Measurement of density of multiphase fluids

Abstract

A multi-phase fluid flows from the flow tube to the U-shaped elbow. Several pressure differences of the multi-phase fluid flowing through the flow tube and the U-shaped elbow are measured. A mixing density of the multiphase fluid is determined based at least on the measured pressure difference.

Description

[0001] Priority claim

[0002] This application claims priority to U.S. patent application No. 17 / 868,545, filed on July 19, 2022, the entire contents of which are incorporated herein by reference. Technical Field

[0003] The present disclosure relates to flow characterization of multiphase fluids. Background Art

[0004] Multiphase fluid is a mixture of multiple material phases. Multiphase fluid can be heterogeneous, and therefore can show complex flow characteristics. The flow characteristics of multiphase fluid in a conduit may for example depend on various factors, such as operating conditions (pressure and temperature), the composition of each phase (and then physical properties such as density and viscosity), the flow of each phase and the physical properties (such as diameter and direction) of the conduit through which the multiphase fluid flows. The characterization of multiphase fluid flow may be difficult sometimes. In some cases, for example in oil and gas operations, it may be important to accurately measure the flow of multiphase fluid mixtures (such as crude oil, natural gas and brine). Summary of the invention

[0005] The present disclosure describes technology related to measuring the density of a multiphase fluid. Certain aspects of the subject matter can be implemented as a system. The system includes a U-bend, a first differential pressure sensor, a second differential pressure sensor, and a computer. The U-bend is configured to circulate a multiphase fluid. The U-bend includes a first conduit, a second conduit, and a connecting conduit. The connecting conduit connects the first conduit to the second conduit. Each of the first conduit and the second conduit has substantially the same cross-sectional flow area for the multiphase fluid flowing through the U-bend. The multiphase fluid flowing through the U-bend flows into the first conduit, flows through the connecting conduit, and then flows out of the second conduit. The multiphase fluid includes a gas phase, an aqueous phase, and an oil phase. A first differential pressure sensor is coupled to the first conduit. The first differential pressure sensor is configured to measure a first differential pressure of the multiphase fluid flowing through the U-bend along the first conduit across a specified differential pressure height. The second differential pressure sensor is coupled to the second conduit. The second differential pressure sensor is configured to measure a second differential pressure of the multiphase fluid flowing through the U-bend along the second conduit across a specified differential pressure height. The computer includes a processor and a computer-readable storage medium. The processor is communicatively coupled to the first differential pressure sensor and the second differential pressure sensor. The computer readable storage medium is coupled to the processor and stores programming instructions for execution by the processor. The programming instructions instruct the processor to perform operations. The operations include: receiving a first differential pressure signal from the first differential pressure sensor. The first differential pressure signal represents a first differential pressure of the multiphase fluid. The operations include: receiving a second differential pressure signal from the second differential pressure sensor. The second differential pressure signal represents a second differential pressure of the multiphase fluid. The operations include: determining a mixed density of the multiphase fluid based at least on a specified differential pressure height and a difference between the first differential pressure and the second differential pressure of the multiphase fluid.

[0006] This aspect and other aspects may include one or more of the following features.

[0007] In some embodiments, the mixed density of the multiphase fluid is determined by the following formula:

[0008]

[0009] Where ρ is the mixed density of the multiphase fluid, ΔP1 is the first pressure difference of the multiphase fluid, ΔP2 is the second pressure difference of the multiphase fluid, g is the acceleration caused by gravity, and h is the specified pressure difference height.

[0010] In some embodiments, the operations performed by the processor include determining the total mass flow rate of the multiphase fluid by the following formula:

[0011]

[0012] Where m T is the total mass flow rate of the multiphase fluid, C dis the flow coefficient, ε is the expansion coefficient, K is the fixed geometric coefficient related to the cross-sectional flow area of ​​the U-bend, ρ is the mixed density of the multiphase fluid, ΔP is the first pressure difference or the second pressure difference of the multiphase fluid, k f is a correction factor for friction based on geometry, and ΔP f is the friction pressure loss.

[0013] In some embodiments, the first differential pressure sensor is a first circumferential pressure sensor that spans the entire circumference of the first conduit. In some embodiments, the second differential pressure sensor is a second circumferential pressure sensor that spans the entire circumference of the second conduit. In some embodiments, the connecting conduit is perpendicular to the first conduit and the second conduit.

[0014] In some embodiments, the operations performed by the processor include receiving as input a gas phase volume fraction of a multiphase fluid. In some embodiments, the operations performed by the processor include receiving as input a gas phase density of a gas phase of a multiphase fluid. In some embodiments, the operations performed by the processor include receiving as input a water phase density of a water phase of a multiphase fluid. In some embodiments, the operations performed by the processor include receiving as input an oil phase density of an oil phase of a multiphase fluid. In some embodiments, the operations performed by the processor include determining the water phase volume fraction of a multiphase fluid by the following formula:

[0015] ρ=ρ g ×α g +ρ a ×α a +ρ o ×(1-α g -α a ),

[0016] where ρ is the mixed density of the multiphase fluid, α g is the gas phase volume fraction of the multiphase fluid, α a is the volume fraction of water phase in the multiphase fluid, ρ g is the gas phase density of the multiphase fluid, ρ a is the water phase density of the multiphase fluid, and ρ o is the oil phase density of the oil phase of the multiphase fluid.

[0017] In some embodiments, the operations performed by the processor include receiving as input a water phase volume fraction of a multiphase fluid. In some embodiments, the operations performed by the processor include receiving as input a gas phase density of a gas phase of the multiphase fluid. In some embodiments, the operations performed by the processor include receiving as input a water phase density of a water phase of the multiphase fluid. In some embodiments, the operations performed by the processor include receiving as input an oil phase density of an oil phase of the multiphase fluid. In some embodiments, the operations performed by the processor include determining the gas phase volume fraction of the multiphase fluid by the following formula:

[0018] ρ=ρ g ×α g +ρ a ×α a +ρ o ×(1-α g -α a ),

[0019] where ρ is the mixed density of the multiphase fluid, α g is the gas phase volume fraction of the multiphase fluid, α a is the volume fraction of water phase in the multiphase fluid, ρ g is the gas phase density of the multiphase fluid, ρ a is the water phase density of the multiphase fluid, and ρ o is the oil phase density of the oil phase of the multiphase fluid.

[0020] Certain aspects of the subject matter can be implemented as methods. A multiphase fluid flows through a U-bend. The multiphase fluid includes a gas phase, a water phase, and an oil phase. The U-bend includes a first conduit, a second conduit, and a connecting conduit. The connecting conduit connects the first conduit to the second conduit. Each of the first conduit and the second conduit has substantially the same cross-sectional flow area for the multiphase fluid flowing through the U-bend. The multiphase fluid flowing through the U-bend flows into the first conduit, flows through the connecting conduit, and then flows out of the second conduit. A first pressure difference of the multiphase fluid across a specified pressure difference height along the first conduit is measured. A second pressure difference of the multiphase fluid across a specified pressure difference height along the second conduit is measured. The mixed density of the multiphase fluid is determined based at least on the specified pressure difference height and the difference between the first pressure difference and the second pressure difference of the multiphase fluid.

[0021] This aspect and other aspects may include one or more of the following features.

[0022] In some embodiments, the mixed density of the multiphase fluid is determined by the following formula:

[0023]

[0024] Where ρ is the mixed density of the multiphase fluid, ΔP1 is the first pressure difference of the multiphase fluid, ΔP2 is the second pressure difference of the multiphase fluid, g is the acceleration caused by gravity, and h is the specified pressure difference height.

[0025] In some embodiments, the total mass flow rate of the multiphase fluid is determined by the following formula:

[0026]

[0027] Where m T is the total mass flow rate of the multiphase fluid, C d is the flow coefficient, ε is the expansion coefficient, K is the fixed geometric coefficient related to the cross-sectional flow area of ​​the U-bend, ρ is the mixed density of the multiphase fluid, ΔP is the first pressure difference or the second pressure difference of the multiphase fluid, k f is a correction factor for friction based on geometry, and ΔP f is the friction pressure loss.

[0028] In some embodiments, the water phase volume fraction of a multiphase fluid is determined by the following formula:

[0029] ρ=ρ g ×α g +ρ a ×α a +ρ o ×(1-α g -α a ),

[0030] where ρ is the mixed density of the multiphase fluid, α g is the gas phase volume fraction of the multiphase fluid, α a is the volume fraction of water phase in the multiphase fluid, ρ g is the gas phase density of the multiphase fluid, ρ a is the water phase density of the multiphase fluid, and ρ o is the oil phase density of the oil phase of the multiphase fluid.

[0031] In some embodiments, the gas phase volume fraction of the multiphase fluid is determined by the following formula:

[0032] ρ=ρ g ×α g +ρ a ×α a +ρ o ×(1-α g -α a ),

[0033] where ρ is the mixed density of the multiphase fluid, α g is the gas phase volume fraction of the multiphase fluid, α a is the volume fraction of water phase in the multiphase fluid, ρg is the gas phase density of the multiphase fluid, ρ a is the water phase density of the multiphase fluid, and ρ o is the oil phase density of the oil phase of the multiphase fluid.

[0034] In some embodiments, a first differential pressure of the multiphase fluid is measured by a first differential pressure sensor coupled to the first conduit. In some embodiments, a second differential pressure of the multiphase fluid is measured by a second differential pressure sensor coupled to the second conduit. In some embodiments, the first differential pressure sensor is a first circumferential pressure sensor that spans the entire circumference of the first conduit. In some embodiments, the second differential pressure sensor is a second circumferential pressure sensor that spans the entire circumference of the second conduit.

[0035] The details of one or more embodiments of the subject matter of the present disclosure are set forth in the accompanying drawings and the description. Other features, aspects, and advantages of the subject matter will become apparent from the description, drawings, and claims. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1A is a schematic diagram of an example apparatus that may be used to measure the density of a multiphase fluid.

[0037] Figure 1B is a schematic diagram of an example apparatus that may be used to measure the density of a multiphase fluid.

[0038] Figure 1C is a schematic diagram of an example apparatus that may be used to measure the density of a multiphase fluid.

[0039] Figure 1D is a schematic diagram of an example apparatus that may be used to measure the density of a multiphase fluid.

[0040] Figure 1E is a schematic diagram of an example apparatus that may be used to measure the flow rate of a multiphase fluid.

[0041] Figure 1F is a schematic diagram of an example apparatus that may be used to measure the flow rate of a multiphase fluid.

[0042] Figure 1G is a schematic diagram of an example apparatus that can be used to measure the water-to-liquid ratio of a multiphase fluid.

[0043] Figure 1H is a schematic diagram of an example apparatus that can be used to measure the density and flow of a multiphase fluid.

[0044] Fig. 1I is a schematic diagram of an example apparatus that can be used to measure density, flow rate, and water-to-liquid ratio of a multiphase fluid.

[0045] Figure 1Jis a schematic diagram of an example apparatus that can be used to measure density, flow rate, and water-to-liquid ratio of a multiphase fluid.

[0046] Figure 2A are schematic diagrams depicting various example pressure tap arrangements.

[0047] Figure 2B are schematic diagrams depicting various example tube arrangements.

[0048] Figure 2C are schematic diagrams depicting various example tube arrangements.

[0049] Figure 2D are schematic diagrams depicting various example tube arrangements.

[0050] Figure 2E are schematic diagrams depicting various example tube arrangements.

[0051] Figure 2F are schematic diagrams depicting various example sensor arrangements.

[0052] Figure 3A is a flow chart depicting an example multiphase fluid flow model.

[0053] Figure 3B is a flow chart depicting an example multiphase fluid flow model for determining density.

[0054] Figure 3C is a flow chart depicting an example multiphase fluid flow model for determining density.

[0055] Figure 3D is a flow chart depicting an example multiphase fluid flow model for determining density.

[0056] Figure 3E is a flow chart depicting an example multiphase fluid flow model for determining flow rates.

[0057] Figure 3F is a flow chart depicting an example multiphase fluid flow model.

[0058] Figure 3G is a flow chart depicting an example multiphase fluid flow model.

[0059] Figure 4 is a flow chart of an example method for measuring the density of a multiphase fluid.

[0060] Figure 5 is a flow chart of an example method for measuring flow of a multiphase fluid.

[0061] Figure 6 is a flow chart of an example method for measuring density and flow of a multiphase fluid.

[0062] Figure 7 is a block diagram of an example computer system. DETAILED DESCRIPTION

[0063] The present disclosure describes density measurement of multiphase fluids. The device described herein can be used to accurately measure the mixed density of a multiphase fluid. The mixed density can then be used to determine other properties of the multiphase fluid, such as based on other known information. The device includes a plurality of connected conduits, the conduit including an elbow (or L-shaped elbow) and a U-shaped elbow. The device includes a plurality of pressure sensors for measuring the pressure difference across each position pair of the flowing multiphase fluid. The measured pressure difference can be compared and manipulated to determine the mixed density of the flowing multiphase fluid.

[0064] The subject matter described in the present disclosure can be implemented in specific embodiments to achieve one or more of the following advantages. The apparatus, system and method described herein can be implemented independently of the use of a radioactive energy source (such as gamma ray attenuation), because the use of a radioactive energy source may be dangerous. The apparatus, system and method described herein can be implemented to accurately determine the mixed density of a multiphase fluid, even in the case where the gas phase is present in a non-negligible amount. The apparatus, system and method described herein can be implemented to accurately determine the mixed density of a multiphase fluid, while taking into account the friction and shear pressure losses of the multiphase fluid. The apparatus, system and method described herein can be implemented to accurately determine the mixed density of a multiphase fluid, even in complex flow states such as slug flow, piston flow and annular flow states. The apparatus, system and method described herein can be implemented to accurately determine the mixed density of a multiphase fluid, even in the case where there is slip (i.e., flow velocity difference) between the gas phase and the liquid phase. The devices, systems and methods described herein can utilize tube geometry (and associated fluid dynamics) to measure relatively simple (and more direct) flow / fluid properties (such as differential pressure) rather than relatively complex (and more indirect) fluid / flow properties (such as electromagnetic (spectral) absorption / transmission) to accurately determine the mixed density of a multiphase fluid. The devices, systems and methods described herein can be implemented in conjunction with other flow metering components to supplement and / or enhance the accuracy of multiphase fluid flow characterization.

[0065] Figure 1A An apparatus 100A is depicted that can be used to measure the density of a multiphase fluid 101. The multiphase fluid 101 can be a 2-phase or 3-phase fluid. For example, the multiphase fluid 101 can include a gas phase 101a and a liquid phase 101b. In some embodiments, the liquid phase 101b includes an aqueous phase 101b' and an oil phase 101b". For example, the multiphase fluid 101 can include a gas phase 101a, an aqueous phase 101b', and an oil phase 101b". As an example, the multiphase fluid 101 can include hydrocarbon gas, hydrocarbon liquid, and water (or brine).

[0066] The device 100A includes a U-bend 102, which is configured to circulate a multiphase fluid 101. The U-bend 102 includes a first conduit 102a, a second conduit 102b, and a connecting conduit 102c. In some embodiments, the second conduit 102b is parallel to the first conduit 102a. In some embodiments, the longitudinal length of the first conduit 102a is substantially the same as the longitudinal length of the second conduit 102b, and the cross-sectional area of ​​the first conduit 102a is substantially the same as the cross-sectional area of ​​the second conduit 102b, so that the friction force component of the pressure drop experienced when the multiphase fluid 101 flows through these components (102a, 102b) of the U-bend 102 is substantially the same for each component. For example, each of the first conduit 102a and the second conduit 102b has substantially the same inner diameter d. The connecting conduit 102c connects the first conduit 102a to the second conduit 102b. In some embodiments, the first conduit 102a, the second conduit 102b and the connecting conduit 102c are integral, so that the U-shaped bend 102 is a single whole, rather than separate and connected together to form the parts of the U-shaped bend 102. In some embodiments, the connecting conduit 102c is perpendicular to the first conduit 102a and the second conduit 102b. The multiphase fluid 101 flowing through the U-shaped bend 102 flows into the first conduit 102a, flows through the connecting conduit 102c, and then flows out from the second conduit 102b. In some embodiments, each of the first conduit 102a, the second conduit 102b and the connecting conduit 102c is made of the same material, so that the friction force experienced by the multiphase fluid 101 flowing through each of the first conduit 102a, the second conduit 102b and the connecting conduit 102c is substantially the same. In some embodiments, the connecting conduit 102b is connected to the first conduit 102a by the first curved elbow 103a. In some embodiments, the connecting conduit 102c is connected to the second conduit 102b by a second curved elbow 103b. In some embodiments, the first conduit 102a, the second conduit 102b, the connecting conduit 102c, the first curved elbow 103a, and the second curved elbow 103b are integral, such that the U-bend 102 is a single unitary entity, rather than separate parts that are coupled together to form the U-bend 102. The first curved elbow 103a and the second curved elbow 103b can be made of the same material as the first conduit 102a, the second conduit 102b, and the connecting conduit 102c, such that the friction experienced by the multiphase fluid 101 flowing through each of the components of the U-bend 102 is substantially the same.

