Measuring density 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 mixture density of the multiphase fluid is determined at least based on the measured differential pressures.
1. A system comprising:
a U-bend configured to flow a multiphase fluid, the multiphase fluid comprising a gas phase, an aqueous phase, and an oil phase, the U-bend comprising:
a first conduit;
a second conduit; and
a connecting conduit connecting the first conduit to the second conduit, wherein each of the first conduit and the second conduit have substantially the same cross-sectional flow area for the multiphase fluid flowing through the U-bend, and the multiphase fluid flowing through the U-bend flows into the first conduit, through the connecting conduit, and out of the second conduit;
a first differential pressure sensor coupled to the first conduit, wherein the first differential pressure sensor is configured to measure a first differential pressure of the multiphase fluid flowing through the U-bend across a specified differential pressure height along the first conduit;
a second differential pressure sensor coupled to the second conduit, wherein the second differential pressure sensor is configured to measure a second differential pressure of the multiphase fluid flowing through the U-bend across the specified differential pressure height along the second conduit; 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; and
determining a mixture density of the multiphase fluid at least based on the specified differential pressure height and a difference between the first differential pressure and the second differential pressure of the multiphase fluid; and
determining a total mass flow rate of the multiphase fluid by:
m T =C d ×ε×K ×√{square root over (2×ρ×(Δ P−k f ×ΔP f ))},
wherein m T the total mass flow rate of the multiphase fluid, C d is a discharge coefficient, ε is an expansion factor, K is a fixed geometry factor related to a cross-sectional flow area of the U-bend, ρ is the mixture density of the multiphase fluid, ΔP is the first differential pressure or the second differential pressure of the multiphase fluid, k f is a geometry-based correction factor for friction, and ΔP f is frictional pressure loss.
2. The system of claim 1 , wherein the mixture density of the multiphase fluid is determined by:
ρ
=
Δ
P
1
-
Δ
P
2
2
×
g
×
h
,
wherein ρ is the mixture density of the multiphase fluid, ΔP 1 is the first differential pressure of the multiphase fluid, ΔP 2 is the second differential pressure of the multiphase fluid, g is an acceleration due to gravity, and h is the specified differential pressure height.
3. The system of claim 2 , wherein the first differential pressure sensor is a first circumferential pressure sensor that spans an entire circumference of the first conduit.
4. The system of claim 3 , wherein the second differential pressure sensor is a second circumferential pressure sensor that spans an entire circumference of the second conduit.
5. The system of claim 4 , wherein the connecting conduit is perpendicular to the first conduit and to the second conduit.
6. The system of claim 5 , wherein a longitudinal length of the first conduit is substantially the same as a longitudinal length of the second conduit.
7. The system of claim 6 , wherein the operations performed by the processor comprise:
receiving, as input, a gas phase volume fraction of the multiphase fluid;
receiving, as input, a gas phase density of a gas phase of the multiphase fluid;
receiving, as input, an aqueous phase density of an aqueous phase of the multiphase fluid;
receiving, as input, an oil phase density of an oil phase of the multiphase fluid; and
determining an aqueous phase volume fraction of the multiphase fluid by:
ρ=ρ g ×α g +ρ a ×α a +ρ o ×(1−α g −α a ),
wherein ρ is the mixture density of the multiphase fluid, α g is the gas phase volume fraction of the multiphase fluid, α g is the aqueous phase volume fraction of the multiphase fluid, ρ g is the gas phase density of the gas phase of the multiphase fluid, ρ a is the aqueous phase density of the aqueous phase of the multiphase fluid, and ρ o is the oil phase density of the oil phase of the multiphase fluid.
8. The system of claim 6 , wherein the operations performed by the processor comprise:
receiving, as input, an aqueous phase volume fraction of the multiphase fluid;
receiving, as input, a gas phase density of a gas phase of the multiphase fluid;
receiving, as input, an aqueous phase density of an aqueous phase of the multiphase fluid;
receiving, as input, an oil phase density of an oil phase of the multiphase fluid; and
determining a gas phase volume fraction of the multiphase fluid by:
ρ=ρ g ×α g +ρ a ×α a +ρ o ×(1−α g −α a ),
wherein ρ is the mixture density of the multiphase fluid, α g is the gas phase volume fraction of the multiphase fluid, α a is the aqueous phase volume fraction of the multiphase fluid, ρ g is the gas phase density of the gas phase of the multiphase fluid, ρ a is the aqueous phase density of the aqueous phase of the multiphase fluid, and ρ o is the oil phase density of the oil phase of the multiphase fluid.
