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Darcy's law is an equation that describes the flow of a fluid flow trough 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 .
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 ...
We notice that the volumetric flow rate is a scalar quantity and that the direction is taken care of by the normal vector of the surface (area) and the volumetric flux (Darcy velocity). In a reservoir model the geometric volume is divided into grid cells, and the area of interest now is the intersectional area between two adjoining cells.
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.
For Reynolds number greater than 4000, the flow is turbulent; the resistance to flow follows the Darcy–Weisbach equation: it is proportional to the square of the mean flow velocity. Over a domain of many orders of magnitude of Re (4000 < Re < 10 8), the friction factor varies less than one order of magnitude (0.006 < f D < 0.06). Within the ...
Pore-structure modelling enables the use Darcy's law to calculate the volumetric flow rate through porous media such as groundwater flow through rock. [12] Further examples occur within the bodies of living organisms, such as blood flow (with plasma being the liquid phase and red blood cells constituting the solid phase. [13]
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 ...
Darcy's law is used for flow in porous media, and works with variables averaged over several pore-widths. In rotating systems, the quasi-geostrophic equations assume an almost perfect balance between pressure gradients and the Coriolis force. It is useful in the study of atmospheric dynamics.