Darcy’s Law and the Role of Gravity forces and Capillary Pressure
1. Since ‘gravity forces’ have a pronounced effect on ‘pressure distribution curves’ for a definite range of injection flow rates;
and in turn, the ‘injection flow rates’ have a pronounced effect on the ‘rate of movement of saturation profiles’; then, to what extent,
the role of ‘gravity term with (positive/negative) dip (inclination/angle) details’ in the extended form of Darcy’s equation plays a crucial role?
2. Since the inclusion of 'capillarity' eliminates the multiple-valued Buckley-Leverett saturation profiles; then, to what extent,
the (sub) pore-scale effects associated with the ‘capillary pressure term’ becomes sensitive, while using the extended form of macroscopic-based Darcy’s law for describing the momentum conservation of multi-phase fluid flow?
Darcy's Law describes the flow of a fluid through a porous medium. The movement of a fluid through porous media is described by the combination of Darcy's law with the principle of conservation of mass in order to express the capillary force or fluid velocity as a function of various other parameters including the effective pore radius, liquid viscosity or permeability ³.
Gravity forces can have a pronounced effect on pressure distribution curves for a definite range of injection flow rates. The Bond number quantifies the ratio of the typical hydrostatic pressure drop over a pore to the capillary pressure ¹. This means that gravity forces can play a crucial role in the extended form of Darcy's equation.
The capillary number is the typical ratio of the viscous pressure drop at pore scale to the capillary pressure ¹. This means that capillarity can also play an important role in the extended form of Darcy's equation. The inclusion of capillarity can eliminate multiple-valued Buckley-Leverett saturation profiles and account for sub-pore-scale effects associated with the capillary pressure term.
(1) Fluid flow through porous media - Wikipedia. https://en.wikipedia.org/wiki/Fluid_flow_through_porous_media.
(2) Competition of gravity, capillary and viscous forces during drainage in .... https://www.sciencedirect.com/science/article/pii/S0360544204001860.
(3) 2.5: Darcy's Law - Flow in a Porous Medium - Geosciences LibreTexts. https://geo.libretexts.org/Courses/University_of_California_Davis/GEL_056%3A_Introduction_to_Geophysics/Geophysics_is_everywhere_in_geology.../02%3A_Diffusion_and_Darcy's_Law/2.05%3A_Darcy's_Law_-_Flow_in_a_Porous_Medium.