# Patent

## Title
Method and apparatus for the measurement of the mass fraction of water in oil-water mixtures

## Abstract

An apparatus for measuring the mass fractions of water and oil in a flowing mixture of oil and water through a pipe includes a sensor portion that measures sound velocity and temperature of the flowing oil water mixture at a first time and at a second time. The apparatus includes a temperature changer in thermal communication with the flowing fluid which changes the temperature of the flowing oil water mixture by a measurable amount between the first time and the second time. A method for measuring water mass fraction in a flowing mixture of oil and water through a pipe includes the steps of measuring sound velocity and temperature of the flowing oil water mixture at a first time with a sensor portion. There is the step of changing the temperature of the flowing oil water mixture by a measurable amount with a temperature changer in thermal communication with the flowing fluid. There is the step of measuring sound velocity and temperature of the flowing oil water mixture at a second time with the sensor portion.

## Background
FIELD OF THE INVENTION
The present invention is related to the measurement of the mass fractions of water and oil in a flowing mixture of oil and water through a pipe. (As used herein, references to the “present invention” or “invention” relate to exemplary embodiments and not necessarily to every embodiment encompassed by the appended claims.) More specifically, the present invention is related to the measurement of the mass fractions of water and oil in a flowing mixture where a temperature changer changes the temperature of the flowing oil water mixture by a measurable amount between a first time and a second time so the mass fraction can be determined from the change in the sound velocity in the mixture for a known change in temperature.
BACKGROUND OF THE INVENTION
This section is intended to introduce the reader to various aspects of the art that may be related to various aspects of the present invention. The following discussion is intended to provide information to facilitate a better understanding of the present invention. Accordingly, it should be understood that statements in the following discussion are to be read in this light, and not as admissions of prior art.
Recent years have seen increased need for an accurate measurement of the water cut—the fraction by volume of water in crude oil relative to the total volume of the mixture. The need has arisen because of the increased use of water and steam for the extraction of crude oil from depleted fields, and because of increased transport of crude by tankers to refineries remote from the field—the transporting tankers often maintain a nominally fixed ballast condition by introducing seawater into oil storage tanks.
Accurate measurement of water cut has proven difficult:

    
    
        1. Several systems that endeavor to correlate the capacitance of the oil water mixtures with water cut are commercially available. These systems suffer however from several technical difficulties: (a) For high water cuts, the mixture's conductance becomes high and capacitance is a poor measure of the water content; and (b) The relationship between the inter-electrode capacitance (or resistance) may not characterize the true mass or volume fraction of water in the flowing fluid, because the distribution of the phases does not correlate with the electrostatic field intensity.
        2. Experiments have shown that, under certain conditions, measurement of the sound velocity of an oil-water mixture can be used to characterize the mass fractions of water and oil in the mixture. There are however several drawbacks to this method: (a) An accurate measure of the sound velocity and specific gravity of each of the two phases is required and (b) The method becomes increasingly inaccurate as the sound velocity and specific gravity of one phase approaches that of the other (this situation can occur with heavy crudes).
        3. Many rely on batch sampling of the flowing process fluid for the measurement of water cut, with the separation and weighing of the phases performed off-line. This method has several obvious drawbacks: (a) It is labor intensive, (b) The uncertainties as to how well the sample represents the whole are difficult to bound, and (c) The sample data are not available in real time to allow action in response to a sudden change in water cut.
    
    


The water cut measurement of the present invention draws on the technology of technique 2 above, but overcomes its difficulties, as well as those of the other techniques, by a unique and hitherto unexploited approach.
BRIEF SUMMARY OF THE INVENTION
The present invention pertains to the measurement of the mass fraction of water in oil-water mixtures. The measurement is performed using ultrasonic transducers. The measurement is based on the fact that the mass fraction is related to the change in the sound velocity in the mixture for a known change in temperature.



BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING
In the accompanying drawings, the preferred embodiment of the invention and preferred methods of practicing the invention are illustrated in which:
FIG. 1 shows change in VOS (at 60 deg F.) vs. WC(%).
FIG. 2 shows sound velocity vs. temperature in pure water at 1000 psia.
FIG. 3 shows change in sound velocity per unit change in fluid temperature for pure water.
FIG. 4 shows sound velocity vs. temperature for several crude oils.
FIG. 5 shows distribution of sensitivities: sound velocity to temperature for 55 crude oils.
FIG. 6 shows change in sound velocity of water oil mixtures per degree F, heavy crude.
FIG. 7 shows change in sound velocity of water oil mixture per degree F, mid range crude.
FIG. 8 shows change in sound velocity of water oil mixtures per degree F, light crude.
FIG. 9 is a flow diagram of measurement of the mass fraction of water, in wateroil mixtures of the present invention.
FIG. 10 shows temperature and sound velocity sensor assembly of the present invention.
FIG. 11 is a block diagram of water mass fraction determination.
FIG. 12 shows water cut vs. change in mixture sound velocity per degree F, dC/dT mixture temperature 100 F.
FIG. 13 shows RTD bridge for differential temperature measurement.
FIG. 14 shows correction to linear water cut determination vs. change in sound velocity/unit change in temperature.



