Patent Description:
The quantification of phase flowrates in an industrial multiphase pipeline may be of value in the petroleum and various other process industries. The development of reliable and accurate multiphase flow meters (MPFMs) has historically proven to be a significant challenge, for example, due to the complexity of industrial multiphase fluid streams. One difficulty in characterizing multiphase flows is the range of flow regimes possible, which describe the geometric arrangement of fluid phases in a pipeline (for example, stratified flow or emulsified flow). Each flow regime may have unique hydrodynamic characteristics such that the response of many multiphase flow measurement techniques is dependent on the flow regime. Furthermore, a greater range of field conditions is being observed in worldwide petroleum production (for example, as a result of increased water content as reservoir lifetimes are extended) such that new developments in MPFM are required to be accurate and robust across a range of flow conditions.

In his doctoral thesis (DOI:<NUM>/5DEDD810E9C14), K. O'Neill describes the development of an earth's field nuclear magnetic resonance multiphase flow meter.

<NPL>)) describe two-phase oil/water flow measurement using an Earth's field nuclear magnetic resonance flow meter.

<NPL>) describe quantitative multiphase flow characterisation using an Earth's field NMR flow meter.

In an example implementation, a fluid measurement system according to claim <NUM> is provided.

In an aspect combinable with the example implementation, the operation of determining a velocity of the gas phase based on the plurality of FID values of the polarized gas phase includes applying a pseudo-1D inversion to the plurality of FID values of the gas phase.

In another aspect combinable with any of the previous aspects, the operation of determining a velocity of the liquid phase based on the plurality of FID values of the polarized liquid phase includes applying another pseudo-1D inversion to the plurality of FID values of the liquid phase.

In another aspect combinable with any of the previous aspects, the operation of determining a content of the liquid phase based on the plurality of FID values of the mixed-phase fluid includes determining an oil-water content of the liquid phase with a 2D probability distribution of the velocity of the liquid phase in the mixed-phase fluid flow based on the applied another 1D inversion of the plurality of FID values of the liquid phase and a model kernel matrix.

In another aspect combinable with any of the previous aspects, at least one of the pseudo-1D inversion or the another psuedo-1D inversion includes a Tikhonov inversion.

In another aspect combinable with any of the previous aspects, the gas source includes a pressurized gas source fluidly coupled to the fluid flow circuit between the fluid mixer and the pre-polarizing permanent magnet.

In another aspect combinable with any of the previous aspects, the at least two liquids include oil and water.

In another aspect combinable with any of the previous aspects, the pre-polarizing magnet is positionable at a plurality of distances apart from the EFNMR detector.

In another aspect combinable with any of the previous aspects, the operation of controlling the EFNMR detector to measure the plurality of FID values of the polarized gas phase includes controlling the EFNMR detector to measure a first plurality of FID values of the polarized gas phase at a first distance of the plurality of distances; and controlling the EFNMR detector to measure a second plurality of FID values of the polarized gas phase at a second distance of the plurality of distances.

In another aspect combinable with any of the previous aspects, the operation of controlling the EFNMR detector to measure the plurality of FID values of the polarized liquid phase includes controlling the EFNMR detector to measure a first plurality of FID values of the polarized liquid phase at a first pulse time duration of a plurality of electromagnet pulse time durations; and controlling the EFNMR detector to measure a second plurality of FID values of the polarized liquid phase at a second pulse time duration of the plurality of electromagnet pulse time durations.

In another aspect combinable with any of the previous aspects, the plurality of FID values of the polarized gas phase include velocity values, and the plurality of FID values of the polarized liquid phase include velocity values and T<NUM> values of the liquid phase.

In another example implementation, a method according to claim <NUM> is provided.

In an aspect combinable with the example implementation, determining a velocity of the gas phase based on the plurality of FID values of the polarized gas phase includes applying a pseudo-1D inversion to the plurality of FID values of the gas phase.

In another aspect combinable with any of the previous aspects, determining a velocity of the liquid phase based on the plurality of FID values of the liquid phase includes applying another pseudo-1D inversion to the plurality of FID values of the liquid phase.

In another aspect combinable with any of the previous aspects, determining a content of the liquid phase based on the plurality of FID values of the mixed-phase fluid includes determining an oil-water content of the liquid phase with a 2D probability distribution of the velocity of the liquid phase in the mixed-phase fluid flow based on the applied another 1D inversion of the plurality of FID values of the liquid phase and a model kernel matrix.

Another aspect combinable with any of the previous aspects further includes separating the liquid phase into a first liquid flow and a second liquid flow with a liquid separator fluidly coupled to a first liquid source and a second liquid source; and inj ecting the gas phase into the liquid phase from a pressurized gas source that is fluidly coupled in the fluid flow circuit between the fluid mixer and the pre-polarizing permanent magnet.

In another aspect combinable with any of the previous aspects, the first liquid includes oil and the second liquid includes water.

Another aspect combinable with any of the previous aspects further includes positioning the pre-polarizing magnet at a plurality of distances apart from the EFNMR detector.

In another aspect combinable with any of the previous aspects, measuring the plurality of FID values of the polarized gas phase with the EFNMR detector includes measuring a first plurality of FID values of the polarized gas phase with the EFNMR detector at a first distance of the plurality of distances; and measuring a second plurality of FID values of the polarized gas phase with the EFNMR detector at a second distance of the plurality of distances.

In another aspect combinable with any of the previous aspects, measuring the plurality of FID values of the polarized liquid phase with the EFNMR detector includes measuring a first plurality of FID values of the liquid phase with the EFNMR detector at a first pulse time duration of a plurality of pulse time durations of the second electromagnet; and measuring a second plurality of FID values of the liquid phase with the EFNMR detector at a second pulse time duration of a plurality of pulse time durations of the second electromagnet.

In another aspect combinable with any of the previous aspects, the plurality of FID values of the polarized gas phase include velocity values, and the plurality of FID values of the liquid phase include velocity values and T<NUM> values of the liquid phase.

Implementations of a fluid measurement system according to the present disclosure may include one or more of the following features. For example, a fluid measurement system may allow for unambiguous phase differentiation as opposed to conventional NMR multi-phase flow meters that do not produce probability distributions of velocity against the NMR spin-lattice relaxation parameter, T<NUM> (and thus composition). As another example, a fluid measurement system according to the present disclosure may utilize a moveable pre-polarizing magnet to allow for phase quantification based on an extent of polarization in the pre-polarization magnet and relaxation following the material leaving this magnetic field before entering an NMR detector. As another example, a fluid measurement system according to the present disclosure may be sensitive to a flow regime of a multi-phase fluid flowing through the system. As another example, a fluid measurement system according to the present disclosure may better measure phase volumetric flowrates as pertains to wet gas flow as compared to conventional NMR systems. For example, a fluid measurement system according to the present disclosure may enable detection of both the NMR liquid and gas signals and, in particular, a presence of a minimal amount of water and/or oil content. In addition, a fluid measurement system according to the present disclosure may utilize NMR signals of a liquid phase that are made discrete from the gas phase and amplified.

The details of one or more implementations of the subject matter described in this disclosure are set forth in the accompanying drawings and the description below.

<FIG> is a schematic illustration of an example implementation of a fluid measurement system <NUM> according to the present disclosure, which is not covered by the claims. In some aspects, the fluid measurement system <NUM> provides for a simultaneous measurement of oil and water volumetric flowrates in a flowing fluid. In the example implementation of fluid measurement system <NUM>, an Earth's field nuclear magnetic resonance (NMR) detection coil is applied to measure free induction decay (FID) signals of a two-phase oil/water flow. A dual polarization measurement assembly of the fluid measurement system <NUM> uses an upstream permanent magnet as well as an electromagnetic pre-polarizing coil. The FID signals with variable pre-polarizing conditions are acquired and fit with a model for the NMR fluid signal using an inversion technique (for example, a 2D Tikhonov regularization algorithm) to determine a joint 2D velocity-T<NUM> probability distribution. The measured velocity-T<NUM> distributions then provides for a calculation of individual phase flowrates in the oil-water fluid.

The utilization of the NMR detection coil may provide multiple measurement options in terms of quantifying the relevant phase fractions of a two-phase system (such as oil and water). The measurement of NMR signals is described by relaxation time constants (T<NUM> and T<NUM>) associated with the fluids of interest, both of which quantify the rate of energy transfer in magnetic resonance processes. The spin-lattice relaxation rate (T1) is a fluid property describing the rate of signal accumulation in a magnetic field, while the spin-spin relaxation rate (T<NUM>) describes the rate of signal decay or dephasing of NMR-active atoms (for example, hydrogen as are used in this disclosure) within a fluid.

In contrast to T<NUM> relaxometry, analysis of T<NUM> relaxation may be a more robust and flexible mechanism to differentiate oil and water. T<NUM> measurements are achieved using multi-pulse acquisition sequences (e.g. CPMG measurements), however T<NUM> signal contrast can be achieved through variation of the pre-polarization conditions, T<NUM> measurements are more sensitive to internal magnetic field gradients arising from susceptibility differences between phases in emulsified flows. In some aspects, T<NUM> measurements may be a more robust approach for fluid relaxometry characterization.

Several inversion techniques may be available to determine a joint 2D velocity-T<NUM> probability distribution. In an example implementation of fluid measurement system <NUM>, the oil-water flow may be quantitatively characterized using a 2D velocity-T<NUM> distributions extracted from measured NMR signal data using Tikhonov regularization. In some aspects, Tikhonov regularization is a robust mathematical inversion technique, useful in determining relevant distributions of parameters. For example, regularization may be effective at handling noisy signal data and may not require any assumptions regarding the shape of the resultant probability distribution.