[0067] The device 100A includes a first pair of pressure sensors 104a, 104b. The pressure sensors 104a, 104b are connected to the first conduit 102a via pressure ports 105a, 105b, respectively. The pressure sensors 104a, 104b are cooperatively configured to measure a first pressure difference of the multiphase fluid 101 flowing through the U-bend 102. The pressure ports 105a, 105b to which the pressure sensors 104a, 104b are respectively connected are spaced apart along the first conduit 102a by a specified pressure difference height h. The device 100A includes a second pair of pressure sensors 104c, 104d. The pressure sensors 104c, 104d are connected to the second conduit 102b via pressure ports 105c, 105d. The pressure sensors 104c, 104d are cooperatively configured to measure a second pressure difference of the multiphase fluid 101 flowing through the U-bend 102. The pressure ports 105c, 105d to which the pressure sensors 104c, 104d are respectively coupled are separated by the same specified differential pressure height h along the second conduit 102b. In other words, the height difference between the pressure ports 105a, 105b of the pressure sensors 104a, 104b is the same as the height difference between the pressure ports 105c, 105d of the pressure sensors 104c, 104d, so that the friction force component of the pressure drop experienced by the multiphase fluid 101 flowing through the first conduit 102a (measured by the pressure sensors 104a, 104b) and flowing through the second conduit 102b (measured by the pressure sensors 104c, 104d) is substantially the same. In some embodiments, the first pair of pressure sensors 104a, 104b is replaced by a first differential pressure sensor coupled to the first conduit 102a via the pressure ports 105a, 105b. In some embodiments, the second pair of pressure sensors 104c, 104d is replaced by a second differential pressure sensor coupled to the second conduit 102b via pressure ports 105c, 105d.

[0068] like Figure 1A As shown, the U-bend 102 can be connected to a flow tube 150 that circulates the multiphase fluid 101. The flow tube 150 includes a first tube 150a and a second tube 150b. The terms "tube" and "conduit" are synonymous. The term "tube" is used in relation to the flow tube 150, and the term "conduit" is used in relation to the U-bend 102, just for consistency / clarity and to avoid confusion. In some embodiments, the U-bend 102 is connected to the flow tube 150 via corner bends 153a, 153b. For example, the first conduit 102a of the U-bend 102 is connected to the first tube 150a of the flow tube 150 via the first corner bend 153a. For example, the second conduit 102b of the U-bend 102 is connected to the second tube 150b of the flow tube 150 via the second corner bend 153b. In some embodiments, as Figure 1A As shown, the corner bends 153a, 153b are 90 degree corner bends. Figure 1A153a, 153b may have different angles, such as in the range from 30 to 150 degrees. In some embodiments, the first conduit 102a, the second conduit 102b, the connecting conduit 102c, the first curved bend 103a, the second curved bend 103b, the first corner bend 153a, the second corner bend 153b and the flow tube 150 are integral, so that the U-bend 102 and the flow tube 150 form a single entity, rather than separate and coupled parts. In some embodiments, the corner bends 153a, 153b are replaced by curved bends (similar to the curved bends 103a, 103b).

[0069] In some embodiments, the inner diameter (d) of the first conduit 102a and the second conduit 102b is different from the inner diameter (D) of the flow tube 150. The change in the cross-sectional flow area between the flow tube 150 and the U-bend 102 can ensure that the pressure difference of the multiphase fluid 101 flowing through the corner bends 153a, 153b depends mainly on the total flow rate of the multiphase fluid 101, rather than on other factors such as friction pressure loss. In some embodiments, the inner diameter (d) of the first conduit 102a and the second conduit 102b can be in the range of half the inner diameter (D) of the flow tube 150 to twice the inner diameter (2D) of the flow tube 150 (i.e., D / 2≤d≤2D).

[0070] In some embodiments, each of the pressure sensors (104a, 104b, 104c, 104d) is at least a threshold distance from the nearest elbow. The threshold distance is long enough to allow the flow of the multiphase fluid 101 to fully develop after the flow disturbance caused by the upstream elbow, or long enough to allow the flow of the multiphase fluid 101 to remain fully developed before approaching the downstream elbow. Without being bound by theory, the sensing method (e.g., the application and / or purpose of the measurement) can determine where the sensor should be placed. For the devices and methods described herein, the threshold distance can be, for example, four times the inner diameter d (i.e., 4d). For example, if the inner diameter (d) of the U-bend 102 is 1 inch, the threshold distance is 4 inches. For example, the pressure port 105a to which the pressure sensor 104a is connected is located on the first conduit 102a, at least 4d away from the corner elbow 153a. For example, the pressure port 105b to which the pressure sensor 104b is connected is located on the first conduit 102a, at least 4d away from the curved elbow 103a. For example, the pressure port 105c to which the pressure sensor 104c is coupled is located on the second conduit 102b at least 4d away from the curved elbow 103b. For example, the pressure port 105d to which the pressure sensor 104d is coupled is located on the second conduit 102b at least 4d away from the corner elbow 153b.

[0071] like Figure 1AAs shown, the device 100A can be communicatively coupled to a computer 700. The computer 700 includes a processor 705 and a memory 707. The processor 705 can be communicatively coupled to the first pair of pressure sensors 104a, 104b (or first differential pressure sensor) and the second pair of pressure sensors 104c, 104d (or second differential pressure sensor). The memory 707 is coupled to the processor 705. The computer 700 is also shown in Figure 7 , which will be described in more detail later. The memory 707 stores programming instructions for execution by the processor 705. The programming instructions may instruct the processor 705 to perform various operations. The operations performed by the processor 705 may include receiving a first differential pressure signal from a first pair of pressure sensors 104a, 104b (or a first differential pressure sensor). The first differential pressure signal may represent a first differential pressure of the multiphase fluid 101 measured by the first pair of pressure sensors 104a, 104b (or a first differential pressure sensor). The operations performed by the processor 705 may include receiving a second differential pressure signal from a second pair of pressure sensors 104c, 104d (or a second differential pressure sensor). The second differential pressure signal may represent a second differential pressure of the multiphase fluid 101 measured by the pressure sensors 104c, 104d (or a second differential pressure sensor). The operations performed by the processor 705 may include determining the total density of the multiphase fluid 101 based at least on the difference between the first differential pressure of the multiphase fluid 101 and the second differential pressure and a specified differential pressure height h.

[0072] In the case where the first conduit 102a and the second conduit 102b are in a vertical orientation (relative to a reference horizontal plane, such as the ground), the differential pressure loss of the multiphase fluid 101 flowing through a vertical distance can be estimated by Equation 1:

[0073] ΔP=ρ×g×h v -ΔP f (1)

[0074] Where ΔP is the total pressure loss of the multiphase fluid 101, ρ is the apparent mixed density of the multiphase fluid 101, g is the acceleration caused by gravity, and h v is the vertical height difference between two reference points (such as the positions of pressure ports 105a, 105b or the positions of pressure ports 105c, 105d), and ΔP f is the pressure loss due to miscellaneous factors such as friction loss and multiphase shear. Therefore, the first pressure difference measured by the first pair of pressure sensors 104a, 104b can be estimated by equation 1a, while the second pressure difference measured by the second pair of pressure sensors 104c, 104d can be estimated by equation 1b:

[0075] ΔP1=ρ×g×h1+ΔP f1 (1a)

[0076] ΔP2=-ρ×g×h2+ΔP f2 (1b)

[0077] The apparent mixed density (ρ) of the multiphase fluid can be determined by obtaining the difference between the first pressure difference and the second pressure difference (ΔP1-ΔP2) and rearranging the resulting equation to solve for ρ. The difference between the first pressure difference and the second pressure difference is shown by Equation 2a:

[0078] ΔP1-ΔP2=ρ×g×h1+ΔP f1 +ρ×g×h2-ΔP f2 (2a)

[0079] Since the flow characteristics of the first conduit 102a and the second conduit 102b are substantially the same, ΔP f1 and ΔP f2 can be assumed to be essentially the same Therefore, Equation 2a can be rewritten as Equation 2b:

[0080] ΔP1-ΔP2=ρ×g×h1+ρ×g×h2(2b)

[0081] At the first pressure difference (ΔP ↑ ) and the second pressure difference (ΔP ↓ ) are each measured across the same vertical distance, but the flow directions are opposite (e.g. Figure 1A In the case of the first pair of pressure sensors 104a, 104b and the second pair of pressure sensors 104c, 104d shown in FIG, the first vertical height (h1) is equal to the second vertical height (h2), that is, h1 = h2. Therefore, equation 2b can be rewritten as equation 2c:

[0082] ΔP1-ΔP2=ρ×g×h1(2c)

[0083] Entering h as the vertical height h1 and rearranging Equation 2c to solve for the total density (ρ) of the multiphase fluid results in Equation 2d:

[0084]

[0085] The first pressure difference (ΔP1) is measured by the first pair of pressure sensors 104a, 104b (or the first differential pressure sensor). The second pressure difference (ΔP2) is measured by the second pair of pressure sensors 104c, 104d (or the second differential pressure sensor). The acceleration of gravity is a known universal constant. Therefore, ΔP1, ΔP2, g, and h can be input into equation 2d to estimate the mixed density (ρ) of the multiphase fluid 101.

[0086] Furthermore, information about friction / shear pressure loss can be estimated by adding the first pressure difference (ΔP1) and the second pressure difference (ΔP2), as shown in Equation 2e:

[0087] ΔP1+ΔP2=ρ×g×h1+ΔP f1 -ρ×g×h2+ΔP f2 (2e)

[0088] As mentioned above, in the case where the first vertical height (h1) is equal to the second vertical height (h2), Equation 2e can be rewritten as Equation 2f:

[0089] ΔP1+ΔP2=ΔP f1 +ΔP f2 (2f)

[0090] As mentioned above, since the flow characteristics of the first conduit 102a and the second conduit 102b are substantially the same, ΔP f1 and ΔP f2 can be assumed to be essentially the same and can be simply replaced by ΔP f , so Equation 2f can be rewritten as Equation 2g:

[0091] ΔP1+ΔP2=2×ΔP f (2g)

[0092] Rearrange Equation 2g to solve for the friction / shear pressure loss (ΔP f ) and obtain equation 2h:

[0093]

[0094] The obtained friction / shear pressure loss (ΔP f ) can be used to determine other correlations and flow characteristics of the multiphase fluid 101. For example, if the apparatus 100A is used in conjunction with a venturi-type flow meter, the friction / shear pressure loss (ΔP f ) can be used to determine the relevance of the variables used in the calculations for a Venturi-type flowmeter. For a Venturi-type flowmeter, the Bernoulli equation can be converted to the form shown in Equation 3a:

[0095]

[0096] Where m T is the total mass flow rate of the multiphase fluid 101, C d is the flow coefficient, ε is the expansion factor, and K is the fixed geometry factor ( Where A is the cross-sectional flow area of ​​the neck (d) of the venturi meter, β is the beta ratio (d / D, where d is the diameter of the neck of the venturi meter and D is the upstream pipe that joins the venturi meter), ΔP is the measured pressure drop, including friction / shear pressure losses, and k f is a geometry-based correction factor used to account for the difference(s) in shape / geometry of the Venturi-type flowmeter(s) (e.g., as in apparatus 100A), ΔP f is the friction / shear pressure loss (e.g., measured by apparatus 100A and Equation 2h), and p is the mixed density of the multiphase fluid 101. For example, the total density (p) and friction / shear pressure loss (ΔP) of the multiphase fluid 101 determined by apparatus 100A are f ) can be compared with the information obtained by the Venturi-type flow meter (e.g., the total mass flow rate m of the multiphase fluid 101). T ) and can be input into Equation 3a.

[0097] The operations performed by the processor 705 may include receiving a gas phase volume fraction (α g ) as input. The operations performed by the processor 705 may include receiving a gas phase density (ρ g ) as input. The operations performed by the processor 705 may include receiving a water phase density (ρ a ) as input. The operations performed by the processor 705 may include receiving the oil phase density (ρ o ) as input. The operations performed by the processor 705 may include at least based on the gas phase volume fraction (α g ), gas density (ρ g ), water phase density (ρ a ), oil phase density (ρ o ) and the total density (ρ) of the multiphase fluid 101 to determine the water phase volume fraction (α a For example, the gas phase volume fraction (α g ), gas density (ρ g ), water phase density (ρ a ), oil phase density (ρ o ) and the total density (ρ) are input into Equation 3b and rearranged to calculate the water phase volume fraction (α) of the multiphase fluid 101. a ):

[0098] ρ=ρ g ×α g +ρ a ×α a+ρ o ×(1-α g -α a )(3b)

[0099] The operations performed by the processor 705 may include receiving a water phase volume fraction (α a ) as input. The operations performed by the processor 705 may include at least based on the water phase volume fraction (α a ), gas density (ρ g ), water phase density (ρ a ), oil phase density (ρ o ) and total density (ρ) to determine the gas phase volume fraction (α g For example, the water phase volume fraction (α a ), gas density (ρ g ), water phase density (ρ a ), oil phase density (ρ o ) and the total density (ρ) are input into Equation 3b and rearranged to calculate the gas phase volume fraction (α g ).

[0100] In some embodiments, the first pair of pressure sensors 104a, 104b and the second pair of pressure sensors 104c, 104d respectively measure the first pressure difference and the second pressure difference of the multiphase fluid 101 flowing through the U-bend 102 multiple times over a period of time. Each first pressure difference and each second pressure difference measured by the first pair of pressure sensors 104a, 104b and the second pair of pressure sensors 104c, 104d respectively can be associated with the time point at which they are measured. Each first pressure difference and each second pressure difference measured by the first pair of pressure sensors 104a, 104b and the second pair of pressure sensors 104c, 104d respectively can take into account the time delay of the multiphase fluid 101 from the first conduit 102a (where the first pair of pressure sensors 104a, 104b are located) through the connecting conduit 102c to the second conduit 102b (where the second pair of pressure sensors 104c, 104d are located). For example, the measured pressure difference can be time-corrected to take into account the delay of the multiphase fluid 101 flowing through the U-bend 102. The time series data may be stored, for example, in the memory 707. The time series data may be used, for example, to train and / or establish a neural network-based classification model, which may be used to accurately identify flow states (e.g., bubbling flow, mist flow, slug flow, turbulent flow, annular flow, stratified flow, or intermittent flow). For example, the time series data may be converted into a spectrogram (e.g., by using a Morlet wavelet transform), and a single-layer two-dimensional image may be compiled from the spectrogram. The neural network (machine learning model) may then analyze the image and identify the flow state of the multiphase fluid 101 flowing through the U-bend 102, for example, based on a comparison with historical data. For example, the time series data may be used to train and / or establish a neural network-based classification model, which may be used to estimate the overall flow rate of the multiphase fluid 101 flowing through the U-bend 102. For example, the time series data may be converted into a spectrogram (e.g., by using a Morlet wavelet transform), and a single-layer two-dimensional image may be compiled from the spectrogram. A neural network (machine learning model) may then analyze the image and estimate the overall flow rate and / or flow rate of the multiphase fluid 101 flowing through the U-bend 102, for example based on a comparison with historical data.

[0101] Figure 1B An apparatus 100B is depicted that can be used to measure the density of a multiphase fluid 101. The apparatus 100B can be used with Figure 1A The device 100A shown in FIG. 1 is substantially similar. In contrast, the device 100B omits the connecting conduit ( Figure 1A102c shown in ). The device 100B includes a U-bend 102, which includes a first conduit 102a and a second conduit 102b. The first conduit 102a is connected to the second conduit 102b by a curved bend 103. In some embodiments, the first conduit 102a, the second conduit 102b, and the curved bend 103 are integral, so that the U-bend 102 is a single entity, rather than separate parts that are coupled together to form the U-bend 102. The curved bend 103 can be made of the same material as the first conduit 102a and the second conduit 102b, so that the friction experienced by the multiphase fluid 101 flowing through each component of the U-bend 102 is substantially the same.

[0102] The device 100B may include a first differential pressure sensor 108a coupled to the first conduit 102a via pressure ports 105a and 105b. The first differential pressure sensor 108a is configured to measure a first differential pressure of the multiphase fluid 101 flowing through the U-bend 102. The pressure ports 105a and 105b are spaced apart by a specified differential pressure height h relative to gravity. The device 100B may include a second differential pressure sensor 108b coupled to the second conduit 102b via pressure ports 105c and 105d. The second differential pressure sensor 108b is configured to measure a second differential pressure of the multiphase fluid 101 flowing through the U-bend 102. The pressure ports 105c and 105d are spaced apart by a specified differential pressure height h relative to gravity. Figure 1B As shown, pressure port 105a does not necessarily need to be at the same vertical height as pressure port 105d, and pressure port 105b does not necessarily need to be at the same vertical height as pressure port 105c. Instead, the vertical distance between pressure port 105a and pressure port 105b should match the vertical distance between pressure port 105c and pressure port 105d. The height difference between pressure ports 105a, 105b of the first differential pressure sensor 108a is the same as the height difference between pressure ports 105c, 105d of the second differential pressure sensor 108b, so that the friction force component of the pressure drop experienced by the multiphase fluid 101 when flowing through the first conduit 102a (measured by the first differential pressure sensor 108a) and flowing through the second conduit 102b (measured by the second differential pressure sensor 108b) is substantially the same.

[0103] Although Figure 1B , but the device 100B may be coupled to a flow tube (such as Figure 1A 150), such as through an angled or curved elbow. Figure 1BNot shown, the first differential pressure sensor 108a and the second differential pressure sensor 108b can be connected to a computer (such as computer 700) to determine the characteristics of the multiphase fluid 101 flowing through the U-bend 102 (such as mixed density, total mass flow rate, water phase volume fraction, gas phase volume fraction, or any combination of these characteristics) (for example, using Equations 1, 1a, 1b, 2a, 2b, 2c, 2d, 2e, 2f, 2g, 2h, 3a, 3b, or any combination of these equations).

