Page 254 - Petroleum Production Engineering, A Computer-Assisted Approach

Guo, Boyun / Computer Assited Petroleum Production Engg 0750682701_chap17 Final Proof page 253 3.1.2007 9:19pm Compositor Name: SJoearun

HYDRAULIC FRACTURING 17/253

Gas

Oil
Water
p tf

H

p wt
p
p e

Figure 17.3 Overburden formation of a hydrocarbon reservoir.

Consider a reservoir rock at depth H as shown in Because of the tectonic effect, the magnitude of the hori-
Fig. 17.3. The in situ stress caused by the weight of the zontal stress may vary with direction. The maximum hori-
overburden formation in the vertical direction is expressed zontal stress may be s h, max ¼ s h, min þ s tect , where s tect is
as called tectonic stress.
rH Based on a failure criterion, Terzaghi presented the
s v ¼ , (17:1) following expression for the breakdown pressure:
144
p bd ¼ 3s h, min s h, max þ T 0 p p , (17:5)
where
s v ¼ overburden stress, psi where T 0 is the tensile strength of the rock.
r ¼ the average density of overburden
formation, lb=ft 3 Example Problem 17.1 A sandstone at a depth of 10,000 ft
H ¼ depth, ft. has a Poison’s ratio of 0.25 and a poro-elastic constant of
0.72. The average density of the overburden formation is
The overburden stress is carried by both the rock grains 165 lb=ft . The pore pressure gradient in the sandstone is
3
and the fluid within the pore space between the grains. The 0.38 psi/ft. Assuming a tectonic stress of 2,000 psi and a
contact stress between grains is called effective stress tensile strength of the sandstone of 1,000 psi, predict the
(Fig. 17.4):
breakdown pressure for the sandstone.
0
s ¼ s v ap p , (17:2)
v
where
0
s ¼ effective vertical stress, psi
v
a ¼ Biot’s poro-elastic constant,
approximately 0.7
p p ¼ pore pressure, psi.
The effective horizontal stress is expressed as
n
0
0
s ¼ s , (17:3)
h
1 n v
where n is Poison’s ratio. The total horizontal stress is
expressed as
Figure 17.4 Concept of effective stress between
0
s h ¼ s þ ap p : (17:4) grains.
h