Fundamentals of Fluid Flow in Porous Media
Multi-phase Saturated Rock Properties:
Dominance of Capillary Forces over Viscous Forces
Viscous force is reflected in the pressure gradient generated by the flow through a porous medium. The pressure gradient is proportional to the viscosity and the fluid velocity and inversely proportional to the conductivity of the medium. Viscous force in a circular capillary tube can be found from eq.(2‑17) or:
- v = fluid velocity, cm/sec
- r = capillary tube radius, cm
- ΔP = pressure loss over length L, (dyne/cm2)
- μ = fluid viscosity, centipoise
- L = length over which pressure loss is measured, cm
As mentioned before for a porous medium, the pressure gradient is given by Darcy’s law.
Now, consider the displacement of oil by water from a capillary tube, at velocity v (Figure 2‑55). For simplicity let us assume that μnw = μw = μ.