9. A method comprising:
flowing a multiphase fluid through 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 each of the first conduit and the second conduit have substantially the same cross-sectional flow area for the multiphase fluid flowing through the U-bend, and the multiphase fluid flowing through the U-bend flows into the first conduit, through the connecting conduit, and out of the second conduit;
measuring a first differential pressure of the multiphase fluid across a specified differential pressure height along the first conduit;
measuring a second differential pressure of the multiphase fluid across the specified differential pressure height along the second conduit;
determining a mixture density of the multiphase fluid at least based on the specified differential pressure height and a difference between the first differential pressure and the second differential pressure of the multiphase fluid; and
determining a total mass flow rate of the multiphase fluid at least based on a discharge coefficient, an expansion factor, a fixed geometry factor related to a cross-sectional flow area of the U-bend, the determined mixture density of the multiphase fluid, the first differential pressure or the second differential pressure, a geometry-based correction factor for friction, and a frictional pressure loss.
10. The method of claim 9 , wherein the mixture density of the multiphase fluid is determined by:
ρ
=
Δ
P
1
-
Δ
P
2
2
×
g
×
h
,
wherein ρ is the mixture density of the multiphase fluid, ΔP 1 is the first differential pressure of the multiphase fluid, ΔP 2 is the second differential pressure of the multiphase fluid, g is an acceleration due to gravity, and h is the specified differential pressure height.
11. The method of claim 10 , wherein the total mass flow rate of the multiphase fluid is determined by:
m T =C d ×ε×K ×√{square root over (2×ρ×(2×ρ×(Δ P−k f ×ΔP f ))},
wherein m T is the total mass flow rate of the multiphase fluid, C d is the discharge coefficient, ε is the expansion factor, K is the fixed geometry factor related to a cross-sectional flow area of the U-bend, ρ is the mixture density of the multiphase fluid, ΔP is the first differential pressure or the second differential pressure of the multiphase fluid, k f is the geometry-based correction factor for friction, and ΔP f is the frictional pressure loss.
12. The method of claim 10 , comprising determining an aqueous phase volume fraction of the multiphase fluid by:
ρ=ρ g ×α g +ρ a ×α a +ρ o ×(1−α g −α a ),
wherein ρ is the mixture density of the multiphase fluid, α a is a gas phase volume fraction of the multiphase fluid, α a is an aqueous phase volume fraction of the multiphase fluid, ρ g is a gas phase density of the gas phase of the multiphase fluid, ρ a is an aqueous phase density of the aqueous phase of the multiphase fluid, and ρ o is an oil phase density of the oil phase of the multiphase fluid.
13. The method of claim 10 , comprising determining a gas phase volume fraction of the multiphase fluid by:
ρ=ρ g ×α g +ρ a ×α a +ρ o ×(1−α g −α a ),
wherein ρ is the mixture density of the multiphase fluid, α g is a gas phase volume fraction of the multiphase fluid, α a is an aqueous phase volume fraction of the multiphase fluid, ρ g is a gas phase density of the gas phase of the multiphase fluid, ρ a is an aqueous phase density of the aqueous phase of the multiphase fluid, and ρ o is an oil phase density of the oil phase of the multiphase fluid.
14. The method of claim 13 , wherein the first differential pressure of the multiphase fluid is measured by a first differential pressure sensor coupled to the first conduit.
15. The method of claim 14 , wherein the second differential pressure of the multiphase fluid is measured by a second differential pressure sensor coupled to the second conduit.
16. The method of claim 15 , wherein the first differential pressure sensor is a first circumferential pressure sensor that spans an entire circumference of the first conduit.
17. The method of claim 16 , wherein the second differential pressure sensor is a second circumferential pressure sensor that spans an entire circumference of the second conduit.