DETAILED DESCRIPTION OF THE INVENTION
Referring now to the drawings wherein like reference numerals refer to similar or identical parts throughout the several views, and more specifically to FIGS. 9 and 10 thereof, there is shown an apparatus 10 for measuring the mass fractions of water and oil in a flowing mixture of oil and water through a pipe 12. The apparatus 10 comprises a sensor portion 14 that measures sound velocity and temperature of the flowing oil water mixture at a first time and at a second time. The apparatus 10 comprises a temperature changer 16 in thermal communication with the flowing fluid which changes the temperature of the flowing oil water mixture by a measurable amount between the first time and the second time.
The sensor portion 14 can include a first sensor portion 18 that measures the sound velocity and temperature of the flowing oil water mixture upstream of the temperature changer 16, and a second sensor portion 20 that measures the sound velocity and temperature of the flowing mixture downstream of the temperature changer 16. The temperature changer 16 can be either a heat exchanger that adds thermal energy to, or a cooler that removes thermal energy from the flowing mixture.
The apparatus 10 can include a controller 22 and processor 24 that determine the mass fraction of the water and oil through an algorithm stored on a computer readable medium which is executed by the controller 22 and processor 24 that relates the mass fraction to the change in the sound velocity in the mixture for a known change in temperature. The oil water mixture can be emulsified so that droplets of a dispersed phase, which is either oil or water, are distributed throughout a continuous phase, which is either water or oil. The disbursal can be achieved by the flowing mixture moving at a velocity sufficient to achieve emulsification with essentially no slip. The apparatus 10 can include a pump 26 in fluid communication with the mixture to ensure the velocity of the sample mixture is made to meet or exceed the emulsification velocity requirement and wherein a portion of the flowing oil water mixture is continuously sampled and passed through the first and second sensor portions 18, 20 and the temperature changer 16 so as to allow determination of the change in mixture sound velocity for a measured change in temperature.
In another embodiment, the apparatus 10 can include a pump 26 in fluid communication with the mixture to ensure the velocity of the sample mixture is made to meet or exceed the emulsification velocity requirement and wherein several portions of the flowing oil water mixture are sampled, either continuously or successively. The samples, either singly or in combination, can pass through the first and second sensor portions 18, 20 and the temperature changer 16 so as to allow the determination of the change in mixture sound velocity for a measured change in temperature for each sample location.
The apparatus 10 can include a sampling arrangement 28 for sampling the fluid in communication with the first sensor portion 18. The sampling arrangement 28 can include a plurality of taps 30 disposed at different radii in the pipe 12 which sample the mixture. The sampling arrangement 28 can include valves 32 for each tap that are maintained open for a period long enough to ensure a representative sound velocity and temperature measurement for the associated tap location.
The first sensor portion 18 can include a sound velocity transducer 34 and a reflecting plug 36. The sound velocity C of the mixture can be determined from the transit time t of a pulse of ultrasound from the transducer that travels to the reflecting plug 36 of the sensor and back to the transducer.
The present invention pertains to a method for measuring a water mass fraction in a flowing mixture of oil and water through a pipe 12. The method comprises the steps of measuring sound velocity and temperature of the flowing oil water mixture at a first time with a sensor portion 14. There is the step of changing the temperature of the flowing oil water mixture by a measurable amount with a temperature changer 16 in thermal communication with the flowing fluid. There is the step of measuring sound velocity and temperature of the flowing oil water mixture at a second time with the sensor portion 14.
The measuring step at a first time can include the step of measuring the sound velocity and temperature of the flowing oil water mixture with a first sensor portion 18 of the sensor portion 14 upstream of the temperature changer 16, and the measuring step at a second time includes the step of measuring the sound velocity and temperature of the flowing oil water mixture with a second sensor portion 20 of the sensor portion 14 downstream of the temperature changer 16. The temperature changer 16 can be either a heat exchanger that adds thermal energy to, or a cooler that removes thermal energy from the flowing mixture.
There can be the step of determining the mass fraction of the water through an algorithm stored on a computer readable medium which is executed by a controller 22 and processor 24 that relates the mass fraction to the change in the sound velocity in the mixture for a known change in temperature.
There can be the step of emulsifying the oil water mixture so that droplets of a dispersed phase, which is either oil or water, are distributed throughout a continuous phase, which is either water or oil, said dispersal achieved by the flowing mixture moving at a velocity sufficient to achieve emulsification with essentially no slip.
There can be the step of pumping the mixture with a pump 26 in fluid communication with the mixture to ensure the velocity of the sample mixture is made to meet or exceed the emulsification velocity requirement and wherein a portion of the flowing oil water mixture is continuously sampled and passed through the first and second sensor portions 18, 20 and the temperature changer 16 so as to allow determination of the change in mixture sound velocity for a measured change in temperature.
In an alternative embodiment, there can be the step of pumping the mixture with a pump 26 in fluid communication with the mixture to ensure the velocity of the sample mixture is made to meet or exceed the emulsification velocity requirement and wherein several portions of the flowing oil water mixture are sampled, either continuously or successively, said samples, either singly or in combination pass through the first and second sensor portions 18, 20 and the temperature changer 16 so as to allow the determination of the change in mixture sound velocity for a measured change in temperature for each sample location.
There can be the step of sampling the fluid with a sampling arrangement 28 in communication with the first sensor portion 18. The sampling step can include the step of sampling the mixture with a plurality of taps 30 disposed at different radii in the pipe 12 of the sampling arrangement 28.
There can be the step of maintaining open valves 32 of each tap of the sampling arrangement 28 for a period long enough to ensure a representative sound velocity and temperature measurement for the associated tap location. There can be the step of determining the sound velocity C of the mixture from the transit time t of a pulse of ultrasound from a transducer that travels to a reflecting plug 36 of the first sensor portion 18 and back to the transducer.
In the operation of the invention, sound velocity—the propagation velocity of a pressure wave through a physical medium—is a function of the ratio of the stiffness and the density of the medium. For a sound velocity measurement to characterize the components of an oil-water mixture, the phases must be dispersed, so that the stiffness and density of each component of the mixture participate in the pressure wave propagation. Furthermore, the length of the pressure wave must be long compared to the dimensions of the dispersed phase, to prevent the multiple phase interfaces in the wave path from excessively scattering the acoustic energy.
When an oil-water mixture flows at a velocity in excess of 4 to 10 feet per second, the mixture starts to emulsify—one of the two phases becomes dispersed. Emulsification is often complete at velocities of 10 feet per second, though higher velocities may be necessary in some circumstances. If the oil fraction is high, the water disperses in the oil; if the water fraction is high, the opposite occurs. But in both cases the droplets of the dispersed phase are small and pulses of ultrasound, at frequencies up to 1 MHz or more can be transmitted and received through distances long enough to make various ultrasonic measurements practical.
Equation (1) below for the sound velocity of an oil-water mixture as a function of the ratio K, the mass of water in the mixture, M1, to the mass of oil in the mixture, M2:

1/C2={(K+1)/(K/SG1+1/SG2)2}[K/(SG1C1)2+1/(SG2C2)2]  1)

    
    
        Here C is the velocity, in the mixture, of sound (or ultrasound—the frequency does not affect the velocity).
        
