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424 PETROPHYSICS: RESERVOIR ROCK PROPERTIES
DARCY’S AND POISEUILLE’S LAWS
Darcy’s law for the linear flow of incompressible fluids in porous and
permeable rocks and Poiseuille’s equation for liquid capillary flow are
quite similar. The general form of Poiseuille’s law for the viscous flow of
liquid through capillary tubes is:
(7.25)
where: r = radius of capillary tube, cm.
Ap = pressure drop, dynes/cm2 (= 1.0133 x lo6 atm).
L = length of capillary tube, cm.
p = viscosity of flowing fluid, Poise.
If the fluid-conducting channels in a porous medium could be
represented by a bundle of parallel capillary tubes of various diameters,
then the flow rate through this system is:
(7.26)
where: nj = number of tubes of radius rj.
N = number of groups of tubes of different radii.
This expression can be rewritten as:
CAP
q = -- (7.27)
PL
where C is the flow coefficient (i njf). It is evident that
E:,
Equation 7.26 is similar to Equation 7.7 (Darcy’s law) where the
coefficient C is equivalent to the permeability. Thus:
where A is the total cross-sectional area, as illustrated in Figure 7.2.
