Method for determining in-situ maximum horizontal stress
A method for obtaining a maximum horizontal stress at a depth of a geological formation, includes: setting an estimate S Hmax of the maximum horizontal stress; conducting an elastoplastic modeling simulation of the geological formation around a wellbore with the estimate S Hmax and obtaining a simulated value ϕ b,1 of a breakout angle, wherein the breakout angle is a half-width of a breakout region; and upon determining that the estimate ϕ b,1 is greater than or equal to a prescribed value and is different from a measured breakout angle ϕ b,m at the depth by more than a threshold value, repeatedly changing the estimate S Hmax and conducting the elastoplastic modeling simulation.
1. A method for obtaining a maximum horizontal stress at a depth of a geological formation, comprising:
setting an estimate S Hmax of the maximum horizontal stress;
conducting an elastoplastic modeling simulation of the geological formation around a wellbore with the estimate S Hmax and obtaining a simulated value ϕ b,1 of a breakout angle, wherein the breakout angle is a half-width of a breakout region,
wherein conducting the elastoplastic modeling simulation comprises:
setting up a calculation region, wherein the calculation region has a boundary that corresponds to a wall of the wellbore;
setting a uniform stress condition for an entirety of the calculation region, wherein the uniform stress condition is represented by the estimate S Hmax , a minimum horizontal stress, and a pore pressure of the geological formation at the depth; and
repeatedly reducing a normal stress that acts perpendicular to the boundary at the boundary by an amount while the uniform stress condition far away from the boundary is maintained and a shear stress at the boundary is maintained to be zero and calculating stress conditions in the calculation region until the normal stress at the boundary is substantially equal to a wellbore pressure above the pore pressure, and
wherein the estimate S Hmax comprises calculating the estimate S Hmax as
S
Hmax
=
ucs
+
Δ
P
W
+
2
P
p
1
-
2
cos
2
θ
b
-
s
hmin
1
+
2
cos
2
θ
b
1
-
2
cos
2
θ
b
,
where
θ b is equal to 90°−ϕ b,m and obtained from a caliper log,
P p is the pore pressure of the geological formation at the depth,
ΔP w is a wellbore pressure P w at the depth above P p ,
S hmin is the minimum horizontal stress at the depth,
ucs is an unconfined compressive strength calculated as
ucs
=
2
c
cos
φ
1
-
sin
φ
,
c is a cohesion of the geological formation at the depth, and
φ is a friction angle of the geological formation at the depth; and
upon determining that the simulated value ϕ b,1 is greater than or equal to a prescribed value and is different from a measured breakout angle ϕ b,m at the depth by more than a threshold value, repeatedly changing the estimate S Hmax and conducting the elastoplastic modeling simulation.
2. The method according to claim 1 , wherein the setting the estimate S Hmax comprises calculating the estimate S Hmax based on an elastic modeling simulation of the geological formation around the wellbore.
3. The method according to claim 1 , wherein the changing the estimate S Hmax comprises:
in response to ϕ b,m >ϕ b,1 , increasing the estimate S Hmax by a first prescribed amount; and
in response to ϕ b,m <ϕ b,1 , decreasing the estimate S Hmax by a second prescribed amount.
4. The method according to claim 1 , further comprising:
determining a safe mud weight window in a drilling of the wellbore based on the estimate S Hmax .
