Generalized Darcy's law including source effect

Conventional Darcy's law for flow description in porous media was derived from a simple experiment carried out by Darcy in 1856 on a linear, homogeneous and sourceless porous medium. In this paper starting from basic Navier-Stokes momentum balance principle, a generalized Darcy's law has been derived that includes the effect of a source/sink term. Navier-Stokes momentum balance of similar nature was attempted by Casulli et al.((1)), also in their studies on porous media flow even though many authors have objected to such analysis. Brinkman((2)) and Hubbert((3)) have also hinted at such application of Navier-Stokes equation to derive the traditional Darcy's law. In deriving the generalized Darcy's law, described in this paper, a similar to Casulli et al.((1)), linear approximation of the stress term has been used. A numerical investigation of the error resulting from not considering the source effect reveals that errors in pressure prediction may range to as high as 500 psi. This is a significant error and cannot be overlooked.