Darcy’s law is widely used to describe the steady-state laminar incompressible single-phase fluid flow in a fully saturated porous medium at the macroscopic-scale. However, in reality, we will be dealing with transient non-laminar compressible multi-phase fluid flow through a saturated porous medium. In this context, it is important to understand the original framework of Darcy’s law; and subsequently, we need to understand clearly, under what circumstances the classical Darcy’s law was extended in order to consider the (a) the differential form of Darcy’s law; (b) the non-linear relation between pressure gradient and fluid velocity; (b) the transient nature of fluid flow; (c) the fluid flow through heterogeneous and anisotropic reservoirs or aquifers. It has been reemphasized from the present study that the presence of weak inertial effect along with the laminar fluid regime causes the ‘non-linear’ relation between the macroscopic pressure gradient and the macroscopic fluid velocity, while the strong inertial effect paves the way for the onset of transient nature of fluid flow.


Darcy’s law; porous medium; differential form; transient flow; inertial effect.

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