Measuring flow rates of multiphase fluids
A multiphase fluid is flowed from a flow pipe to a U-bend. Several differential pressures of the multiphase fluid flowing through the flow pipe and U-bend are measured. A total flow rate of the multiphase fluid is determined at least based on the measured differential pressures. In some cases, flow rates of each of the phases of the multiphase fluid can be determined at least based on the measured differential pressures.
1. A system comprising:
a U-bend configured to flow a multiphase fluid, the U-bend comprising:
a first conduit;
a second conduit, wherein a cross-sectional flow area of the first conduit is substantially the same as a cross-sectional flow area of the second conduit; and
a connecting conduit connecting the first conduit to the second conduit;
a third conduit configured to flow the multiphase fluid, the third conduit having a cross-sectional flow area that is different from the cross-sectional flow area of the first conduit;
a first bend connecting the third conduit to the first conduit;
a fourth conduit configured to flow the multiphase fluid, the fourth conduit parallel to and in-line with the third conduit, the fourth conduit having a cross-sectional flow area that is substantially the same as the cross-sectional flow area of the third conduit;
a second bend connecting the fourth conduit to the second conduit;
a first differential pressure sensor coupled to the third conduit and to the first conduit, wherein the first differential pressure sensor is configured to measure a first differential pressure of the multiphase fluid across the first bend;
a second differential pressure sensor coupled to the second conduit and to the fourth conduit, wherein the second differential pressure sensor is configured to measure a second differential pressure of the multiphase fluid across the second bend; and
a computer, comprising:
a processor communicatively coupled to the first differential pressure sensor and to the second differential pressure sensor; and
a computer-readable storage medium coupled to the processor and storing programming instructions for execution by the processor, the programming instructions instructing the processor to perform operations comprising:
receiving a first differential pressure signal from the first differential pressure sensor, the first differential pressure signal representing the first differential pressure of the multiphase fluid;
receiving a second differential pressure signal from the second differential pressure sensor, the second differential pressure signal representing the second differential pressure of the multiphase fluid;
receiving, as input, a mixture density of the multiphase fluid; and
determining a total flow rate of the multiphase fluid at least based on the first differential pressure, the second differential pressure, and the mixture density of the multiphase fluid.
2. The system of claim 1 , wherein the first differential pressure sensor is coupled to the third conduit at a first location and to the first conduit at a second location, and the first location and the second location are separated by a specified height with respect to gravity.
3. The system of claim 2 , wherein the second differential pressure sensor is coupled to the second conduit at a third location and to the fourth conduit at a fourth location, and the third location and the second location are separated by the specified height with respect to gravity.
4. The system of claim 3 , wherein the total flow rate of the multiphase fluid is determined as a first total mass flow rate of the multiphase fluid at least based on a first differential pressure equation:
m T1 =C d1 ×ε 1 ×K 1 ×√{square root over (2×ρ×(Δ P 1 −ρ×g×h ))},
wherein m T1 is the first total mass flow rate of the multiphase fluid, C d1 is a first discharge coefficient, ε 1 is a first expansion factor, K 1 is a first fixed geometry factor proportional to the cross-sectional flow area of the first conduit, ΔP 1 is the first differential pressure, ρ is the mixture density of the multiphase fluid, g is an acceleration due to gravity, and h is the specified height.
5. The system of claim 4 , wherein the total flow rate of the multiphase fluid is determined as a second total mass flow rate of the multiphase fluid at least based on a second differential pressure equation:
m T2 =C d2 ×ε 2 ×K 2 ×√{square root over (2×ρ×(Δ P 2 +ρ×g×h ))},
wherein m T2 is the second total mass flow rate of the multiphase fluid, C d2 is a second discharge coefficient, ε 2 is a second expansion factor, K 2 is a second fixed geometry factor proportional to the cross-sectional flow area of the fourth conduit, ΔP 2 is the second differential pressure, ρ is the mixture density of the multiphase fluid, g is the acceleration due to gravity, and h is the specified height.
6. The system of claim 5 , wherein the operations performed by the processor comprise comparing the first total mass flow rate of the multiphase fluid and the second total mass flow rate of the multiphase fluid to determine an adjustment of the first discharge coefficient (C d1 ) or an adjustment of the second discharge coefficient (C d2 ).
7. The system of claim 6 , wherein the first total mass flow rate (m T1 ) is equal to the second total mass flow rate (m T2 ), the mixture density of the multiphase fluid is a first mixture density of the multiphase fluid, and the operations performed by the processor comprise determining a second mixture density of the multiphase fluid at least based on a combined differential pressure equation:
ρ
2
=
Z
×
Δ
P
1
-
Δ
P
2
g
×
(
1
+
Z
)
,
wherein ρ 2 is the second mixture density of the multiphase fluid, ΔP 1 is the first differential pressure, ΔP 2 is the second differential pressure, g is the acceleration due to gravity, and Z is defined by:
Z
=
(
C
d
1
×
ε
1
×
K
1
C
d
2
×
ε
2
×
K
2
)
2
,
wherein C d1 is the first discharge coefficient, ε 1 is the first expansion factor, K 1 is the first fixed geometry factor, C d2 is the second discharge coefficient, ε 2 is the second expansion factor, and K 2 is the second fixed geometry factor.