Generally, the example inversion technique used in fluid measurement system <NUM> includes a discretized probability distribution vector of a variable (p), which may be expressed as a function of an experimentally acquired NMR signal (s) via a model kernel matrix (M) with the generalized linear inverse problem:
<MAT>.

Regularization may provide a method of determining a realistic probability distribution, p, from Eq. (<NUM>). A stable inversion in the presence of experimental noise may be achieved by applying a penalty function. In Tikhonov regularization, the following expression is minimized in order to determine p:
<MAT>
where α is a smoothing parameter and Q is a smoothing operation matrix. In this example, Q is designed to calculate the finite second derivative of the resultant probability distribution to ensure smoothness. The first term in Eq. (<NUM>), ∥Mp-s∥<NUM>, is the residual norm while the second term, ∥Qp∥<NUM>, is a penalty function. The smoothing parameter is used to optimize the compromise between finding the true solution (minimizing the residual norm) and limiting the impact of noise on the solution (minimizing the penalty function). In this example, the value of α is selected using a generalized cross-validation (GCV) method, which has been widely validated for NMR data interpretation. This method sequentially removes a data point in the solution (s) and determines the value of the smoothing parameter which predicts the removed point with the best accuracy. This may be repeated for each data point in s, and a GCV score is determined as a function of α. The value of α that minimizes this GCV score is the optimal smoothing parameter.

Two-dimensional NMR measurements may be useful in probing local surroundings as well as providing chemical information for complex systems. Such systems can be characterized by distributions of measured parameters (e.g., T<NUM>, T<NUM> or self-diffusion coefficients (D)); therefore appropriate data analysis methods may be required to provide reliable interpretation of results. Tikhonov regularization is extrapolated to such 2D data in this example, and is used in the example implementation to produce 2D probability distributions of T<NUM> and velocity for the multiphase oil-water flow.

The example implementation of the fluid measurement system <NUM> shown in <FIG> includes the following components. An oil tank <NUM> holds oil <NUM> and is fluidly coupled to an oil pump <NUM> that is in turn fluidly coupled to a fluid mixer <NUM>. A water tank <NUM> holds water <NUM> and is fluidly coupled to a water pump <NUM> that is in turn fluidly coupled to the fluid mixer <NUM>. As shown in <FIG>, lines that connect such components represent a conduit <NUM> or connected portions of conduit <NUM> through which the oil <NUM>, the water <NUM>, and an oil-water fluid <NUM> is circulated by the pumps <NUM> and <NUM>. A pre-polarizing permanent magnet <NUM> is positioned around or adjacent to the conduit downstream of the fluid mixer <NUM> to receive the oil-water fluid <NUM>. Positioned a variable distance <NUM> downstream from the pre-polarizing permanent magnet <NUM> is an EFNMR detector <NUM> that includes an electromagnet <NUM> and a radio-frequency coil <NUM>. A control system <NUM>, shown communicably coupled to the EFNMR detector <NUM>, is operable to control the operation of and receive measurements from the EFNRM detector <NUM>. The control system <NUM> may also be communicably coupled (wirelessly or wired) to one or more of the referenced components of fluid measurement system <NUM> to control the operation of, and receive data (such as measurements) from, such components.

An oil-water separator <NUM> is positioned downstream of the EFNMR detector <NUM> to receive the oil-water fluid <NUM> and separate the oil-water fluid <NUM> back into the constituents of oil <NUM> and water <NUM>. Such constituents are circulated back to their respective tanks <NUM> and <NUM>. As shown in the example implementation of fluid measurement system <NUM>, valves <NUM> are positioned in the conduit to shut-off or modulate (or both) a flow of the oil <NUM>, the water <NUM>, or the oil-water fluid <NUM>. As further shown, an oil flow meter <NUM> is positioned between the oil pump <NUM> and the fluid mixer <NUM>. A water flow meter <NUM> is positioned between the water pump <NUM> and the fluid mixer <NUM>. Both flow meters <NUM> and <NUM> may measure a flow rate of their respective constituents and, in some aspects, provide such flow rate values to the control system <NUM>.

In this example, the pre-polarizing permanent magnet <NUM> is a <NUM> T Halbach array located the variable distance <NUM> (LPD) upstream of the EFNMR detector <NUM>. In some aspects, the Halbach array can be shifted such that the polarization detection separation distance <NUM> is between <NUM> and <NUM>. In some aspects, shorter distances are not achievable due to the stray field from the Halbach array interfering with the EFNMR detector <NUM> and larger distances are impractical for a realistic flow metering system construction.

The combination of the EFNMR detector <NUM> and radio-frequency coil <NUM> may be used to excite and detect an NMR signal (for example, at about <NUM>, the <NUM>H Larmor frequency at the local Earth's magnetic field). The radio-frequency coil <NUM> may include a coaxial solenoid of diameter <NUM>, operating at <NUM> A to produce an <NUM> mT magnetic field, which can be used to provide a polarization field to generate magnetization at the EFNMR detector <NUM>. The illustrated combined polarization scheme (simultaneously using the pre-polarizing magnet <NUM> and the electromagnet <NUM> of the EFNMR detector <NUM>) is discussed later. The EFNMR detector <NUM>, in some aspects, includes an external resistive Q-switch, which enables the acquisition delay time to be reduced from <NUM> to <NUM>, allowing earlier acquisition of free induction decay (FID) signals.

As shown, oil <NUM> and water <NUM> are stored separately in oil tank <NUM> and water tank <NUM>, respectively. Pump <NUM> may be a close-coupled centrifugal pump (for example, Calpeda NM32-20A). Flow meter <NUM> includes an in-line rotameter (for example, Stubbe DFM350, <NUM>-<NUM><NUM>/h). In some aspects, such as to mirror a composition of subterranean water, as well as to reduce a separation time of oil-in-water emulsions during operation of the fluid measurement system <NUM>, the water <NUM> may be concentrated with sodium chloride (for example, <NUM> wt%). The addition of salt causes an increase in the water density and viscosity. Pump <NUM> may be a centrifugal pump (for example, Calpeda MXHLM803). Flow meter <NUM> includes an in-line rotameter (for example, Stubbe DFM350).

In some aspects, both flow meters <NUM> and <NUM> are calibrated using gravimetric measurement of fluid outflow in order to account for the used fluid viscosities and densities. The individual fluid flowrates can be varied using associated valves <NUM>. The oil-water separator <NUM> may be a gravimetric oil/water separator (separation volume of <NUM>) in order to split the oil <NUM> and the water <NUM> before returning to their individual storage tanks <NUM> and <NUM>, respectively.

The example implementation of flow measurement system <NUM> may use a model for the NMR signal acquired by the EFNMR detector <NUM> for fluid moving through the flow metering section. In some aspects, the measured NMR signal is a composite of three contributions: development of signal magnetization during polarization (SP), signal attenuation from intermediate decay between the polarization magnet and the EFNMR detector <NUM> (SPD), and signal attenuation following excitation (SD). In some aspects, during the development of the NMR signal model for the fluid measurement system <NUM>, the fluid is considered to be discretized into separate fluid elements. When an individual fluid element is moving through a particular one of the flow meters <NUM> or <NUM> with a velocity, v, the signal contribution of this fluid element to the overall FID signal acquired at the EFNMR detector <NUM> is given by:
<MAT>
where te is the time since a radio-frequency excitation pulse by the radio-frequency coil <NUM>, SOH is the NMR signal after an infinite time in the magnetic field of the pre-polarizing permanent magnet <NUM>, LP is the length of the pre-polarizing permanent magnet <NUM>, LPD is the polarization detection separation distance <NUM>, LD is the length of the radio-frequency coil <NUM>, T<NUM> is the spin-lattice relaxation time, and T*<NUM> is the effective spin-spin relaxation time.

The example implementation of the fluid measurement system <NUM> uses T<NUM> differentiation in order to quantify the oil <NUM> and the water <NUM> in the oil-water fluid <NUM>. In order to obtain an indication of the spin-lattice relaxation rates expected under flow, T<NUM> measurements of the stationary fluids (the water <NUM> and the oil <NUM>) can be performed (using standard NMR measurement techniques) to determine log-mean T<NUM> values (T<NUM>, LM) for the oil <NUM> and the water <NUM>. The fast spin-lattice relaxation of the oil <NUM> may introduce difficulty in terms of obtaining a measurement with a reasonable signal-to-noise-ratio (SNR) for the oil <NUM>. The signal attenuation during intermediate decay (SPD) is anticipated to be significant for the oil <NUM> due to its low T<NUM> (relative to the water <NUM>), particularly at low velocities (for example, <<NUM>/s). Measurements of the SNR (calculated as the ratio of the initial FID signal (at t = tdelay = <NUM>) to standard deviation of the measured noise) may be obtained with only the oil <NUM> flowing through the fluid measurement system <NUM> at velocities of <NUM>-<NUM>/s. In some aspects, FID measurements are obtained using scan averages (Nscans = <NUM>) at a separation distance <NUM> of <NUM>.

The radio-frequency coil <NUM> and accompanying electromagnet <NUM> that is incorporated with the EFNMR detector <NUM> (and used for stationary fluid measurements) was previously considered unsuitable for flowing measurements with water, as the outflow effect does not allow sufficient time for polarization and detection to occur within the radio-frequency coil <NUM>. However, the application of the radio-frequency coil <NUM> and accompanying electromagnet <NUM> can be considered useful for fluids with low T<NUM> at low velocity. FID measurements of the oil <NUM> can be obtained using only the radio-frequency coil <NUM> (without the pre-polarizing permanent magnet <NUM>) and the accompanying electromagnet <NUM>, which is applied for a pre-polarizing time of <NUM>. Thus, the combination of the two polarizing mechanisms (the pre-polarizing permanent magnet <NUM> and the electromagnet <NUM>) may be effective at different oil velocity ranges.

