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Ind. Eng. Chem. Res. 1993,32, 998-1002
Volume Fraction Measurements of Water in Oil by an Ultrasonic Technique Costas Tsourist and Lawrence L. Tavlarides* Phaedron Technologies, Inc., P.O. Box 446, Syracuse, New York 13210, and Department of Chemical Engineering and Materials Science, Syracuse University, Syracuse, New York 13244-1190
An ultrasonic technique developed previously is extended for measurements of volume fractions of water in oil a t low phase fractions and for long path lengths. The technique is applied on a number of stirred vessels of 10-cm diameter and lo-, 20-, 30-, and 50-cm length and on a continuousflow apparatus. Experiments for a l-m-length column suggest meaningful measurements can be obtained for this length as well. Results demonstrate the utility of the ultrasonic technique t o measure volume fractions as low as 0.005. The travel time of sound through the liquid dispersion permits the estimation of the volume fraction of the two phases by a linear model which considers sound reflection through the drop and refraction on the drop interface. This model works well for volume fractions higher than 5 % . An empirical model is applied for volume fractions lower than 5 % . The relative error in the measurements is of the order of 10%.
Introduction In many industrial processes, there is a need to contact two liquid immiscible phases in mixing vessels either for the separation of a chemical species (solvent extraction) or for a chemical reaction to occur. In such processes, mixing is provided by agitation of the two phases in order to increase the contact area between the two phases. Depending on the initial conditions of mixing, one of the two phases forms drops which are surrounded by the other phase. The drop phase is called the "dispersed phase" (d),the surrounding phase is called the "continuous phase" (c), and both phases together are referred to as the "dispersion". The volume fraction of each phase is defined as the ratio of the volume of each phase over the total volume. The drop size of the dispersed phase depends on the physical properties of the two phases (viscosities, densities, interfacial tension), on the volume fraction of the dispersed phase, on the geometry of the contacting equipment, and on the agitation intensity. Very small colorless drops, up to 1 mm in diameter, form a graycolored emulsion. An accurate, reliable, and continuous measurement of the volume fraction of one phase dispersed in another fluid is of great importance in the control and safety of process vessels. Examples include the control of pulsed liquid extraction columns (Schon et al., 1986)or centrifugal contactors (Aparo et al., 1987) used for the reprocessing of nuclear waste fuel in the nuclear industry and the control of extractors for the separation and recovery of valuable and strategic metals such as cobalt and nickel (Jacobs et al., 1985)and vanadium (Rice, 1983)in hydrometallurgical processing. Important examples in the oil industry can also be cited for the need to accurately monitor the volumetric phase fraction. Most of the crude oil produced in the world today is transported from the areas of production to refineries by means of pipelines. The first example refers to a recently developed (Wyslouzi et al., 1987)method of transporting heavy (viscous) crude oil in the form of an oil-water emulsion with water content as
* To whom correspondence should be addressed at Department of Chemical Engineering and Materials Science, Syracuse University, Syracuse, NY 13244-1190. + Present address: Oak Ridge National Laboratory, P.O.Box 2008, Oak Ridge, T N 37831-6226.
high as 58 vol % . Since oil is an expensive commodity, it is important that the volume fraction of water in the flowing mixture be accurately measured. The second example to cite is that of crude oil shipped in pipelines without emulsification. Such oil contains small amounts of water, about 1 vol 5%. Although the percentages are small (Berto, 1982),because of the huge volumes involved, water content must be accurately known. The most common method of measuring oiltwater ratios in commercial use is the measurement of the dielectric constant by means of a capacitance probe. However, capacitance probes are subject to coating by paraffins, which render them inaccurate in a short period of time. Another method involvesthe laboratory analysis of samples,but this method is labor intensive, requires a substantial amount of time to complete the test, and does not allow the continuous monitoring of the fluid-fluid system. The ultrasonic technique described in this work is shown to fulfill the monitoring requirements of both extreme cases occurring in the oil industry as cited above.