            K, as noted above, is defined as the ratio of the mass of water M1 to the mass of oil M2. [K is more precisely defined as the ratio of the mass flow rate of water W1 to the mass flow rate of oil W2.] From this definition, the mass fraction of water with respect to the total mass is K/(K+1).
            SG1 is the specific gravity of the water in the mixture under the conditions of the measurement/
            SG2 is the specific gravity of the oil in the mixture under the conditions of the measurement.
            C1 is the velocity of sound in the water in the mixture for the conditions of the measurement (i.e., the temperature, and, weakly, the pressure of the mixture and the salinity of the water).
            C2 is the velocity of sound in the oil in the mixture for the conditions of the measurement. For crude oils, this variable depends on the molecular specifics of the crude, its temperature, and, again weakly, its pressure.
        
        
    
    


FIG. 1 plots the sound velocity measured for a mixture of water and oil, each having known properties, against the mass fraction of water in the mixture, for a limited range of water mass fractions (0 to 10%). It should be noted that this document uses the term “water cut” as a synonym for the mass fraction of water, K/(K+1), as defined above. Strictly speaking water cut is the volume fraction of water. The relationship between the two terms is straightforward, if the specific gravities of the constituents are known. The volume fraction of water in the mixture V1/(V1+V2) is given by M1v1/(M1v1+M2v2) where v1 and v2 are the specific volumes of the water and oil respectively. This expression can be converted to the following form: V1/(V1+V2)=Kv1/(Kv1+v2).
FIG. 1 also plots the mixture sound velocity calculated using equation (1) against the water mass fraction. The calculated mixture sound velocity (the “mass weighted” velocity of the figure) is lower than the measured velocity by about 0.1%. [A volume weighted calculated velocity, on the other hand, is about 0.07% higher than the measured sound velocity. The volume weighted figure is of doubtful physical significance.] The source of the discrepancy between sound velocity predicted by equation (1) and the measured sound velocity may be due to the configuration of the experiment (as noted in the reference) but may also be due to slip—the velocity of the dispersed phase, water in this case, is not necessarily the same as that of the continuous phase. Equation (1) takes no account of slip. Furthermore, slip can vary with the specifics of the measurement. To achieve full emulsification a fluid velocity of 10 feet/second or more is required; at this velocity droplets are very small. At velocities above 10 feet/second, the drag forces on a droplet, which pull it along with a velocity approaching that of the continuous phase, overwhelm the gravitational forces on the droplet, leading to little or no slip. The velocity was in the 3 to 4 feet/second range. At this velocity, the drag forces on the larger droplets of the dispersed phase do not overwhelm gravitational forces and the water droplets will tend to travel at a lower velocity than the continuous oil phase.
Reiterating, slip can be avoided and emulsification assured if the mixture sound velocity is measured where the direction of flow is horizontal, and the fluid velocity is in excess of 10 feet/second. Any measurement using sound velocity as a determinant for water cut must adhere to this requirement.
A re-examination of equation (1) reveals several drawbacks to the use of mixture sound velocity alone to measure water cut. More specifically, the sound velocities of the constituent phases must be known precisely, for the conditions of the measurement, specifically the temperature of both phases and the salinity of the water phase. This becomes evident from the scale of FIG. 1—an oil temperature change of 3° F. can change the mixture sound velocity by 250 in/sec, which corresponds to a 10% change in water cut. Thus if one is to make a determination of water cut to within, say, ±1%, he must measure temperature to better than ±0.3° F., on an absolute basis.
As noted in the background section above, an additional difficulty with the direct use of mixture sound velocity to measure water cut arises if the constituent sound velocities and densities are equal or nearly so. This can readily be seen in equation (1); changes in K will produce no change in mixture sound velocity when the two phases have the same specific gravity and sound velocity.
The means for measurement of water cut proposed herein exploits the responses of the constituents of a water-oil mixture to a chance in temperature. The response of the sound velocity of water to an increase in temperature is very different from the response of the sound velocity of oil. The difference is evident from the data of FIGS. 2, 3, 4 and 5. The data of the figures describe the behavior of sound velocity with temperature for the temperature range in which most water cut measurements are made: 40° F. to 140° F. FIG. 2 plots the sound velocity of water against temperature; FIG. 3 plots the incremental change in sound velocity of water per degree Fahrenheit. FIG. 4 plots the sound velocity of four typical crudes covering a range of specific gravities, again against temperature. FIG. 5 is a bar chart showing the incremental change in sound velocity per degree Fahrenheit for 55 different crudes, in the temperature range of interest.
The difference in the responses of constituent sound velocities to a change in temperature is evident from a comparison of FIGS. 3 and 5. In water, an increase in temperature produces a change in sound velocity ranging from +7 fps/° F. at low temperatures to near zero at temperatures at the upper end of the range of interest. In most crude oils, an increase in temperature produces a change in sound velocity of about −6.7 fps/° F.±0.3 fps/° F., over the full temperature range. For all crudes the incremental change is negative, in contrast to that of water, which is either positive or zero, depending on its temperature.
The principles of the proposed means for water cut measurement are illustrated in FIGS. 6, 7, and 8 which show the sound velocity changes for a 1° F. increase in mixture temperature over water mass fractions ranging from zero to 100%. FIG. 6 represents the response of a typical heavy crude, FIG. 7, a medium crude, and FIG. 8, a light crude. Each figure shows the sound velocity response for three different mixture temperatures covering the full range of potential applications: 40° F., 100° F., and 140° F. A comparison of the figures shows the strengths of a measurement using the proposed means for a mixture temperature change of only 1° F.:

    
    