In some aspects, the pre-polarizing permanent magnet <NUM> may provide a much stronger signal across a broad range of velocities compared to the electromagnet <NUM>. However, the electromagnet <NUM> may be able to fill a void for low velocity (<<NUM>/s) and low T<NUM> (<NUM>-<NUM>) fluids (such as the oil <NUM>) where the pre-polarizing permanent magnet <NUM> may have a poor SNR due to intermediate signal decay between polarization and detection. By combining the polarizing methods in a dual polarization mechanism, the flow metering system <NUM> may measure signals across a range of velocities (<NUM>-<NUM>/s) and fluid T<NUM> values (<NUM>-<NUM>). In some aspects, such combined measurements may always incorporate the pre-polarizing permanent magnet <NUM>, with the option of additional re-polarization using the electromagnet <NUM> once the oil-water fluid <NUM> reaches the EFNMR detector <NUM>.

In some aspects, measurement of the fluid T<NUM> under flow may utilize an independent variable to observe signal contrast according to T<NUM>. For measurements obtained using the pre-polarizing permanent magnet <NUM> alone, an example independent variable is the separation distance <NUM>, which can easily be adjusted via movement of the pre-polarizing permanent magnet <NUM>. Signal contrast due to the electromagnet <NUM>, however, can be observed by varying the pre-polarization time (tpolz). Thus variable separation distances (<NUM>-<NUM>) may be used to measure signal contrast for fluids with higher T<NUM> (and/or at high velocities), while the variable pre-polarization time (<NUM>-<NUM>) may be used to measure signal contrast for low T<NUM> fluids with low velocity.

In some aspects of the fluid measurement system <NUM>, the secondary polarization mechanism) may be incorporated into the NMR model. In some aspects, the introduction of the dual polarization mechanism involves the application of the electromagnet <NUM> in some of the FID measurements to provide additional re-polarization, while the pre-polarizing permanent magnet <NUM> is applied as it is fixed around the conduit in which the oil-water fluid <NUM> circulates. For aspects where the electromagnet <NUM> is not applied (in other words, the pre-polarizing permanent magnet <NUM> alone is used for pre-polarization), the effective signal polarization due to the pre-polarizing permanent magnet <NUM> just prior to excitation (SPH), including the intermediate signal decay term, can be considered as:
<MAT>
where SOH is the overall signal magnetization after an infinite time in the field generated by the pre-polarizing permanent magnet <NUM> and LPH is the effective length of the pre-polarizing permanent magnet <NUM>. A fraction of the oil-water fluid <NUM> which is not polarized (xNP) upon reaching the EFNMR detector <NUM> can be considered as:
<MAT>.

Equation (<NUM>) represents oil-water fluid <NUM> which was either not polarized at the pre-polarizing permanent magnet <NUM> or has decayed to its original energy state during the residence time between pre-polarization and detection (for example, by EFNMR detector <NUM>). The effective signal polarization of a stationary fluid due to the electromagnet <NUM> can be described by the T<NUM> signal development:
<MAT>
where Soc is overall signal magnetization after an infinite time in the field of the radio-frequency coil <NUM>, tpolz is the polarization time, and tPE is the polarization-excitation delay (for example, <NUM>). In some aspects, a limit may be imposed on the polarization time for measurements conducted on the flowing oil-water fluid <NUM>; the effective polarization time may be limited by the fluid residence time in the radio-frequency coil <NUM>. A fluid element traveling with velocity, v, will leave the radio-frequency coil <NUM> (for example, with an effective length LPC of <NUM>) after a residence time τPC = LPC/v. Thus, Equation (<NUM>) can be updated for a flowing fluid:
<MAT>
where
<MAT>.

In this example, the polarization-excitation delay term (tPE) is included to account for fluid which would leave the radio-frequency coil <NUM> during the delay time. The incorporation of the minimization term may effectively restrict a range of useful polarization times according to the velocity of the oil-water fluid <NUM>; larger pre-polarization times (tpolz > <NUM>) may be ineffective as the fluid will flush through the radio-frequency coil <NUM> before sufficient polarization can be achieved. When combining the dual effects of the pre-polarizing permanent magnet <NUM> and the radio-frequency coil <NUM>, oil-water fluid <NUM> that is not polarized upon reaching the EFNMR detector <NUM> (quantified by Eq. (<NUM>)) can be re-polarized by the radio-frequency coil <NUM>. Therefore, the combined signal polarization (SP) is modelled by:
<MAT>.

If the radio-frequency coil <NUM> is not applied (in other words, τPC = tpolz = <NUM>) then SP = SPH, meaning that the overall signal polarization is just the signal polarization due to the pre-polarizing permanent magnet <NUM>. The overall model for the NMR signal of a the oil-water fluid <NUM> can be considered as:
<MAT>
where SP is defined in Eq. (<NUM>).

The example implementation of flow metering system <NUM> may apply multiple NMR "pulse and collect" sequences in order to acquire FID measurements. In the case where the dual polarization scheme is utilized, the polarization pulse is applied for a polarization time, tpolz, followed by a <NUM> degrees radio frequency pulse by the radio-frequency coil <NUM> to excite the oil-water fluid <NUM>. Then, the FID is detected in the EFNMR detector <NUM> by the same radio-frequency coil <NUM>.

An example "pulse and collect" sequence diagram is shown in <FIG>, which illustrates a sequence diagram <NUM>. The sequence diagram <NUM> shows illustrative definitions of timing parameters, including; the length of the polarization pulse (tpolz), the delay between polarization and excitation (tPE), the acquisition delay (tdelay) and the acquisition time (ta). The time since excitation (te) is the combination of the acquisition delay and acquisition time (for example, te = tdelay + ta). The use of the pulse and collect measurement implies that the measured FID signal incorporates spin-spin relaxation (T<NUM>) as well as decay due to magnetic field inhomogeneity in the Earth's field (T<NUM>, I). These effects may be combined into an effective spin-spin relaxation (T*<NUM>) with the assumption that the magnetic field inhomogeneity causes exponential signal decay behavior. However, the signal decay due to field inhomogeneity can often be non-exponential; therefore assuming an exponential decay can result in significant error during signal analysis. Experimental FID measurements using the EFNMR detector <NUM> have previously been observed to produce a half-Gaussian line shape. The field inhomogeneity signal decay (I) can be described by the following half-Gaussian model:
<MAT>
where te is the time since excitation and RI is a Gaussian relaxation rate constant accounting for the rate of signal decay introduced by magnetic field inhomogeneity. A FID signal (SFID), which incorporates half-Gaussian decay behavior can be described by the following model equation:
<MAT>
where SE is the polarized signal prior to excitation and T<NUM> is the spin-spin relaxation constant for a given fluid. The field inhomogeneity signal decay (I(te)) can effectively be calibrated via measurement of the CPMG decay signal (SCPMG) as well as a standard pulse and collect FID measurement of stationary water (SFID). The field inhomogeneity decay is determined using:
<MAT>.

In some aspects, the movement of the pre-polarizing permanent magnet <NUM> is observed to interfere with the Earth's field homogeneity and therefore the inhomogeneity decay function must be measured at each relevant separation distance <NUM>. The model for NMR signal of a flowing fluid (Eq. (<NUM>)) is updated in consideration of the observed FID behavior:
<MAT>
where I(te, LPD) is the measured field inhomogeneity distribution at a given separation distance <NUM> (LPD). The final FID component to be considered for flow measurements is the T<NUM> signal decay of the oil-water fluid <NUM> under flow. The measured T<NUM> relaxation during circulation of the oil-water <NUM> may be a function of the fluid phase composition considering the differing T<NUM> relaxation rates for the oil <NUM> and the water <NUM>. The simultaneous measurement of fluid T<NUM> distribution with velocity and T<NUM> under flow may be difficult; therefore a T<NUM>/T<NUM> ratio is introduced in order to link the modelled T<NUM> decay to the measured T<NUM> decay. The T<NUM>/T<NUM> ratio is defined as RT = T<NUM>/T<NUM> and is specified about the oil/water T<NUM> cutoff of T<NUM>,C = <NUM>; with oil (T<NUM> < <NUM>) having RT = <NUM> and water (T<NUM> <NUM>) using RT = <NUM> (determined from stationary fluid relaxation measurements). The T<NUM>/T<NUM> ratio is introduced into the model for NMR signal of a flowing fluid:
<MAT>.

This effectively removes T<NUM> from the model equation, leaving velocity (v) and spin-lattice relaxation in the Earth's field (T<NUM>) as the only dependent variables. The incorporation of the T<NUM>/T<NUM> ratio assumes that the ratio is constant as a function of T<NUM>. This assumption is reasonable; the fluid T<NUM>/T<NUM> ratio should only change in the presence of diffusive decay (which influences T<NUM> but not T<NUM>). Diffusional decay will occur for, for example, emulsified flows (where droplets are present) however for such flows at higher velocities (v > <NUM>/s) T<NUM> relaxation becomes much less important as the FID is increasingly dominated by the flush-out effect.

Regarding the flush-out effect, the oil-water fluid <NUM>, as previously described, may be subjected to a dual-polarization scheme. As described, the scheme enables the polarization of the NMR signal from the pre-polarizing permanent magnet <NUM> (of variable position) to be combined with the polarization of the NMR signal from the electromagnet <NUM> (which was applied for a variable time). The transition of polarized magnetization from the pre-polarizing permanent magnet <NUM> into the field of the pre-polarizing field of the electromagnet <NUM> may include consideration of the operation of the EFNMR detector <NUM>.