The Ultrasonic Technique The ultrasonic technique for measuring volume fractions of phases in dispersive systems is based on velocity differences of sound in the two phases. Figure 1 shows measurements of the sound velocity in some liquids of interest as a function of temperature. Measuring the travel time of sound through the dispersion and comparing it with the travel times through pure phases enables one to calculate the volume fraction of each phase in the dispersion. The basic components of the technique are shown in Figure 2. Bonnet and Tavlarides (1987) showed that the time-average model given by eq 1 provides an estimate of the phase fraction of the dispersed phase with reasonable accuracy. @=-
t* - t , td
- tc
Here @ is the dispersed-phase volume fraction, t* is the travel time through the dispersion measured after mixing is provided, and t, and t d are the continuous-phase and the dispersed-phase travel times, respectively, measured a priori in pure phases. The travel times in pure phases, t, and t d , are referred to as calibration measurements. The
0888-5885/93/2632-0998$04.00/00 1993 American Chemical Society
Ind. Eng. Chem. Res., Vol. 32, No. 5, 1993 999
1250
2z
20
2,
in
2s
I
30
Ternperdure ("C)
F i r e I. Soundveloeityofvariousliquidsutmtnncesvatemperature; s = specific gravity.
t
+ J generator
Figure 2. Experimental setup of the ultrasonic technique.
estimated error in the calculation of the volume fraction by eq 1is *0.017. This error includes the error introduced by the measuring equipment and the local fluctuations of the volume fraction due to the stochastic nature of the turbulent regime at mixing conditions. Four measurements are obtained and an average is calculated for each data point. Yi and Tavlarides (1990) and Tsouris and Tavlarides (1990a) improved the accuracy of the calculation by considering refraction and reflection phenomena of sound on the droplet-water interface. The final form of the model is
where gd and g, are correction factors calculated by the sound velocities in pure phases as follows (see Yi and Tavlarides, 1990; Tsouris and Tavlarides, 199Oa): gd= (1/y2)[1- (1- y2)3/2~for y 5 1
(3)
gd = 1/yz for y 2 1
(4)
or
+
g, = 1 ;[I Y
3 - (1- y2)3/21 - [I - (1- y2)5/z~ -
sy3
2
y2for y 5 1 (5) 5
or
where
ultrasonic velocity in the dispersed phase = ultrasonic velocity in the continuous phase The last term in eq 6 is a result of total reflection of the sound wave on the droplet surface, which was erroneously omitted in eq 13b in Tsouris and Tavlarides (199Oa). According to the analysis presented in that article, total reflection occurs only when y 2 1at the projected area of a droplet of diameter d included between rmm= d12y and dl2. A data acquisition system has also been developed (Tsourisetal., 1990)whichutilizes the ultrasonictechnique for continuous on-linemonitoring and control of extraction columns (Tsouris and Tavlarides, 1990b). Requirements for Low Phase Fraction Measurements. Thevolume phase fractionofthedispersed phase measured by the ultrasonic technique prior to this work was in the range of 6-75 vol % (Kirou et al., 1988). The aasociatedabsoluteerrorwasreportedtobe*l.7%volume fraction units (Bonnet and Tavlarides, 1987). Accurate measurements of low volume fractions, of the order of 1%,required improvement of the accuracy of the technique. Furthermore, the technique was expected to be sensitiveto temperature variations at low dispersed-phase volume fractions. An error analysis based on the dependence of sound velocity on temperature in water and oil showed that the relative error increases as the dispersedphase fraction decreases. In the range of 1%dispersedphase volume fraction, corrections for acoustical-velocity changesduetosmallvariationsintemperature areessential to prevent meaningless values of 6 to be calculated (viz., negative values can be obtained). Improvementshave been achieved in the technique by using high-frequency ultrasonic transducers and by correcting for temperature variations to overcome these difficulties. Volume Fraction Measurements in Stirred Vessels Experimental Setup. The experimental setup in this case includes stirred-tank and column