Page 135 - Petrophysics 2E

108 PETROPHYSICS: RESERVOIR ROCK PROPERTIES

Equating Equations 3.10 and 3.1 1 and solving for k gives:

(3.12)

By definition, porosity is

(3.13)

Substituting 4 = nn?/@ from Equation 3.13 into Equation 3.12, one
obtains a simpler relationship between permeability and porosity for
pores of the same size and radii equal to r:

(3.14)

where k is in cm2 (1 an2 = 1.013 x lo8 darcys) or in pm2 (1 mD =
9.871 x 10-4pm2) and 4) is a fraction.

Let svP be the internal surface area per unit of pore volume, where the
surface area As for n capillary tubes is n(2nrL) and the pore volume Vp is
n(nr;?L):

(3.15)

Let svgr be the specific surface area of a porous material or the total
area exposed within the pore space per unit of grain volume. For a
bundle of capillary tubes, the total area exposed, At, is equivalent to the
internal surface area As; and the grain volume, Vg. is equal to &L(l-9).
Thus

(3.16)

Combining Equations 3.15 and 3.16 gives:

SVg' svp (")

1-4) (3.17)