        The left intercept (for 0% water cut) for all three figures is the same—−6.7 fps/° F. FIG. 5 shows that this figure is characteristic of many crudes, regardless of their specific gravity. FIG. 5 also shows that unlike water (FIG. 3), the slopes all the crude sound velocity-temperature curves are negative. Crude oil properties are well understood. The left intercept of the mixture sound velocity/temperature change vs. water cut curve can be firmly and accurately anchored for any crude.
        The right intercept (for 100% water cut) is likewise readily and precisely established using a temperature measurement of modest accuracy. The sound velocity versus temperature curve for pure water (FIG. 2) is extremely well documented in the scientific literature; the effect of salinity is likewise well documented and, with respect to the curve's slope, small. Accordingly, a measurement of the mixture temperature to within, say, ±2° F. allows the determination of the right intercept with precision, as illustrated by FIG. 3.
        The measurement does not depend heavily on knowledge of the sound velocities and specific gravities of the constituents. This follows from the shapes of the curves in FIGS. 6, 7, and 8. Between the two intercepts the curves do not depart greatly from a linear relationship (the curve for heavy crude at 40° F. is essentially linear). Scoping calculations, described in Appendix A, indicate that the proposed means can measure water cut with an accuracy of better than ±0.7% throughout the full range of water cuts (0% to 100%). This conclusion is subject to the following conditions:
        Constituent sound velocities and gravities are established by a temperature measurement of ±2° F.,
        A salinity estimate within a few thousand ppm is available,
        The oil source is known and properties are established using existing oil property data bases, and
        The oil water mixture is subjected to a 2° F. temperature increase (or decrease) to establish the change in mixture sound velocity with a change in temperature.
    
    


Implementation
FIGS. 9 and 10 illustrate one implementation of the present technique for water cut measurement. FIG. 9 shows an oil water mixture flowing in a pipe 12. The diameter of the pipe 12 is selected so as to maintain the mixture velocity above 10 feet per second, to ensure emulsification and minimal slip. The sample arrangement (4 taps 30 located at different radii within the pipe 12) enhances the precision of the measurement. Locating the taps 30 according to the rules of numerical integration (e.g., Gaussian quadrature) and weighting the mass fractions at each location as prescribed by the integration method allows the calculation of bulk average water cut with lower uncertainty.
The sample tap arrangement allows sampling to proceed from each tap in turn, through the operation of the solenoid valves S1 through S4. Each valve is maintained open for a period long enough to ensure representative sound velocity and temperature measurements for the associated tap location. The metering pump 26 ensures that the velocity of the mixture in the sample piping is maintained above that necessary to minimize slip and maintain emulsification.
FIG. 10 shows one arrangement of sensors for the measurement of sound velocity and temperature. The diameter of the sensor piping is chosen to ensure that, given the flow rate of the sample pump 26, the mixture remains emulsified. A sensor of the requisite accuracy—an RTD or thermocouple—measures the temperature of the incoming sample mixture. The sensor is located at the 90° inlet bend to ensure a measurement representative of the sample liquid. The sample is then directed through a second 90° bend in which is located a piezoceramic sound velocity transducer 34. The transducer is operated in the pulse echo mode. With appropriate signal processing, the sound velocity C of the mixture can be determined from the transit time t of a pulse of ultrasound that travels to the reflecting plug 36 of the sensor and back to the transducer:

C=2L/t  2)

Where L is the distance from the transducer face to the reflecting plug, and

    
    
        t is the round trip transit time in the fluid.
    
    


The diameter and frequency of the ultrasonic transducer and the configuration of the sensor tube are chosen to ensure that, given the diameter of the sensor assembly in the way of the transit time measurement, the walls of the sensor assembly due not interfere with the transit of the pulse. In addition this section of the sensor assembly is horizontal, to avoid gravitationally induced slip in the sample mixture. The effect of fluid velocity on the sound velocity measurement is intrinsically nullified by the pulse echo arrangement.
It should be noted that the pulse transit time measurements will include the travel times of the pulse through non fluid media—the delays of the cable, electronics, and the acoustic “window” of the transducer assembly. These delays can be calculated (or measured offline). In any event, a highly accurate determination of the delay in non fluid media is not required because the method relies entirely on the difference in sound velocities of the mixture at two different temperatures. Means for dealing with the difference in the delays of the two measurements in a manner consistent with the accuracy goals of the measurement are discussed further in Appendix A.
The electric heater downstream of the inlet sensor assembly in FIG. 9 raises the temperature of the mixture by a preset amount. As shown in Appendix A, the digitally based transit time measurement allows the determination of the difference in sound velocities, hot vs. cold, to within a few parts in 100,000, a temperature increase of as little as 2° F. is sufficient to produce an accurate measurement of the change in mixture sound velocity. Note that the proposed means can work just as effectively if the temperature of the sample is cooled by 2° F. The heater-cooler choice would be based on the temperature of the incoming oil-water mixture and the amount of power required to affect the heating versus the cooling.
Downstream of the heater (or cooler), the sample mixture is directed thorough the second sound velocity and temperature sensor assembly. After passing through this sensor assembly, the mixture is returned to the pipe 12 from which it was extracted.
It should be pointed out that the data processing of the proposed system should account for the transport delay through the piping and the heater (or cooler) between the sensors which measure sound velocity and temperature at the upstream and downstream locations. The data processing must take the difference between the measurements at the hot (or cold) sensor and the measurements at the inlet sensor taken earlier by an amount equal to the transport delay. This measure is necessary because the water cut may vary in time; failure to account for the transport delay will introduce “noise” and possibly biases into the water cut measurement.
To obtain the water cut, the data from each sample are processed as shown in the flow chart of FIG. 11. An iterative procedure is shown. Because of the water cut-sound velocity relationships are nearly linear, it is expected that 2 or 3 iterations will produce a water cut result that is within 0.1 to 0.2%.
Heater power and flow rate affect the performance of the sample system illustrated in FIG. 9. Clearly, the system cost is minimized if power and flow rate requirements are low. On the other hand, accuracy is enhanced with increased temperature rise (or fall). And larger ultrasonic transducers can be accommodated in larger sensor pipe 12 diameters, which require higher flow. Larger transducers maximize the strength of the received ultrasonic signals while still avoiding interaction of the acoustic wave with the pipe 12 wall. Design tradeoffs are illustrated in the table below.