contactors, the components of the ultrasonic technique as shown in Figure 2, feed tanks and pumps for both phases, a thermocouple connected with a thermistor, and a storage tank. Glass vessels of lo-, 20-, 30-, 50-, and 100-cm length and 10.2-cm diameter were used to test the effect of the sound path length on the signal and the measurements. Special machining on the 10-cm glass vessel permits housing of the transducers for volume fraction measurements in a horizontal direction. Housing for the transducers is also available in the top and bottom stainless-steel plates of the tank for axial measurements. The first transducer (transmitting) is excited by an electric pulse sent by the pulse generator (HP5052PR). The same pulse is directed to the digitizing oscilloscope (HP54201A) for triggering. The transmitting tranducer during excitation creates a sound wave which travels through the liquid medium and is received by the second transducer (receiver). An electric signal is created by the receiver transducer which is amplified by an amplifier and sent to the oscilloscope for the estimation of the sound travel time. A measurable signal has been obtained in all cases for pure fluids and dispersions, even for the 100-cm-lengthcolumncontactor. For the mixing of the two immiscible liquids inside the vessels, six-blade impellers of the Rushton type of 4-cm diameter and vertical baffles for each vessel have been fabricated. Videoscan ultrasonictransducers ranging in frequencies of0.5-10 MHzof diameters0.5and Loin. have been tried. The highest frequencytransducers gave the best resolution (0.5 ns), but t h e signal was very weak. Inter-
1000 Ind. Eng. Chem. Res., Vol. 32, No. 5, 1993 0.06
7
/ I
Actuol Volume
i
/ O
c/
0.00 0.00
I
0.d5
0.10
I
I
0.15
0.20
,
0.25
0.30
0.35
Fraclion
,
0.40
J
0.45
Actual Volume Fraction
Figure 3. (a, top) Experimentalvs actuallow volume fraction results of toluene dispersed in water. (b, bottom) Experimental vs actual high volume fraction results of toluene dispersed in water.
mediate-range transducers worked well in terms of resolution (1.0 ns) and signal intensity in the range up to 3% dispersed-phase volume fraction. The travel time of sound through the liquid medium was obtained as the time between the electric pulse (rise part of square wave) and the time at which the maximum intensity wave is received by the oscilloscope. This time includes also the transmittance time of the electric signal which is assumed to be negligible as compared to the travel time of sound through the liquid. The temperature was precisely monitored (AO.01 "C)during the measurement for the correction of the sound travel time through pure phases (to td).
Results. Measurements were obtained for low values of the dispersed-phase volume fraction in the range of 0.005-0.05and high values in the range of 0.05-O.40 from all vessels (10, 20, 30, and 50 cm) for the water (continuous)-toluene (dispersed) system. Equation 2 has been employed for the calculations. Results are compared to the true values of the volume fraction in Figure 3 for all vessels. The agreement between the calculated and actual values of the dispersed-phase volume fraction is very good. The maximum error occurs at the lowest phase fraction of 0.005,where the average relative error is 8%. Over this entire data set the average relative error is 4.2%. Experiments were also executed with toluene continuous and water dispersed. In this system, the sound wave travels from a low-density continuum to high-density dispersedphase droplets. This configuration creates sound reflection phenomena which elongate the sound-wave path length in the continuous phase. Equation 2 accounts for this elongation. Experiments were conducted for low-volume phase fractions of water, between 0.005 and 0.05, in the
w OD0.0
0 10
020
0.30
0.40
Actual Volume Fraction
Figure 4. (a, top) Low volume fraction results from the 10-cmdiameter vessel for the toluene (continuous)-water (dispersed) system: A, calculated using eq 2; 0, calculated using eq 7 with g = 0.55. (b, bottom) High volume fraction results from the 10-cmdiameter vessel for the toluene (continuous)-water (dispersed)system.
