This paper presents a method of determining the volume fractions of two liquid components in a two-phase flow by measuring the speed of sound through the composite fluid and the instantaneous temperature. Two separate algorithms are developed, based on earlier modeling work by Urick (Urick, 1947, “A Sound Velocity Method for Determining the Compressibility of Finely Divided Substances,” J. Appl. Phys., 18(11), pp. 983–987) and Kuster and Toksöz (Kuster and Toksöz, 1974, “Velocity and Attenuation of Seismic Waves in Two-Phase Media: Part 1. Theoretical Formulations,” Geophysics, 39(5), pp. 587–606). The main difference between these two models is the representation of the composite density as a function of the individual densities; the former uses a linear rule-of-mixtures approach, while the latter uses a nonlinear fractional formulation. Both approaches lead to a quadratic equation, the root of which yields the volume fraction (φ) of one component, subject to the condition 0φ1. We present results of a study with mixtures of crude oil and process water, and a comparison of our results with a Coriolis meter. The liquid densities and sound speeds are calibrated at various temperatures for each fluid component, and the coefficients are used in the final algorithm. Numerical studies of sensitivity of the calculated volume fraction to temperature changes are also presented.

References

References
1.
Whitaker
,
T. S.
, 1996, “
Multiphase Flow Measurement: Current and Future Developments [for Offshore Industry Use]
,” Institution of Electrical Engineers (IEE) Colloquium on Advances in Sensors for Fluid Flow Measurement, London, UK,
IEE
, pp.
1/1
111
.
2.
Thorn
,
R.
,
Johansen
,
G. A.
, and
Hammer
,
E. A.
, 1999, “
Three-Phase Flow Measurement in the Offshore Oil Industry: Is There a Place for Process Tomography?
,” First World Congress on Industrial Process Tomography, Buxton, Greater Manchester, April 14–17, pp.
228
235
.
3.
Jaworski
,
A. J.
, and
Meng
,
G.
, 2009, “
On-Line Measurement of Separation Dynamics in Primary Gas/Oil/Water Separators: Challenges and Technical Solutions—A Review
,”
J. Petrol. Sci. Eng.
,
68
(
1–2
), pp.
47
59
.
4.
Jaworski
,
A. J.
, and
Dyakowski
,
T.
, 2005, “
Measurements of Oil–Water Separation Dynamics in Primary Separation Systems Using Distributed Capacitance
,”
Flow Meas. Instrum.
,
16
(
2–3
), pp.
113
127
.
5.
Meng
,
G.
,
Jaworski
,
A. J.
, and
White
,
N. M.
, 2006, “
Composition Measurements of Crude Oil and Process Water Emulsions Using Thick-Film Ultrasonic Transducers
,”
Chem. Eng. Process.
,
45
(
5
), pp.
383
391
.
6.
Tsouris
,
C.
, and
Tavlarides
,
L. L.
, 1993, “
Volume Fraction Measurements of Water in Oil by an Ultrasonic Technique
,”
Ind. Eng. Chem. Res.
,
32
(
5
), pp.
998
1002
.
7.
Jana
,
A. K.
,
Mandal
,
T. K.
,
Chakrabarti
,
D. P.
,
Das
,
G.
, and
Das
,
P. K.
, 2007, “
An Optical Probe for Liquid–Liquid Two-Phase Flows
,”
Meas. Sci. Tech.
,
18
(
5
), pp.
1563
1575
.
8.
García-Golding
,
F.
,
Giallorenzo
,
M.
,
Moreno
,
N.
, and
Chang
,
V.
, 1995, “
Sensor for Determining the Water Content of Oil-in-Water Emulsion by Specific Admittance Measurement
,”
Sensor. Actuator. A: Phys.
,
47
(
1–3
), pp.
337
341
.
9.
Johansen
,
G. A.
,
Frøystein
,
T.
,
Hjertakery
,
B. T.
, and
Olsen
,
Ø.
, 1996, “
A Dual Sensor Flow Imaging Tomographic System
,”
Meas. Sci. Tech.
,
7
(
3
), pp.
297
307
.
10.
Yang
,
Y.
,
Scott
,
B.
, and
Cregger
,
B.
, 1990, “
The Design, Development and Field Testing of a Water-Cut Meter Based on a Microwave Technique
,” 65th Annual Technology Conference of the Society of Petroleum Engineers
(SPE)
, New Orleans, LA, Sept. 23–16, pp.
775
782
.
11.
Heindel
,
T. J.
, 2011, “
A Review of X-ray Flow Visualization With Applications to Multiphase Flows
,”
ASME J. Fluids Eng.
,
133
(
7
), p.
074001
.
12.
Abro
,
E.