[0104] Figure 1C An apparatus 100C is depicted that can be used to measure the density of a multiphase fluid 101. The apparatus 100C can be used with Figure 1A The device 100A shown in FIG. 1 is substantially similar. In contrast, the device 100C includes a plurality of pressure sensor pairs coupled to the first conduit 102a and a plurality of pressure sensor pairs coupled to the second conduit 102b. Figure 1C The device 100C shown in FIG. 1 includes two pairs of pressure sensors (104a, 104b and 104a', 104b') mounted in a parallel configuration coupled to the first conduit 102a, but in other embodiments, additional pairs of pressure sensors may be included. Figure 1C The device 100C shown in includes two pairs of pressure sensors (104c, 104d and 104c', 104d') connected to the second conduit 102b and installed in a parallel configuration, but in other embodiments, additional pressure sensor pairs may be included. The redundancy of the pressure sensor can be used to provide a more accurate pressure measurement (e.g., by averaging the measured pressure). The redundancy of the pressure sensor can also be used to identify a fault in one or more pressure sensors, for example, if the deviation of the pressure reading provided by one or more pressure sensors from the remaining pressure sensors exceeds a threshold deviation. In some embodiments, each pair of pressure sensors can be replaced by a differential pressure sensor. For example, the pressure sensor pair 104a, 104b can be replaced by a first differential pressure sensor, the pressure sensor pair 104a', 104b' can be replaced by a second differential pressure sensor, the pressure sensor pair 104c, 104d can be replaced by a third differential pressure sensor, and the pressure sensor pair 104c', 104d' can be replaced by a fourth differential pressure sensor. The redundancy of the differential pressure sensor can be used to provide a wider measurement range (e.g., by using sensors with different but overlapping ranges).

[0105] Figure 1D An apparatus 100D is depicted that can be used to measure the density of a multiphase fluid 101. The apparatus 100D can be used with Figure 1A The device 100A shown in FIG. 1 is substantially similar. In contrast, the device 100D includes more than two pressure sensors coupled to the first conduit 102a and more than two pressure sensors coupled to the second conduit 102b. Figure 1D 100D includes six pressure sensors (104a, 104b, 104c, 104d, 104e, 104f) coupled to the first conduit 102a, but the device 100D may include fewer pressure sensors (such as three, four or five) or more pressure sensors (such as seven or more) coupled to the second conduit 102b. Figure 1D 100D includes six pressure sensors (104a', 104b', 104c', 104d', 104e', 104f') coupled to the second conduit 102b, but the device 100D may include fewer pressure sensors (such as three, four or five) or more pressure sensors (such as seven or more) coupled to the second conduit 102b. Ideally, the device 100D will include the same number of pressure sensors coupled to the first conduit 102a as the number of pressure sensors coupled to the second conduit 102b. Figure 1D As shown, pressure sensors (104a, 104b, 104c, 104d, 104e, 104f) are mounted in a series configuration on the first conduit 102a, and pressure sensors (104a', 104b', 104c', 104d', 104e', 104f') are mounted in a series configuration on the second conduit 102b.

[0106] In some cases, pressure sensors 104a and 104b may be considered a first pair for first conduit 102a, corresponding to pressure sensors 104a' and 104b' as a corresponding first pair for second conduit 102b. In some cases, pressure sensors 104b and 104c may be considered a second pair for first conduit 102a, corresponding to pressure sensors 104b' and 104c' as a corresponding second pair for second conduit 102b. In some cases, pressure sensors 104c and 104d may be considered a third pair for first conduit 102a, corresponding to pressure sensors 104c' and 104d' as a corresponding third pair for second conduit 102b. In some cases, pressure sensors 104d and 104e may be considered a fourth pair for first conduit 102a, corresponding to pressure sensors 104d' and 104e' as a corresponding fourth pair for second conduit 102b. In some cases, pressure sensors 104e and 104f can be considered as the fifth pair of first conduit 102a, corresponding to pressure sensors 104e' and 104f' as the corresponding fifth pair of second conduit 102b. These pairs can be used to measure the segmented pressure gradient along the first conduit 102a and the second conduit 102b. For example, the segmented pressure gradient data can be averaged to more accurately calculate the density of the multiphase fluid 101 flowing through the U-bend.

[0107] In some cases, pressure sensors 104a and 104c can be considered as a first pair of first conduit 102a, corresponding to pressure sensors 104a' and 104c' as a corresponding first pair of second conduit 102b. In some cases, pressure sensors 104b and 104d can be considered as a second pair of first conduit 102a, corresponding to pressure sensors 104b' and 104d' as a corresponding second pair of second conduit 102b. In some cases, pressure sensors 104c and 104e can be considered as a third pair of first conduit 102a, corresponding to pressure sensors 104c' and 104e' as a corresponding third pair of second conduit 102b. In some cases, pressure sensors 104d and 104f can be considered as a fourth pair of first conduit 102a, corresponding to pressure sensors 104d' and 104f' as a corresponding fourth pair of second conduit 102b. Similarly, these pairs can be used to measure segmented pressure gradients along first conduit 102a and second conduit 102b. For example, the segmented pressure gradient data may be averaged to more accurately calculate the density of the multiphase fluid 101 flowing through the U-bend.

[0108] In some cases, pressure sensors 104a and 104d can be considered as a first pair of first conduit 102a, corresponding to pressure sensors 104a' and 104d' as a corresponding first pair of second conduit 102b. In some cases, pressure sensors 104b and 104e can be considered as a second pair of first conduit 102a, corresponding to pressure sensors 104b' and 104e' as a corresponding second pair of second conduit 102b. In some cases, pressure sensors 104c and 104f can be considered as a third pair of first conduit 102a, corresponding to pressure sensors 104c' and 104f' as a corresponding third pair of second conduit 102b. Similarly, these pairs can be used to measure segmented pressure gradients along first conduit 102a and second conduit 102b. For example, the segmented pressure gradient data can be averaged to more accurately calculate the density of the multiphase fluid 101 flowing through the U-bend.

[0109] In some cases, pressure sensors 104a and 104e can be considered as a first pair of first conduit 102a, corresponding to pressure sensors 104a' and 104e' as a corresponding first pair of second conduit 102b. In some cases, pressure sensors 104b and 104f can be considered as a second pair of first conduit 102a, corresponding to pressure sensors 104b' and 104f' as a corresponding second pair of second conduit 102b. Similarly, these pairs can be used to measure segmented pressure gradients along first conduit 102a and second conduit 102b. For example, the segmented pressure gradient data can be averaged to more accurately calculate the density of the multiphase fluid 101 flowing through the U-bend.

[0110] In some cases, pressure sensors 104a and 104f may be considered a first pair for first conduit 102a, with pressure sensors 104a' and 104f' being a corresponding first pair for second conduit 102b. In this case, device 100D and Figure 1A The device 100A shown is substantially the same.Any combination or sub-combination of the pressure sensor pairs described above may be considered a suitable implementation of the device 100D.

[0111] In some embodiments, any pair of pressure sensors connected to the first conduit 102a can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104a, 104b can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104a, 104c can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104a, 104d can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104a, 104e can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104a, 104f can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104b, 104c can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104b, 104d can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104b, 104e can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104b, 104f can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104b, 104e can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104b, 104f can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104c, 104d can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104b, 104e can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104b, 104f can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104c, 104d can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104c, 104e can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104c, 104f can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104d, 104e can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104d, 104f can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104e, 104f can be replaced by a differential pressure sensor.

[0112] In some embodiments, any pair of pressure sensors connected to the second conduit 102b can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104a', 104b' can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104a', 104c' can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104a', 104d' can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104a', 104e' can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104a', 104f' can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104b', 104c' can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104b', 104d' can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104b', 104e' can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104b', 104f' can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104b', 104c' can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104b', 104d' can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104b', 104e' can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104b', 104f' can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104c', 104d' can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104c', 104e' can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104c', 104f' can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104d', 104e' can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104d', 104f' can be replaced by a differential pressure sensor. For example, a pair of pressure sensors 104e', 104f' can be replaced by a differential pressure sensor.

[0113] Figure 1E An apparatus 100E is depicted that can be used to measure the total mass flow rate of a multiphase fluid 101. The apparatus 100E can be used with Figure 1A 100E is substantially similar to the device 100A shown in FIG. 100A. Compared to the device 100A, the first pair of pressure sensors 104a, 104b and the second pair of pressure sensors 104c, 104d are located at different positions on the device 100E. The first pressure sensor 104a is connected to the pressure port 105a on the first tube 150a (third conduit) of the flow tube 150. The second pressure sensor 104b is connected to the pressure port 105b on the first conduit 102a of the U-bend 102. The third pressure sensor 104c is connected to the pressure port 105c on the second conduit 102b of the U-bend 102. The fourth pressure sensor 104d is connected to the pressure port 105d on the second tube 150b (fourth conduit) of the flow tube 150. In some embodiments, the first pair of pressure sensors 104a, 104b is replaced by a first differential pressure sensor. In some embodiments, the second pair of pressure sensors 104c, 104d is replaced by a second differential pressure sensor.

[0114] The first pair of pressure sensors 104a, 104b (or first differential pressure sensors) are configured to measure a first differential pressure of the multiphase fluid 101. The first differential pressure includes the pressure loss of the multiphase fluid 101 flowing through the first corner bend 153a. The second pair of pressure sensors 104c, 104d (or second differential pressure sensors) are configured to measure a second differential pressure of the multiphase fluid 101. The second differential pressure includes the pressure loss of the multiphase fluid 101 flowing through the second corner bend 153b. The operations performed by the processor 705 may include receiving a first differential pressure signal from the first pair of pressure sensors 104a, 104b (or first differential pressure sensors). The first differential pressure signal may represent the first differential pressure of the multiphase fluid 101 measured by the pressure sensors 104a, 104b (or first differential pressure sensors). The operations performed by the processor 705 may include receiving a second differential pressure signal from the second pair of pressure sensors 104c, 104d (or second differential pressure sensors). The second differential pressure signal may represent a second differential pressure of the multiphase fluid 101 measured by the pressure sensors 104c, 104d (or a second differential pressure sensor). The operations performed by the processor 705 may include determining a total flow rate of the multiphase fluid 101 based at least on the first differential pressure, the second differential pressure, the difference between the first differential pressure and the second differential pressure of the multiphase fluid 101, and the total density of the multiphase fluid 101. The total density of the multiphase fluid 101 may be measured, for example, by a separate multiphase flow meter. For example, the device 100E may include features from the device 100A that may be used to determine a mixed density (ρ) of the multiphase fluid 101.

[0115] The total flow rate of the multiphase fluid 101 can be determined in a variety of ways. As a first example, the total flow rate of the multiphase fluid 101 can be determined using the first pressure difference through equation 4a (neglecting friction pressure losses):

[0116]

[0117] Where m T1 is the total mass flow rate of the multiphase fluid 101, C d1 is the empirically characterized flow coefficient, ε1 is the expansion factor, and K1 is the fixed geometric factor ( Where A1 is the cross-sectional flow area of ​​the throat of the first corner elbow 153a, and β1 is the beta ratio (d / D, where d is the inner diameter of the first conduit 102a and D is the inner diameter of the first tube 150a), ΔP1 is the first pressure difference measured by the pressure sensors 104a, 104b (or the first differential pressure sensor), ρ is the mixed density of the multiphase fluid 101, g is the acceleration caused by gravity, and h v is the vertical height difference between the pressure ports 105a and 105b to which the pressure sensors 104a and 104b (or the first differential pressure sensor) are connected. d1) can be determined empirically, for example based on historical data or corrected using real-time data.

[0118] As a second example, the total mass flow rate of the multiphase fluid 101 (neglecting friction pressure losses) can be determined using the second pressure difference by Equation 4b:

[0119]

[0120] Where m T2 is the total mass flow rate of the multiphase fluid 101, C d2 is the empirically characterized flow coefficient, ε2 is the expansion factor, and K2 is the fixed geometric factor ( Wherein, A2 is the cross-sectional flow area of ​​the throat of the second corner elbow 153b, and β2 is the beta ratio (D / d, where d is the inner diameter of the second conduit 102b, and D is the inner diameter of the second tube 150b), ΔP2 is the second pressure difference measured by the pressure sensors 104c, 104d (or the second differential pressure sensor), ρ is the mixed density of the multiphase fluid 101, g is the acceleration caused by gravity, and h v is the vertical height difference between the pressure ports 105c, 105d to which the pressure sensors 104c, 104d (or the second differential pressure sensor) are connected. Flow coefficient (C d2 ) can be determined empirically, for example based on historical data or corrected using real-time data.

[0121] Operations performed by processor 705 may include comparing the total mass flow rate (m) determined by equations 4a and 4b. T1 , m T2 ) to determine the convection coefficient (C d1 , C d2 ). Equation 4a can be rewritten as: T1 =C d1 × Y1, where Y1 is simply substituted into the right side of equation 4a (including the measured parameters ΔP1 and ρ and the predetermined parameters ε1 and K1), excluding the flow coefficient C d1 . Equation 4b can be rewritten as: m T2 =C d2 × Y2, where Y2 simply replaces the right side of Equation 4b (including the measured parameters ΔP2 and ρ and the predetermined parameters ε2 and K2), excluding the flow coefficient C d1 Because the total mass flow rate does not change as the multiphase fluid 101 flows through the device 100E, m T1 =m T2 Therefore, C d1 ×Y1=C d2 ×Y2. Due to this relationship, given C d1and the measured parameters Y1 and Y2, C can be calculated d2 Similarly, given C d2 and the measured parameters Y1 and Y2, C can be calculated d1 Therefore, as an on-site self-check, the flow coefficient (C d1 , C d2 ) consistency and accuracy. Other techniques (such as least squares minimization) may be used additionally or alternatively to accurately calculate the flow coefficient (C d1 , C d2 ).

[0122] The first pressure difference (ΔP1) measured by the pressure sensors 104a, 104b (or the first differential pressure sensor) and the second pressure difference (ΔP2) measured by the pressure sensors 104c, 104d (or the second differential pressure sensor) can be used to calculate the mixed density (ρ) of the multiphase fluid 101.

[0123] Equation 4a can be rearranged into Equation 5a:

[0124]

[0125] Equation 4b can be rearranged into Equation 5b:

[0126]

[0127] As previously mentioned, when the multiphase fluid 101 flows through the device 100E, the total mass flow rate does not change, so m T1 =m T2 For simplicity, the variable Z is defined by Equation 5c:

[0128]

[0129] Combining Equations 5a, 5b, and 5c and then solving for the mixture density (ρ) yields Equation 5d:

[0130]

[0131] For example, equation 5d may be used to verify the accuracy of the mixture density (ρ) determined by any of the devices 100A, 100B, 100C, or 100D.

[0132] In some embodiments, the distance between the first pressure sensor 104a and the second pressure sensor 104b is substantially the same as the distance between the third pressure sensor 104c and the fourth pressure sensor 104d. In a specific example, the device 100E has the following dimensions. The inner diameter (d) of the U-bend 102 (the first conduit 102a, the second conduit 102b, and the connecting conduit 102c) is approximately 2.067 inches (Nominal Pipe Size (NPS) 2" Schedule 40). The inner diameter (D) of the first tube 150a and the second tube 150b is approximately 3.068" (NPS 3" Schedule 40). Dimension A is the length of a straight tube (i.e., a tube without any bends) of the first tube 150a upstream of the first pressure sensor 104a. Dimension A is also the length of a straight tube of the second tube 150b downstream of the fourth pressure sensor 104d. Dimension A is the minimum length of a straight tube to ensure minimal interference from turbulence and friction, which may affect the measurement results of the first pair of pressure sensors 104a, 104b and the measurement results of the second pair of pressure sensors 104c, 104d. In some embodiments, Dimension A is at least five times the inner diameter (D) of the first tube 150a (A≥5D). Dimension B is the length of a straight tube of the first tube 150a downstream of the first pressure sensor 104a and upstream of the first corner bend 153a. Dimension B is also the length of a straight tube of the second tube 150b downstream of the second corner bend 153b and upstream of the fourth pressure sensor 104d. Similarly, Dimension B is the minimum length of a straight tube to ensure minimal interference from turbulence and friction. Small length, turbulence and friction interference may affect the measurement results of the first pair of pressure sensors 104a, 104b and the measurement results of the second pair of pressure sensors 104c, 104d. In some embodiments, dimension B is at least five times the inner diameter (D) of the first tube 150a (B≥5D). Dimension C is the length of the straight pipe of the first conduit 102a downstream of the first corner bend 153a and upstream of the second pressure sensor 104b. Dimension C is also the length of the straight pipe of the second conduit 102b downstream of the third pressure sensor 104c and upstream of the second corner bend 153b. Similarly, dimension C is the minimum length of the straight pipe to ensure that the interference of turbulence and friction is minimized, and the interference of turbulence and friction may affect the measurement results of the first pair of pressure sensors 104a, 104b and the measurement results of the second pair of pressure sensors 104c, 104d. In some embodiments, dimension C is at least five times the inner diameter (d) of the U-bend 102 (C≥5d).

[0133] Figure 1F An apparatus 100F is depicted that can be used to measure the total mass flow rate of a multiphase fluid 101. The apparatus 100F can be used with Figure 1E The device 100E shown in FIG. 1 is substantially similar. In contrast, the device 100F omits the connecting conduit ( Figure 1E102c shown in ). The device 100F includes a U-bend 102, which includes a first conduit 102a and a second conduit 102b. The first conduit 102a is connected to the second conduit 102b by a curved bend 103. In some embodiments, the first conduit 102a, the second conduit 102b, and the curved bend 103 are integral, so that the U-bend 102 is a single entity, rather than separate parts that are coupled together to form the U-bend 102. The curved bend 103 can be made of the same material as the first conduit 102a and the second conduit 102b, so that the friction experienced by the multiphase fluid 101 flowing through each component of the U-bend 102 is substantially the same.

[0134] like Figure 1F As shown, the U-bend 102 can be connected to a flow tube 150 that allows the multiphase fluid 101 to circulate. The flow tube 150 includes a first tube 150a and a second tube 150b. In some embodiments, the U-bend 102 is connected to the flow tube 150 through curved bends 153c, 153d. For example, the first conduit 102a of the U-bend 102 is connected to the first tube 150a of the flow tube 150 through the first curved bend 153c. For example, the second conduit 102b of the U-bend 102 is connected to the second tube 150b of the flow tube 150 through the second curved bend 153d. In some embodiments, the first conduit 102a, the second conduit 102b, the curved bend 103, the first curved bend 153c, the second curved bend 153d and the flow tube 150 are integral, so that the U-bend 102 and the flow tube 150 form a single entity, rather than separate and connected parts.