10-cm vessel. Results obtained from eq 2 (triangles in Figure 4a) show that the model underpredicts the volume fraction by as much as 20%. At higher volume fractions, however, obtained in the same vessel, eq 2 provides a good estimation of the volume fraction as shown in Figure 4b. The circles in Figure 4a show calculated volume fractions by an empirical model which considers a correction factor g in the time-average model as follows: (7) The mean value of g was estimated to be 0.55. Equation 7 is suggested in the case of low volume fraction measurements of a denser liquid dispersed into a lighter liquid. In this case, the theoretically derived eq 2 underpredicts the volume fraction. The value of the factor g is obtained from calibration measurements by using samples of known volume fraction. The study was further expanded to include dispersedphase volume fraction measurements in the kerosene (continuous)-water (dispersed) system. The behavior of this system was similar to the behavior of the toluene (continuous)-water (dispersed) system. Experimental results obtained in the 10-cm vessel are compared to the actual volume fractions in Figure 5. In this figure, triangles represent calculations using eq 2 whereas circles represent results from the empirical relation (7). The mean value of g in this case was found to be 0.59. A number of repetitive experiments have been executed for both systems, toluene (continuous)-water (dispersed) and kerosene (continuous)-water (dispersed) as shown on the
Ind. Eng. Chem. Res., Vol. 32, No. 5, 1993 1001 Table 1. Results from a Pipe Flow. calcd "01
1 2 3 4
1 1 1 1
BV
(RE)
a
4elurl Volum Fradlon
Figure 5. Low phase fraction results in the 10-em-diametervessel for the kerosene (continuous)-water (dispemd)system: A, calculated using eq 2; 0, calculated using eq 7 with g = 0.59.
,water wnk
W
stainless-Steel Pipe
-
- - - - - - - - ~lO.Zrn 635 cm
T
4
Figure 6. Experimental setup for volume fraction meamrements in a continuous-flow apparatus.
figures. The maximum error obtained by the empirical relation occwa in thelowestvolumefractionmeasurements where the average relative error is of order 14%. The average relative error over both data seta for this low range of dispersed phase fraction is 7.3%. It should be noted here that Yi and Tavlarides (1990) found no effect of the drop size over the range of 50-3000 pm. No effort was made to examine the drop-size effects for the experiments reported here. Volume Fraction Measurements on a Flow Apparatus The feasibility to measure low volume fractions in a flow apparatus is also demonstrated in this work. Experiments were executed a t the laboratories of the Chemical Engineering Department of the University of South Carolina. The experimental setup and results are described below. Experimental Setup. The experimental apparatus is shown in Figure 6. Kerosene is pumped from a feed tank through a test section, where the ultrasonic transducers have been installed, and then to the storage tank. Water is introduced in the kerosene line by a secondary delivery system. More details about the experimental setup are given elsewhere (Hanzevack et al., 1987). The mean flow rates of both kerosene and water are estimated by the total volume of each fluid pumped during a measured
0.66 1.36 1.35 1.14
0.59 1.15 1.12 1.15
-10.6 -15.4 -17.0 +0.9 -10.5
calcd "01
0.67 1.30 1.24 1.27
+2
4 -7 +11 +6
RE, relative error.
period of time. The mean flow rates of the two phases are used for the estimation of the actual volume fraction. The test section is a stainless-steel pipe of 63.5-cm length and 10.2-cm diameter. Threaded transducers have been installed on the test section in a vertical configuration for sound travel-time measurements. Results. Four experiments were conducted at low volume fraction betweed 0.0066 andO.0136 under avelocity of 1m/s. The experimental results are shown in Table I, where a comparison between the calculated volume fractions by using eqs 2 and 7 and the actual values are made. Again, the theoretical model, eq 2, underpredicts low volume fractions by a mean value of 10.5% of the actual value. The g value for the empirical model, eq 7, calculated by minimizing the error between the calculated and the actual values of the volume fraction was found to he 0.69. This value differs by 15% from theg value found in the stirred batch system where a different-grade kerosenewasused. Thedifferenceisattributed todifferent physical properties of the two kerosenes. Summarizing, the agreement of the calculated with the actual volume fraction values is a very good indication of the potential of the ultrasonic technique for dispersedphase volume fraction measurements in continuous flows. The theoretical model predicts very well the volume fraction of the dispersed phase when the sound velocity in the continuous phase is higher than in the dispersed phase. In the case at which the sound velocity in the dispersed phase is higher than in the continuous phase, the model provides a good estimation for high values of volume fraction. However, low volume fractions are underestimated by a mean value of 15-20% of the actual value in a stirred vessel and by 10% in a continuous flow through pipe. If more accurate calculations are needed in this range, an empirical model can be employed which requires preliminary experiments for the estimation of an empiricalfadorg. Comparedtothelaser image processing technique developed by Hanzevack et al. (1987) to monitor two-phase flows, the ultrasonic technique shows the following advantages: (a) the ultrasonic technique can measure the phase fraction with good accuracy even if the flow is stratified into layers; (b) it works for all liquid mediums and not only for liquid media which are transparent to light; (c) it can be installed easily on the liquid delivery system; and (d) it is less expensive. Furthermore, to provide good accuracy, the laser image processing technique requires multiple point measurements radially at a cross-sectional area, whereas a single measurement is adequate for the ultrasonic technique to give the same results. Acknowledgment The assistance of Mr. Richard Gunther during the execution of the experiments is gratefully acknowledged. Also, the authors are indebted to Dr. E. Hanzevack, who made his research facilities available for experiments on flow apparatus.
