Darcy's law

Darcy's law is an equation that describes the flow of a fluid through a porous medium. The law was formulated by Henry Darcy based on results of experiments on the flow of water through beds of sand, forming the basis of hydrogeology, a branch of earth sciences. It is analogous to Ohm's law in electrostatics, linearly relating the volume flow rate of the fluid to the hydraulic head difference (which is often just proportional to the pressure difference) via the hydraulic conductivity. Darcy's law was first determined experimentally by Darcy, but has since been derived from the Navier–Stokes equations via homogenization methods. It is analogous to Fourier's law in the field of heat conduction, Ohm's law in the field of electrical networks, and Fick's law in diffusion theory. One application of Darcy's law is in the analysis of water flow through an aquifer; Darcy's law along with the equation of conservation of mass simplifies to the groundwater flow equation, one of the basic relationships of hydrogeology. Morris Muskat first refined Darcy's equation for a single-phase flow by including viscosity in the single (fluid) phase equation of Darcy. It can be understood that viscous fluids have more difficulty permeating through a porous medium than less viscous fluids. This change made it suitable for researchers in the petroleum industry. Based on experimental results by his colleagues Wyckoff and Botset, Muskat and Meres also generalized Darcy's law to cover a multiphase flow of water, oil and gas in the porous medium of a petroleum reservoir. The generalized multiphase flow equations by Muskat and others provide the analytical foundation for reservoir engineering that exists to this day. Darcy's law, as refined by Morris Muskat, in the absence of gravitational forces and in a homogeneously permeable medium, is given by a simple proportionality relationship between the instantaneous flux (units of : m3/s, units of : m2, units of : m/s) through a porous medium, the permeability of the medium, the dynamic viscosity of the fluid , and the pressure drop over a given distance , in the form This equation, for single phase (fluid) flow, is the defining equation for absolute permeability (single phase permeability).