[0135] The device 100F may include a first differential pressure sensor 108a, which is connected to the first tube 150a and the first conduit 102a via pressure ports 105a and 105b, respectively. The first differential pressure sensor 108a is configured to measure a first differential pressure of the multiphase fluid 101 flowing through the first curved elbow 153c. The pressure ports 105a and 105b are separated by a specified differential pressure height h relative to gravity. The device 100B may include a second differential pressure sensor 108b, which is connected to the second conduit 102b and the second tube 150b via pressure ports 105c and 105d, respectively. The second differential pressure sensor 108b is configured to measure a second differential pressure of the multiphase fluid 101 flowing through the second curved elbow 153d. The pressure ports 105c and 105d are separated by a specified differential pressure height h relative to gravity. Figure 1FAs shown, pressure port 105a does not necessarily need to be at the same vertical height as pressure port 105d, and pressure port 105b does not necessarily need to be at the same vertical height as pressure port 105c. Instead, the vertical distance between pressure port 105a and pressure port 105b should match the vertical distance between pressure port 105c and pressure port 105d. The height difference between pressure ports 105a, 105b of the first differential pressure sensor 108a is the same as the height difference between pressure ports 105c, 105d of the second differential pressure sensor 108b, and the horizontal distance between pressure ports 105a, 105b of the first differential pressure sensor 108a is the same as the horizontal distance between pressure ports 105c, 105d of the second differential pressure sensor 108b, so that the friction force component of the pressure drop experienced by the multiphase fluid 101 flowing through the first curved elbow 153c (measured by the first differential pressure sensor 108a) and flowing through the second curved elbow 153d (measured by the second differential pressure sensor 108b) is substantially the same.

[0136] although Figure 1F Not shown, the first differential pressure sensor 108a and the second differential pressure sensor 108b can be connected to a computer (such as computer 700) to determine characteristics (such as mixed density, total mass flow rate, or both) of the multiphase fluid 101 flowing through the U-bend 102 (e.g., using Equations 4a, 4b, 5a, 5b, 5c, 5d, or any combination of these equations).

[0137] Figure 1G An apparatus 100G is depicted that can be used to measure the water-to-liquid ratio of a multiphase fluid 101. The apparatus 100G can be used with Figure 1A Compared to the apparatus 100A, the apparatus 100G includes dynamic pressure sensors 106a, 106b, 106c coupled to the U-bend 102. Figure 1G100G is shown as including three dynamic pressure sensors 106a, 106b, 106c, but the device 100G may include fewer dynamic pressure sensors (such as two dynamic pressure sensors) or more dynamic pressure sensors (such as four dynamic pressure sensors or more than four dynamic pressure sensors). The dynamic pressure sensors 106a, 106b, 106c measure the dynamic pressure of the multiphase fluid 101 flowing through the U-bend 102, rather than the static pressure of the multiphase fluid 101. The dynamic pressure sensors 106a, 106b, 106c may be located at any position along the U-bend 102. In some embodiments, the dynamic pressure sensors 106a, 106b, 106c are connected to the first conduit 102a of the U-bend 102. In some embodiments, the dynamic pressure sensors 106a, 106b, 106c are connected to the second conduit 102b of the U-bend 102. In some embodiments, a first portion of the dynamic pressure sensors 106a, 106b, 106c (e.g., one or two of the dynamic pressure sensors 106a, 106b, 106c) is coupled to the first conduit 102a of the U-bend 102, and the remaining portion of the dynamic pressure sensors 106a, 106b, 106c is coupled to the second conduit 102b of the U-bend 102. The dynamic pressure sensors 106a, 106b, 106c may be evenly or randomly distributed along the U-bend 102.

[0138] The dynamic pressure measurements made by the dynamic pressure sensors 106a, 106b, 106c can be cross-correlated (e.g., by the processor 705) to determine the acoustic velocity of the multiphase fluid 101 flowing through the U-bend 102. The acoustic velocity of the multiphase fluid 101 and the total density (ρ) of the multiphase fluid 101 can then be used to determine the water-to-liquid ratio of the multiphase fluid 101. The water-to-liquid ratio of the multiphase fluid 101 is the ratio of the volume of the water phase 101b' to the sum of the volume of the water phase 101b' and the volume of the oil phase 101b" (liquid phase 101b) (i.e., the ratio of (volume of 101b') / (volume of 101b'+volume of 101b"), which is the same as the ratio of (volume of 101b') / (volume of 101b)). For example, the speed of sound of the multiphase fluid 101 and the total density (ρ) of the multiphase fluid 101 may be compared to plots of various phase curves (gas / oil, gas / water, oil / water) to determine the water-to-liquid ratio.

[0139] Figure 1H An apparatus 100H is depicted that can be used to measure density, total flow, and phase flow of a multiphase fluid 101. The apparatus 100H can be used with Figure 1A The device 100A shown in FIG. Figure 1E100E is substantially similar to the device 100A shown in FIG. 100A. For example, the device 100H may be a combination of the device 100A and the device 100E. The first pressure sensor 104a is coupled to the first pressure port 105a on the first tube 150a (third conduit) of the flow tube 150. The second pressure sensor 104b is coupled to the second pressure port 105b on the first conduit 102a of the U-bend 102. The third pressure sensor 104c is coupled to the third pressure port 105c on the second conduit 102b of the U-bend 102. The fourth pressure sensor 104d is coupled to the fourth pressure port 105d on the second tube 150b (fourth conduit) of the flow tube 150. The fifth pressure sensor 104e and the sixth pressure sensor 104f are respectively coupled to the fifth pressure port 105e and the sixth pressure port 105f on the first conduit 102a of the U-bend 102. The fifth pressure port 105e and the sixth pressure port 105f are separated by a specified height h along the first conduit 102a. The seventh pressure sensor 104g and the eighth pressure sensor 104h are respectively connected to the seventh pressure port 105g and the eighth pressure port 105h on the second conduit 102b of the U-bend 102. The seventh pressure port 105g and the eighth pressure port 105h are separated by a specified height h along the second conduit 102b. In some embodiments, the first pressure sensor 104a and the second pressure sensor 104b are replaced by the first differential pressure sensor. In some embodiments, the third pressure sensor 104c and the fourth pressure sensor 104d are replaced by the second differential pressure sensor. In some embodiments, the fifth pressure sensor 104e and the sixth pressure sensor 104f are replaced by the third differential pressure sensor. In some embodiments, the seventh pressure sensor 104g and the eighth pressure sensor 104h are replaced by the fourth differential pressure sensor.

[0140] The first pair of pressure sensors 104a, 104b (or first differential pressure sensors) are configured to measure a first differential pressure of the multiphase fluid 101. The first differential pressure includes the pressure loss of the multiphase fluid 101 flowing through the first corner bend 153a. The second pair of pressure sensors 104c, 104d (or second differential pressure sensors) are configured to measure a second differential pressure of the multiphase fluid 101. The second differential pressure includes the pressure loss of the multiphase fluid 101 flowing through the second corner bend 153b. The third pair of pressure sensors 104e, 104f (or third differential pressure sensors) are configured to measure a third differential pressure of the multiphase fluid 101. The fourth pair of pressure sensors 104g, 104h (or fourth differential pressure sensors) are configured to measure a fourth differential pressure of the multiphase fluid 101. The operations performed by the processor 705 may include receiving a first differential pressure signal from the first pair of pressure sensors 104a, 104b (or first differential pressure sensors). The first differential pressure signal may represent a first differential pressure of the multiphase fluid 101 measured by the pressure sensors 104a, 104b (or the first differential pressure sensor). The operations performed by the processor 705 may include receiving a second differential pressure signal from a second pair of pressure sensors 104c, 104d (or the second differential pressure sensor). The second differential pressure signal may represent a second differential pressure of the multiphase fluid 101 measured by the pressure sensors 104c, 104d (or the second differential pressure sensor). The operations performed by the processor 705 may include receiving a third differential pressure signal from a third pair of pressure sensors 104e, 104f (or the third differential pressure sensor). The third differential pressure signal may represent a third differential pressure of the multiphase fluid 101 measured by the pressure sensors 104e, 104f (or the third differential pressure sensor). The operations performed by the processor 705 may include receiving a fourth differential pressure signal from a fourth pair of pressure sensors 104g, 104h (or the fourth differential pressure sensor). The fourth differential pressure signal may represent a fourth differential pressure of the multiphase fluid 101 measured by the pressure sensors 104g, 104h (or a fourth differential pressure sensor). The operations performed by the processor 705 may include determining a total density of the multiphase fluid 101 based at least on the specified height (h) and the difference between the third differential pressure and the fourth differential pressure. The operations performed by the processor 705 may include determining a total flow rate of the multiphase fluid 101 based at least on the first differential pressure and the second differential pressure of the multiphase fluid 101 and the total density of the multiphase fluid 101.

[0141] The mixed density of the multiphase fluid 101 can be determined in a variety of ways. As a first example, the mixed density (ρ) of the multiphase fluid 101 can be determined by equation 2d customized for the device 100H, where ΔP1 is the third pressure difference measured by the third pair of pressure sensors 104e, 104f (or the third differential pressure sensor), ΔP2 is the fourth pressure difference measured by the fourth pair of pressure sensors 104g, 104h (or the fourth differential pressure sensor), and h2 is the specified height (h). As a second example, the mixed density (ρ) of the multiphase fluid 101 can be determined by equation 5d customized for the device 100H, where ΔP1 is the third pressure difference measured by the third pair of pressure sensors 104e, 104f (or the third differential pressure sensor), and ΔP2 is the fourth pressure difference measured by the fourth pair of pressure sensors 104g, 104h (or the fourth differential pressure sensor).

[0142] The total flow rate of the multiphase fluid 101 can be determined in various ways. As a first example, the total flow rate of the multiphase fluid 101 can be determined using the first pressure difference using Equation 4a. As a second example, the total flow rate of the multiphase fluid 101 can be determined using the second pressure difference using Equation 4b. The operations performed by the processor 705 can include comparing the total flow rates (m) determined by Equations 4a and 4bc. T1 ,m T2 ) to determine the flow coefficient (C d1 ,C d2 ) adjustments.

[0143] In some embodiments, the distance between the first pressure sensor 104a and the second pressure sensor 104b is substantially the same as the distance between the third pressure sensor 104c and the fourth pressure sensor 104d. In a specific example, the device 100D has the following dimensions. The inner diameter (d) of the U-bend 102 (the first conduit 102a, the second conduit 102b, and the connecting conduit 102c) is approximately 2.067 inches (NPS 2" Schedule 40). The inner diameter (D) of the first tube 150a and the second tube 150b is approximately 3.068" (NPS 3" Schedule 40). Dimension A is the length of the first tube 150a that is straight (i.e., a tube without any bends) upstream of the first pressure sensor 104a. Dimension A is also the length of the second tube 150b that is straight downstream of the fourth pressure sensor 104d. Dimension A is the minimum straight tube length to ensure minimal turbulence and friction interference that may affect the measurements of the first pair of pressure sensors 104a, 104b and the measurements of the second pair of pressure sensors 104c, 104d. In some embodiments, Dimension A is at least the first tube 150b. Dimension B is the length of the straight pipe of the first pipe 150a downstream of the first pressure sensor 104a and upstream of the first corner bend 153a. Dimension B is also the length of the straight pipe of the second pipe 150b downstream of the second corner bend 153b and upstream of the fourth pressure sensor 104d. Similarly, Dimension B is the minimum length of the straight pipe to ensure minimal interference from turbulence and friction, which may affect the measurement results of the first pair of pressure sensors 104a, 104b and the second pair of pressure sensors. 104c, 104d. In some embodiments, dimension B is at least five times the inner diameter (D) of the first tube 150a (B ≥ 5D). Dimension C is the length of the straight tube of the first conduit 102a downstream of the first corner bend 153a and upstream of the second pressure sensor 104b. Dimension C is also the length of the straight tube of the second conduit 102b downstream of the third pressure sensor 104c and upstream of the second corner bend 153b. Similarly, dimension C is the minimum length of the straight tube to ensure minimal interference from turbulence and friction, turbulence and friction may affect the measurement results of the first pair of pressure sensors 104a, 104b and the measurement results of the second pair of pressure sensors 104c, 104d. In some embodiments, dimension C is at least five times the inner diameter (d) of the U-bend 102 (C ≥ 5d). In some embodiments, between the second pressure sensor 104b and the fifth pressure sensor 104e, along the longitudinal length of the first conduit 102a of the U-bend 102, there is a straight pipe with a length of at least twice the inner diameter (d) of the U-bend 102 (≥ 2d).In some embodiments, between the eighth pressure sensor 104h and the third pressure sensor 104c, along the longitudinal length of the second conduit 102b of the U-bend 102, there is a straight pipe whose length is at least twice the inner diameter (d) of the U-bend 102 (≥2d). Dimension E is the length of the straight pipe of the first conduit 102a downstream of the sixth pressure sensor 104f and upstream of the first curved bend 103a. Dimension E is also the length of the straight pipe of the second conduit 102b downstream of the second curved bend 103b and upstream of the seventh pressure sensor 104g. Similarly, dimension E is the minimum length of the straight pipe to ensure minimal interference from turbulence and friction, which may affect the measurement results of the third pair of pressure sensors 104e, 104f and the measurement results of the fourth pair of pressure sensors 104g, 104h. In some embodiments, dimension E is at least five times the inner diameter (d) of the U-bend 102 (E≥5d).

[0144] Fig. 1I An apparatus 100I is depicted that can be used to measure density, flow rate, and water-to-liquid ratio of a multiphase fluid 101. The apparatus 100I can be used with Figure 1A The device 100A shown, Figure 1E The device 100E shown, Figure 1G The equipment shown is 100G and Figure 1H The device 100H shown is substantially similar. For example, the device 100I can be a combination of the device 100G and the device 100H. For example, the device 100I can be a replica of the device 100H, which also includes dynamic pressure sensors 106a, 106b, 106c (similar to the device 100G) coupled to the U-bend 102. Therefore, the device 100I can perform all functions that the device 100G and the device 100H can perform.

[0145] although Fig. 1I100I is shown as including three dynamic pressure sensors 106a, 106b, 106c, but the device 100I may include fewer dynamic pressure sensors (such as two dynamic pressure sensors) or more dynamic pressure sensors (such as four dynamic pressure sensors or more than four dynamic pressure sensors). The dynamic pressure sensors 106a, 106b, 106c measure the dynamic pressure of the multiphase fluid 101 flowing through the U-bend 102, rather than the static pressure of the multiphase fluid 101. The dynamic pressure sensors 106a, 106b, 106c may be located at any position along the U-bend 102. In some embodiments, the dynamic pressure sensors 106a, 106b, 106c are coupled to the first conduit 102a of the U-bend 102. In some embodiments, the dynamic pressure sensors 106a, 106b, 106c are coupled to the second conduit 102b of the U-bend 102. In some embodiments, a first portion of the dynamic pressure sensors 106a, 106b, 106c (e.g., one or two of the dynamic pressure sensors 106a, 106b, 106c) is coupled to the first conduit 102a of the U-bend 102, and the remaining portion of the dynamic pressure sensors 106a, 106b, 106c is coupled to the second conduit 102b of the U-bend 102. The dynamic pressure sensors 106a, 106b, 106c may be evenly or randomly distributed along the U-bend 102.

[0146] The dynamic pressure measurements made by the dynamic pressure sensors 106a, 106b, 106c can be cross-correlated (e.g., by the processor 705) to determine the acoustic velocity of the multiphase fluid 101 flowing through the U-bend 102. The acoustic velocity of the multiphase fluid 101 and the total density (ρ) of the multiphase fluid 101 can then be used to determine the water-to-liquid ratio of the multiphase fluid 101. For example, the acoustic velocity of the multiphase fluid 101 and the total density (ρ) of the multiphase fluid 101 can be compared to plots of various phase curves (gas / oil, gas / water, oil / water) to determine the water-to-liquid ratio.

[0147] Figure 1J An apparatus 100J is depicted that can be used to measure density, flow rate, and water-to-liquid ratio of a multiphase fluid 101. The apparatus 100J can be used with Figure 1H The device 100H shown in FIG. 1 is substantially similar. In contrast, the device 100J omits the connecting conduit ( Figure 1H102c shown in ). The device 100J includes a U-bend 102, which includes a first conduit 102a and a second conduit 102b. The first conduit 102a is connected to the second conduit 102b by a curved bend 103. In some embodiments, the first conduit 102a, the second conduit 102b, and the curved bend 103 are integral, so that the U-bend 102 is a single entity, rather than separate parts that are coupled together to form the U-bend 102. The curved bend 103 can be made of the same material as the first conduit 102a and the second conduit 102b, so that the friction experienced by the multiphase fluid 101 flowing through each component of the U-bend 102 is substantially the same.

[0148] like Figure 1J As shown, the U-bend 102 can be connected to a flow tube 150 that allows the multiphase fluid 101 to circulate. The flow tube 150 includes a first tube 150a and a second tube 150b. In some embodiments, the U-bend 102 is connected to the flow tube 150 through curved bends 153c, 153d. For example, the first conduit 102a of the U-bend 102 is connected to the first tube 150a of the flow tube 150 through the first curved bend 153c. For example, the second conduit 102b of the U-bend 102 is connected to the second tube 150b of the flow tube 150 through the second curved bend 153d. In some embodiments, the first conduit 102a, the second conduit 102b, the curved bend 103, the first curved bend 153c, the second curved bend 153d and the flow tube 150 are integral, so that the U-bend 102 and the flow tube 150 form a single entity, rather than separate and connected parts.

