Method of fracturing a subterranean formation at optimized and pre-determined conditions
View Patent ↗During a hydraulic fracturing treatment operation, one of three operational parameters may be modified in a successive stage by adjustment of another operational parameter to attain a fracture of length D PST . The operational parameters include the proppant size, viscosity of the transport fluid and injection rate of the transport fluid.
1. A method of hydraulic fracturing a subterranean formation in multiple stages to create or enlarge a fracture of length, D PST , the method comprising:
(a) pumping into the formation in a first stage a transport fluid containing a proppant, the transport fluid having an apparent viscosity, μ fluid1 , defined by Equation (I):
μ fluid1 =(1 /A )× q i ×(1 /D PST ) B ×( C TRANS )×(Δ SG PS )×( d 2 prop1 ) (I)
wherein:
A is the multiplier and B is the exponent from the Power Law equation of velocity of the transport slurry vs. distance for the fracture geometry;
q i is the injection rate per foot of injection height of μ fluid1 ;
C TRANS is the transport coefficient;
Δ SG PS is SG prop −SG fluid , SG prop being the specific gravity of the proppant and SG fluid being the specific gravity of the transport fluid; and
d prop1 is the median diameter of the proppant pumped in the transport fluid in the first stage;
(b) determining the requisite apparent viscosity of the transport fluid of a successive stage, μ fluid2 , wherein the transport fluid of the successive stage contains a proppant, and wherein the median diameter of the proppant pumped in the transport fluid in the successive stage, d prop2 is known and is different from the median diameter of the proppant pumped in the transport fluid in the first stage and further wherein A, B, q i , C TRANS , and Δ SG PS for the first stage and the successive stage are the same, μ fluid2 determined from Equation (II):
(
u
fluid
2
)
=
(
d
prop
2
)
2
×
(
u
fluid
1
)
(
d
prop
1
)
2
;
(
II
)
(c) pumping the transport fluid of the successive stage into the formation.
2. The method of claim 1 , wherein the proppant of the first and the successive stage is an ultra lightweight (ULW) proppant.
3. The method of claim 1 , wherein the transport fluid in the first stage and the successive stage is slickwater.
4. The method of claim 1 , wherein the fracture geometry has a 1:1 to 5:1 aspect ratio.
5. The method of claim 1 , wherein step (b) precedes step (a).
6. The method of claim 1 , wherein the proppant is sand.
7. A method of hydraulic fracturing a subterranean formation in multiple stages to create or enlarge a fracture of length, D PST , the method comprising:
(a) pumping into the formation in a first stage a transport fluid containing a proppant, the transport fluid having an apparent viscosity of μ fluid1 at a rate of injection defined by Equation (V):
q i =[1/( D PST ) B ]×[(1 /A )× C TRANS ×( d 2 prop1 )×(1/μ fluid1 )×(Δ SG PS )]; (V)
wherein:
A is the multiplier and B is the exponent from the Power Law equation of velocity of the transport slurry vs. distance for the fracture geometry;
q i is the injection rate per foot of injection height of μ fluid1 ;
C TRANS is the transport coefficient;
μ fluid1 is the apparent viscosity of the transport fluid;
Δ SG PS is SG prop −SG fluid , SG prop being the specific gravity of the proppant and SG fluid being the specific gravity of the transport fluid; and
d prop1 is the median diameter of the proppant pumped in the transport fluid in the first stage;
(b) determining the requisite rate of injection, q i2 , for a transport fluid having an apparent viscosity of μ fluid2 for a second stage, wherein the transport fluid of the successive stage contains a proppant, and and further wherein the median diameter of the proppant pumped in the transport fluid in the successive stage, d pop2 is known and is different from d prop1 and further wherein A, B, C TRANS , Δ SG PS and the apparent viscosity of the transport fluids for the first stage and the successive stage are the same, q i2 determined from Equation (VI):
(
q
i
2
)
=
(
d
prop
1
)
2
×
(
q
i
1
)
(
d
prop
2
)
2
;
(
VI
)
and
(c) pumping the transport fluid of the successive stage into the formation.
8. The method of claim 7 , wherein the proppant of the first stage and the successive stage is an ultra lightweight (ULW) proppant.
