Darcy’s Law in Variable Density Groundwater Systems

Although Darcy’s law is one of the fundamental equations used in hydrogeology to describe the movement of groundwater through an aquifer, it has limitations. In this book, we focus on Darcy’s law for one-dimensional flow in a homogeneous porous medium. We begin with a review of the hydraulic head form of Darcy’s law that is familiar to most groundwater hydrologists and discuss the concept of head as a hydraulic potential. Using a thought experiment, we show that the head form of Darcy’s law cannot work for a hypothetical system with variable groundwater denisty. This leads us to the pressure-based form of Darcy’s law, which is more universal and can be used to compute flux in systems with elevated and/or variable-density groundwater. Finally, through illustrative examples, we demonstrate how the pressure-based form can be used to evaluate horizontal and vertical fluxes in flow systems that are not amenable to analysis with the head form of Darcy’s law.