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Darcy's law is an equation that describes the flow of a fluid through a porous medium and through a Hele-Shaw cell.The law was formulated by Henry Darcy based on results of experiments [1] on the flow of water through beds of sand, forming the basis of hydrogeology, a branch of earth sciences.
The SI unit for permeability is the square metre (m 2).A practical unit for permeability is the darcy (d), or more commonly the millidarcy (md) (1 d ≈ 10 −12 m 2). The name honors the French Engineer Henry Darcy who first described the flow of water through sand filters for potable water supply.
The porous medium equation name originates from its use in describing the flow of an ideal gas in a homogeneous porous medium. [6] We require three equations to completely specify the medium's density , flow velocity field , and pressure : the continuity equation for conservation of mass; Darcy's law for flow in a porous medium; and the ideal gas equation of state.
However, the use of Darcy's law alone does not produce accurate results for heterogeneous media like shale, and tight sandstones, where there is a huge proportion of nanopores. This necessitates the use of a flow model that considers the weighted proportion of various flow regimes like Darcy flow, transition flow, slip flow, and free molecular ...
The above form for Darcy's law is sometimes also called Darcy's extended law, formulated for horizontal, one-dimensional, immiscible multiphase flow in homogeneous and isotropic porous media. The interactions between the fluids are neglected, so this model assumes that the solid porous media and the other fluids form a new porous matrix through ...
The collision cross section per volume or collision cross section density is , and it is related to the mean free path by l = 1 2 C σ {\displaystyle l={\frac {1}{{\sqrt {2}}C\sigma }}} Combining the kinetic equations for molecular motion with the defining equation of shear viscosity gives the well known equation for shear viscosity for dilute ...
A mass balance must be performed, and used along with Darcy's law, to arrive at the transient groundwater flow equation. This balance is analogous to the energy balance used in heat transfer to arrive at the heat equation. It is simply a statement of accounting, that for a given control volume, aside from sources or sinks, mass cannot be ...
The Darcy velocity is not the velocity of a fluid particle, but the volumetric flux (frequently represented by the symbol ) of the fluid stream. The fluid velocity in the pores v a {\displaystyle \mathbf {v} _{a}} (or short but inaccurately called pore velocity) is related to Darcy velocity by the relation