For example, the EFNMR detector <NUM> utilizes the electromagnet <NUM> in order to achieve reasonable signal sensitivity due to the increased polarizing field strength (~<NUM> mT compared to the Earth's Field strength of ~ <NUM>µT). In using the pre-polarizing field, it may be necessary to ensure that the full pre-polarized magnetization can be detected by allowing an adiabatic field discharge. The field discharge from the polarizing field strength to Earth's field strength may be sufficiently slow to ensure an adiabatic field transition. The non-adiabatic transition occurring for the polarization coil "switch on" may be important for the particular EFNMR detector <NUM> with a dual polarization scheme.

For example, the oil-water fluid <NUM> entering the EFNMR detector <NUM> will have previously been magnetized or polarized by the upstream pre-polarizing permanent magnet <NUM> and therefore possess an initial magnetization. The rate of polarizing field accumulation may be too fast (for example, the time for field "switch-on" is too short) and therefore the flowing oil-water fluid <NUM> experiences a non-adiabatic transition from Earth's field to polarizing field. In some aspects, this means that the pre-magnetized signal (due to the pre-polarizing permanent magnet <NUM>) may not be able to fully re-orientate from the Earth's field to the pre-polarizing field. Consequently, a signal loss may be observable between a single-polarizing scheme (in other words, where only the pre-polarizing permanent magnet <NUM> is used) and a dual-polarizing scheme (in other words, where the pre-polarizing permanent magnet <NUM> and the electromagnet <NUM> are used simultaneously).

The impact of the non-adiabatic field change on the measured signals is incorporated into the NMR model. For example, the oil-water fluid <NUM> within the conduit (or pipeline) is separated into regions of significance based on the fluid position relative to the polarization and detection zones of the EFNMR detector <NUM>. These regions are illustrated in <FIG> and a description of the signal attenuation for each region is provided below the figure. As shown, <FIG> illustrates a schematic diagram <NUM> of a conduit through which the oil-water fluid <NUM> flows as it enters a detection region of the EFNMR detector <NUM>.

<FIG> illustrates three regions of fluid within the pipeline; the initial fluid, intermediate fluid and outside fluid. The "initial fluid" region is fluid in the detection region of the EFNMR detector <NUM> when the electromagnet <NUM> is switched on. The detection zone (for example, of length LD = <NUM>) reflects the sensitivity of the EFNMR detector <NUM> along the axis parallel to the pipeline. The majority of the fluid in the detection region will experience an adiabatic transition as the signal sensitivity is strongest towards the center of the radio-frequency coil <NUM>. However, a full adiabatic transition between fields may not be possible due to the time of coil switch-on; thus a small fraction of the polarized fluid (kP) will not transition from Earth's field to the pre-polarizing field resulting in signal loss.

The "intermediate fluid" region is fluid outside the detection zone of the EFNMR detector <NUM> but still within the polarization zone (for example, of length LP = <NUM>) of the radio-frequency coil <NUM>. This portion of oil-water fluid <NUM> is in two regions either side of the detection zone (for example, both of length Li = <NUM>). This region has significantly poorer sensitivity relative to the detection zone. The impact of the non-adiabatic transition may result in a more significant fraction of fluid (ki) experiencing a non-adiabatic transition.

The "outside fluid" region may not be impacted by the non-adiabatic transition as this portion of the oil-water fluid <NUM> is not within the polarizing region of the electromagnet <NUM>. It may be assumed that this portion, which moves from outside the polarizing region to within the polarizing region, may effectively experience an adiabatic transition. For example, the electromagnet <NUM> will have a "polarization profile" involving changing field strength with length. The velocity of the oil-water fluid <NUM> may be low enough such that the fluid will experience a gradual change in field strength as it moves into the polarizing region. There may be no signal change of the outside fluid initially, however this outside fluid becomes important as it moves into the detection zone replacing fluid which has experienced a signal change.

The effect of the non-adiabatic transition may depend on the type of fluid (in other words, initial, intermediate or outside) and the relative fraction of each fluid in the EFNMR detector <NUM> at a given time. In order to aid the understanding of the signal loss model, <FIG> shows a table <NUM> that provides a description of position, quantification of the relevant fluid fractions, and a visual depiction of the regions within the detection zone for five different cases at different times since the polarization switch on.

Table <NUM> considers five different cases (A-E) at variable time since the polarization switch-on (tps) of the radio-frequency coil <NUM>. Case A is the initial position (tps = <NUM>) where the "initial fluid" alone is fully inside the detector zone of the EFNMR detector <NUM>. Case B shows the "intermediate fluid" flushing into the detection zone, while the "initial fluid" is flushing out of the detector zone. Case C has the "intermediate fluid" fully within the detection zone, which may only apply if LI≤ LD. The "outside fluid" is beginning to flush into the detection zone while the final fraction of the "initial fluid" is still flushing out of the detection zone. In Case D the "initial fluid" has now completely left the detection zone and the "intermediate fluid" is now flushing out of the detection zone. Finally, in Case E, the "intermediate fluid" has completely left the detection zone and the "outside fluid" will completely fill the EFNMR detector <NUM>.

In Case E, the EFNMR detector <NUM> is now filled with oil-water fluid <NUM>, which was not impacted by the non-adiabatic transition. Thus, the NMR signal will effectively be the same as if the fluid was polarized by the pre-polarizing permanent magnet <NUM>. In order to quantify the signal variation due to non-adiabatic field transition (SNA) at a given time since polarization pulse (tps), the following equation is applied:
<MAT>
where xP is the fraction "initial fluid" within the detection zone, xi is the fraction of "intermediate fluid" within the detection zone and xo is the fraction of "outside fluid" within the detection zone. In some aspects, SNA replaces SP in Eq. (<NUM>).

The values of xP, xI, and xO are determined by selecting the relevant case (according to the time since polarization) from Table <NUM>, whilst kP and ki are fractions of the "initial fluid" and "intermediate fluid" which observe non-adiabatic field transitions. The fraction parameters (kP and kI) are determined by empirically fitting the parameters to signal loss measurements for water as a function of fluid velocity and time since the polarization pulse.

In some aspects, the fluid measurement system <NUM> may determine a velocity-T<NUM> distribution via a 2D inversion. Therefore, the velocity and T<NUM> distributions must be measured simultaneously as a joint 2D velocity-T<NUM> distribution. This may require consideration in the application of 2D inversion techniques. The model for NMR signal of a flowing fluid (Eq. (<NUM>)) now effectively describes the relationship between the experimental parameters (for example, LPD, tpolz, and te) and the measured parameters (v and T<NUM>) and is used as the model kernel function for 2D inversion. The kernel function can be considered in terms of the "direct" and "indirect" dimensions; the direct measurement is obtained from the single-shot FID signal which is detected (SD), while the indirect measurement corresponds to variation in the pre-polarizing conditions (SP). The model kernel function can be simplified as: <MAT> where
<MAT>
where SP has been previously described in Eq. (<NUM>). The kernel function may be non-separable as the measured parameters (v and T<NUM>) are present in both the direct and indirect dimensions. Therefore, a full kernel matrix (for example, a non-separable matrix) may be constructed to avoid undesirable consequences during data analysis. A pseudo-1D inversion may be applied (using appropriate matrix manipulation) with the full kernel matrix in order to determine the 2D velocity-T<NUM> probability distribution. The relevant linear inverse problem can be written as:
<MAT>
where s(LPD, tpolz, te) are the experimentally acquired NMR signals, M(LPD, tpolz, te, v, T<NUM>) is the model kernel matrix described in Eq. (<NUM>), and P(v, T<NUM>) is the joint 2D probability distribution to be determined. The NMR signals consist of FID measurements acquired at variable pre-polarizing conditions (for example, variable distance <NUM> (LPD) and variable time, tpolz) organized into a stacked signal vector. The row elements of the model kernel matrix describe changes in signal with respect to the experimental parameters (in other words, LPD, tpolz, and te) and correspond to the signal vector components. The column elements of the model kernel matrix describe changes in the measured signal with respect to the measured parameters (v and T<NUM>) and correspond to the solution vector components. The probability distribution vector (p) is determined using, for example, 1D Tikhonov regularization (via Eq. (<NUM>)). The resultant probability distribution vector is rearranged into the final 2D distribution (P(v, T<NUM>)). The inversion procedure may take into account matrix arrangement and manipulation procedures. In some, aspects, the 1D distributions (p(v) and p(T<NUM>)) may be readily determined by projecting the 2D distribution onto the relevant 1D axis.

The fluid measurement system <NUM> may apply a particular matrix manipulation technique for a pseudo-1D inversion. For example, the NMR signals from the EFNMR detector <NUM> include FID measurements (with nF points recorded for each FID) acquired at variable pre-polarizing conditions (for example, distance <NUM> and tpolz). The FID measurements may be compressed using window-averaging in order to obtain signal matrices of reasonable size for inversion processing. The FID signals are divided into nw equally sized windows or bins (FID signals may generally be dominated by a linear outflow effect; therefore using equally spaced windows is appropriate). The data points within each bin may be averaged to provide a compressed FID signal of size nw. If FID measurements are acquired at nL different separation distances (for varying distances <NUM>) and nT different polarization times, tpolz (for additional pre-polarization at the radio-frequency coil <NUM>), then there are npp = nL + nT pre-polarization conditions.

Thus, the effective NMR measured signals will be of size nw×npp (in other words, a 2D data matrix of npp compressed FIDs each of length nw). The signal matrix (S) may be unwrapped into a 1D signal column vector (s). If the solution matrix (P) for the probability distribution is to be of size mv×mT1 then the relevant model kernel matrix (K) will be of size n×m (where n = nwnpp and m = mvmT1). The row elements of the model kernel matrix describe changes in signal with respect to the experimental parameters (in other words, LPD, tpolz and te) and correspond to the signal vector components. The column elements of the model kernel matrix may describe changes in the measured signal with respect to the measured parameters (v and T<NUM>) and correspond to the solution vector components.

