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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 movement of a fluid through porous media is described by the combination of Darcy's law with the principle of conservation of mass in order to express the capillary force or fluid velocity as a function of various other parameters including the effective pore radius, liquid viscosity or permeability. [3]
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.
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 ...
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.
Hele-Shaw flow is defined as flow taking place between two parallel flat plates separated by a narrow gap satisfying certain conditions, named after Henry Selby Hele-Shaw, who studied the problem in 1898. [1] [2] Various problems in fluid mechanics can be approximated to Hele-Shaw flows and thus the research of these flows is of importance ...
Henry Philibert Gaspard Darcy (French: [ɑ̃ʁi daʁsi]; 10 June 1803 – 3 January 1858) was a French engineer who made several important contributions to hydraulics, including Darcy’s law for flow in porous media.
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]