1002 Ind. Eng. Chem. Res., Vol. 32, No. 5, 1993
Nomenclature g = empirical correction factor in eq 7 g, = correction factor for the continuous-phase path length (eq 2) gd = correction factor for the dispersed-phase path length (eq 2) s = specific gravity t* = travel time through the dispersion t, = travel time through the continuous phase t d = travel time through the dispersed phase y = (ultrasonic velocity through the dispersed phase)/ (ultrasonic velocity through the continuous phase) 4 = dispersed-phase volume fraction Literature Cited Aparo, M.; Casarci, M.; Moccia, A.; Siepe, V.; Vicini, C. Pilot Plant Tests of In-Line Process Instrumentations for Feedback Control of Solvent Extraction Operations for a Co-Processing Flowsheet. Abstracts of Papers, International eonference on Nuclear Fuel Reprocessing and Waste Management, RECOD '87; SociBt.4 Francaise d'Energie NuclBaire: Paris, 1987;Proceedings Vol. 1, pp 423-429. Berto, F. J. Control Program Halves Crude Losses. Oil Gas J. 1982, Dee 27,p 173. Bonnet. J. C.: Tavlarides. L. L. An Ultrasonic Technioue for Disoersed Phase Holdup Measurements. Znd. Eng. Chem. Res. 19g7, 26, 811. Hanzevack, E. L.; Bowers, Jr., C. B.; Ju, C.-H. Study of Two-Phase Flow by Laser Image Processing. AZChE J. 1987, 33, 2003.
Jacobs, J. J.; Allard, M.; Behmo, S.; Moreau, J. Nickel and Cobalt Extraction UsingOrganic Compounds;Pergamon Press: Oxford, 1985. Kirou, V.; Tavlarides, L. L.; Tsouris, C. Flooding, Holdup and Drop Size Measurements in a Multistage Column Extractor. AZChE J. 1988, 34, 289. Rice, N. M. Commercial Processes for Chromium and Vanadium. In Handbook ofSolvent Extraction;Lo,T.C., Baird, M. H. I., Hanson, C., Eds.; Wiley: New York, 1983;p 25.4. Schon, J.; Bleyl, H. J.; Ertel, D.; Hamberger, E.; Kluth, M.; Petrich, G.; Riffel, W. Transient Behavior of Purex Pulsed Columns. Abstracts of Papers,International Solvent Extraction Conference, ISEC '86;DECHEMA: Frankfurt am Main, 1986;Preprints Vol. 1, pp 399-404. Tsouris, C.; Tavlarides, L. L. Comments on Model for Holdup Measurements in Liquid Dispersions Using an Ultrasonic Technique. Znd. Eng. Chem. Res. 19908, 29, 2170. Tsouris, C.; Tavlarides, L. L. Control of Extraction Columns. Abstracts of Papers, Annual AIChE Meeting, Chicago, IL, Nov 11-16,1990;AIChE: New York, 1990b. Tsouris, C.; Tavlarides, L. L.; Bonnet, J. C. Application of the Ultrasonic Technique for Holdup Monitoring for the Control of Extraction Columns. Chem. Eng. Sci. 1990, 45, 305. Yi, J.; Tavlarides, L. L. Model for Hold-up Measurements in Liquid Dispersions Using an Ultrasonic Technique. Znd. Eng. Chem. Res. 1990, 29, 475. Wyslouzi, B. E.; Kessick, M. A.; Masliyah, J. H. Pipeline Flow Behavior of Heavy Crude Oil Emulsions. Can. J. Chem. Eng. 1987, 65,353.
Receiued for reuiew February 19, 1993 Accepted March 1, 1993