The measured signals (s) have now been appropriately manipulated such that the signal vector is of length n = nwnp and the model kernel (K) has been manipulated to provide a matrix of size n×m in order to solve the solution vector (p) of length m with 1D Tikhonov regularization. The vector and matrix are also of appropriate size to ensure reasonable computational efficiency. In some aspects, the smoothing operation matrix (Q) must be carefully constructed to calculate the finite second difference across 2D solution space (hence approximating the second derivative of the P). The resultant solution is returned as a vector (p) is of length m and is reshaped into the final 2D distribution (P of size mv×mT1).

Once the joint 2D velocity-T<NUM> probability distribution is determined, such distribution can be used to calculate individual phase flowrates of the oil <NUM> and the water <NUM>. The oil and water phases are distinguished with a T<NUM> cutoff value (T<NUM>,C), which is used to differentiate the oil <NUM> and the water <NUM> (for example, similar to T<NUM> cut-offs used to differentiate bound fluid and free fluid in NMR analysis of rock cores). In some aspects, a cut-off of T<NUM>,C = <NUM> is used (calculated as the geometric mean of the T<NUM> values for the oil (<NUM>) and water (<NUM>)). The relevant signal contribution of each liquid is calculated by integrating over the relevant region of the joint probability distribution:
<MAT>
<MAT>
where Soil and Swater are the oil and water signal contribution to the model fit respectively, T<NUM>,min and T<NUM>,max define the bounds of the discretized T<NUM> range, and vmax is the maximum value in the discretized velocity range. The phase fractions can be calculated from the relevant signal contribution of each phase:
<MAT>
<MAT>
where xw is the water phase fraction (water-cut), xo is the oil phase fraction, and HIoil is the hydrogen index for the oil <NUM>, which has been determined by comparing the measured signal intensity of the oil and water samples obtained during CPMG measurements in an NMR rock core analyzer (for example, a Magritek <NUM> NMR rock core analyzer). The individual phase velocity distributions (p(vo) and p(vw) for oil and water respectively) are determined by integrating the relevant regions of the 2D distribution:
<MAT>
<MAT>.

The mean velocity for each phase (vM,o and vM,w for the oil <NUM> and the water <NUM>, respectively) can then be determined by calculating the expected value for each phase velocity distribution:
<MAT>.

Finally, individual phase volumetric flowrates (qo and qw for the oil <NUM> and the water <NUM>, respectively) can be calculated:
<MAT>
where A is the internal cross-sectional area of the conduit <NUM>. The phase flowrates of the oil <NUM> and the water <NUM>, which are measured from the NMR signal analysis methodology, in some aspects, can be verified against independent flowrate measurements from the flow meters <NUM> and <NUM>, respectively, of single-phase flow obtained prior to mixing the oil <NUM> and the water <NUM> into the oil-water fluid <NUM> by the fluid mixer <NUM>.

An example operation process <NUM> executed with the fluid measurement system <NUM> is shown in <FIG>. Process <NUM> includes a description of steps in a procedure applied to measure the fluid flowrates using the fluid measurement system <NUM>. The procedure, in this example, is applied with the control system <NUM> executing. for example, Prospa software (from Magritek, New Zealand) to capture twenty FID measurements at varying separation distance <NUM> (LPD) and twenty FID measurements at varying pre-polarization times (tpolz). Once the FID data has been recorded, it may be imported into, for example, Matlab R2017b, for signal processing and analysis.

A series of pre-processing steps may be applied to the imported FID data such that the FID data is suitable for inversion. For example, a Gaussian noise filter may be implemented on the measured FID spectrums primarily to remove the influence of <NUM> mains noise. The FIDs may then be truncated at the point where the SNR reaches <NUM> (in other words, data with SNR < <NUM> is removed), such that the baseline noise does not influence the signal and introduce artifacts in the resulting 2D velocity-T<NUM> distribution.

The truncated signals may then be window-averaged such that the data is of appropriate size for computationally efficient inversion. The processed FID data may then be fit with the appropriate 2D velocity-T<NUM> distribution using the NMR flow model (Eq. (<NUM>)) via the 2D Tikhonov regularization inversion (Eq. (<NUM>)). The 2D regions of the velocity-T<NUM> distribution may be appropriately integrated in order to determine the relevant signal contribution of each phase (according to Eqs. (<NUM>) and (<NUM>)). The signal contributions may be corrected for the oil hydrogen index in order to quantify volumetric fluid fractions (according to Eqs. (<NUM>) and (<NUM>)). The expected value of each of the individual phase velocity distributions may be calculated in order to quantify mean velocity (according to Eq. (<NUM>)). Finally, the individual volumetric flowrates for the water <NUM> and the oil <NUM> may be calculated from the volumetric phase fractions and phase mean velocities (using Eq. (<NUM>)).

As previously described, the resultant individual volumetric flowrates determined according to the FID data and inversion process may be checked against the independent flowrate measurements from the flow meters <NUM> and <NUM> for accuracy. Such analysis may also include consideration of the range of liquid-liquid flow regimes within the conduit <NUM> of the oil-water fluid <NUM>. There may be six different oil/water flow regimes including; stratified flow (St), stratified flow with mixing at the interface (St w/ mix), a dispersion of oil-in-water over a free water layer (Do/w & w), a dual dispersion of water-in-oil over oil-in-water (Do/w & Dw/o), a full oil-in-water emulsion (Eo/w) and a full water-in-oil emulsion (Ew/o). Experimental executions with the fluid measurement system <NUM> included twenty-one experimental flow measurements in three flow regime: stratified with mixing (<NUM> measurements), dispersion of oil-in-water and water (<NUM> measurements), and full oil-in-water emulsions (<NUM> measurement). <FIG> illustrates a table <NUM> that shows a summary for the three relevant flow regimes including the appropriate region on a flow regime map, a schematic and a photograph.

Further, a graph <NUM> that shows an experimental matrix of oil and water superficial velocities to be used for verification of the NMR flow measurement procedure is illustrated in <FIG>. The water superficial velocities range from <NUM> to <NUM>/s (corresponding to flowrates of <NUM>-<NUM><NUM>/h) and the oil superficial velocities range from <NUM> to <NUM>/s (corresponding to flowrates of (<NUM>-<NUM>) m<NUM>/h). The visually observed flow regime for each measurement point is indicated by the marker type and shade on graph <NUM>, with the flow regime boundaries indicated with black lines. Here, the experiments with the fluid measurement system <NUM> were conducted with saline tap water as the water <NUM> and canola oil as the oil <NUM>, with a pipe diameter of <NUM> of conduit <NUM>, density ratio of <NUM>, and a viscosity ratio of <NUM>.

Two-phase flow measurements were performed for each of the <NUM> flow measurement points displayed in the graph <NUM> and each measurement was analyzed according to the NMR flow measurement procedure of the present disclosure. <FIG> illustrates a graph <NUM> that compares the NMR measured flowrates according to the present disclosure for each individual phase to the corresponding flow meter (<NUM> or <NUM>) measured phase volumetric flowrates for both the oil <NUM> and the water <NUM>. The visually observed flow regime for each measurement is indicated according to the marker shape in graph <NUM>.

<FIG> shows the NMR measured flowrates compare very well to the measured flowrates (by the flow meters <NUM> and <NUM>) for both the oil <NUM> and the water <NUM>. The absolute errors appear to be slightly higher for the water measurements in the oil-in-water emulsion flow regime. A statistical comparison between the flow measurement techniques is performed in order to quantify the relative performance in each flow regime. The mean error (ME) quantifies how well an observed measurement (in other words, flowrate measurements according to the EFNMR detector <NUM> and control system <NUM>) matches a reference measurement (in other words, flowrate measurement by the flow meters <NUM> and <NUM>). The mean error for a sample (of size N) is:
<MAT>
where zi,obs is the observed measurement of the variable of interest (flowrate measurements according to the EFNMR detector <NUM> and control system <NUM>) for sample, i, and zi,ref is the reference measurement of the property of interest (flowrate measurement by the flow meters <NUM> and <NUM>) for sample, i. The root-mean-square error (RMSE) quantifies accuracy in terms of the standard deviation of the residual errors of observed measurements relative to a reference measurement. The RMSE for a set of flow measurements (of sample size N) is:
<MAT>.

<FIG> illustrates a graph <NUM> that represents the mean error and <FIG> illustrates a graph <NUM> that represents the root mean square error of the observed measurements relative to the reference measurements. The summary statistics are presented for both oil and water measurements across the three observed flow regimes, as well as the overall values across all <NUM> measurements.

<FIG> further demonstrates the good agreement between the observed measured flowrates and the reference measured flowrates. In graph <NUM>, the mean error is less than <NUM><NUM>/h across all flow regimes; except for the oil flowrate measurement in the dispersion of oil-in-water and water flow regime. This flow regime only had three experiments, and the example presented in graphic <NUM> of <FIG> (with a deviation of about <NUM><NUM>/h) demonstrates the source of this discrepancy. For mid-range oil velocities (about <NUM>/s) there is loss of measurement sensitivity due to the poor SNR measured in this velocity-T<NUM> range. The velocity is between the effective regions of the two polarizing mechanisms; the pre-polarizing magnet <NUM> achieves improved polarization at higher velocities, whilst the electromagnetic radio-frequency coil <NUM> achieves improved polarization at lower velocities.

The root mean square errors in graph <NUM> also demonstrate the excellent agreement between flow measurement techniques. There is good agreement in the stratified with mixing flow regime (RMSE < <NUM><NUM>/h for both oil and water), as the two-phase flow stream is not emulsified and the low overall flowrate gives the fluid sufficient residence time for the two phases to separate in the fluid separation tank <NUM>. The flowrate agreement is marginally poorer for the oil-in-water emulsion, primarily due to the reduced separation efficiency, particularly at higher flowrates. The oil-in-water emulsion flow regime results in an emulsified mixture to be separated in the fluid separation tank <NUM>.