[0149] The device 100J may include a first differential pressure sensor 108a, which is connected to the first tube 150a and the first conduit 102a via pressure ports 105a and 105b, respectively. The first differential pressure sensor 108a is configured to measure a first differential pressure of the multiphase fluid 101 flowing through the first curved elbow 153c. The pressure ports 105a and 105b are separated by a specified differential pressure height h relative to gravity. The device 100B may include a second differential pressure sensor 108b, which is connected to the second conduit 102b and the second tube 150b via pressure ports 105c and 105d, respectively. The second differential pressure sensor 108b is configured to measure a second differential pressure of the multiphase fluid 101 flowing through the second curved elbow 153d. The pressure ports 105c and 105d are separated by a specified differential pressure height h relative to gravity. Figure 1FAs shown, pressure port 105a does not necessarily need to be at the same vertical height as pressure port 105d, and pressure port 105b does not necessarily need to be at the same vertical height as pressure port 105c. Instead, the vertical distance between pressure port 105a and pressure port 105b should match the vertical distance between pressure port 105c and pressure port 105d. The height difference between pressure ports 105a, 105b of the first differential pressure sensor 108a is the same as the height difference between pressure ports 105c, 105d of the second differential pressure sensor 108b, and the horizontal distance between pressure ports 105a, 105b of the first differential pressure sensor 108a is the same as the horizontal distance between pressure ports 105c, 105d of the second differential pressure sensor 108b, so that the friction force component of the pressure drop experienced by the multiphase fluid 101 flowing through the first curved elbow 153c (measured by the first differential pressure sensor 108a) and flowing through the second curved elbow 153d (measured by the second differential pressure sensor 108b) is substantially the same.

[0150] The device 100J may include a third differential pressure sensor 108c coupled to the first conduit 102a via pressure ports 105e and 105f. The third differential pressure sensor 108c is configured to measure a third differential pressure of the multiphase fluid 101 flowing through the U-bend 102. The pressure ports 105e and 105f are separated by a specified differential pressure height h relative to gravity. The device 100J may include a fourth differential pressure sensor 108d coupled to the second conduit 102b via pressure ports 105g and 105h. The fourth differential pressure sensor 108d is configured to measure a fourth differential pressure of the multiphase fluid 101 flowing through the U-bend 102. The pressure ports 105g and 105h are separated by a specified differential pressure height h relative to gravity. Figure 1J As shown, pressure port 105e does not necessarily need to be at the same vertical height as pressure port 105h, and pressure port 105f does not necessarily need to be at the same vertical height as pressure port 105g. Instead, the vertical distance between pressure port 105e and pressure port 105f should match the vertical distance between pressure port 105g and pressure port 105h. The height difference between pressure ports 105e, 105f of the third differential pressure sensor 108c is the same as the height difference between pressure ports 105g, 105h of the fourth differential pressure sensor 108d, so that the friction force component of the pressure drop experienced by the multiphase fluid 101 flowing through the first conduit 102a (measured by the third differential pressure sensor 108c) and flowing through the second conduit 102b (measured by the fourth differential pressure sensor 108d) is substantially the same.

[0151] although Figure 1JNot shown, but the first differential pressure sensor 108a, the second differential pressure sensor 108b, the third differential pressure sensor 108c and the fourth differential pressure sensor 108d can be connected to a computer (such as computer 700) to determine the characteristics of the multiphase fluid 101 flowing through the U-bend 102 (such as mixed density, total mass flow rate, water phase volume fraction, gas phase volume fraction, or any combination of these characteristics) (for example, using Equations 1, 1a, 1b, 2a, 2b, 2c, 2d, 2e, 2f, 2g, 2h, 3a, 3b, 4a, 4b, 5a, 5b, 5c, 5d, or any combination of these equations).

[0152] Any of the devices 100A, 100B, 100C, 100D, 100E, 100F, 100G, 100H, 100I, or 100J may be combined with any of the following components to obtain additional information about the multiphase fluid 101: a flow meter (such as a venturi-type flow meter), a water content meter that measures the water fraction or water-to-liquid ratio, a dynamic pressure sensor, a temperature sensor, or a strain gauge. Where a dynamic pressure sensor is included, the dynamic pressure sensor may be located on the same pressure tap as any pressure sensor (100A, 100B, 100C, 100D, 100E, 100F, 100G, 100H, 100I, or 100J) already included in the device.

[0153] Figure 2A Schematic diagrams depicting various example pressure tap arrangements. Each of views (i), (ii) and (iii) is a cross-sectional view of a tube (e.g., a first conduit 102a or a second conduit 102b). Any of the pressure sensors (104a, 104b, 104c, 104d, 104e, 104f, 104a', 104b', 104c', 104d', 104e', 104f') can have the form shown in view (i), (ii) or (iii). In view (i), the pressure sensor includes a single pressure tap. In view (ii), the pressure sensor includes various (such as four) pressure taps distributed around the circumference of the conduit. In view (ii), the pressure sensor can obtain four simultaneous readings (one reading for each of the four pressure taps), and average the four simultaneous readings to obtain an average pressure reading at a specific axial position along the conduit. Although shown as having four pressure taps in view (ii), the pressure sensor may have fewer pressure taps (such as two or three) or more pressure taps (such as five or more). In view (iii), the pressure sensor includes circumferential pressure taps that completely span the entire circumference of the conduit. The circumferential pressure taps shown in view (iii) may be Figure 2AThe most accurate of all the views (i), (ii) and (iii) shown in .

[0154] Figure 2B Schematic diagrams depicting various example tube arrangements. Each of views (i), (ii), (iii), (iv) and (v) shows a tube arrangement that can be used in addition to or in place of the tube arrangements already described with respect to apparatus 100A, 100B, 100C, 100D, 100E, 100F, 100G, 100H, 100I and 100J. ΔP1 is a first pressure difference of the multiphase fluid 101 flowing through the corresponding tube arrangement. ΔP2 is a second pressure difference of the multiphase fluid 101 flowing through the corresponding tube arrangement. ΔP1 can be measured by a pair of pressure sensors or a single differential pressure sensor. Similarly, ΔP2 can be measured by a pair of pressure sensors or a single differential pressure sensor. The first pressure difference (ΔP1) and the second pressure difference (ΔP2) measured from any of these pipe arrangements can be used, for example, to determine properties of the multiphase fluid 101 flowing through the corresponding pipe arrangement (such as mixing density, total mass flow rate, water phase volume fraction, gas phase volume fraction, or any combination of these properties) (for example, using Equations 1, 1a, 1b, 2a, 2b, 2c, 2d, 2e, 2f, 2g, 2h, 3a, 3b, or any combination of these equations).

[0155] As an example, view (i) can be considered the base case, which generally complies with Figure 1A and 1B . The pipe arrangements of the devices 100A and 100B are shown in the figures, respectively. Although the pipe arrangement of view (ii) is substantially similar to the pipe arrangement of view (i), the first conduit 102a and the second conduit 102b of view (ii) are not necessarily straight pipes. In view (iii), the connecting conduit (102c) is omitted, and the first conduit 102a and the second conduit 102b are connected by a corner bend. Although the pipe arrangement of view (iv) is substantially similar to the pipe arrangement of view (i), it is vertically flipped so that the multiphase fluid 101 flowing through the pipe arrangement of view (iv) first flows downward and then flows upward. Although the pipe arrangement of view (v) is substantially similar to the pipe arrangement of view (i), the first conduit 102a and the second conduit 102b are coiled (i.e., include coiled pipes).

[0156] Figure 2CSchematic diagrams depicting various example tube arrangements. The tube arrangements shown in each of views (i), (ii), (iii), (iv) and (v) can be used in addition to or in place of the tube arrangements already described with respect to devices 100A, 100B, 100C, 100D, 100E, 100F, 100G, 100H, 100I and 100J. ΔP1 is a first pressure difference of a multiphase fluid 101 across a first elbow (bend or corner) flowing through each tube arrangement. ΔP2 is a second pressure difference of a multiphase fluid 101 across a second elbow (bend or corner) flowing through each tube arrangement. ΔP1 can be measured by a pair of pressure sensors or a single differential pressure sensor. Similarly, ΔP2 can be measured by a pair of pressure sensors or a single differential pressure sensor. The first pressure difference (ΔP1) and the second pressure difference (ΔP2) measured from any of these pipe arrangements can be used, for example, to determine properties (such as mixture density, total mass flow rate, or both) of the multiphase fluid 101 flowing through the corresponding pipe arrangement (e.g., using Equations 4a, 4b, 5a, 5b, 5c, 5d, or any combination of these equations).

[0157] For example, view (i) can be considered the base case, which usually meets Figure 1E and 1F . Although the pipe arrangement of view (ii) is substantially similar to the pipe arrangement of view (i), the first conduit 102a and the second conduit 102b of view (ii) deviate from the vertically oriented pipe (i.e., they are arranged at a non-zero angle relative to the vertical orientation) and are not necessarily straight pipes. Similarly, in view (iii), although the first conduit 102a and the second conduit 102b deviate from the vertically oriented pipe, they are straight pipes connected to the corner bend pipe. Although the pipe arrangement of view (iv) is substantially similar to the pipe arrangement of view (i), it is vertically flipped so that the multiphase fluid 101 flowing through the pipe arrangement of view (iv) first flows downward and then flows upward. Although the pipe arrangement of view (v) is substantially similar to the pipe arrangement of view (i), the first conduit 102a and the second conduit 102b are coiled (i.e., include coiled pipes).

[0158] Figure 2DSchematic diagrams depicting various example pipe arrangements. Each of views (i), (ii), (iii) and (iv) shows a pipe arrangement that can be used in addition to or in place of the pipe arrangements already described with respect to devices 100A, 100B, 100C, 100D, 100E, 100F, 100G, 100H, 100I and 100J. ΔP1 is a first pressure difference of a multiphase fluid 101 across a first elbow (bend or corner) flowing through each pipe arrangement. ΔP2 is a second pressure difference of a multiphase fluid 101 across a second elbow (bend or corner) flowing through each pipe arrangement. ΔP1 can be measured by a pair of pressure sensors or a single differential pressure sensor. Similarly, ΔP2 can be measured by a pair of pressure sensors or a single differential pressure sensor. ΔP3 is a third pressure difference of a multiphase fluid 101 flowing through a first conduit 102a of a corresponding pipe arrangement. ΔP4 is the fourth pressure difference of the multiphase fluid 101 flowing through the second conduit 102b of the corresponding pipe arrangement. ΔP3 can be measured by a pair of pressure sensors or a single pressure difference sensor. Similarly, ΔP4 can be measured by a pair of pressure sensors or a single pressure difference sensor. The first pressure difference (ΔP1), the second pressure difference (ΔP2), the third pressure difference (ΔP3) and the fourth pressure difference (ΔP4) measured from any of these pipe arrangements can be used, for example, to determine the characteristics of the multiphase fluid 101 flowing through the corresponding pipe arrangement (such as mixed density, total mass flow rate, water phase volume fraction, gas phase volume fraction or any combination of these characteristics) (for example, using equations 1, 1a, 1b, 2a, 2b, 2c, 2d, 2e, 2f, 2g, 2h, 3a, 3b, 4a, 4b, 5a, 5b, 5c, 5d or any combination of these equations).

[0159] For example, view (i) can be considered the base case, which usually meets Figure 1H and 1J 100H and 100J are shown in the figure. Although the pipe arrangement of view (ii) is substantially similar to the pipe arrangement of view (i), the first conduit 102a and the second conduit 102b of view (ii) deviate from the vertically oriented pipe and are connected by a corner bend. In the pipe arrangement of view (iii), the first pipe 150a and the second pipe 150b of the flow tube 150 are not in line with each other. Although the pipe arrangement of view (iv) is substantially similar to the pipe arrangement of view (i), it is vertically flipped so that the multiphase fluid 101 flowing through the pipe arrangement of view (iv) flows downward first and then upward.

[0160] Figure 2ESchematic diagrams depicting various example pipe arrangements. The pipe arrangements shown in each of views (i), (ii), (iii) and (iv) can be used in addition to or in place of the pipe arrangements already described with respect to devices 100A, 100B, 100C, 100D, 100E, 100F, 100G, 100H, 100I and 100J. ΔP1 is a first pressure difference of a multiphase fluid 101 across a first elbow (bend or corner) flowing through each pipe arrangement. ΔP2 is a second pressure difference of a multiphase fluid 101 across a second elbow (bend or corner) flowing through each pipe arrangement. ΔP1 can be measured by a pair of pressure sensors or a single differential pressure sensor. Similarly, ΔP2 can be measured by a pair of pressure sensors or a single differential pressure sensor. ΔP3 is a third pressure difference of a multiphase fluid 101 flowing through a first conduit 102a of a corresponding pipe arrangement. ΔP4 is a fourth pressure difference of a multiphase fluid 101 flowing through a second conduit 102b of a corresponding pipe arrangement. ΔP3 can be measured by a pair of pressure sensors or a single differential pressure sensor. Similarly, ΔP4 can be measured by a pair of pressure sensors or a single differential pressure sensor. The first differential pressure (ΔP1), the second differential pressure (ΔP2), the third differential pressure (ΔP3), and the fourth differential pressure (ΔP4) measured from any of these pipe arrangements can be used, for example, to determine the properties of the multiphase fluid 101 flowing through the corresponding pipe arrangement (such as mixed density, total mass flow rate, water phase volume fraction, gas phase volume fraction, or any combination of these properties) (e.g., using equations 1, 1a, 1b, 2a, 2b, 2c, 2d, 2e, 2f, 2g, 2h, 3a, 3b, 4a, 4b, 5a, 5b, 5c, 5d, or any combination of these equations).

[0161] Although the pipe arrangement of view (i) is similar to Figure 1H and 1J The pipe arrangements of the apparatuses 100H and 100J shown in FIG. 1 and 100B are substantially similar, but the first conduit 102a and the second conduit 102b of view (i) are not necessarily straight pipes. In the pipe arrangement of view (ii), the first conduit 102a and the second conduit 102b form a loop. Although the pipe arrangement of view (iii) is similar to Figure 2D The tube arrangement of view (i) is substantially similar to that of view (ii), but the first conduit 102a and the second conduit 102b are coiled (i.e., comprise coiled tubes). While the tube arrangement of view (iv) is substantially similar to the tube arrangement of view (ii), the first conduit 102a and the second conduit 102b form a corner loop, wherein the straight portions of the tubes are located between the corner bends. Furthermore, in the tube arrangement of view (iv), the first tube 150a and the second tube 150b of the flow tube 150 are not in line with each other.

[0162] Figure 2FSchematic diagrams depicting various example sensor arrangements. Any of the sensor arrangements shown in views (i), (ii), (iii), (iv) and (v) may be applied (alone or in combination) in addition to or in place of the sensor arrangements already described with respect to devices 100A, 100B, 100C, 100D, 100E, 100F, 100G, 100H, 100I and 100J.

[0163] As an example, view (i) can be considered the base case, which generally complies with Figure 1B , 1F 1 and 1J, respectively. The pressure sensor arrangement of view (ii) includes two pressure sensors that measure the static pressure at their respective locations. The difference between the measured static pressures can be determined as a pressure difference (similar to a differential pressure sensor). The pressure sensor arrangement of view (ii) is similar to Figure 1A , 1C , 1D, 1E, 1G, 1H and 1I respectively shown in the apparatus 100A, 100C, 100D, 100E, 100G, 100H and 100I are substantially similar. Although the differential pressure sensor arrangement in view (iii) is substantially similar to view (i), it includes redundant differential pressure sensors arranged in parallel across the same pipe length, which is similar to Figure 1C Although the differential pressure sensor arrangement in view (iv) is substantially similar to the differential pressure sensor arrangement in view (i), it includes an additional differential pressure sensor configured in series across the length of the pipe, which is similar to the differential pressure sensor arrangement in view (iv). Figure 1D The differential pressure sensor arrangement shown in the apparatus 100D in FIG. 1 is substantially similar. The sensor arrangement in view (v) includes a plurality of strain sensors (such as strain gauges) disposed along the length of the pipe. The measured strain can be correlated with the pressure, so that similar calculations can be performed to determine the characteristics of the flowing multiphase fluid 101.

[0164] Figure 3A 300A. For example, any of the devices 100H, 100I, or 100J may be used to implement the model 300A to characterize a multiphase fluid, such as the multiphase fluid 101. At box 301a, the pressure and temperature of the multiphase fluid 101 are determined (e.g., using pressure and temperature sensors). At box 303a, various properties (such as density, viscosity, and speed of sound) of the phases (gas phase 101a, water phase 101b', and oil phase 101b") of the multiphase fluid 101 are determined. For example, the gas phase density (ρ g ), water phase density of water phase 101b' (ρ a) and the oil phase density (ρ o At block 305a, the total flow rate (m ) of the multiphase fluid 101 is determined. T ) (e.g., using a differential pressure sensor such as in apparatus 100D). At block 307a, the mixed density (ρ) of the multiphase fluid 101 is determined (e.g., using a differential pressure sensor such as in apparatus 100A). At block 309a, the water-to-liquid ratio (R) of the multiphase fluid 101 is determined. WL ) (e.g., using a dynamic pressure sensor such as in apparatus 100E). At block 311a, based at least on the densities of the phases (determined at block 303a), the mixed density (ρ) of the multiphase fluid 101 (determined at block 307a), and the water-to-liquid ratio (R WL ) (determined at block 309a) to determine the gas volume fraction (α g ):ρ=(ρ a ×R WL +ρ o ×(1-R WL ))×(1-α g )+ρ g ×α g At block 313a, based on the gas volume fraction (α g ) and the total volume flow rate (Q) to determine the gas flow rate (Q) of the gas phase 101a g ): Q g =α g ×Q. At block 313a, based on the water-to-liquid ratio (R WL ), gas volume fraction (α g ) and the total flow rate (Q) to determine the water phase flow rate (Q) of the water phase 101b' a ): Q a =R WL ×(1-α g )×Q. At block 313a, based on the water-to-liquid ratio (R WL ), gas volume fraction (α g ) and the total volume flow rate (Q) to determine the oil phase flow rate (Q) of the oil phase 101b″ o ): Q o =(1-R WL )×(1-α g )×Q.

