Page 49 - Geology and Geochemistry of Oil and Gas

26 OIL- AND GAS-BEARING ROCKS

Fig. 2.3. Permian carbonate outcrops. Relationship between the permeability and porosity due to di-
ssilution (leaching) (after Kerans et al., 1994). Porosity (%): 1–0-5; 2–6-10; 3–11-30.

k 2
V g ¼ Dp (2.6)
2m
where k is the gas permeability.
If the fracture opening is at least 10 mm, fractured reservoir permeability may be
calculated using the following equation:
4
3
k ¼ 8:5 10 w =b (2.7)
where b is the spacing between the fractures (m).
The classical hydrodynamic equation for narrow linear channels (fractures) is
3
q ¼ w aDp=12mL (2.8)
3
where q is the volumetric rate of flow (cm /s), w the height of fracture (cm), a the
width of fracture (cm, a wŠ), L the length of fracture (cm), Dp the pressure drop
½
2
2
(dyn/cm ), and m the viscosity (dyn/cm ).
For laminar flow, Witherspoon et al. (1980) proposed the following equation:
6
3
q ¼ 5:11 10 ðw Dpa=lmÞ (2.9)
where q is the volumetric rate of flow in (bbl/day), w the width (or aperture) of a
fracture (in); Dp the pressure drop (psi), a the width of fracture face (f), l the length
of the fracture (f), and m the viscosity of the fluid (cP).
Jones et al. (1988) suggested the following equations for open, rough fractures
with single-phase flow:

3
4
q ¼ 5:06 10 aðDpw =flrÞ 0:5 (2.10)
5
k ¼ 5:39 10 mðwl=DprÞ 0:5 (2.11)
where q ¼ the volumetric rate of flow (bbl/day), k ¼ the permeability (darcys),
3
r ¼ the density of flowing fluid (lb/ft ), and f ¼ the friction factor (dimensionless).