Analytical solutions for groundwater and soil vapor flow to a partially penetrating well with non-uniform radial flux along the screen

Analytical functions for groundwater and soil air flow toward an extraction well with non-uniform radial flux (NUF) along the screen and finite-thickness skin are derived via the Laplace and finite Fourier transforms and Fredholm integral equation. The flow domain is simulated as a homogeneous layer of uniform thickness and infinite extent. For groundwater extraction, the layer represents an unconfined, leaky-boundary flux, or confined aquifer. For soil vapor extraction (SVE), the flow domain represents a vadose zone with unrestricted flow of atmospheric air across the ground surface or a vadose zone covered by a leaky-boundary flux confining layer. The new groundwater flow solution constitutes a general well function that reduces to special cases such as constant flowrate pumping, constant drawdown pumping, and slug test. The new SVE well function avoids the common practice of lumping the flowrate and wellhead pressure into a single variable and allows the well to be either pressure- or flow-controlled.; Simulations based on the established P or P2 linearization of the governing air-flow equation yield results that are practically indistinctive for steady SVE, but the deviation increases with applied wellhead pressure for transient SVE, indicating the range of the validity of the linearization.; The new solutions allow for non-uniform radial flux distribution along the well screen instead of the commonly assumed, but less realistic, uniform flux. The deviation in drawdown or pressure of the uniform flux (UF) from NUF solutions depends on the length of the extraction well screen, relative positions of the extraction and observation well screens, soil properties, and duration of extraction.; Ignoring the non-uniform radial flux in aquifer test analysis under some conditions can lead to errors, up to a few hundred percent, in the estimates of aquifer properties. Application to field SVE test data indicates that estimates of horizontal and vertical soil-air permeability by non-uniform flux model are similar to those obtained with uniform flux model for extraction wells with short screens. Least squares fitting of transient data revealed the dependence of the three estimated parameters: air-filled soil porosity and horizontal and vertical permeability.