[0165] Figure 3B300B is a flow chart depicting an example multiphase fluid flow model. For example, any one of the devices 100A, 100B, 100C, 100D, 100H, 100I, or 100J can be used to implement the model 300B to characterize a multiphase fluid, such as a multiphase fluid 101. At box 301b, a first pressure difference (ΔP1) and a second pressure difference (ΔP2) of the flowing multiphase fluid 101 are measured. The first pressure difference (ΔP1) is measured across a specified pressure difference height (h) in a first direction. The second pressure difference (ΔP2) is measured across a specified pressure difference height (h) in a second direction (different from the first direction). The first direction and the second direction cause the multiphase fluid 101 to flow generally upward through the specified pressure difference height (h) in one direction of the first direction or the second direction, and generally flow downward through the specified pressure difference height (h) in the other direction. For example, the multiphase fluid 101 generally flows upward through the specified pressure difference height (h) in the first direction, and generally flows downward through the specified pressure difference height (h) in the second direction. For example, the multiphase fluid 101 flows generally downward through a specified pressure differential height (h) in a first direction and generally upward through a specified pressure differential height (h) in a second direction.

[0166] At block 303b, the friction pressure loss (ΔP ) of the flowing multiphase fluid 101 is calculated based on the first pressure difference (ΔP1) and the second pressure difference (ΔP2) measured at block 301b. f The friction pressure loss (ΔP ) may be calculated at block 303b by, for example, equation 2h. f ). At block 305b, the mixed density (ρ) of the multiphase fluid 101 is calculated based on the first pressure difference (ΔP1) and the second pressure difference (ΔP2) measured at block 301b. The mixed density (ρ) may be calculated at block 305b by, for example, equation 2d. At block 307b, the gas phase volume fraction (α ) of the multiphase fluid 101 is calculated based on the mixed density (ρ) determined at block 305b. g The gas phase volume fraction (α ) may be calculated at block 307b by, for example, equation 3b. g In some embodiments, the density of the liquid phase (ρ l ) and gas phase density (ρ g )) Calculate the gas phase volume fraction (α) at ​​block 307b g In such embodiments, the gas phase volume fraction (α ) can be calculated by Equation 6a. g ).

[0167]

[0168] In some embodiments, the total mass flow rate (m TThe total mass flow rate (m) may be determined, for example, by a mass flow meter and / or by any of equations 3a, 4a, or 4b. T ). The multiphase fluid flow model 300B assumes that the slip ratio (S) of the multiphase fluid 101 is substantially equal to 1. The slip ratio (S) is the ratio of the velocity of the gas phase to the velocity of the liquid phase (including the water phase and the oil phase) in the flowing multiphase fluid 101.

[0169] Figure 3C 300C is a flow chart depicting an example multiphase fluid flow model. For example, any one of the devices 100A, 100B, 100C, 100D, 100H, 100I, or 100J can be used to implement the model 300C to characterize a multiphase fluid, such as a multiphase fluid 101. At box 301c, a first pressure difference (ΔP1) and a second pressure difference (ΔP2) of the flowing multiphase fluid 101 are measured. The first pressure difference (ΔP1) across a specified pressure difference height (h) is measured in a first direction. The second pressure difference (ΔP2) across a specified pressure difference height (h) in a second direction (different from the first direction) is measured. The first direction and the second direction cause the multiphase fluid 101 to flow generally upward through the specified pressure difference height (h) in one direction of the first direction or the second direction, and generally flow downward through the specified pressure difference height (h) in the other direction. For example, the multiphase fluid 101 generally flows upward through the specified pressure difference height (h) in the first direction, and generally flows downward through the specified pressure difference height (h) in the second direction. For example, the multiphase fluid 101 flows generally downward through a specified pressure differential height (h) in a first direction and generally upward through a specified pressure differential height (h) in a second direction.

[0170] At block 303c, the friction pressure loss (ΔP ) of the flowing multiphase fluid 101 is calculated based on the first pressure difference (ΔP1) and the second pressure difference (ΔP2) measured at block 301c. f The friction pressure loss (ΔP ) may be calculated at block 303c, for example, by equation 2h. f At block 305c, the apparent mixed density (ρ) of the multiphase fluid 101 is estimated based on the first pressure difference (ΔP1) and the second pressure difference (ΔP2) measured at block 301c. app The apparent mixing density (ρ ) may be estimated at block 305c, for example, by equation 2d. app At block 307c, based on the apparent mixing density (ρ app ) to calculate the void fraction (λ g The void fraction (λ) may be calculated at block 307c, for example, by Equation 6b. g ).

[0171]

[0172] At block 309c, various operating conditions and / or properties (such as pressure, temperature, and salinity) of the flowing multiphase fluid 101 are determined. The conditions and / or properties determined at block 309c may be measured, for example, by external sensors (such as pressure sensors, temperature sensors, and brine samplers). At block 311c, the water-to-liquid ratio (R WL ). This can be done, for example, by external sensors (such as dynamic pressure sensors, such as Figure 1G The device 100G shown in FIG. 100B measures the water-to-liquid ratio (R) determined at block 311c. WL At block 313c, the density of each phase of the flowing multiphase fluid 101 (such as the density of the gas phase (ρ g ), the density of the water phase (ρ a ) and the density of the oil phase (ρ o )). For example, the density of each phase of the flowing multiphase fluid 101 may be determined at block 313c based on the operating conditions (pressure and temperature) of the flowing multiphase fluid 101 determined at block 309c. At block 313c, the density of the liquid phase (ρ l , including the density of the water phase and the oil phase). The density of each phase of the flowing multiphase fluid 101 and the water-liquid ratio (R WL ), the density of the liquid phase (ρ l The density of the liquid phase (ρ) can be determined at block 313c by equation 6c. l ).

[0173] ρ l =ρ a R WL +ρ o (1-R WL (6c) In some embodiments, the liquid phase density (ρ) determined at block 313c may be l ) and gas phase density (ρ g ) At block 307c the void fraction (λ g ).

[0174] At block 315c, based on the void fraction (λ) determined at block 307c g ) and the slip rate (S) of the flowing multiphase fluid 101 to calculate the gas phase volume fraction (α g ). In block 315c, it is used to determine the gas phase volume fraction (α g The slip ratio (S) of the gas phase can be measured, for example, by an external sensor or assumed to be substantially equal to 1 as an initial guess. At block 317c, based on the gas phase volume fraction (α ) determined at block 315c, g), the gas phase density (ρ g ) and the liquid phase density (ρ) determined at block 313c l ) is used to calculate the mixed density (ρ) of the multiphase fluid 101. The mixed density (ρ) may be determined at block 317c by equation 6d.

[0175] ρ=α g ρ g +(1-α g )ρ l (6d)

[0176] In some embodiments, the total mass flow rate (m T The total mass flow rate (m) may be determined, for example, by a mass flow meter and / or by any of equations 3a, 4a, or 4b. T In some embodiments, the blocks in the dashed box of the multiphase fluid flow model 300C (blocks 315c, 317c, determining the total mass flow rate (m T ) and determining the slip ratio (S). In some embodiments, the blocks in the dashed box of the multiphase fluid flow model 300C (blocks 315c, 317c, determining the total mass flow rate (m T ) and determine the slip ratio (S) until the calculated values ​​converge to the final value.

[0177] Figure 3D 300D. For example, any one of the devices 100A, 100B, 100C, 100D, 100H, 100I, or 100J can be used to implement the model 300D to characterize a multiphase fluid, such as the multiphase fluid 101. At box 301d, a first pressure difference (ΔP1) and a second pressure difference (ΔP2) of the flowing multiphase fluid 101 are measured. The first pressure difference (ΔP1) across a specified pressure difference height (h) is measured along a first direction. The second pressure difference (ΔP2) across a specified pressure difference height (h) along a second direction (different from the first direction) is measured. The first direction and the second direction cause the multiphase fluid 101 to flow generally upward through the specified pressure difference height (h) in one direction of the first direction or the second direction, and generally downward through the specified pressure difference height (h) in the other direction. For example, the multiphase fluid 101 generally flows upward through the specified pressure difference height (h) in the first direction, and generally flows downward through the specified pressure difference height (h) in the second direction. For example, the multiphase fluid 101 flows generally downward through a specified pressure differential height (h) in a first direction and generally upward through a specified pressure differential height (h) in a second direction.

[0178] At block 303d, the friction pressure loss (ΔP ) of the flowing multiphase fluid 101 is calculated based on the first pressure difference (ΔP1) and the second pressure difference (ΔP2) measured at block 301d. f The friction pressure loss (ΔP ) may be calculated at block 303d, for example, by equation 2h. f At block 305d, the apparent mixed density (ρ) of the multiphase fluid 101 is estimated based on the first pressure difference (ΔP1) and the second pressure difference (ΔP2) measured at block 301d. app The apparent mixing density (ρ ) may be estimated at block 305d, for example, by equation 2d. app ).

[0179] At block 307d, various operating conditions and / or properties (such as pressure, temperature, and salinity) of the flowing multiphase fluid 101 are determined. The conditions and / or properties determined at block 307d may be measured, for example, by external sensors (such as pressure sensors, temperature sensors, and brine samplers). At block 309d, the densities of the various phases of the flowing multiphase fluid 101 (such as the density of the gas phase (ρ g ), the density of the water phase (ρ a ) and the density of the oil phase (ρ o )). At block 309d, the densities of the various phases of the flowing multiphase fluid 101 may be determined, for example, based on the operating conditions (pressure and temperature) of the flowing multiphase fluid 101 determined at block 307d. At block 311d, the gas phase volume fraction (α g The gas phase volume fraction (α ) determined at block 311d may be measured, for example, by an external sensor such as an ultrasonic sensor. g ).

[0180] At block 313d, based on the gas volume fraction (α g ) and the slip rate (S) of the flowing multiphase fluid 101 to calculate the void fraction (λ) of the multiphase fluid 101 g ). At block 313d, it is used to determine the void fraction (λ g The slip ratio (S) of the liquid phase (ρ) can be measured, for example, by an external sensor or assumed to be substantially equal to 1 as an initial guess. At block 315d, the liquid phase (ρ l , including the density of the water phase and the oil phase). The apparent mixed density (ρ app ), the densities of the various phases of the flowing multiphase fluid 101 determined at block 309d, and the void fraction (λ) determined at block 313d g ) to determine the density of the liquid phase (ρ l The density of the liquid phase (ρ) may be calculated at block 315d, for example, by Equation 6e.l ).

[0181]

[0182] At block 317d, based on the gas phase density (ρ g ), the gas phase volume fraction (α g ) and the liquid phase density (ρ l ) calculates the mixed density (ρ) of the multiphase fluid 101. The mixed density (ρ) may be determined at block 317c by equation 6d.

[0183] In some embodiments, the total mass flow rate (m T The total mass flow rate (m) may be determined, for example, by a mass flow meter and / or by any of equations 3a, 4a, or 4b. T In some embodiments, the blocks in the dashed box of the multiphase fluid flow model 300D (blocks 313d, 315d, 317d, determining the total mass flow rate (m T ) and determining the slip ratio (S). In some embodiments, the blocks in the dashed box of the multiphase fluid flow model 300D (blocks 313d, 315d, 317d, determining the total mass flow rate (m T ) and determine the slip ratio (S) until the calculated value converges to the final value. At box 319, the water-to-liquid ratio (R WL ). R can be solved at block 319d by rearranging Equation 6c. WL To determine the water-liquid ratio (R WL ).

[0184] Figure 3E 300E is a flow chart depicting an example multiphase fluid flow model 300E. For example, the model 300E can be implemented using any of the devices 100E, 100F, 100H, 100I, or 100J to characterize a multiphase fluid, such as multiphase fluid 101. At box 301e, a first pressure differential (ΔP1) and a second pressure differential (ΔP2) of the flowing multiphase fluid 101 are measured. The first pressure differential (ΔP1) is measured across a first bend in the pipe. The second pressure differential (ΔP2) is measured across a second bend in the pipe. The multiphase fluid 101 generally flows upward through either the first bend or the second bend, and generally flows downward through the other of the first bend or the second bend. For example, the multiphase fluid 101 generally flows upward through the first bend, and generally flows downward through the second bend. For example, the multiphase fluid 101 generally flows downward across the first bend and generally flows upward across the second bend. About Figure 1E , 1F , 1H, 1I and 1J respectively provide examples. At block 303e, either the first pressure difference (ΔP1) or the second pressure difference (ΔP2) measured at block 301e is selected for further calculation in model 300E.

[0185] At block 305e, the void fraction (λ g The void fraction (λ) determined at block 305e may be measured, for example, by an external sensor such as an ultrasonic sensor. g At block 307e, various operating conditions and / or properties (such as pressure, temperature, and salinity) of the flowing multiphase fluid 101 are determined. The conditions and / or properties determined at block 307e may be measured, for example, by external sensors (such as pressure sensors, temperature sensors, and brine samplers). At block 309e, the water-to-liquid ratio (R WL ). This can be accomplished, for example, by external sensors (such as dynamic pressure sensors, such as Figure 1G The device 100G shown in FIG. 1 measures the water-to-liquid ratio (R) determined at block 309e. WL At block 311e, the density of each phase of the flowing multiphase fluid 101 (such as the density of the gas phase (ρ g ), the density of the water phase (ρ a ) and the density of the oil phase (ρ o )). The density of each phase of the flowing multiphase fluid 101 may be determined at block 311e, for example based on the operating conditions (pressure and temperature) of the flowing multiphase fluid 101 determined at block 307e. At block 311e, the liquid phase (ρ l , including the density of the water phase and the oil phase). The density of each phase of the flowing multiphase fluid 101 and the water-liquid ratio (R ) determined at block 309e can be determined at block 311e based on the density of each phase of the flowing multiphase fluid 101 and the water-liquid ratio (R WL ) to determine the density of the liquid phase (ρ l The density of the liquid phase (ρ) can be determined at block 311e by equation 6c. l In some embodiments, the liquid phase density (ρ l ) and gas phase density (ρ g ) At block 305e, the void fraction (λ g ).

[0186] At block 313e, based on the void fraction (λ) determined at block 305e, g ) and the slip rate (S) of the flowing multiphase fluid 101 to calculate the gas phase volume fraction (αg ). In block 313e, it is used to determine the gas phase volume fraction (α g The slip ratio (S) of the gas phase (α) can be measured, for example, by an external sensor or assumed to be substantially equal to 1 as an initial guess. At block 315e, based on the gas phase volume fraction (α) determined at block 313e, g ), the gas phase density (ρ g ) and the liquid phase density (ρ) determined at block 311e l ) to calculate the mixed density (ρ) of the multiphase fluid 101. The mixed density (ρ) can be determined at block 315e by equation 6d. At block 317e, the total mass flow rate (m T Total mass flow rate (m T ) may be determined at block 317e, for example, by a mass flow meter and / or by any of equations 4a or 4b based on the pressure differential selected at block 303e. In some embodiments, the blocks in the dashed box of the multiphase fluid flow model 300E (blocks 313e, 315e, 317e, and determining the slip ratio (S)) are executed simultaneously (e.g., executed in parallel). In some embodiments, the blocks in the dashed box of the multiphase fluid flow model 300E (blocks 313e, 315e, 317e, and determining the slip ratio (S)) are iteratively executed (e.g., executed in series) until the calculated values ​​converge to the final value.

[0187] Figure 3F is a flow chart depicting an example multiphase fluid flow model 300F. For example, the model 300F can be implemented using any of the devices 100H, 100I, or 100J to characterize a multiphase fluid, such as the multiphase fluid 101. At box 301f, a first pressure difference (ΔP1) and a second pressure difference (ΔP2) of the flowing multiphase fluid 101 are measured. The first pressure difference (ΔP1) is measured across a first bend in the pipe. The second pressure difference (ΔP2) is measured across a second bend in the pipe. The multiphase fluid 101 generally flows upward through either the first bend or the second bend, and generally flows downward through the other of the first bend or the second bend. For example, the multiphase fluid 101 generally flows upward through the first bend, and generally flows downward through the second bend. For example, the multiphase fluid 101 generally flows downward across the first bend, and generally flows upward across the second bend. About Figure 1E , 1F , 100F, 100H, 100I, and 100J shown in FIGS. 1A, 1B, 1C, and 1D, respectively, provide examples.

[0188] At box 303f, a third pressure difference (ΔP3) and a fourth pressure difference (ΔP4) of the flowing multiphase fluid 101 are measured. The third pressure difference (ΔP1) is measured across a specified pressure difference height (h) in a first direction. The second pressure difference (ΔP2) across a specified pressure difference height (h) in a second direction (different from the first direction) is measured. The first direction and the second direction cause the multiphase fluid 101 to flow upward approximately across the specified pressure difference height (h) in one direction of the first direction or the second direction, and flow downward approximately across the specified pressure difference height (h) in the other direction. For example, the multiphase fluid 101 flows upward approximately across the specified pressure difference height (h) in the first direction and flows downward approximately across the specified pressure difference height (h) in the second direction. For example, the multiphase fluid 101 flows downward approximately across the specified pressure difference height (h) in the first direction and flows upward approximately across the specified pressure difference height (h) in the second direction.

[0189] At block 305f, the friction pressure loss (ΔP ) of the flowing multiphase fluid 101 is calculated based on the third pressure difference (ΔP 3 ) and the fourth pressure difference (ΔP 4 ) measured at block 303f. f ). Friction pressure loss (ΔP f ) can be calculated at block 305f by, for example, equation 2h. At block 307f, the apparent mixed density (ρ) of the multiphase fluid 101 is estimated based on the third pressure difference (ΔP3) and the fourth pressure difference (ΔP4) measured at block 303f. app The apparent mixing density (ρ) may be estimated at block 307f by, for example, equation 2d. app At box 309f, based on the apparent mixing density (ρ app ) to calculate the void fraction (λ g The void fraction (λ) may be calculated at block 309f by, for example, Equation 6b. g ).

