Combining the Neuman and Boulton models for flow to a well in an unconfined aquifer

Abstract

A Laplace transform solution is presented for flow to a well in a homogeneous, water-table aquifer with noninstanta-neous drainage of water from the zone above the water table. The Boulton convolution integral is combined with Darcy's law and used as an upper boundary condition to replace the condition used by Neuman. Boulton's integral derives from the assumption that water drained from the unsaturated zone is released gradually in a manner that varies exponentially with time in response to a unit decline in hydraulic head, whereas the condition used by Newman assumes that the water is released instantaneously. The result is a solution that reduces to the solution obtained by Neuman as the rate of release of water from the zone above the water table increases. A dimensionless fitting parameter, γ , is introduced that incorporates vertical hydraulic conductivity, saturated thickness, specific yield, and an empirical constant α 1 , similar to Boulton's α . Results show that theoretical drawdown in water-table piezometers is amplified by noninstantaneous drainage from the unsaturated zone to a greater extent than drawdown in piezometers located at depth in the saturated zone. This difference provides a basis for evaluating γ by type-curve matching in addition to the other dimensionless parameters. Analysis of drawdown in selected piezometers from the published results of two aquifer tests conducted in relatively homogeneous glacial outwash deposits but with significantly different hydraulic conductivities reveals improved comparison between the theoretical type curves and the hydraulic head measured in water-table piezometers.