Page 254 - Geology and Geochemistry of Oil and Gas

220 MATHEMATICAL MODELING IN PETROLEUM GEOLOGY

where d i is the average diameter of grains which constitute an ith grain-size fraction
with weight content of C i in wt%. (Total grain-size distribution is expressed as
follows: C 1 þ C 2 þ þ C i þ þ C n ¼ 100%.)
Inasmuch as one of the main influences on the specific surface area is caused by
the clay content, C cl , the empirical equation developed for the reservoir rocks is as
follows:

s g ¼ 75ð1 fÞC cl þ 532ð1 fÞð75C cl þ 532Þð1 fÞ (11.26)

Assuming that f ave ¼ 0:25, the average correlation between s g and C cl will be as
follows:

s g ¼ 56:3C cl þ 400 (11.27)

In order to determine the permeability from porosity and specific surface area, one
has to solve Eq. 11.23 for permeability

2
k ¼ f=ð2s Þ (11.28)
p
Inasmuch as a porous rock is more complex than a bundle of capillary tubes, a
constant K cf is introduced. Thus, the equation for permeability becomes
2
k ¼ f=ðK cf s Þ (11.29)
p
Eq. 11.29 is the familiar Kozeny–Carman equation. Carman (1937, in: Bury-
akovsky et al., 2001, p. 304) noted that the constant K cf is actually a complex
combination of two variables: shape factor for pores, s hf , and tortuosity factor, t:

K cf ¼ ðs hf ÞðtÞ (11.30)

Tortuosity is equal to the square of the ratio of effective length L e to the length
parallel to the overall direction of flow of pore channels L:
2
t ¼ ðL e =LÞ (11.31)
Thus, the Kozeny–Carman constant K cf is a function of both the shape of each
particular pore tube and its orientation relative to the overall direction of fluid flow.
Using the multivariable linear regression analysis, Chilingarian et al. (1990) de-
veloped an empirical expression for permeability in terms of porosity, specific sur-
face area, and irreducible fluid saturation for carbonate reservoir rocks, with very
high (40.9) coefficient of correlation between porosity and permeability.
This research resolved the age-long controversy whether there is a correlation
between porosity and permeability of carbonate rocks or not. By simply introducing
two additional variables (specific surface area and irreducible fluid saturation), there
is correlation between the porosity and permeability. Microfractures do not con-
tribute much to the porosity (fo1%) but are very permeable.