[0190] At block 311f, various operating conditions and / or properties (such as pressure, temperature, and salinity) are determined regarding the flowing multiphase fluid 101. The conditions and / or properties determined at block 311f may be measured, for example, by external sensors (such as pressure sensors, temperature sensors, and brine samplers). At block 313f, the water-to-liquid ratio (R WL ). This can be done, for example, by external sensors (such as dynamic pressure sensors, such as Figure 1G The device 100G shown in FIG. 100B measures the water-to-liquid ratio (R) determined at block 313f. WL At block 315f, the density of each phase of the flowing multiphase fluid 101 (such as the density of the gas phase (ρ g ), the density of the water phase (ρ a) and the density of the oil phase (ρ o )). The density of each phase of the flowing multiphase fluid 101 can be determined at block 315f, for example, based on the operating conditions (pressure and temperature) of the flowing multiphase fluid 101 determined in block 311f. At block 315f, the liquid phase (ρ l , including the density of the water phase and the oil phase). The density of each phase of the flowing multiphase fluid 101 and the water-liquid ratio (R ) determined at block 315f can be determined at block 313f. WL ) to determine the density of the liquid phase (ρ l The density of the liquid phase (ρ) can be determined at block 315f by equation 6c. l In some embodiments, the density of the liquid phase (ρ ) may be determined at block 309f based on the density of the liquid phase (ρ ) determined at block 315f. l ) and the density of the gas phase (ρ g ) to calculate the void fraction (λ g ).

[0191] In block 317f, based on the void fraction (λ g ) and the slip rate (S) of the flowing multiphase fluid 101 to calculate the gas phase volume fraction (α g ). In block 317f, it is used to determine the gas phase volume fraction (α g The slip ratio (S) of the gas phase can be measured, for example, by an external sensor or assumed to be substantially equal to 1 as an initial guess. At block 319f, based on the gas phase volume fraction (α g ), the gas phase density (ρ g ) and the liquid phase density (ρ) determined at block 315f l ) is used to calculate the mixed density (ρ) of the multiphase fluid 101. The mixed density (ρ) can be determined at block 319f by equation 6d.

[0192] Based on the friction pressure loss (ΔP f ) determines the friction coefficient (q) of the flowing multiphase fluid 101 h At block 323f, the horizontal flow dynamic pressure (f d ) and vertical flow dynamic pressure (q v The horizontal flow dynamic pressure (q ) determined at block 323f may be measured, for example, by an external sensor such as a dynamic pressure sensor. h ) and vertical flow dynamic pressure (q v ). In some embodiments, by Equation 6f h Determine the horizontal flow dynamic pressure (q h ). In some embodiments, by Equation 6fv Determine the vertical flow dynamic pressure (q v In some embodiments, the friction coefficient (f) is determined at block 321f by equation 6g. d ), which depends on the horizontal flow dynamic pressure (q h ) and vertical flow dynamic pressure (q v ) (e.g., via a sensor or via Equation 6f h and 6f v) .

[0193]

[0194] In equation 6f h A h is the cross-sectional flow area of ​​the horizontal flow of the multiphase fluid 101. In Equation 6f v A v is the cross-sectional flow area of ​​the vertical flow of the multiphase fluid 101. In Equation 6g, h is the specified pressure difference height, and D v It is the inner diameter of the conduit in which the flow direction of the multiphase fluid 101 is generally upward or generally downward.

[0195] At block 325f, the total mass flow rate (m T The total mass flow rate (m) may be determined at block 325f. T ), for example, by a mass flow meter and / or by any of equations 4a or 4b. Total mass flow (m T ) can be determined at block 325f based on the first pressure difference (ΔP1) and the second pressure difference (ΔP2) measured at block 301f, the mixed density (ρ) determined at block 319f, the friction coefficient (f) determined at block 321f, and the pressure difference (ΔP2) measured at block 301f. d ) and the horizontal flow dynamic pressure (q h ) and vertical flow dynamic pressure (q v In some embodiments, the total mass flow rate (m) is determined at block 325f by equation 6h. T ).

[0196]

[0197] Among them C d is the empirically characterized flow coefficient, ε is the expansion factor, and K is the fixed geometric factor ( Where A is the cross-sectional flow area of ​​the elbow throat, β is the beta ratio (d / D, where d is the inside diameter downstream of the elbow and D is the inside diameter upstream of the elbow), ΔP Lis the pressure difference across the elbow (select one of the first pressure difference (ΔP1) or the second pressure difference (ΔP2)), g is the acceleration caused by gravity, y is the vertical height difference between the pressure ports of the differential pressure sensor, x is the horizontal distance between the pressure ports of the differential pressure sensor, and D′ h is the equivalent (effective) inner diameter of the cross-sectional flow area for horizontal flow of the multiphase fluid 101, and D v ' is the equivalent (effective) inner diameter of the cross-sectional flow area for vertical flow of the multiphase fluid 101.

[0198] In some embodiments, the boxes in the dashed box of the multiphase fluid flow model 300F (boxes 317f, 319f, 321f, 323f, 325f and determining the slip ratio (S)) are executed simultaneously (e.g., executed in parallel). In some embodiments, the boxes in the dashed box of the multiphase fluid flow model 300F (boxes 317f, 319f, 321f, 323f, 325f and determining the slip ratio (S)) are iteratively executed (e.g., executed in series) until the calculated values ​​converge to the final value. At box 327f, various volume flow rates of the multiphase fluid 101 are determined. The various volume flow rates determined at box 327f may include the total volume flow rate (Q of the multiphase fluid 101). T ), the gas phase volume flow rate (Q g ), the liquid phase volume flow rate (Q l , including water phase and oil phase), the oil phase volume flow rate (Q o ) and the water phase volume flow rate (Q a ). It can be obtained by Equation 6j t 、6j g 、6j l 、6j o and 6j a The various volumetric flow rates determined at block 327f are calculated.

[0199]

[0200] Q g =Q T α g (6j g )

[0201] Q l =Q T (1-α g ) (6j l )

[0202] Q o =Q T (1-R WL ) (6j o )

[0203] Q a =Q T R WL (6j a )

[0204] Figure 3G 300G is a flow chart depicting an example multiphase fluid flow model. For example, any one of the devices 100H, 100I or 100J can be used to implement the model 300G to characterize a multiphase fluid, such as a multiphase fluid 101. At box 301g, various operating conditions (such as pressure and temperature) about the flowing multiphase fluid 101 are determined. The various operating conditions determined at box 301g can be measured, for example, by external sensors (such as pressure sensors and temperature sensors). The various operating conditions determined at box 301g can include, for example, differential pressure measurements. At box 303g, the salinity of the water phase of the multiphase fluid 101 is measured. The salinity of the water phase of the multiphase fluid 101 can be measured at box 303g, for example, using a salinity sensor. In some embodiments, the salinity sensor includes an electrode for generating an electric current to measure the conductivity of the water phase of the multiphase fluid 101. At box 305g, the fluid properties (such as density) of each phase (such as a gas phase, a water phase, and an oil phase) of the multiphase fluid 101 are determined. The fluid properties of each phase can be determined at block 305g based on the operating conditions measured at block 301g and the salinity of the water phase measured at block 303g. At block 307g, the void fraction (λ) of the multiphase fluid 101 is determined. g The void fraction (λ) may be determined at block 307g, for example, using an external sensor (such as an ultrasonic sensor) and / or by Equation 6b. g At block 309g, the water-to-liquid ratio (R WL At block 309g, the water-to-liquid ratio (R ) may be determined, for example, using an external sensor such as a dynamic pressure sensor. WL At block 311g, determine the liquid phase (ρ l , including the density of the water phase and the oil phase). At block 311g, the density of each phase of the flowing multiphase fluid 101 and the water-to-liquid ratio (R WL ) to determine the density of the liquid phase (ρ l At block 311g, the density of the liquid phase (ρ) may be determined, for example, by Equation 6c. l ).

[0205] At block 313g, based on the void fraction (λ) determined at block 307g, g ) and the slip rate (S) of the flowing multiphase fluid 101 to calculate the gas phase volume fraction (α g). In block 313g, it is used to determine the gas phase volume fraction (α g The slip ratio (S) of the gas phase (α) can be measured, for example, by an external sensor or assumed to be substantially equal to 1 as an initial guess. At box 315g, based on the gas phase volume fraction (α) determined at box 313g, g ), the gas phase density (ρ g ) and the liquid density (v l ) to calculate the mixed density (ρ) of the multiphase fluid 101. The mixed density (ρ) can be determined at block 315g, for example, by equation 6d. At block 317g, the total mass flow rate (m T The total mass flow rate (m) may be determined at block 317g. T ), for example, by a mass flow meter and / or by any of equations 4a or 4b. In some embodiments, the boxes in the dashed box of the multiphase fluid flow model 300G (boxes 313g, 315g, 317g and determining the slip ratio (S)) are executed simultaneously (e.g., executed in parallel). In some embodiments, the boxes in the dashed box of the multiphase fluid flow model 300G (boxes 313g, 315g, 317g and determining the slip ratio (S)) are iteratively executed (e.g., executed in series) until the calculated value converges to the final value.

[0206] At block 319g, various volumetric flow rates of the multiphase fluid 101 are determined. The various volumetric flow rates determined at block 319g may include the total volumetric flow rate (Q T ), the gas phase volume flow rate (Q g ), the liquid phase volume flow rate (Q l , including water phase and oil phase), the oil phase volume flow rate (Q o ) and the water phase volume flow rate (Q a ). It can be obtained by Equation 6j t 、6j g 、6j l 、6j o and 6j a The various volumetric flow rates determined at block 319g are calculated.

[0207] Figure 44 is a flow chart of an example method 400 for measuring the density of a multiphase fluid 101. For example, the method 400 may be implemented using any of the apparatuses 100A, 100B, 100C, 100D, 100H, 100I, or 100J. At block 402, a multiphase fluid (such as the multiphase fluid 101) flows through a U-bend (such as the U-bend 102). The multiphase fluid 101 may include a gas phase 101a, a water phase 101b' and an oil phase 101b". As described above, the U-bend 102 includes a first conduit 102a, a second conduit 102b and a connecting conduit 102c. The first conduit 102a is parallel to the second conduit 102b. The connecting conduit 102c connects the second conduit 102b to the first conduit 102a. Each of the first conduit 102a, the second conduit 102b and the connecting conduit 102c has substantially the same cross-sectional flow area for the multiphase fluid 101 flowing through the U-bend 102. The multiphase fluid 101 flowing through the U-bend 102 flows into the first conduit 102a, flows through the connecting conduit 102c, and then flows out of the second conduit 102b. At box 404, the first pressure drop of the multiphase fluid 101 along the first conduit 102a across a specified pressure difference height (h) is measured. A first pressure difference (ΔP1) of the multiphase fluid 101 can be measured, for example, at box 404 by a first pair of pressure sensors 104a, 104b. At box 406, a second pressure difference (ΔP2) of the multiphase fluid 101 along the second conduit 102b across a specified pressure difference height (h) is measured. For example, the second pressure difference (ΔP2) of the multiphase fluid 101 can be measured at box 406 by a second pair of pressure sensors 104c, 104d. At box 408, a mixture density (ρ) of the multiphase fluid 101 is determined based on at least a difference between the first pressure difference (ΔP1) and the second pressure difference (ΔP2) of the multiphase fluid 101 (measured at boxes 404 and 406, respectively) and the specified pressure difference height (h). For example, the mixture density (ρ) of the multiphase fluid 101 can be determined at box 406 using equation 2d.

[0208] In some embodiments, method 400 includes determining a gas phase volume fraction (α) of multiphase fluid 101 based on at least g ), the gas density (ρ g ), water phase density (ρ a ), the oil phase density (ρ o ) and the mixed density (ρ) of the multiphase fluid 101 to determine the water phase volume fraction (α a For example, the gas phase volume fraction (α g ), gas density (ρ g ), water phase density (ρ a), oil phase density (ρ o ) and the mixture density (ρ) are input into Equation 3b and rearranged to calculate the water phase volume fraction (α a ).

[0209] In some embodiments, method 400 includes determining a volume fraction of a water phase (α) of multiphase fluid 101 based on at least a ), the gas density (ρ g ), water phase density (ρ a ), the oil phase density (ρ o ) and the mixed density (ρ) of the multiphase fluid 101 to determine the gas phase volume fraction (α g For example, the water phase volume fraction (α a ), gas density (ρ g ), water phase density (ρ a ), oil phase density (ρ o ) and the mixture density (ρ) are input into Equation 3b and rearranged to calculate the gas phase volume fraction (α g ).

[0210] Figure 5is a flow chart of an example method 500 for measuring the total flow of a multiphase fluid 101. For example, the method 500 may be implemented using any of the apparatuses 100E, 100H, 100I, or 100J. At block 502, a multiphase fluid (such as the multiphase fluid 101) flows from a flow tube (such as the flow tube 150) to a U-bend (such as the U-bend 102). The multiphase fluid 101 may include a gas phase 101a, a water phase 101b' and an oil phase 101b". As described above, the U-bend 102 includes a first conduit 102a, a second conduit 102b and a connecting conduit 102c. The connecting conduit 102c connects the first conduit 102a to the second conduit 102b. The multiphase fluid 101 flowing through the U-bend 102 flows into the first conduit 102a, flows through the connecting conduit 102c, and then flows out of the second conduit 102b. The flow pipe 150 includes a first pipe 150a (third conduit) and a second pipe 150b (fourth conduit). The first pipe 150a passes through the first bend. A tube (such as the first corner bend 153a) is connected to the first conduit 102a of the U-bend 102. The second tube 150b is connected to the second conduit 102b of the U-bend 102 through a second bend (such as the second corner bend 153b). Flowing the multiphase fluid 101 from the flow tube 150 to the U-bend 102 at block 502 includes flowing the multiphase fluid 101 from the first tube 150a of the flow tube 150 through the first corner bend 153a to the first conduit 102a of the U-bend 102. At block 504, the multiphase fluid 101 is flowed from the U-bend 102 to the flow tube 150. At block 504 Flowing the multiphase fluid 101 from the U-bend 102 to the flow tube 150 includes flowing the multiphase fluid 101 from the second conduit 102b of the U-bend 102 through the second corner bend 153b to the second tube 150b of the flow tube 150. At block 506, a first pressure differential of the multiphase fluid 101 is measured between a first location on the first tube 150a of the flow tube 150 and a second location on the first conduit 102a of the U-bend 102. For example, the first pressure differential of the multiphase fluid 101 can be measured at block 506 by a first pressure sensor 104a coupled to the first tube 150a of the flow tube 150 at the first location. At block 508, a second differential pressure of the multiphase fluid 101 is measured between a third position on the second conduit 102b of the U-bend 102 and a fourth position on the second tube 150b of the flow tube 150. At block 508, the second differential pressure of the multiphase fluid 101 may be measured by a third pressure sensor 104c coupled to the second conduit 102b of the U-bend 102 at the third position and a fourth pressure sensor 104d coupled to the second tube 150b of the flow tube 150 at the fourth position.At block 510, a total flow rate of the multiphase fluid 101 is determined based on at least the first pressure differential (measured at block 506), the second pressure differential (measured at block 508), the difference between the first pressure differential and the second pressure differential, and the total density of the multiphase fluid 101. For example, the total mass flow rate (m) of the multiphase fluid 101 may be determined at block 510 using Equation 4a. T1 For example, the total mass flow rate (m ) of the multiphase fluid 101 may be determined at block 510 using Equation 4b. T2 In some embodiments, the method 500 includes comparing the total flow rate (m ) of the multiphase fluid 101 determined at block 510 to the total flow rate (m ) of the multiphase fluid 101 determined at block 510. T1 ,m T2 ) (e.g., determined by Equations 4a and 4b) to determine the adjustment of the flow coefficient (e.g., C d1 ,C d2 ).