TABLE 1







Sample System Design Tradeoffs


Minimum Flow Velocity 10 fps, Sp. Gravity 1.0, Sp.


Heat 1.0 btu/#/° F.











System 1
System 2
System 3





Temperature increase
1° F.
1° F.
2° F.


(or decrease)





Heater Power for increase
2 kW
5 kW
5 kW


Flow Rate
14 gpm
34 gpm
17 gpm


Sensor Pipe Diameter
0.75 in.
1.2 in
0.83 in









Appendix A defines the algorithms and analyzes the uncertainties in the measurement System 3 of the table above. It concludes that uncertainties in the measurement of water cut with this system are about ±1⁄2% water cut at water cuts near 0% and 100%. The uncertainties increase to about ±2⁄3% water cut in the mid range of water cuts (20% to 70%). Increasing the heating (or cooling) so as to double the temperature increase (or decrease) in system 3 would halve these uncertainties.
Implementation methods other than those illustrated in FIGS. 9 and 10 are possible. For example, in some pipelines a heater is employed at the head end, to increase oil temperature and thereby reduce pumping power requirements. Conventional temperature instruments upstream and downstream of the heater, along with conventional ultrasonic transducers (which can be mounted external to the upstream and downstream pipe) will provide inputs to a system that determines water cut using an algorithm similar to that of FIG. 11. Again, data processing for such installations must account for the transport delay between the cold and hot sensor locations.
Although the invention has been described in detail in the foregoing embodiments for the purpose of illustration, it is to be understood that such detail is solely for that purpose and that variations can be made therein by those skilled in the art without departing from the spirit and scope of the invention except as it may be described by the following claims.
Appendix A—Algorithm and Uncertainties for the Water Cut Calculation
Summary
This analysis establishes that systems of the type described herein, wherein the temperature of an emulsified oil-water mixture is increased or decreased 2° F., can measure water cut with an accuracy of better than ±0.67% water cut over the full range of water cuts. Accuracy approaches ±0.5% water cut at water cuts near 0% and 100%. These accuracies are calculated for System 3 herein. The accuracies can be halved, roughly, if heating (or cooling) is increased so as to double the temperature change.
Analysis
Design tradeoffs for systems to measure the water cut of a sample of a flowing water-oil mixture are given in a table herein. FIGS. 9 and 10 depict the arrangement of the sample measurement systems. In System 3 herein, a 5 kW heater provides a temperature rise of 2° F. for a sample flow rate of 17 gpm. This flow rate in a 0.83 inch diameter pipe 12 produces a fluid velocity of 10 feet/sec, which is assumed sufficient to ensure an emulsified sample with little slip. This system will be used as a reference to establish the accuracy of the measurements of the change in sound velocity and the change in temperature, as well as the accuracy of other fluid properties used to calculate the accuracy of the water cut determination over the full water cut range.
The accuracy objective for the water cut measurement—in the order of ±1% water cut—implies requirements on the accuracy of the measurements of the changes in mixture sound velocity ΔC and changes in mixture temperature ΔT produced by the heater of the reference system. An input mixture temperature in the 100° F. range was chosen for the analysis. For this mixture temperature, the mixture sound velocity change per unit temperature change, dC/dT, varies from −81 inches per second per ° F. at 0% water, to +36 inches per second per ° F. at 100% water cut. FIG. 12, produced from the analyses supporting the present invention, shows that, for a heavy crude, intermediate values of water cut are related to dC/dT by what is essentially a straight line connecting these end points. The medium and lighter crudes in this example share the same end points, but depart from linearity because of the differences in the properties of the constituents, specifically sound velocity and density (which is strongly correlated with sound velocity). A sensitivity analysis performed in support of the present invention demonstrated that, with an approximate knowledge of the constituent properties, a correction could be applied to the linear relationship to achieve good water cut accuracy (a quantitative analysis of this correction is given later in this analysis). But for all oils, the overall accuracy of the water cut determination rests on the accuracy of the dC/dT measurement: for this example, 1.17 inches per second per degree F per % water cut. For the two degree F change in the temperature of the sample of the reference system, this amounts to a 2.34 inch/sec change in sound velocity for a 1% change in water cut. So the issues are: (1) Can a change in mixture sound velocity of 2.34 inches per second be measured with sufficient accuracy to support a ±1% water cut measurement? and (2) Can a change in mixture temperature of 2° F. be measured with sufficient accuracy to support a ±1% water cut measurement?
Before addressing these issues, it should be noted that at product temperatures lower than the 100° F. assumed, the slope becomes higher; therefore the burden on the measurement accuracies of the change in sound velocity and the change in temperature is eased. On the other hand at higher product temperatures, 140° F., for example, the slope is lower. But in this case the designer has the option of cooling the sample by, say, 5 or 10° F., using the ambient as a heat sink. For these conditions, cooling requires the expenditure of very little power hence the burden on the measurements of the reduced slope can be economically offset by a much increased temperature change.
Algorithm for the Determination of ΔC, the Change in Mixture Sound Velocity
The sound velocity of crude oil-water mixtures is in the order of 55,000 inches per second, so that the requirement to detect and measure a change of 2.34 inches/second amounts to a precision requirement of about 1 part in 24,000. The sound velocity C as measured by the sensor assemblies of FIG. 10 is given as:

C=2L/t  A-1)

    
    
        Here L is the distance in the fluid from the face of the transducer window to the reflecting plug, and
        
            t is the transit time in the fluid
        
        
    
    


As stated above, the time that is measured will include not only the transit time in the fluid but the delays in the transmission of energy from a transmitter through cables, transducers, acoustic windows and signal detection electronics. Assuming for the moment that the non fluid delays, τ, and path lengths for each sensor are equal, the sound velocities as measured by the sensors upstream (C) and downstream (H) of the heater element are, respectively:

CC=2L/(tC−τ)  A-2A)

CH=2L/(tH−τ)=2L/(tC+Δt−τ)  A-2B)

Here Δt is the difference in transit time produced by heating the fluid in the heater.
The difference in sound velocities, ΔC is given by