8. The system of claim 7 , wherein the first differential pressure sensor is a first circumferential pressure sensor that spans an entire circumference of the first conduit.
9. The system of claim 8 , wherein the second differential pressure sensor is a second circumferential pressure sensor that spans an entire circumference of the second conduit.
10. The system of claim 9 , wherein each of the first bend and the second bend are 90-degree angled bends.
11. A method comprising:
flowing a multiphase fluid from a flow pipe to a U-bend, wherein the multiphase fluid comprises a gas phase, an aqueous phase, and an oil phase, and the U-bend comprises:
a first conduit;
a second conduit; and
a connecting conduit connecting the first conduit to the second conduit, wherein the multiphase fluid flowing through the U-bend flows into the first conduit, through the connecting conduit, and out of the second conduit;
flowing the multiphase fluid from the U-bend to the flow pipe, wherein:
the flow pipe comprises a third conduit and a fourth conduit;
the third conduit of the flow pipe is connected to the first conduit of the U-bend by a first bend;
the fourth conduit of the flow pipe is connected to the second conduit of the U-bend by a second bend;
flowing the multiphase fluid from the flow pipe to the U-bend comprises flowing the multiphase fluid from the third conduit of the flow pipe through the first bend to the first conduit of the U-bend; and
flowing the multiphase fluid from the U-bend to the flow pipe comprises flowing the multiphase fluid from the second conduit of the U-bend through the second bend to the fourth conduit of the flow pipe;
measuring a first differential pressure of the multiphase fluid between a first location on the third conduit of the flow pipe and a second location on the first conduit of the U-bend, wherein the first location and the second location are separated by a specified height along the first conduit of the U-bend;
measuring a second differential pressure of the multiphase fluid between a third location on the second conduit of the U-bend and a fourth location on the fourth conduit of the flow pipe, wherein the third location and the fourth location are separated by the specified height along the second conduit of the U-bend; and
determining a total flow rate of the multiphase fluid at least based on the first differential pressure, the second differential pressure, and a mixture density of the multiphase fluid.
12. The method of claim 11 , wherein the total flow rate of the multiphase fluid is determined as a first total mass flow rate of the multiphase fluid at least based on a first differential pressure equation:
m T1 =C d1 ×ε 1 ×K 1 ×√{square root over (2×ρ×(Δ P 1 −ρ×g×h ))},
wherein m T1 is the first total mass flow rate of the multiphase fluid, C d1 is a first discharge coefficient, ε 1 is a first expansion factor, K 1 is a first fixed geometry factor proportional to the cross-sectional flow area of the first conduit, ΔP 1 is the first differential pressure, ρ is the mixture density of the multiphase fluid, g is an acceleration due to gravity, and h is the specified height.
13. The method of claim 12 , wherein the total flow rate of the multiphase fluid is determined as a second total mass flow rate of the multiphase fluid at least based on a second differential pressure equation:
m T2 =C d2 ×ε 2 ×K 1 ×√{square root over (2×ρ×(Δ P 2 −ρ×g×h ))},
wherein m T2 is the second total mass flow rate of the multiphase fluid, C d2 is a second discharge coefficient, ε 2 is a second expansion factor, K 2 is a second fixed geometry factor proportional to the cross-sectional flow area of the fourth conduit, ΔP 2 is the second differential pressure, ρ is the mixture density of the multiphase fluid, g is the acceleration due to gravity, and h is the specified height.
14. The method of claim 13 , wherein the first total mass flow rate (m T1 ) is equal to the second total mass flow rate (m T2 ), the mixture density of the multiphase fluid is a first mixture density of the multiphase fluid, and the operations performed by the processor comprise determining a second mixture density of the multiphase fluid at least based on a combined differential pressure equation:
ρ
2
=
Z
×
Δ
P
1
-
Δ
P
2
g
×
(
1
+
Z
)
,
wherein ρ 2 is the second mixture density of the multiphase fluid, ΔP 1 is the first differential pressure, ΔP 2 is the second differential pressure, g is the acceleration due to gravity, and Z is defined by:
Z
=
(
C
d
1
×
ε
1
×
K
1
C
d
2
×
ε
2
×
K
2
)
2
,
wherein C d1 is the first discharge coefficient, ε 1 is the first expansion factor, K 1 is the first fixed geometry factor, C d2 is the second discharge coefficient, ε 2 is the second expansion factor, and K 2 is the second fixed geometry factor.
15. The method of claim 14 , comprising comparing the first total mass flow rate of the multiphase fluid and the second total mass flow rate of the multiphase fluid to determine an adjustment of the first discharge coefficient (C d1 ) or an adjustment of the second discharge coefficient (C d2 ).
16. The method of claim 15 , wherein the first differential pressure is measured by a first differential pressure sensor coupled to the third conduit of the flow pipe at the first location and coupled to the first conduit of the U-bend at the second location, the second differential pressure is measured by a second differential pressure sensor coupled to the second conduit of the U-bend at the third location and coupled to the fourth conduit of the flow pipe at the fourth location.
17. The method of claim 16 , wherein the first differential pressure sensor is a first circumferential pressure sensor that spans an entire circumference of the first conduit.
18. The method of claim 17 , wherein the second differential pressure sensor is a second circumferential pressure sensor that spans an entire circumference of the second conduit.
19. The method of claim 18 , wherein each of the first bend and the second bend are 90-degree angled bends.