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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 .
A version of the multiphase flow equation, before it is discretized and used in reservoir simulators, is thus Q a = − μ a − 1 A ⋅ K r a ⋅ K ⋅ ( ∇ P a − ρ a g ) {\displaystyle Q_{a}=-\mu _{a}^{-1}\mathbf {A} \cdot \mathbf {K} _{ra}\cdot \mathbf {K} \cdot \left(\nabla P_{a}-\rho _{a}\mathbf {g} \right)} where a = w, o, g
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 ...
An example of multiphase flow on a smaller scale would be within porous structures. 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 ]
Darcy's law, in hydrogeology, describes the flow of a fluid (such as water) through a porous medium (such as an aquifer). Davis's law, in anatomy, describes how soft tissue models along imposed demands. Corollary to Wolff's law. De Morgan's laws apply to formal logic regarding the negation of pairs of logical operators.
Diagram showing definitions and directions for Darcy's law. Darcy's law states that the volume of flow of the pore fluid through a porous medium per unit time is proportional to the rate of change of excess fluid pressure with distance. The constant of proportionality includes the viscosity of the fluid and the intrinsic permeability of the soil.
The darcy is referenced to a mixture of unit systems. A medium with a permeability of 1 darcy permits a flow of 1 cm 3 /s of a fluid with viscosity 1 cP (1 mPa·s) under a pressure gradient of 1 atm/cm acting across an area of 1 cm 2. Typical values of permeability range as high as 100,000 darcys for gravel, to less than 0.01 microdarcy for ...