, and
Johansen
,
G. A.
, 1999, “
Improved Void Fraction Determination by Means of Multibeam Gamma-Ray Attenuation Measurements
,”
Flow Meas. Instrum.
,
10
(
2
), pp.
99
108
.
13.
Meng
,
G.
,
Jaworski
,
A. J.
, and
Kimber
,
J. C. S.
, 2006, “
A Multi-Electrode Capacitance Probe for Phase Detection in Oil-Water Separation Processes: Design, Modelling and Validation
,”
Meas. Sci. Tech.
,
17
(
4
), pp.
881
894
.
14.
Yang
,
M.
, 2011, “
Measurement of Oil in Produced in Water
,”
Produced Water: Environmental Risks and Advances in Mitigation Technologies
,
Springer
,
New York
, pp.
57
88
.
15.
Bonnet
,
J. C.
, and
Tavlarides
,
L. L.
, 1987, “
Ultrasonic Technique for Dispersed-Phase Holdup Measurements
,”
Ind. Eng. Chem. Res.
,
26
(
4
), pp.
811
815
.
16.
Yi
,
J.
, and
Tavlarides
,
L. L.
, 1990, “
Model for Hold-Up Measurements in Liquid Dispersions Using an Ultrasonic Technique
,”
Ind. Eng. Chem. Res.
,
29
(
3
), pp.
475
482
.
17.
Tsouris
,
C.
, and
Tavlarides
,
L. L.
, 1990, “
Comments on ‘Model for Hold-Up Measurements in Liquid Dispersion Using an Ultrasonic Technique
’,”
Ind. Eng. Chem. Res.
,
29
(
10
), pp.
2170
2172
.
18.
Soong
,
Y.
,
Gamwo
,
I. K.
,
Harke
,
F. W.
,
Blackwell
,
A. G.
,
Schehl
,
R. R.
, and
Zarochak
,
M. F.
, 1997, “
Measurement of Solids Concentration by an Ultrasonic Transmission Technique
,”
Chem. Eng. Tech.
,
20
(
1
), pp.
47
52
.
19.
Krause
,
D.
,
Schöck
,
T.
,
Hussein
,
M. A.
, and
Becker
,
T.
, 2011, “
Ultrasonic Characterization of Aqueous Solutions With Varying Sugar and Ethanol Content Using Multivariate Regression Methods
,”
J. Chemometrics
,
25
(
4
), pp.
216
223
.
20.
Atkinson
,
C. M.
, and
Kytömaa
,
H. K.
, 1992, “
Acoustic Wave Speed and Attenuation in Suspensions
,”
Int. J. Multiphase Flow
,
18
(
4
), pp.
577
592
.
21.
Atkinson
,
C. M.
, and
Kytömaa
,
H. K.
, 1993, “
Acoustic Properties of Solid-Liquid Mixtures and the Limits of Ultrasound Diagnostics—I: Experiments
,”
ASME J. Fluid. Eng.
,
115
(
4
), pp.
665
675
.
22.
Urick
,
R. J.
, 1947, “
A Sound Velocity Method for Determining the Compressibility of Finely Divided Substances
,”
J. Appl. Phys.
,
18
(
11
), pp.
983
987
.
23.
Kuster
,
G. T.
, and
Toksöz
,
M. N.
, 1974, “
Velocity and Attenuation of Seismic Waves in Two-Phase Media: Part 1. Theoretical Formulations
,”
Geophysics
,
39
(
5
), pp.
587
606
.
24.
McClements
,
D. J.
, and
Povey
,
M. J. W.
, 1989, “
Scattering of Ultrasound by Emulsions
,”
J. Phys. D: Appl. Phys.
,
22
(
1
), pp.
38
47
.
25.
McClements
,
D. J.
, 1991, “
Ultrasonic Characterisation of Emulsions and Suspensions
,”
Adv. Colloid Interfac.
,
37
(
1-2
), pp.
33
72
.
26.
Caleap
,
M.
,
Drinkwater
,
B. W.
, and
Wilcox
,
P. D.
, 2012, “
Effective Dynamic Constitutive Parameters of Acoustic Metamaterials With Random Microstructure
,”
New J. Phys.
,
14
(
3
), p.
033014
.
27.
Ament
,
W. S.
, 1953 “
Sound Propagation in Gross Mixtures
,”
J. Acoust. Soc. Am.
,
25
(
4
), pp.
638
641
.
28.
Veil
,
J. A.
,
Puder
,
M. G.
,
Elcock
,
D.
, and
Redweik
,
R. J.
, 2004, “
A White Paper Describing Produced Water From Production of Crude Oil, Natural Gas, and Coal Bed Methane,” Argonne National Laboratory, Technical Report
.
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