Darcy's Law

Part 10, Chapter 10: Flow Physics, Governing Equations, and Initialization

The Law of Flow Through Rock

Darcy's law says the volumetric flow rate through rock is set by four things, q=k Aμ ΔPLq = \dfrac{k,A}{\mu},\dfrac{\Delta P}{L}: the permeability k, the cross-sectional area A, the inverse of the viscosity, and the pressure gradient, the drop divided by the length.

Darcy's lawPin 2000Pout 1500pressure (psi)distance through rock (flow ->)Darcy: rate = k A times the pressure gradient, over viscosity. The profile stays straight; permeability and viscosity set the flux.

Why the Profile Is Straight

For steady incompressible flow the same rate must cross every slice of the rock, so the gradient is constant and the pressure falls in a straight line. Permeability and viscosity do not bend that line; they set how much fluid flows for a given gradient.

Permeability and Viscosity

Doubling the permeability doubles the rate; doubling the viscosity halves it. This one law, applied face by face across the grid, is the flow engine inside every reservoir simulator.

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