Page 209 - Introduction to Petroleum Engineering

196 WELL COMPLETIONS

Example 10.6 Density of Brine‐saturated Rock
Find the density of rock saturated with saline water. The water density is
65 lb /ft , specific gravity of rock grains is 2.65, and rock porosity is 0.22.
3
m
Answer
Rock density is the weighted average of the water and grain densities:
=
ρ Rock (02265. )( lb /ft 3 − )( . )( . lb/ft 3 lb //ft 3
m ) =143
m ) +(1 0222 65 62 4.
m

Example 10.7 Overburden Stress Gradient

Find the overburden stress gradient if the overburden density is 160 lb /ft . The
3
overburden stress gradient is σ /h = ρg. Express your result in psi/ft. m
v
Answer
Substitute overburden density into σ /h = ρg and convert units:
v
 

2
m )( 32
σ v =   (160 lb /ft 3 ft/s )  1 1ft 2  = 111 psi/ft

.

h   32 lb ft /s   144in. 2  
2

  m  
   lb f   
The following example shows how to calculate horizontal stresses.
Example 10.8 Suite of Stresses
Find the stresses in a sandstone layer at depth of 10 000 ft. Assume overburden
stress gradient is 1.0 psi/ft, formation pressure is 4500 psi, Biot’s constant is
0.95, Poisson’s ratio for the sandstone is 0.25, and the tectonic stress is 2000 psi.

Answer
Apply Equations 10.12–10.16 with the physical values provided:
σ =10000 psi
v
(
.
σ =10000 psi − 0954500 psi) = 5725 psi
ve
.
025 (5725 psi)
σ = =1908 psi
he
− 25.
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