Generalized Darcy's law with source and heterogeneity effects

Steady state Darcy's law has long been used (since 1856) for pressure predi ction from continuity equation in porous media fluid now. Effects of a sour ce term, heterogeneity such as spatial porosity variation and unsteady natu re of flow on Darcy-equivalent velocity have been investigated in this pape r. In absence of Darcy type experimental observation in presence of these t hree factors, an analytical Navier-Stokes equation type investigation has b een presented. These model equations are based on a new "pore average veloc ity" concept rather than conventional superficial velocity concept. Large p ressure prediction errors are indicated for individual factors (source or h eterogeneity) ranging to as high as 1,000 psi (7,000 kpa) for typical time steps (10 days) used in petroleum reservoir simulation. For implicit formul ation unbounded pressure errors may result. There appears to be a severe ne ed for time step limitation which makes modelling difficult and impractical .