ΔC=CH−CC=2L[1/(tC+Δt−τ)−1/(tC−τ)]  A-3)

Multiplying both terms in the brackets by the product (tC+Δt−τ)(tC−τ) the following expression is obtained for ΔC:

ΔC=2L[(tC−τ)−(tC+Δt−τ)]/[(tC+Δt−τ)(tC−τ)]  A-4)

Carrying out the algebra in Equation (A-4):

ΔC=−2LΔt/[(tC+Δt−τ)(tC−τ)]≅−2LΔt/(tC−τ)2  A-4A)

The approximation of equation (A-4A) is justified as follows: For the sensors of the reference system, a path length L of 5 inches has been selected. With this path length, a 1⁄2 inch diameter, 3 MHz transducer produces a focused beam that does not interact with the 0.83 inch diameter tubular walls of the sensor. The net transit time in the fluid (tC−τ) for a packet of 3 MHz acoustic energy with these parameters is nominally 167 μseconds at the inlet temperature of 100° F. The change in sound velocity produced by 2° F. of heating causes a change in transit time, Δt, of 6.5 nanoseconds for a change in water cut of 1%. Relative to tC the Δt can therefore be neglected in the denominator product.
Uncertainty in the Determination of the Change in Mixture Sound Velocity
The uncertainty in the change in sound velocity ∂ΔC is found by taking the differential of equation A-4A. The result of this procedure is as follows:

∂ΔC=2L/(tC−τ)2[−∂Δt+2Δt/(tC−τ)∂(tC−τ)−Δt ∂L/L]  A-5)

The uncertainties in path length ∂L and net transit time ∂(tC−τ) are dominated by biases that do not vary with operating conditions. Their net impact can be determined by measuring the Δt with the heater or cooler off (that is, with no temperature change between the two sensors). In this condition ∂ΔC=ΔC=0. The measured residual Δt, ∂Δt0, characterizes the net residual biases in transit time and path length, including those due to differences between the lengths and non fluid delays of the upstream and downstream sensors.

∂Δt0=[2Δt/(tC−τ)∂(tC−τ)−Δt ∂L/L]0  A-6)

Accordingly, the uncertainty in ΔC due to uncertainties in path length and non fluid delays can be minimized by algebraically combining ∂Δt0 with the measured Δt when the sample is being heated. It should be noted however that the correction ∂Δt0 is subject to the same time measurement uncertainties as is the measurement of Δt, which uncertainties are described in the paragraphs that follow.
The residual uncertainty in ΔC is due to uncertainties in the time difference Δt between the transit times measured by the hot and cold sound velocity sensors under operating conditions. Elements of the Δt uncertainty are given in Table A-1 below.







TABLE A-1







Uncertainty Elements in Time Difference Measurements









Time Difference




Uncertainty Element
Value
Basis













Clock dt
6.5 × 10−4
ns
The same clock will be used for both hot and cold





measurements. Long term wander tends to cancel in





each t measurement. Clock accuracy is specified at ±0.01%.





The figure given is 0.01% of the reference Δt.


Clock resolution
0.016
ns
The uncertainty in a single measurement (0.625 ns) is





reduced by multiple samples (60 seconds of sampling





at a 50 Hz rate = 3000 samples). The uncertainties in





each time measurement are combined as the root sum





squares.


Random noise
0.14
ns
A signal/random noise ratio of 10 was assumed.





Uncertainty is reduced by multiple samples, as above.


Coherent noise
1.88
ns
A conservative signal/coherent noise ratio of 40 was





assumed.


Δt error
1.88
ns
Root sum squares of above elements, since they are


Reference System


not systematically correlated with one another









These same uncertainties also apply to the measurement, with zero temperature change, of the net bias ∂Δt0 due to differences in path length and non fluid delay. Thus the total uncertainty in the measurement of dC/dT, the change in sound velocity with temperature for the reference system is given by:

∂ΔC=2L/(tC−τ)2[(∂Δt)2+(∂Δt0)2]1/2=CC[(∂Δt)2+(∂Δt0)2]1/2/(tC−τ)  A-7)

Substituting numbers for the reference system:

∂ΔC=55,000 in/s[(1.88 ns)2+(1.88 ns)2]1/2(167,000 ns)=0.88 inches/second  A-7A)

Relative to the change in mixture sound velocity ΔC brought about by the 2° F. temperature change of the reference system—2.34 inches/second/% water cut—the uncertainty in the sound velocity contributes an uncertainty in the measurement of a 1% change in water cut of 0.88/2.34=0.376 of 1%. Thus the differential sound velocity measurement uncertainty degrades the ability to measure a 1% change in water cut by ±0.38%.
Uncertainty in the Determination of the Mixture Temperature Change, ΔT, Aggregate Uncertainty in the Determination of dC/dT
The ±0.38% figure does not account for the uncertainty in the measurement of temperature rise, ΔT, which is also used to determine dC/dT. For effective measurement of water cut, the temperature measurement system must be designed to measure precisely the difference in the temperatures of the mixture upstream and downstream of the heat addition (or heat removal) device. FIG. 13 shows a sample schematic of a system for this purpose, using precision RTDs for both the hot leg and cold leg temperature measurements. Each RTD has a resistance of 100Ω at 32° F. with a sensitivity of approximately 0.214Ω/° F. The 2° F. temperature rise of the reference system produces a differential voltage of 0.418 mv between each leg of the resistance bridge. For this analysis it has been assumed that this voltage can be measured within ±0.1 mv; thus the accuracy of the measurement of the temperature rise in the reference system is 0.1/0.418=0.24 for a 1% change in water cut or ±0.24% water cut.
As with the sound velocity differential, biases in the resistance bridge differential can be readily eliminated by measuring the differential voltage when no there is zero temperature difference between the “hot” and “cold” measurements (that is, no heating or cooling). Again, however, the differential voltage measurement with no heating or cooling is subject to its assumed uncertainty of ±0.1 mv. Accordingly the overall uncertainty of the temperature rise measurement is given by the root sum square of the uncertainty in the zero bias determination and the uncertainty in the determination with heating or [2×(0.24%)2]1/2=±0.34%.
The aggregate accuracy for the slope measurement dC/dT is the root sum square of the sound velocity and temperature components or [(0.38%)2+(0.34%)2]1/2=±0.51%.
Uncertainties in the Water Cut Determination of Lighter Oils; Algorithm for the Correction of a Linear Water Cut-dC/dT Relationship
The slope uncertainty calculated in the preceding section applies, in and of itself, to the water cut determination near 0% and 100% water cut. However, as FIG. 12 shows, in the mid range of water cuts, the relationship between water cut and dC/dT departs from linearity by an amount dependent on the sound velocities and specific gravities of the constituents of the mixture—the lighter the crude, the greater the departure. The amount of the departure depends on the differences between the sound velocity and density of the crude from those of water. As noted previously, the densities of the crude and the water are strongly correlated with their sound velocities.
The correction to a linear relationship between water cut and dC/dT can be calculated iteratively using the water cut determined using the linear (heavy oil) water cut vs. dC/dT curve and calculating the hot and cold mixture sound velocities, C(TH) and C(TC) respectively, using the mixture sound velocity equation (1). The operative equations are reproduced below.

