Page 559 - Petrophysics

526 PETROPHYSICS: RESERVOIR ROCK PROPERTIES

unit Area
At

Figure 8.19. Effect of fracture shape on the permeability-porosity relationship.

EFFECT OF FRACTURE SHAPE

Consider a fracture with an elliptical cross-section as shown in Figure
8.19. Assuming a type 1 naturally fractured reservoir, the specific surface
area per unit pore volume, S,, is:

Ase
s, = - (8.52)
VP

where Ase is the surface area of the elliptl:al fracture and is given by:

Ase = 7~ b.75 (wf + hf) - 0.5-1 L (8.53)

and

7C
Vp = -WfhfL (8.54)
4
Combining the above three equations, and simplifying:

1
1
2
= 3 (- + -) - - (8.55)
Wf hf 46G
Since l/hf << l/wf, the above equation reduces to:

3 2
h=(wy)-m (8.56)