated for any combination of K ratios, PW distance from the interface, pumping rates, or aquifer properties; as long as S is constant.