The efficiency of separation is dependent on the residence time of the mixture within the separator <NUM>. For example, for the measurement displayed in graphic <NUM> of <FIG>, the overall fluid flowrate is <NUM><NUM>/h, which means for a separation volume of <NUM>, the separation residence time will be about <NUM>. This may not be enough to achieve full separation of the oil and water emulsion; therefore the oil will contaminate the water storage tank <NUM> and vice versa. This is may be more problematic for the oil tank <NUM>, where the unseparated emulsion (which is denser than the pure oil phase <NUM>) may sink to the bottom of the tank <NUM>. The tank outlet may then discharge the emulsion. This causes the water fraction to increase gradually throughout the duration of the NMR flow measurement sequence. This results in slightly poorer comparison errors (RMSE of <NUM><NUM>/h for water and <NUM><NUM>/h for oil) in the oil-in-water flow regime. However the overall flow measurement performance (RMSE of <NUM><NUM>/h for water and <NUM><NUM>/h for oil) is still very good for two-phase oil/water measurements.

The EFNMR flow measurement procedure according to the present disclosure is also analyzed with respect to three example measurements from each of the three measurable flow regimes. <FIG> illustrate the measured the 2D velocity-T<NUM> probability distributions with a particular graphic (<NUM>, <NUM>, <NUM>) for a particular flow regime. Graphic <NUM> shows an example measurement from the stratified with mixing flow regime with a water flowrate of <NUM><NUM>/h and an oil flowrate of <NUM><NUM>/h. Graphic <NUM> shows a measurement from the dispersion of oil-in-water and water flow regime for a water flowrate of <NUM><NUM>/h and an oil flowrate of <NUM><NUM>/h. Graphic <NUM> presents an example distribution from the oil-in-water emulsion flow regime at a water flowrate of <NUM><NUM>/h and an oil flowrate of <NUM><NUM>/h. For each measurement, the 2D velocity-T<NUM> distribution has been fit to the experimentally measured FID signals with the model kernel given by Eq. (<NUM>). Each 2D velocity-T<NUM> distribution is projected into the relevant marginal 1D probability distributions with the velocity distributions also segregated into the relevant phase velocity probability distributions for the oil <NUM> and the water <NUM>.

Each of the examples presented in <FIG> are also individually analyzed. The 2D velocity-T<NUM> distribution illustrated in graphic <NUM> shows two separate regions with distinguishable T<NUM> relaxation. The distribution is reflective of the stratified with mixing flow regime consisting of two segregated layers of fluid in the pipe cross section with water on the bottom layer and oil on the top layer. The oil region (T<NUM>,LM = <NUM>, vM = <NUM>/s) displays a lower velocity relative to the water region (T<NUM>,LM = <NUM>, vM = <NUM>/s). The measured velocity difference is capturing the velocity slip that exists between the two liquid phases in the stratified flow regime. The oil <NUM> has a much higher viscosity (<NUM> cP) relative to the saline water (about <NUM> cP). The lower viscosity results in a higher fluid-wall frictional force for the oil <NUM> leading to a lower velocity relative to the water <NUM>. Note that for the similar flowrates of <NUM><NUM>/h and <NUM><NUM>/h for water and oil respectively, the higher water velocity will correspond to a higher oil fraction. The accuracy of the measurement for this example is excellent; the EFNMR measured oil flowrate (<NUM><NUM>/h) deviates from the flow meter <NUM> measured oil flowrate (<NUM><NUM>/h) by only <NUM><NUM>/h, whilst the water flowrate (<NUM><NUM>/h) deviates from the flow meter <NUM> measured water flowrate (<NUM><NUM>/h) by about <NUM><NUM>/h.

The 2D velocity-T<NUM> distribution in graphic <NUM> for the dispersion of oil-in-water above a water layer measurement displays three distinct regions. The region at short T<NUM> corresponds to the dispersed oil droplets in the top layer (fraction = <NUM>%, T<NUM>,LM = <NUM>, vM = <NUM>/s). The large dispersing water region at the lower velocity (fraction = <NUM>%, T<NUM>,LM = <NUM>, vM = <NUM>/s) corresponds to water with oil droplets dispersed within it. The small "free water" region at high velocity (fraction = <NUM>%, T<NUM>,LM = <NUM>, vM = <NUM>/s) is water from the water only layer (at the base of the conduit <NUM>). The free water layer is relatively small (<NUM>%) as the oil flowrate is relatively high for a dispersion of oil-in-water and water flow, meaning that the two-phase flow is beginning to approach the flow regime boundary and transition towards a dual dispersion flow. The measurement is able to capture the anticipated velocity slip for this example; the fluids within the dispersion layer (for example, the dispersed oil drops and the water phase containing the oil) both have very similar velocities which is anticipated for a continuous layer. The water only phase (on the bottom layer of the conduit <NUM>) is observed to be at marginally higher velocity relative to the dispersion components. This is expected as the dispersion will be more viscous relative to the water only phase. The EFNMR measured water flowrate (qw,nmr = <NUM><NUM>/h) matches the flow meter <NUM> measured water flowrate (qw,rot = <NUM><NUM>/h) very well. However the EFNMR measured oil flowrate (qo,nmr = <NUM><NUM>/h) is under predicted relative to the flow meter <NUM> measured oil flowrate. (qo,rot = <NUM><NUM>/h). This discrepancy can be attributed to the poor SNR of oil flows at intermediate velocities.

The 2D distribution in graphic <NUM> displays a small region at short T<NUM> corresponding to the emulsified oil (T<NUM>,LM = <NUM>, vM = <NUM>/s) and a large region at high T<NUM> corresponding to water (T<NUM>,LM = <NUM>, vM = <NUM>/s). The velocity slip ratio is determined to be <NUM> from the measured velocity-T<NUM> distribution. For this measurement, the EFNMR measured water flowrate (qw,nmr = <NUM><NUM>/h) is over-predicted relative to the flow meter <NUM> measured flowrate (qw,rot = <NUM><NUM>/h). The EFNMR measured oil flowrate (qo,nmr = <NUM><NUM>/h) is reasonably close to the flow meter <NUM> measured flowrate (qo,rot = <NUM><NUM>/h). The suggested source of discrepancy for the water flowrate measurement is inadequate residence time required for separation of the oil-in-water emulsion.

Turning now to <FIG>, this figure illustrates another example implementation of a fluid measurement system <NUM> according to the present disclosure, which is covered by the claims. Fluid measurement system <NUM> may be substantially similar to the fluid measurement system <NUM>, and in this figure, like reference symbols indicate like components of the fluid measurement system <NUM>. However, as shown in <FIG>, fluid measurement system <NUM> includes electromagnets <NUM> and <NUM>. In this example, the electromagnet <NUM> creates a pulsed magnetic field gradient. Electromagnet <NUM>, in some aspects, is aligned with the radio-frequency coil <NUM> of the EFNM detector <NUM> (for example, fits around the coil <NUM>). The electromagnet <NUM> creates a reasonably homogeneous polarizing field. In some aspects, the electromagnet <NUM> can fit externally about the electromagnet <NUM> or may be positioned immediately upstream (in other words, between the EFNMR detector <NUM> and the pre-polarizing permanent magnet <NUM>) of the electromagnet <NUM>.

In some aspects, the oil-water fluid <NUM> comprises both a liquid phase (for example, a mix of liquid oil <NUM> and liquid water <NUM>) and a gas <NUM> (for example, methane or other hydrocarbon gas) that is introduced into the oil-water fluid <NUM> with a compressor <NUM>. Thus, with respect to the fluid measurement system <NUM>, the oil-water fluid <NUM> is a mixed-phase fluid <NUM>.

In some aspects, the pre-polarizing magnet <NUM> and the first electromagnet <NUM> are operated in combination with the pre-polarizing permanent magnet <NUM>, the radio-frequency coil <NUM>, and the EFNMR detector <NUM>, to determine the velocities of the liquid and gas phases of the mixed-phase fluid <NUM>, as well as the oil-water content of the liquid phase of the mixed-phase fluid <NUM>. For example, a velocity of the liquid phase of the mixed-phase fluid <NUM> may be determined as follows. As the mixed-phase fluid <NUM> is circulated through the pre-polarizing permanent magnet <NUM>, an initial polarization of the gas phase is applied to the mixed-phase fluid <NUM> by the pre-polarizing permanent magnet <NUM>. As the initially polarized mixed-phase fluid <NUM> flows through the EFNRM detector <NUM> and during acquisition of the FID values with the radio-frequency coil <NUM>, the electromagnet <NUM> is energized to produce the pulsed magnetic field gradient that suppresses the NMR acquired signals from the gas phase (which is faster flowing and diffusing relative to the liquid phase) of the mixed phase fluid <NUM>. The electromagnet <NUM> is also operated to produce the reasonably homogenous magnetic field to polarize the liquid phase of the mixed-phase fluid <NUM>. Based on the acquired signals in this operation, the EFNRM detector <NUM> determines a velocity of the liquid phase only of the mixed-phase fluid <NUM>. Such velocities may be determined, for example, based on a pseudo-1D inversion to the acquired FID values of the liquid phase, as previously described.