9. The method of claim 7 , wherein the transport fluid of the first stage and the successive stage is slickwater.
10. The method of claim 7 , wherein the fracture geometry has a 1:1 to 5:1 aspect ratio.
11. The method of claim 7 , wherein step (b) precedes step (a).
12. A method of hydraulic fracturing a subterranean formation in multiple stages to create or enlarge a fracture of length, D PST , the method comprising:
(a) pumping into the formation in a first stage a transport fluid containing a proppant, the transport fluid having an apparent viscosity of μ fluid1 at a rate of injection, q i1 , defined by Equation (V):
q i1 =[1/( D PST ) B ]×[(1 /A )× C TRANS ×( d 2 prop )×(1/μ fluid )×(Δ SG PS )]; (V)
wherein:
A is the multiplier and B is the exponent from the Power Law equation of velocity of the transport slurry vs. distance for the fracture geometry;
C TRANS is the transport coefficient;
Δ SG PS is SG prop −SG fluid , SG prop being the specific gravity of the proppant and SG fluid being the specific gravity of the transport fluid; and
d prop is the median diameter of the proppant pumped in the transport fluid in the first stage;
(b) determining the requisite rate of injection, q i2 , for a transport fluid of a successive stage having an apparent viscosity of μ fluid2 wherein the transport fluid of the successive stage contains a proppant, and and further wherein the median diameter of the proppant pumped in the transport fluid in the successive stage is the same as that of the proppant pumped in the first stage, the apparent viscosity of the transport fluid of the successive stage, μ fluid2 is known and is different from the μ fluid1 and further wherein A, B, C TRANS , and Δ SG PS for the first stage and the successive stage are the same, q i2 determined from Equation (VI):
q
i
2
=
q
i
1
×
μ
fluid
2
μ
fluid
1
;
(
VI
)
and
(c) pumping the transport fluid of the successive stage into the formation.
13. The method of claim 12 , wherein the proppant of the first stage and the successive stage is an ultra lightweight (ULW) proppant.
14. The method of claim 12 , wherein the transport fluid of the first stage and the successive stage is slickwater.
15. The method of claim 12 , wherein the fracture geometry has a 1:1 to 5:1 aspect ratio.
16. The method of claim 12 , wherein step (b) precedes step (a).
17. A method of hydraulic fracturing a subterranean formation in multiple stages to create or enlarge a fracture of length, D PST , the method comprising:
(a) pumping into the formation in a first stage a transport fluid containing a proppant, the transport fluid having an apparent viscosity of μ fluid1 , defined by Equation (I):
μ fluid1 =(1 /A )× q i ×(1 /D PST ) B ×( C TRANS )×(Δ SG PS )×( d 2 prop ) (I)
wherein:
A is the multiplier and B is the exponent from the Power Law equation of velocity of the transport slurry vs. distance for the fracture geometry;
q i is the injection rate of μ fluid1 ;
C TRANS is the transport coefficient;
Δ SG PS is SG prop −SG fluid , SG prop being the specific gravity of the proppant and SG fluid being the specific gravity of the transport fluid; and
d prop is the median diameter of the proppant pumped in the transport fluid in the first stage;
(b) determining the requisite apparent viscosity of the transport fluid of a successive stage, μ fluid2 , wherein the transport fluid of the successive stage contains a proppant, and wherein the median diameter of the proppant pumped in the first stage and the successive stage are the same, the rate of injection of the transport fluid of the successive stage, q i2 , is known and is different from q i1 and further wherein A, B, C TRANS , and Δ SG PS for the first stage and the successive stage are the same, μ fluid2 determined from Equation (XIX):
μ
fluid
2
=
q
i
2
×
μ
fluid
1
q
i
1
;
(
XIX
)
and
(c) pumping the transport fluid of the successive stage into the formation.
18. The method of claim 17 , wherein the proppant is an ultra lightweight (ULW) proppant.
19. The method of claim 17 , wherein the transport fluid is slickwater.
20. The method of claim 17 , wherein the fracture geometry has a 1:1 to 5:1 aspect ratio.
21. The method of claim 17 , wherein step (b) precedes step (a).