[0211] Figure 66 is a flow chart of an example method 600 for measuring mixed density, total flow, and phase flow of a multiphase fluid 101. For example, the method 600 may be implemented using any of the apparatuses 100H, 100I, or 100J. At block 602, a multiphase fluid (such as the multiphase fluid 101) flows from a flow tube (such as the flow tube 150) to a U-bend (such as the U-bend 102). The multiphase fluid 101 may include a gas phase 101a, a water phase 101b' and an oil phase 101b". As described above, the U-bend 102 includes a first conduit 102a, a second conduit 102b and a connecting conduit 102c. The connecting conduit 102c connects the first conduit 102a to the second conduit 102b. The multiphase fluid 101 flowing through the U-bend 102 flows into the first conduit 102a, flows through the connecting conduit 102c, and then flows out of the second conduit 102b. The flow pipe 150 includes a first pipe 150a (third conduit) and a second pipe 150b (fourth conduit). The first pipe 150a passes through the first bend. A tube (such as the first corner bend 153a) is connected to the first conduit 102a of the U-bend 102. The second tube 150b is connected to the second conduit 102b of the U-bend 102 through a second bend (such as the second corner bend 153b). Flowing the multiphase fluid 101 from the flow tube 150 to the U-bend 102 at block 602 includes flowing the multiphase fluid 101 from the first tube 150a of the flow tube 150 through the first corner bend 153a to the first conduit 102a of the U-bend 102. At block 604, the multiphase fluid 101 is flowed from the U-bend 102 to the flow tube 150. At block 604 Flowing the multiphase fluid 101 from the U-bend 102 to the flow tube 150 includes flowing the multiphase fluid 101 from the second conduit 102b of the U-bend 102 through the second corner bend 153b to the second tube 150b of the flow tube 150. At block 606, a first pressure differential of the multiphase fluid 101 is measured between a first location on the first tube 150a of the flow tube 150 and a second location on the first conduit 102a of the U-bend 102. For example, the first pressure differential of the multiphase fluid 101 can be measured at block 606 by a first pressure sensor 104a coupled to the first tube 150a of the flow tube 150 at the first location. At block 608, a second differential pressure of the multiphase fluid 101 is measured between a third position on the second conduit 102b of the U-bend 102 and a fourth position on the second tube 150b of the flow tube 150. At block 608, the second differential pressure of the multiphase fluid 101 may be measured by a third pressure sensor 104c coupled to the second conduit 102b of the U-bend 102 at the third position and a fourth pressure sensor 104d coupled to the second tube 150b of the flow tube 150 at the fourth position.At box 610, a third pressure differential of the multiphase fluid 101 across a specified height (such as a specified height h) is measured along the longitudinal length of the first conduit 102a of the U-bend 102. At box 610, the third pressure differential of the multiphase fluid 101 may be measured by a third pair of pressure sensors 104e, 104f coupled to the first conduit 102a. At box 612, a fourth pressure differential of the multiphase fluid 101 across a specified height (h) is measured along the longitudinal length of the second conduit 102b of the U-bend 102. At box 612, the fourth pressure differential of the multiphase fluid 101 may be measured by a fourth pair of pressure sensors 104g, 104h coupled to the second conduit 102b. At box 614, a mixture density (ρ) of the multiphase fluid 101 is determined based on at least the difference between the third pressure differential (ΔP3) and the fourth pressure differential (ΔP4) of the multiphase fluid 101 (measured at boxes 610 and 612, respectively) and the specified height (h). For example, the mixture density (ρ) of the multiphase fluid 101 may be determined at block 614 using Equation 2d, where ΔP1 replaces the third pressure differential (ΔP3) measured at block 610 by the third pair of pressure sensors 104e, 104f, ΔP2 replaces the fourth pressure differential (ΔP4) measured at block 612 by the fourth pair of pressure sensors 104g, 104h, and h2 replaces the specified height (h). At block 616, the total flow rate of the multiphase fluid 101 is determined based on at least the first pressure differential (measured at block 606), the second pressure differential (measured at block 608), and the mixture density of the multiphase fluid 101 (determined at block 614). For example, the total mass flow rate (m) of the multiphase fluid 101 may be determined at block 616 using Equation 4a. T1 For example, the total mass flow rate (m ) of the multiphase fluid 101 may be determined at block 616 using Equation 4b. T2 ).

[0212] In some embodiments, the method 600 includes comparing the total flow rate (m) of the multiphase fluid 101 determined at block 616 with the total flow rate (m) of the multiphase fluid 101 determined at block 616. T1 ,m T2 ) (e.g., determined by Equations 4a and 4b) to determine the flow coefficient (C d1 ,C d2). In an embodiment in which method 600 is performed by device 100G, method 600 may include measuring various dynamic pressures of the multiphase fluid 101 flowing through the U-bend 102. The dynamic pressure of the multiphase fluid 101 may be measured, for example, by dynamic pressure sensors 106a, 106b, 106c. The dynamic pressure measurements made by the dynamic pressure sensors 106a, 106b, 106c may be cross-correlated (e.g., by processor 705) to determine the sound velocity of the multiphase fluid 101 flowing through the U-bend 102. The sound velocity of the multiphase fluid 101 and the mixed density (ρ) of the multiphase fluid 101 may then be used to determine the water-to-liquid ratio of the multiphase fluid 101. For example, the sound velocity of the multiphase fluid 101 and the mixed density (ρ) of the multiphase fluid 101 may be compared to plots of various phase curves (gas / oil, gas / water, oil / water) to determine the water-to-liquid ratio.

[0213] Figure 7 is a block diagram of an example computer 700 for providing computing functions associated with the algorithms, methods, functions, processes, flows, and programs described in this specification, according to an embodiment. The illustrated computer 700 is intended to cover any computing device, such as a server, a desktop computer, a laptop / notebook computer, one or more processors in these devices, or any other processing device, including physical or virtual instances (or both) of computing devices. In addition, the computer 700 may include a computer that includes an input device, such as a keypad, a keyboard, a touch screen, or other device that can accept user information, and an output device that conveys information related to the operation of the computer 700 (including digital data, visual, audio information, or a combination of information).

[0214] Computer 700 includes interface 704. Although Figure 7 704, two or more interfaces 704 may be used depending on the particular needs, desires, or particular implementation of the computer 700. Figure 7700 is not shown, but the computer 700 can be connected to the network communication. The interface 704 is used by the computer 700 to communicate with other systems connected to the network in a distributed environment. Generally, the interface 704 includes logic encoded in software or hardware (or a combination of software and hardware), and is operable to communicate with the network. More specifically, the interface 704 may include software supporting one or more communication protocols associated with the communication, so that the hardware of the network or interface is operable to transmit physical signals inside and outside the computer 700 shown. The interface 704 may include a control interface, which may be used to connect the computer 700 to the control. In some embodiments, the control interface is a group of relays, a group of MOSFET power controllers, a serial peripheral interface (SPI) or a field bus, etc. The interface 704 may include a sensor interface, which may be used to connect the computer 700 to a sensor. In some embodiments, the sensor interface is a group of analog-to-digital converters (ADC) and I2C bus, a serial peripheral interface (SPI) bus or a field bus, etc. The interface 704 may include a man-machine interface, which may be used by a user to interact with the computer 700. In some embodiments, the human-machine interface includes a monitor or touch screen configured to display information to a user, for example.

[0215] Computer 700 includes processor 705. Processor 705 may be a microprocessor, a multi-core processor, a multi-threaded processor, an ultra-low voltage processor, an embedded processor, or a virtual processor. In some embodiments, processor 705 may be part of a system on a chip (SoC), where processor 705 and other components of computer 700 are formed as a single integrated electronic package. In some embodiments, processor 705 may include a processor from Santa Clara, California processors from Advanced Micro Devices, Inc. (AMD) of Sunnyvale, California, or processors from ARM Holdings, LTD. of Cambridge, England. Any number of other processors from other vendors may also be used. Although Figure 7705, but two or more processors may be used depending on the specific needs, expectations, or specific implementations of the computer 700. Typically, the processor 705 executes instructions and manipulates data to perform the operations of the computer 700 and any algorithms, methods, functions, processes, flows, and programs described in this specification. The processor 705 may communicate with other components of the computer 700 via a bus. The bus may include any number of technologies, such as an industry standard architecture (ISA), an extended ISA (EISA), a peripheral component interconnect (PCI), a peripheral component interconnect extension (PCIx), PCI express (PCIe), or any number of other technologies. The bus may be a proprietary bus, for example, for a system based on a SoC. Other bus technologies may also be used in addition to or in place of the above-mentioned technologies.

[0216] The computer 700 may also include a database 706 that may store data for the computer 700 or other components that may be connected to the network (or a combination of both). Figure 7 A single database 706 is shown, but two or more databases (of the same or combined type) may be used depending on the specific needs, expectations, or specific implementations of the computer 700 and the functions described. Although the database 706 is shown as an integral part of the computer 700, the database 706 may be external to the computer 700. The database 706 may be used to store information persistently, such as data, applications, operating systems, and the like. The database 706 may be a non-volatile RAM, a solid-state disk drive, or a flash drive, and the like. In some embodiments, the database 306 will include a hard drive, such as a micro hard drive, a conventional hard drive, or a hard drive array, such as associated with a DCS or cloud server.

[0217] The computer 700 also includes a memory 707 that can store data for the computer 700 or other components that can be connected to the network (or a combination of both). Figure 7707 is shown as a single memory 707, but two or more memories (of the same or combined type) 707 may be used depending on the specific needs, expectations, or specific implementations of the computer 700 and the functions described. Although the memory 707 is shown as an integrated component of the computer 700, the memory 707 may be external to the computer 700. The memory 707 may be a temporary or non-temporary storage medium. In some embodiments, such as in PLCs and other process control units, the memory 707 is integrated with a database 706 for long-term storage of programs and data. The memory 707 may include any number of volatile and non-volatile storage devices, such as volatile random access memory (RAM), static random access memory (SRAM), flash memory, etc. In smaller devices (such as PLCs), the memory 707 may include registers associated with the processor 705 itself.

[0218] The memory 707 stores computer readable instructions that can be executed by the processor 705. When the computer readable instructions are executed, the processor 705 performs operations such as receiving a first differential pressure signal from the first pair of pressure sensors 104a, 104b; receiving a second differential pressure signal from the second pair of pressure sensors 104c, 104d; and determining the total density of the multiphase fluid 101 based on at least the difference between the first differential pressure and the second differential pressure of the multiphase fluid 101 and the specified differential pressure height h. The computer 700 may also include a power supply 714. The power supply 714 may include a rechargeable or non-rechargeable battery that may be configured to be user replaceable or non-user replaceable. The power supply 714 may be hardwired. There may be any number of computers 700 associated with or external to the computer system containing the computer 700, each of which communicates via a network. In addition, the terms "customer", "user", "operator" and other appropriate terms may be used interchangeably as needed without departing from the present specification. Furthermore, this specification contemplates that many users may use one computer 700 , or that one user may use multiple computers 700 .

[0219] Although this specification contains many specific implementation details, these details should not be interpreted as limitations on the scope of the claimed protection, but should be interpreted as descriptions of features that may be specific to a particular embodiment. Certain features described in the context of separate embodiments in this specification may also be implemented in combination in a single embodiment. Conversely, the various features described in the context of a single embodiment may also be implemented individually or in any sub-combination in multiple embodiments. In addition, although the previously described features may be described as working in certain combinations, and even initially claimed as such, in some cases, one or more features in the claimed combination may be deleted from the combination, and the claimed combination may be directed to a sub-combination or a variation of the sub-combination.

[0220] As used in this disclosure, the terms "a", "an" or "the" are used to include one or more than one, unless the context clearly dictates otherwise. Unless otherwise indicated, the term "or" is used to refer to a non-exclusive "or". The expression "at least one of A and B" has the same meaning as "A, B, or A and B". In addition, it should be understood that the expressions or terms used in this disclosure (not otherwise defined) are for descriptive purposes only and not for limiting purposes. The use of any section headings is intended to aid in reading this document and should not be construed as limiting; information related to the section heading may appear within or outside that particular section.

[0221] As used in this disclosure, the terms "about" or "approximately" can allow a value or range to vary to a certain degree, for example, within 10%, within 5%, or within 1% of a stated value or limit of a stated range.

[0222] As used in this disclosure, the term "substantially" refers to a majority or majority, such as at least about 50%, 60%, 70%, 80%, 90%, 95%, 96%, 97%, 98%, 99%, 99.5%, 99.9%, 99.99%, or at least about 99.999% or more.

[0223] Values ​​expressed in range format should be interpreted in a flexible manner to include not only the values ​​explicitly indicated as range limits, but also all individual values ​​or subranges contained within the range, as if each value and subrange were explicitly indicated. For example, a range of "0.1% to about 5%" or "0.1% to 5%" should be interpreted to include about 0.1% to about 5%, as well as individual values ​​(e.g., 1%, 2%, 3% and 4%) and subranges (e.g., 0.1% to 0.5%, 1.1% to 2.2%, 3.3% to 4.4%) within the indicated range. Unless otherwise indicated, the statement "X to Y" has the same meaning as "about X to about Y". Similarly, unless otherwise indicated, the statement "X, Y or Z" has the same meaning as "about X, about Y or about Z".

[0224] Specific embodiments of the subject matter have been described. It will be clear to those skilled in the art that other embodiments, variations and permutations of the described embodiments are within the scope of the following claims. Although operations are described in a particular order in the drawings or claims, it should not be understood as requiring that these operations be performed in the particular order shown or in a continuous order, or requiring that all of the operations shown (some operations may be considered optional) be performed to achieve the desired results. In some cases, multitasking or parallel processing (or a combination of multitasking and parallel processing) may be advantageous and performed as needed.

[0225] Furthermore, the separation or integration of the various system modules and components in the aforementioned embodiments should not be understood as requiring such separation or integration in all embodiments, and it should be understood that the described components and systems may generally be integrated together or packaged into multiple products.

[0226] Therefore, the above exemplary embodiments do not limit or restrict the present disclosure. Other changes, substitutions and modifications are also possible without departing from the spirit and scope of the present disclosure.

Claims

1. A system comprising: A U-shaped bend pipe is configured to allow a multiphase fluid to flow, wherein the multiphase fluid includes a gas phase, a water phase, and an oil phase, and the U-shaped bend pipe includes: - 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 has 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, flows through the connecting conduit, and then flows 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 along the first conduit across a specified differential pressure height; 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 along the second conduit across the specified differential pressure height; and Computers, including: - a processor communicatively coupled to the first differential pressure sensor and the second differential pressure sensor; and - a computer-readable storage medium coupled to the processor and storing programming instructions executed 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 a 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 a second differential pressure of the multiphase fluid; and A mixed density of the multiphase fluid is determined based on at least the designated pressure differential altitude and a difference between the first pressure differential and the second pressure differential of the multiphase fluid.

2. The system of claim 1, wherein the mixed density of the multiphase fluid is determined by: Wherein ρ is the mixed density of the multiphase fluid, ΔP1 is the first pressure difference of the multiphase fluid, ΔP2 is the second pressure difference of the multiphase fluid, g is the acceleration caused by gravity, and h is the specified pressure difference altitude.

3. The system of claim 2, wherein the operations performed by the processor include determining the total mass flow rate of the multiphase fluid by: Where m T is the total mass flow rate of the multiphase fluid, C d is the flow coefficient, ε is the expansion coefficient, K is a fixed geometric coefficient related to the cross-sectional flow area of ​​the U-bend, ρ is the mixed density of the multiphase fluid, ΔP is the first pressure difference or the second pressure difference of the multiphase fluid, k f is a correction factor for friction based on geometry, and ΔP f is the friction pressure loss. 4 . The system of claim 3 , wherein the first differential pressure sensor is a first circumferential pressure sensor spanning the entire circumference of the first conduit.

5. The system of claim 4, wherein the second differential pressure sensor is a second circumferential pressure sensor spanning the entire circumference of the second conduit. The system of claim 5 , wherein the connecting conduit is perpendicular to the first conduit and the second conduit.

7. The system of claim 6, wherein a longitudinal length of the first conduit is substantially the same as a longitudinal length of the second conduit.

8. The system of claim 7, wherein the operations performed by the processor include: 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 a water phase density of a water phase of the multiphase fluid; receiving as input an oil phase density of an oil phase of the multiphase fluid; and The water phase volume fraction of the multiphase fluid is determined by the following formula: p=p g ×a g +r a ×a a +r o ×(1-a g -a a ), where ρ is the mixed density of the multiphase fluid, α g is the gas phase volume fraction of the multiphase fluid, α a is the water 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 water phase density of the water phase of the multiphase fluid, and ρ o is the oil phase density of the oil phase of the multiphase fluid.

9. The system of claim 7, wherein the operations performed by the processor include: receiving as input a water 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 a water phase density of a water phase of the multiphase fluid; receiving as input an oil phase density of an oil phase of the multiphase fluid; and The gas phase volume fraction of the multiphase fluid is determined by the following formula: p=p g ×a g +r a ×a a +r o ×(1-a g -a a ), where ρ is the mixed density of the multiphase fluid, α g is the gas phase volume fraction of the multiphase fluid, α a is the water 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 water phase density of the water phase of the multiphase fluid, and ρ o is the oil phase density of the oil phase of the multiphase fluid.

10. A method comprising: A multiphase fluid is caused to flow through a U-bend pipe, wherein the multiphase fluid comprises a gas phase, a water phase, and an oil phase, and the U-bend pipe 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 has 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, flows through the connecting conduit, and then flows 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 along the second conduit across the specified differential pressure height; and A mixed density of the multiphase fluid is determined based on at least the designated pressure differential altitude and a difference between the first pressure differential and the second pressure differential of the multiphase fluid.

11. The method of claim 10, wherein the mixed density of the multiphase fluid is determined by the following formula: Wherein ρ is the mixed density of the multiphase fluid, ΔP1 is the first pressure difference of the multiphase fluid, ΔP2 is the second pressure difference of the multiphase fluid, g is the acceleration caused by gravity, and h is the specified pressure difference altitude.

12. The method of claim 11, comprising determining the total mass flow rate of the multiphase fluid by the following formula: Where m T is the total mass flow rate of the multiphase fluid, C d is the flow coefficient, ε is the expansion coefficient, K is a fixed geometric coefficient related to the cross-sectional flow area of ​​the U-bend, ρ is the mixed density of the multiphase fluid, ΔP is the first pressure difference or the second pressure difference of the multiphase fluid, k f is a correction factor for friction based on geometry, and ΔP f is the friction pressure loss.

13. The method of claim 11, comprising determining the water phase volume fraction of the multiphase fluid by the following formula: p=p g ×a g +r a ×a a +r o ×(1-a g -a a ), where ρ is the mixed density of the multiphase fluid, α g is the gas phase volume fraction of the multiphase fluid, α a is the water 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 water phase density of the water phase of the multiphase fluid, and ρ o is the oil phase density of the oil phase of the multiphase fluid.

14. The method of claim 11, comprising determining the gas phase volume fraction of the multiphase fluid by the following formula: p=p g ×a g +r a ×a a +r o ×(1-a g -a a ), where ρ is the mixed density of the multiphase fluid, α g is the gas phase volume fraction of the multiphase fluid, α a is the water 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 water phase density of the water phase of the multiphase fluid, and ρ o is the oil phase density of the oil phase of the multiphase fluid.

15. The method of claim 14, wherein the first differential pressure of the multiphase fluid is measured by a first differential pressure sensor coupled to the first conduit.

16. The method of claim 15, wherein the second differential pressure of the multiphase fluid is measured by a second differential pressure sensor coupled to the second conduit.

17. The method of claim 16, wherein the first differential pressure sensor is a first circumferential pressure sensor spanning the entire circumference of the first conduit.

18. The method of claim 17, wherein the second differential pressure sensor is a second circumferential pressure sensor spanning the entire circumference of the second conduit.

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