5. A system, comprising:
a logging system coupled to a plurality of logging tools; and
a formation breakout simulator comprising a computer processor, wherein the formation breakout simulator is coupled to the logging system, the formation breakout simulator comprising functionality for:
setting an estimate S Hmax of a maximum horizontal stress;
conducting an elastoplastic modeling simulation of a geological formation around a wellbore with the estimate S Hmax and obtaining a simulated value ϕ b,1 of a breakout angle, wherein the breakout angle is a half-width of a breakout region,
wherein conducting the elastoplastic modeling simulation comprises:
setting up a calculation region, wherein the calculation region has a boundary that corresponds to a wall of the wellbore;
setting a uniform stress condition for an entirety of the calculation region, wherein the uniform stress condition is represented by the estimate S Hmax , a minimum horizontal stress, and a pore pressure of the geological formation at the depth; and
repeatedly reducing a normal stress that acts perpendicular to the boundary at the boundary by an amount while the uniform stress condition far away from the boundary is maintained and a shear stress at the boundary is maintained to be zero and calculating stress conditions in the calculation region until the normal stress at the boundary is substantially equal to a wellbore pressure above the pore pressure, and
wherein the estimate S Hmax comprises calculating the estimate S Hmax as
s
Hmax
=
ucs
+
Δ
P
W
+
2
P
p
1
-
2
cos
2
θ
b
-
S
hmin
1
+
2
cos
2
θ
b
1
-
2
cos
2
θ
b
,
where
θ b is equal to 90°−ϕ b,m and obtained from a caliper log,
P p is the pore pressure of the geological formation at the depth,
ΔP w is a wellbore pressure P w at the depth above P p ,
S hmin is the minimum horizontal stress at the depth,
ucs is an unconfined compressive strength calculated as
ucs
=
2
c
cos
φ
1
-
sin
φ
,
c is a cohesion of the geological formation at the depth, and
φ is a friction angle of the geological formation at the depth; and
upon determining that the simulated value ϕ b,1 is greater than or equal to a prescribed value and is different from a measured breakout angle ϕ b,m at the depth by more than a threshold value, repeatedly changing the estimate S Hmax and conducting the elastoplastic modeling simulation.
6. The system according to claim 5 , wherein the setting the estimate S Hmax comprises calculating the estimate S Hmax based on an elastic modeling simulation of the geological formation around the wellbore.
7. The system according to claim 5 , wherein the changing the estimate S Hmax comprises:
in response to ϕ b,m >ϕ b,1 , increasing the estimate S Hmax by a first prescribed amount; and
in response to ϕ b,m <ϕ b,1 , decreasing the estimate S Hmax by a second prescribed amount.
8. The system according to claim 5 , wherein the formation breakout simulator further comprises functionality for:
determining a safe mud weight window in a drilling of the wellbore based on the estimate S Hmax .
9. A non-transitory computer readable medium storing instructions executable by a computer processor, the instructions comprising functionality for:
setting an estimate S Hmax of a maximum horizontal stress;
conducting an elastoplastic modeling simulation of a geological formation around a wellbore with the estimate S Hmax and obtaining a simulated value ϕ b,1 of a breakout angle,
wherein the breakout angle is a half-width of a breakout region,
wherein conducting the elastoplastic modeling simulation comprises:
setting up a calculation region, wherein the calculation region has a boundary that corresponds to a wall of the wellbore;
setting a uniform stress condition for an entirety of the calculation region, wherein the uniform stress condition is represented by the estimate S Hmax , a minimum horizontal stress, and a pore pressure of the geological formation at the depth; and
repeatedly reducing a normal stress that acts perpendicular to the boundary at the boundary by an amount while the uniform stress condition far away from the boundary is maintained and a shear stress at the boundary is maintained to be zero and calculating stress conditions in the calculation region until the normal stress at the boundary is substantially equal to a wellbore pressure above the pore pressure, and
wherein the estimate S Hmax comprises calculating the estimate S Hmax as
s
Hmax
=
ucs
+
Δ
P
W
+
2
P
p
1
-
2
cos
2
θ
b
-
s
hmin
1
+
2
cos
2
θ
b
1
-
2
cos
2
θ
b
,
where
θ b is equal to 90°−ϕ b,m and obtained from a caliper log,
P p is the pore pressure of the geological formation at the depth,
ΔP w is a wellbore pressure P w at the depth above P p ,
S hmin is the minimum horizontal stress at the depth,
ucs is an unconfined compressive strength calculated as
ucs
=
2
c
cos
φ
1
-
sin
φ
,
c is a cohesion of the geological formation at the depth, and
φ is a friction angle of the geological formation at the depth; and
upon determining that the simulated value ϕ b,1 is greater than or equal to a prescribed value and is different from a measured breakout angle ϕ b,m at the depth by more than a threshold value, repeatedly changing the estimate S Hmax and conducting the elastoplastic modeling simulation.
10. The non-transitory computer readable medium according to claim 9 , wherein the setting the estimate S Hmax comprises calculating the estimate S Hmax based on an elastic modeling simulation of the geological formation around the wellbore.
11. The non-transitory computer readable medium according to claim 9 , wherein the changing the estimate S Hmax comprises:
in response to ϕ b,m >ϕ b,1 , increasing the estimate S Hmax by a first prescribed amount; and
in response to ϕ b,m <ϕ b,1 , decreasing the estimate S Hmax by a second prescribed amount.