Effect of Unsaturated Flow on Delayed Response of Unconfined Aquifiers to Pumping

A new analytical solution is presented for the delayed response process characterizing flow to a partially penetrating well in an unconfined aquifer. The new solution generalizes that of Neuman [1972, 1974] by accounting for unsaturated flow above the water table. Axially symmetric three-dimensional flow in the unsaturated zone is described by a linearized version of Richards' equation in which hydraulic conductivity and water content vary exponentially with incremental capillary pressure head relative to its air entry value (defining the interface between the saturated and unsaturated zones). Unsaturated soil properties are characterized by an exponent κ having the dimension of inverse length and a dimensionless exponent κD = κb where b is initial saturated thickness. Our treatment of the unsaturated zone is similar to that of Kroszynski and Dagan [1975] who however have ignored internal (artesian) aquifer storage. It has been suggested by Boulton [1954, 1963, 1970] and Neuman [1972, 1974], and is confirmed by our solution, that internal storage is required to reproduce the early increase in drawdown characterizing delayed response to pumping in typical aquifers. According to our new solution such aquifers are characterized by relatively large κ_ D values, typically 10 or larger; in the limit as κD tends to infinity (the soil unsaturated water retention capacity becomes insignificant and/or aquifer thickness become large), unsaturated flow becomes unimportant and our solution reduces to that of Neuman. In typical cases corresponding to κD larger than or equal to 10, unsaturated flow is found to have little impact on early and late dimensionless time behaviors of drawdown measured wholly or in part at some distance below the water table; unsaturated flow causes drawdown to increase slightly at intermediate dimensionless time values that represent transition from an early artesian dominated to a late water-table dominated flow regime. The increase in drawdown during this transition period is caused by delayed drainage from the unsaturated zone, whose relatively small effect is superimposed on the more pronounced phenomenon of delay in water table decline relative to artesian head drops below it. Delayed drainage from the unsaturated zone becomes less and less important as κD increases; as it approaches infinity, this effect dies out completely and drawdown is controlled entirely by delayed decline in the water table. The unsaturated zone has major impact on drawdown at intermediate time, and significant impact at early and late times, in the atypical case of small κD values (1 or less), becoming the dominant factor as κD approaches zero (the soil water retention capacity becomes very large and/or saturated thickness becomes insignificant).