1/[C(TC)]2={(K+1)/(K/SG1(TC)+1/SG2(TC))2}[K/(SG1(TC)C1(TC))2+1/(SG2(TC)C2(TC))2]  A-8)

1/[C(TH)]2={(K+1)/(K/SG1(TH)+1/SG2(TH))2}[K/(SG1(TH)C1(TH))2+1/(SG2(TH)C2(TH))2]  A-9)

Here, the properties subscripted 1 are those of the water in the mixture; the variables subscripted 2 are those of the oil. The variable K is the ratio of water mass flow rate to oil mass flow rate. On a mass basis, water cut equals K/(K+1).
The difference in the calculated mixture sound velocities is then compared with the measured difference. If they are not the same within a selected tolerance ( ̃0.1%), the water cut is adjusted until they are.
FIG. 14 has been constructed using this methodology. Analysis of FIG. 14 indicates that for a given measurement of dC/dT, the correction from a linear relationship between water cut and dC/dT is linearly proportional to the difference between the water sound velocity for the conditions of the measurement C1(TC) and the oil sound velocity, C2(TC)—that is, [C1(TC)−C2(TC)].
As shown in the flow chart of FIG. 11, the variables C1(TC) and C2(TC) are determined with the measured mixture temperature TC as an entry variable to look-up tables, which characterize the sound velocities of the water and the crude as a function of their temperature. The tables are constructed from published data for saline water and crude oils. Inputs by the user for water salinity and for the crude oil source focus the look-up.
Experimental studies suggest that the accuracy with which the tables represent the actual sound velocity of saline water at a given temperature is equal to or better than ±36 inches/sec—equivalent to about 1° F. at the 100° F. temperature of this example. The accuracy with which the dependence of the oil sound velocity on its temperature is less certain, but can probably be established within ±160 inches per second or better by a one-shot experiment where a sample of the mixture is extracted, the oil separated from the water, and the sound velocity of the pure oil measured at several temperatures in the temperature range of interest.
The temperature used to establish the constituent sound velocities, TC is determined from the voltage measured across the cold (heater inlet) RTD in the resistance bridge of FIG. 13. Experience shows that an accuracy of between ±1 and ±2° F. can be achieved with the arrangement of the figure. This performance is achieved by ensuring low self heating of the RTDs (which the low current of the bridge circuit of FIG. 13 ensures) and low resistance RTD connections. Thermal insulation of the exterior of the sensor assembly from its surroundings is also desired, to reduce the effect of ambient temperature on the measurement. Heat transfer between the mixture and the RTD is inhibited by the low conductivity of the oil; hence the temperature measurement is vulnerable to variations in exterior temperature, where wind and rainwater may facilitate heat transfer between the air and the exterior of the RTD assembly.
The uncertainties in the correction to the linear dC/dT vs. water cut curve are summarized and combined in Table A-2 below. It should be noted that the error due to the temperature measurement itself, line 3 of the table, systematically affects the sound velocity of both the oil and the water; the uncertainty given reflects the systematic (algebraically additive) effect. The aggregate uncertainty due to the water and oil sound velocities, line 4 of the table, is translated into an uncertainty in water cut using the data implicit in FIG. 14. As calculated in the table, the uncertainty due to constituent properties for the reference system is ±0.44%







TABLE A-2





Uncertainties in the correction to a linear water cut vs. dC/dT curve
















1. Uncertainty in correlation of sound velocity
±36 inches per second


and temperature for saline water



2. Uncertainty in correlation of sound velocity
±160 inches per second


and temperature for the crude oil of the



application



3. Uncertainty in the measurement of C1 − C2
±234 inches per second


due to a ±2° F. uncertainty in the



measurement of TC



4. Aggregate uncertainty due to constituent
±286 inches per second


sound velocities (root sum squares of



1, 2, and 3)



5. Maximum water cut change light vs.
14.9%


heavy oil for a fixed dC/dT, FIG. 14



6. Maximum sound velocity difference,
9600 inches per second


light vs. heavy oil



7. Maximum uncertainty in water cut
±0.44% water cut


determination due to uncertainty in constituent



sound velocities.



[line 4/line 6] × line 5









Aggregate Uncertainty of the Water Cut Measurement
The ±0.44% uncertainty due to constituent properties is a maximum; as can be seen in FIG. 14 the corrections to a linear water cut vs. dC/dT relationship approach the 14.9% used in the table above only in the mid range of water cuts. In this range the total measurement uncertainty of the reference system is the root sum squares of the slope uncertainty, ±0.51% and the constituent uncertainty ±0.44% or ±0.67%. Thus, over the range of water cuts from 0% to 100% the uncertainty of the water cut measurement of the reference system lies between ±0.51% and 0.67% water cut depending on the water cut itself.

