Simulation of Complex Groundwater Flow Processes in Low-Fidelity Radial Flow Model Using a Mathematical Representation of the Variation of Vertical Hydraulic Conductivity With Depth

Abstract

Numerical groundwater models are key tools to calculate the deployable output from pumped boreholes. Their calibration requires undertaking multiple runs to optimise the parameter values. To maintain computational efficiency, the hydrogeological complexity of fractured and weathered aquifers is often represented in numerical models using a simplified approach consisting of a mathematical equation that describes the vertical variation of horizontal hydraulic conductivity ($K_h$) value with depth. In this article, we present the inclusion of the variation of the vertical hydraulic conductivity ($K_v$) with depth to a radial flow model. We derive the mathematical equation controlling the flow vertically between the numerical nodes. We show that the inclusion of $K_v$ variation with depth have a limited impact on the shape of the time drawdown curve at the early times of a pumping test but its significance is higher at later times. This also has a measurable impact on the water level inside the pumped borehole especially when the variations of both $K_h$ and $K_v$ are accounted for. We use a simple linear variation of $K_v$ with depth but the method is also applicable to complex profile of aquifer heterogeneity if this complexity can be represented using polynomial approximation. This illustrates the applicability of the proposed method to a wide range of weathered aquifer settings.