A velocity of the gas phase of the mixed-phase fluid <NUM> may be determined as follows. As the mixed-phase fluid <NUM> is circulated through the pre-polarizing permanent magnet <NUM>, an initial polarization of the gas phase is applied to the mixed-phase fluid <NUM> by the pre-polarizing permanent magnet <NUM>. As the initially polarized mixed-phase fluid <NUM> flows through the EFNRM detector <NUM> and during acquisition of the FID values with the radio-frequency coil <NUM>, neither electromagnet <NUM> nor <NUM> is energized. Based on the acquired signals in this operation, the EFNRM detector <NUM> determines a velocity of the gas phase only of the mixed-phase fluid <NUM>. Such velocities may be determined, for example, based on a pseudo-1D inversion to the acquired FID values of the gas phase, as previously described.

The content distribution of the oil <NUM> and water <NUM> in the liquid phase may also be determined by the fluid measurement system <NUM> in similar fashion to the previous operations described with reference to the fluid measurement system <NUM> of <FIG>. For example, as the mixed-phase fluid <NUM> circulates through the EFNMR detector <NUM>, the electromagnet <NUM> is energized subsequent to an initial polarization of the mixed-phase fluid <NUM> by the pre-polarizing permanent magnet <NUM>. In this operation, the electromagnet <NUM> is energized and the homogeneous polarizing field is generated. In some aspects, the separation distance <NUM> of the fluid measurement system <NUM> may be greater than <NUM>, which may be larger than the distance typically used in fluid measurement system <NUM>. As described previously, the oil-water content of the liquid phase of the mixed-phase fluid <NUM> is determined according to the T<NUM> differences for the FID signals from the EFNMR detector <NUM>.

Turning now to <FIG>, this figure illustrates a flowchart that describes an example method <NUM> for determining oil-water content in an oil-water fluid, which is not covered by the claims. In some aspects, all or part of the example method <NUM> can be implemented by or with the control system <NUM> and, more generally, the fluid measurement system <NUM> shown in <FIG>. Method <NUM> may begin at step <NUM>, which includes circulating a mixed oil-water liquid flow through a fluid flow circuit that comprises an oil source and a water source. For example, the oil <NUM> and the water <NUM> may be circulated (by pumps <NUM> and <NUM>, respectively) from tanks <NUM> and <NUM> (respectively) to the fluid mixer <NUM> and mixed into the oil-water fluid <NUM>.

Method <NUM> may continue at step <NUM>, which includes circulating the mixed oil-water liquid flow through a pre-polarizing magnet. For example, the oil-water fluid <NUM> is circulated through conduit <NUM> and into the pre-polarizing magnet <NUM>. In some aspects, the pre-polarizing magnet <NUM> is a Halbach array.

Method <NUM> may continue at step <NUM>, which includes polarizing the mixed oil-water liquid flow with the pre-polarizing magnet to an initial polarization. For example, the pre-polarizing magnet <NUM> polarizes the oil-water fluid <NUM> to the initial polarization by, for example, applying the <NUM> T Halbach array, which is located at a particular distance (LPD) from an EFNMR detector <NUM>. The distance may be varied, for example, between <NUM> and <NUM>.

Method <NUM> may continue at step <NUM>, which includes circulating the polarized mixed oil-water liquid flow at the initial polarization to an Earth's field nuclear magnetic resonance (EFNMR) detector that includes a radio-frequency (RF) coil and a surrounding electromagnet. For example, once the oil-water fluid <NUM> is polarized by the pre-polarizing magnet <NUM>, the oil-water fluid <NUM> is circulated to the EFNMR detector <NUM>.

Method <NUM> may continue at step <NUM>, which includes further polarizing the polarized mixed oil-water liquid flow with the surrounding electromagnet. For example, once within the polarization area of the electromagnet, the fluid is additionally polarized by the electromagnet of the EFNRM detector <NUM> (in other words, in a dual-polarization scheme).

Method <NUM> may continue at step <NUM>, which includes measuring fluid induction decay (FID) values of the additionally polarized mixed oil-water liquid flow with the EFNMR detector. For example, the dually-polarized oil-water fluid <NUM> flows through the EFNMR detector, in which the FID values are measured. In some aspects, the FID values include relaxation time constants (T<NUM> and T<NUM>) associated with the fluids of interest, both of which quantify the rate of energy transfer in magnetic resonance processes. The spin-lattice relaxation rate (T<NUM>) is a fluid property describing the rate of signal accumulation in a magnetic field, while the spin-spin relaxation rate (T<NUM>) describes the rate of signal decay or dephasing of hydrogen atoms within a fluid. In some aspects, the FID values are a function of velocity and T<NUM> values.

In some aspects, step <NUM> may be repeated for multiple, different separation distances <NUM> between the pre-polarizing magnet <NUM> and the EFNMR detector <NUM>. For example, the pre-polarizing magnet <NUM> may be positioned at a first, particular separation distance <NUM> (for example, about <NUM>). A first set of FID values of the polarized gas phase may be measured with the EFNMR detector at the first, particular separation distance <NUM>. Then, the pre-polarizing magnet <NUM> may be positioned at a second, particular separation distance <NUM> (for example, about <NUM>). A second set of FID values of the polarized gas phase may be measured with the EFNMR detector at the second, particular separation distance <NUM>.

Method <NUM> may continue at step <NUM>, which includes transforming the measured FID values from a non-adiabatic transition from an Earth's field to a polarizing field to an effective adiabatic transition from the Earth's field to the polarizing field. For example, in some aspects, the transformation of the measured FID values from a non-adiabatic transition from an Earth's field to a polarizing field to an effective adiabatic transition from the Earth's field to the polarizing field includes determining a location of a particular portion of the dual polarized oil-water fluid <NUM> relative to a detection zone of the EFNMR detector <NUM>. In some aspects, that determination based on a start time of the additional polarization (for example, tpolz) of the polarized mixed oil-water fluid <NUM>. As previously described, for example, the portion of the oil-water fluid <NUM> may be an initial portion, an intermediate portion, or an outside portion. At the start time of the additional polarization, for instance, the initial portion may be fully inside the detection region of the EFNMR detector <NUM>, while the intermediate and outside portions are fully outside such region. As the oil-water fluid <NUM> circulated to and through the EFNMR detector <NUM>, at a time greater than a ratio of a combined length of the separation distance <NUM> and a length of a region just outside of the detection region (for example, LI) to a velocity of the oil-water fluid <NUM>, the outside portion may be fully within the detection region. This outside portion, in some aspects, may be independent of the non-adiabatic transition from the Earth's field to the polarizing field. Thus, the portion of FID values that correspond to the outside portion of the polarized oil-water fluid <NUM> may be selected to transform the measured FID values from a non-adiabatic transition from an Earth's field to a polarizing field to an effective adiabatic transition from the Earth's field to the polarizing field.

Method <NUM> may continue at step <NUM>, which includes determining a velocity of the oil in the mixed oil-water liquid flow and a velocity of the water in the mixed oil-water liquid flow based on differences in NMR signal relaxation properties of the transformed FID values. For example, once the transformed FID values are determined in step <NUM>, the velocities of the oil <NUM> and the water <NUM> may be determined according to the T<NUM> properties of the transformed FID values. In some aspects, this determination includes applying a pseudo-1D inversion to the transformed FID values. The pseudo 1D-inversion, in some aspects, may be a Tikhonov inversion. Then, a 2D probability distribution (P) of the velocity of the oil <NUM> in the oil-water fluid <NUM> and the velocity of the water <NUM> in the oil-water fluid <NUM> is determined based on the applied 1D inversion of the transformed FID values and a model kernel matrix (M) (as described in Eq. (<NUM>)). The model kernel matrix may be a function of a polarization pulse time of the electromagnet, a distance <NUM> between the pre-polarizing magnet <NUM> and the EFNMR detector <NUM>, a start time of a radio-frequency signal acquisition from the radio-frequency coil <NUM>, and the NMR signal relaxation properties (T<NUM>) of the transformed FID values, as previously described.

Method <NUM> may continue at step <NUM>, which includes determining an oil content and a water content of the mixed oil-water liquid flow from the transformed plurality of FID values based on differences in NMR signal relaxation properties of the transformed FID values. For example, the oil and water content can be determined according to, for example, the mean velocities (Eq. (<NUM>)) and, from these, the individual phase volumetric flowrates (Eq. (<NUM>)).

Turning now to <FIG>, this figure illustrates a flowchart that describes an example method <NUM> for determining one or more fluid properties of a mixed-phase fluid, which is covered by the claims. In some aspects, all or part of the example method <NUM> can be implemented by or with the control system <NUM> and, more generally, the fluid measurement system <NUM> shown in <FIG>. Method <NUM> may begin at step <NUM>, which includes circulating a mixed-phase fluid flow through a fluid flow circuit that includes at least two liquid sources and a fluid mixer that mixes a liquid from each of the at least two liquid sources into the mixed-phase fluid flow. For example, a first liquid, such as the oil <NUM>, and a second liquid, such as the water <NUM>, may be mixed by the fluid mixer <NUM> and circulated (for example, by pumps <NUM> and <NUM>) through the conduit <NUM>. In some aspects, a gas phase <NUM> from gas source <NUM> is injected into the mixed liquid phase downstream of the fluid mixer <NUM>. In some aspects, the gas phase may be a hydrocarbon gas.

Method <NUM> may continue at step <NUM>, which includes circulating the mixed-phase fluid flow through a pre-polarizing magnet. For example, the mixed-phase fluid <NUM> is circulated through the pre-polarizing magnet <NUM> within the conduit <NUM>.

Method <NUM> may continue at step <NUM>, which includes polarizing a gas phase of the mixed-phase fluid flow to an initial polarization with the pre-polarizing magnet. For example, the pre-polarizing magnet <NUM> may be operated (for example, by the control system <NUM>) to generate a homogeneous polarization field to polarize the mixed-phase fluid <NUM> (including a gas phase within the fluid <NUM>) to an initial polarization.

