Patent Grant
8880363
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.
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:
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.
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.
In the accompanying drawings, the preferred embodiment of the invention and preferred methods of practicing the invention are illustrated in which:
Referring now to the drawings wherein like reference numerals refer to similar or identical parts throughout the several views, and more specifically to
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 dispersal 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. [“no slip” means the velocities of the two components of the mixture are equal.]
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 two 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.
A derivation of the relationship between the sound velocity of a mixture of oil and water and the sound velocities and other properties of its constituents follows.
In the absence of slip* the specific volume v of the mixture of oil and water is given by: * The term slip is used to describe a state in which one phase of a two phase mixture is traveling at a different mass velocity than the other phase. The absence of slip means that the two mass velocities are equal
v=Xv1+(1−X)v2 1)
Here The subscripts 1 and 2 refer to water and oil respectively
The mixture density, ρ is the reciprocal of the specific volume:
ρ=1/v 2)
The densities of the mixture components are similarly related to their specific volumes.
The sound velocity c of the mixture is related to the mixture density by the following:
c2=g∂P/∂ρ|s 3)
Here g is the gravitational constant
Similar relationships apply to the sound velocities of the mixture components.
Expressing equation 2 as a differential:
dρ=−dv/v2 4)
Using this relationship to express the reciprocal of the sound velocity in terms of pressure and specific volume:
1/c2=−(1/gv2)∂v/∂P|s 5)
Or:
∂v/δP|s=−(gv2)/c2 6)
The partial derivative of equation (1) with respect to pressure at constant entropy yields the relationship between the sound velocity of the mixture and its constituents:
∂v/∂P|s=X(∂v1/∂P|s)+(1−X)(∂v2/∂P|s) 7)
Or
(−gv2)/c2=X(−gv12)/c12+(1−X)(−gv22)/c22 8)
Canceling the (−g) term from both sides of equation (8):
v2/c2=X(v12/c12)+(1−X)(v22/c22) 9)
It is noted that equation (9) is the square of the acoustic admittance of the mixture—the admittance characterizing the velocity/pressure quotient of the two mixture components in parallel.
V1/(V1+V2)=Xv1/(Xv1+(1−X)v2).
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 (9) 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 change 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
The difference in the responses of constituent sound velocities to a change in temperature is evident from a comparison of
The principles of the proposed means for water cut measurement are illustrated in
Algorithm
The instrument utilizes measurements or estimates of the change in mixture properties with a measured change in temperature dT. Taking the derivative of equation (9) with respect to temperature:
d/dT(v2/c2)=Xd/dT(v12/c12)+(1−X)d/dT(v22/c22) 10)
2v/c2dv/dT−2v2/c3dc/dT=X(2v1/c12dv1/dT−2v12/c13dc1/dT)+(1−X)(2v2/c22dv2/dT−2v22/c23dc2/dT) 11)
Here, again, the terms without subscripts refer to mixture properties, those with the subscript 1 refer to water properties, those with the subscript 2 refer to oil properties.
The term dv/dT on the left side of equation (11) can be expressed in terms of its constituents by taking the derivative of equation (1) with respect to temperature:
dv/dT=Xdv1/dT+(1−X)dv2/dT 12)
If the expression of equation (12) is substituted for dv/dT in equation 11 and the result solved for the mass fraction of water X, an expression of the following form is obtained:
X=B/A 13)
Here:
B=dc/dT(v2/c3)−dc2/dT(v22/c23)−dv2/dT(v/c2−v2/c22) 14)
A=dv1/dT(v/c2−v1/c12)−dv2/dT(v/c2−v2/c22)+dc1/dT(v12/c13)−dc2/dT(v22/c23) 15)
All of the terms on the right hand sides of equations (14) and (15) are measured or can be estimated with reasonable accuracy from look-up tables. More specifically:
As noted previously, the petroleum industry generally characterizes the presence of water in a petroleum product as “water cut”. Also as noted above, water cut is defined as the volume fraction of water present in an oil-water mixture. For a homogenous mixture without slip, volume fraction is related to the mass fraction X as determined by the algorithm of equations (13), 14) and (15) as follows:
VF=Xv1/[Xv1+(1−X)v2] 16)
Implementation
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.
C=2L/t 2)
Where L is the distance from the transducer face to the reflecting plug, and
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
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.
To obtain the water cut, the algorithm described by equations (13), (14), (15), and (16) above is employed.
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.
Heater power and flow rate affect the performance of the sample system illustrated in
Appendix A 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 ±½% water cut at water cuts near 0% and 100%. The uncertainties increase to about ±⅔% 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
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.
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.
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.
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
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
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 ½ 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 ΔL 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)−ΔtΔL/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.
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.
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%.
Aggregate Uncertainty of the Water Cut Measurement
The ±0.44% uncertainty due to constituent properties is a maximum; as can be seen in
This is a continuation-in-part of U.S. patent application Ser. No. 12/383,431 filed Mar. 24, 2009 now U.S. Pat. No. 8,532,943.
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| Number | Date | Country | |
|---|---|---|---|
| 20110246099 A1 | Oct 2011 | US |
| Number | Date | Country | |
|---|---|---|---|
| Parent | 12383431 | Mar 2009 | US |
| Child | 13066354 | US |