## Claims

1. An apparatus for measuring the mass fractions of water and oil in a flowing mixture of oil and water through a pipe comprising:
a sensor portion that measures sound velocity and temperature of the flowing oil water mixture at a first time and at a second time;
a temperature changer in thermal communication with the flowing fluid which changes the temperature of the flowing oil water mixture by a measurable amount between the first time and the second time, the sensor portion includes a first sensor portion that measures the sound velocity and temperature of the flowing oil water mixture upstream of the temperature changer, and a second sensor portion that measures the sound velocity and temperature of the flowing mixture downstream of the temperature changer, the first sensor portion includes a sound velocity transducer and a reflecting plug, the sound velocity C of the mixture determined from the transit time t of a pulse of ultrasound from the transducer that travels to the reflecting plug of the first sensor portion and back along axial flow with the flowing fluid to the transducer, the sound velocity transducer producing pulses of ultrasound at frequencies up to 1 MHz, the sound velocity transducer and the reflecting plug being a fixed distance; and
a pump in fluid communication with the mixture to ensure the flowing mixture is moving at a velocity sufficient to achieve emulsification with no slip, wherein the oil water mixture is emulsified so that droplets of a dispersed phase, which is either oil or water, are distributed throughout a continuous phase, which is either water or oil, said dispersal achieved by the flowing mixture moving at a velocity sufficient to achieve emulsification with no slip.

2. The apparatus as described in claim 1 wherein the temperature changer is either a heat exchanger that adds thermal energy to, or a cooler that removes thermal energy from the flowing mixture.

3. The apparatus as described in claim 2 including a controller and processor that determines the mass fraction of the water and oil through an algorithm stored on a non-transitory computer readable medium which is executed by the controller and processor that relates the mass fraction to the change in the sound velocity in the mixture for a known change in temperature.

4. The apparatus as described in claim 2 wherein the pump in fluid communication with the mixture ensures the velocity of the sample mixture is made to meet or exceed the emulsification velocity requirement and wherein a portion of the flowing oil water mixture is continuously sampled and passed through the first and second sensor portions and the temperature changer so as to allow determination of the change in mixture sound velocity for a measured change in temperature.

5. The apparatus as described in claim 2 wherein the pump in fluid communication with the mixture to ensure the velocity of the sample mixture is made to meet or exceed the emulsification velocity requirement and wherein several portions of the flowing oil water mixture are sampled, either continuously or successively, said samples, either singly or in combination pass through the first and second sensor portions and the temperature changer so as to allow the determination of the change in mixture sound velocity for a measured change in temperature for each sample location.

6. The apparatus as described in claim 5 including a sampling arrangement for sampling the fluid in communication with the first sensor portion.

7. The apparatus as described in claim 6 wherein the sampling arrangement includes a plurality of taps disposed at different radii in the pipe which sample the mixture.

8. The apparatus as described in claim 7 wherein the sampling arrangement includes valves for each tap that are maintained open for a period long enough to ensure a representative sound velocity and temperature measurement for the associated tap location.

9. A method for measuring water mass fraction in a flowing mixture of oil and water through a pipe comprising the steps of:
pumping the flowing mixture with a pump in fluid communication with the mixture to ensure the flowing mixture is moving at a velocity sufficient to achieve emulsification with no slip, wherein the oil water mixture is emulsified so that droplets of a dispersed phase, which is either oil or water, are distributed throughout a continuous phase, which is either water or oil, said dispersal achieved by the flowing mixture moving at a velocity sufficient to achieve emulsification with no slip;
measuring sound velocity and temperature of the flowing oil water mixture at a first time with a sensor portion, the measuring step at a first time includes the step of measuring the sound velocity and temperature of the flowing oil water mixture with a first sensor portion of the sensor portion upstream of a temperature changer;
determining the sound velocity C of the mixture from the transit time t of a pulse of ultrasound from a sound velocity transducer that travels along axial flow with the flowing fluid to a reflecting plug of the first sensor portion and back along the axial flow with the flowing fluid to the sound velocity transducer, the sound velocity transducer producing pulses of ultrasound at frequencies up to 1 MHz, the sound velocity transducer and the reflecting, plug being a fixed distance;
changing the temperature of the flowing oil water mixture by a measurable amount with the temperature changer in thermal communication with the flowing fluid; and
measuring sound velocity and temperature of the flowing oil water mixture at a second time with the sensor portion, the measuring step at a second time includes the step of measuring the sound velocity and temperature of the flowing oil water mixture with a second sensor portion of the sensor portion downstream of the temperature changer.

10. The method as described in claim 9 wherein the temperature changer is either a heat exchanger that adds thermal energy to, or a cooler that removes thermal energy from the flowing mixture.

11. The method as described in claim 10 including the step of determining the mass fraction of the water through an algorithm stored on a computer readable medium which is executed by a controller and processor that relates the mass fraction to the change in the sound velocity in the mixture for a known change in temperature.

12. The method as described in claim 11 wherein the step of pumping the mixture with the pump in fluid communication with the mixture includes the step of pumping the mixture to ensure the velocity of the sample mixture is made to meet or exceed the emulsification velocity requirement and wherein a portion of the flowing oil water mixture is continuously sampled and passed through the first and second sensor portions and the temperature changer so as to allow determination of the change in mixture sound velocity for a measured change in temperature.

13. The method as described in claim 11 wherein the step of pumping the mixture with a pump in fluid communication with the mixture includes the step of pumping the mixture to ensure the velocity of the sample mixture is made to meet or exceed the emulsification velocity requirement and wherein several portions of the flowing oil water mixture are sampled, either continuously or successively, said samples, either singly or in combination pass through the first and second sensor portions and the temperature changer so as to allow the determination of the change in mixture sound velocity for a measured change in temperature for each sample location.

14. The method as described in claim 13 including the step of sampling the fluid with a sampling arrangement in communication with the first sensor portion.

15. The method as described in claim 14 wherein the sampling step includes the step of sampling the mixture with a plurality of taps disposed at different radii in the pipe of the sampling arrangement.

16. The method as described in claim 15 including maintaining open valves of each tap of the sampling arrangement for a period long enough to ensure a representative sound velocity and temperature measurement for the associated tap location.