Method <NUM> may continue at step <NUM>, which includes measuring a plurality of fluid induction decay (FID) values of the polarized gas phase with the EFNMR detector. For example, once polarized to the initial polarization, the mixed-phase fluid <NUM> is circulated a particular distance <NUM> (LPD) to the EFNMR detector <NUM>, which includes the first electromagnet <NUM>, the second electromagnet <NUM>, and the radio-frequency coil <NUM>. The polarized gas phase, flows through the EFNMR detector <NUM>, in which the FID values of the gas phase are measured. In some aspects, the FID values include relaxation time constants (T<NUM> and T<NUM>) associated with the gas phase, both of which quantify the rate of energy transfer in magnetic resonance processes. The spin-lattice relaxation rate (T<NUM>) is a fluid property describing the rate of signal accumulation in a magnetic field, while the spin-spin relaxation rate (T<NUM>) describes the rate of signal decay or dephasing of hydrogen atoms within a fluid. In some aspects, the FID values are a function of velocity and T<NUM> values.

Method <NUM> may continue at step <NUM>, which includes determining a velocity of the gas phase based on the FID values of the polarized gas phase. For example, in some aspects, determining the velocity of the gas phase includes applying a pseudo-1D inversion, such as a Tikhonov inversion, to the measured FID values of the gas phase. In some aspects, for example, such a pseudo-1D inversion includes applying a discretized probability distribution vector of a variable (p) may be expressed as a function of the measured FID values (in other words, NMR signal (s)) via a model kernel matrix (M) as described in Eq. <NUM> and subsequent equations according to the present disclosure. By step <NUM> (or step <NUM>), the initial polarization of the liquid phase of the mixed-phase fluid <NUM> may be decayed by the time the mixed-phase fluid <NUM> has reached the radio-frequency coil <NUM> of the EFNMR detector <NUM>; thus, the FID measurements taken in step <NUM> are only of the gas phase of the mixed-phase fluid <NUM>.

Method <NUM> may continue at step <NUM>, which includes producing a pulsed magnetic field gradient with the first electromagnet to suppress one or more signals acquired by the EFNMR detector with the first electromagnet and measuring FID values of the liquid phase of the mixed-phase fluid. For example, the first electromagnet <NUM> may produce a pulsed magnetic field gradient to suppress the NMR signals taken from the gas phase of the mixed-phase fluid <NUM>. Simultaneously, FID measurements may be taken of the liquid phase of the mixed-phase fluid <NUM> with the NMR detector <NUM> while the second electromagnet <NUM> is producing a reasonably homogeneous magnetic field to polarize the liquid phase during step <NUM>.

In some aspects, step <NUM> may be repeated for multiple, different pulse time durations of the second electromagnet <NUM>. For example, the second electromagnet <NUM> may be operated at a first, particular pulse time duration (tpolz). A first set of FID values of the polarized liquid phase may be measured with the EFNMR detector at the first, particular pulse time duration. Then, the second electromagnet <NUM> may be operated at a second, particular pulse time duration. A second set of FID values of the polarized liquid phase may be measured with the EFNMR detector at the second, particular pulse time duration.

Method <NUM> may continue at step <NUM>, which includes producing a homogeneous polarizing field to polarize the liquid phase of the mixed-phase fluid with the second electromagnet. For example, as the first electromagnet <NUM> suppresses one or more signals from the gas phase and measuring FID values of the liquid phase of the mixed-phase fluid, the second electromagnet <NUM> produces the homogenous magnetic field to polarize the liquid phase of the mixed-phase fluid <NUM>.

Method <NUM> may continue at step <NUM>, which includes determining a velocity of the liquid phase based on the FID values of the polarized liquid phase. For example, as with the gas phase, the velocity of the liquid phase may be determined by applying a pseudo-1D inversion, such as a Tikhonov inversion, to the measured FID values of the liquid phase. In some aspects, for example, such a pseudo-1D inversion includes applying a discretized probability distribution vector of a variable (p) may be expressed as a function of the measured FID values (in other words, NMR signal (s)) via a model kernel matrix (M) as described in Eq. <NUM> and subsequent equations according to the present disclosure.

Method <NUM> may continue at step <NUM>, which includes determining a content of the liquid phase based on the FID values of the liquid phase of the mixed-phase fluid. For example, in the case of the liquid phase being a mixture or combination of oil and water, an oil-water content of the liquid phase of the mixed-phase fluid <NUM> is determined with a 2D probability distribution of the velocity of the liquid phase in the mixed-phase fluid <NUM> based on the applied 1D inversion of the FID values of the liquid phase and a model kernel matrix, as described according to step <NUM> of method <NUM>.

<FIG> is a schematic illustration of an example controller <NUM> (or control system) for controlling operations of a fluid measurement system according to the present disclosure. For example, the controller <NUM> may include or be part of the control system <NUM> shown in <FIG> and <FIG>. The controller <NUM> is intended to include various forms of digital computers, such as printed circuit boards (PCB), processors, digital circuitry, or otherwise parts of a fluid measurement system. Additionally the system can include portable storage media, such as, Universal Serial Bus (USB) flash drives. For example, the USB flash drives may store operating systems and other applications. The USB flash drives can include input/output components, such as a wireless transmitter or USB connector that may be inserted into a USB port of another computing device.

The controller <NUM> includes a processor <NUM>, a memory <NUM>, a storage device <NUM>, and an input/output device <NUM>. Each of the components <NUM>, <NUM>, <NUM>, and <NUM> are interconnected using a system bus <NUM>. The processor <NUM> is capable of processing instructions for execution within the controller <NUM>. The processor may be designed using any of a number of architectures. For example, the processor <NUM> may be a CISC (Complex Instruction Set Computers) processor, a RISC (Reduced Instruction Set Computer) processor, or a MISC (Minimal Instruction Set Computer) processor.

In one implementation, the processor <NUM> is a single-threaded processor. In another implementation, the processor <NUM> is a multi-threaded processor. The processor <NUM> is capable of processing instructions stored in the memory <NUM> or on the storage device <NUM> to display graphical information for a user interface on the input/output device <NUM>.

The memory <NUM> stores information within the controller <NUM>.

The storage device <NUM> is capable of providing mass storage for the controller <NUM>.

The input/output device <NUM> provides input/output operations for the controller <NUM>.

The features described can be implemented in digital electronic circuitry, or in computer hardware, firmware, software, or in combinations of them. The apparatus can be implemented in a computer program product tangibly embodied in an information carrier, for example, in a machine-readable storage device for execution by a programmable processor; and method steps can be performed by a programmable processor executing a program of instructions to perform functions of the described implementations by operating on input data and generating output. The described features can be implemented advantageously in one or more computer programs that are executable on a programmable system including at least one programmable processor coupled to receive data and instructions from, and to transmit data and instructions to, a data storage system, at least one input device, and at least one output device. A computer program is a set of instructions that can be used, directly or indirectly, in a computer to perform a certain activity or bring about a certain result.

Additionally, such activities can be implemented via touchscreen flat-panel displays and other appropriate mechanisms.

The features can be implemented in a control system that includes a back-end component, such as a data server, or that includes a middleware component, such as an application server or an Internet server, or that includes a front-end component, such as a client computer having a graphical user interface or an Internet browser, or any combination of them. Examples of communication networks include a local area network ("LAN"), a wide area network ("WAN"), peer-to-peer networks (having ad-hoc or static members), grid computing infrastructures, and the Internet.

While this specification contains many specific implementation details, these should not be construed as limitations on the scope of any inventions or of what may be claimed, but rather as descriptions of features specific to particular implementations of particular inventions.

Claim 1:
A fluid measurement system, comprising:
a fluid flow circuit that comprises at least two liquid sources (<NUM>, <NUM>), a gas source (<NUM>), and a fluid mixer (<NUM>) that mixes at least two liquids (<NUM>, <NUM>) from the at least two liquid sources (<NUM>, <NUM>) to form a liquid phase of a mixed-phase fluid (<NUM>) that also includes a gas phase (<NUM>) from the gas source (<NUM>);
a pre-polarizing magnet (<NUM>) positioned to receive the mixed-phase fluid flow from the fluid mixer (<NUM>);
an Earth's field nuclear magnetic resonance EFNMR detector (<NUM>) that comprises a radio-frequency RF coil (<NUM>), a first electromagnet (<NUM>), and a second electromagnet (<NUM>), the EFNMR detector (<NUM>) positioned to receive the mixed-phase fluid from the pre-polarizing magnet (<NUM>); and
a control system (<NUM>) communicably coupled to the pre-polarizing magnet (<NUM>) and the EFNMR detector (<NUM>) and configured to perform operations comprising:
controlling (<NUM>) the pre-polarizing magnet (<NUM>) to polarize at least the gas phase of the mixed-phase fluid flow to an initial polarization;
controlling (<NUM>) the EFNMR detector (<NUM>) to measure a plurality of free induction decay - FID - values of the polarized gas phase;
determining (<NUM>) a velocity of the gas phase based on the plurality of FID values of the polarized gas phase;
controlling (<NUM>) the first electromagnet (<NUM>) to produce a pulsed magnetic field gradient to suppress one or more signals acquired by the EFNMR detector;
controlling (<NUM>) the EFNMR detector (<NUM>) simultaneously with the production of the pulsed magnetic field gradient to measure a plurality of FID values of the liquid phase of the mixed-phase fluid;
controlling (<NUM>) the second electromagnet (<NUM>) to generate a homogeneous polarizing field to polarize the liquid phase of the mixed-phase fluid;
determining (<NUM>) a velocity of the liquid phase based on the plurality of FID values of the polarized liquid phase of the mixed-phase fluid; and
determining (<NUM>) a content of the liquid phase based on the plurality of FID values of the liquid phase of the mixed-phase fluid.