Ind. Eng. Chem. Res. 1993,32, 1212-1217
1212
Flow of Oil-in-Water Emulsions through Orifice and Venturi Meters Rajinder Pal Department of Chemical Engineering, University of Waterloo, Waterloo, Canada N2L 3G1
The applicability of conventional orifice and venturi meters to monitor the flow rate of oil/water emulsions was investigated. The discharge coefficients were determined for various unstable and surfactant-stabilized oil-in-water emulsions using a single orifice and a single venturi. The oil concentration was varied over a wide range of 0-84.32 vol % . The metering results indicate that orifice and venturi meters are feasible flow measuring devices for emulsions. The usual calibration curves of discharge coefficient versus Reynolds number (obtained from single-phase Newtonian fluids) are valid for the stable emulsions, both Newtonian and non-Newtonian. In the latter case, one needs to use the generalized Reynolds number instead of the conventional one. The orifice and venturi discharge coefficients for the unstable emulsions tend to deviate from the single-phase curves a t low values of Reynolds number although the agreement is good a t high Reynolds numbers. Based on the experimental data, empirical expressions for the orifice and venturi discharge coefficients are given. modified to
Introduction An "emulsion" is a two-phase oil/water system where one of the phases is dispersed as globules (droplets) in the other. The phase which is present in the form of globules is referred to as the "dispersed phase", and the phase which forms the matrix in which these globules are suspended is called the "continuous phase" (sometimesreferred to as dispersion medium or suspending medium). Many industrial products of commercial importanceare encountered or handled in the form of emulsions. Books have been written describing the industrial application of emulsion systems (Torrey, 1984;Bennett et al., 1968; Friberg, 1976; Lissant, 1974). The industries where emulsions are of considerable importance include petroleum, food, polymer, paints, cosmetic, pharmaceutical, agriculture, textile, paper, leather, polish, printing, etc. The measurement of the flow rate of emulsions is required in many of the industrial processes where large volumes of emulsions are handled. However, despite the industrial importance, little published work is available on metering of emulsions. It is due to this lack of information that the present work was undertaken. The main objective of this work was to investigate the applicabilityof conventional orifice and venturi meters to emulsion metering.
Q = C ~ o C 2 ( b P ) / p ( l 19?1'/~ where CD is the discharge coefficient given by
-
CD = cc[(1 @)/(a2- a1C:@
Q = AoCC[2(bP)/p(l- C,2@4)11/2
+ m)11/2
CD = f ( B f l & )
(4) The foregoing discussion can also be applied to venturi meters, except that the downstream pressure tap is located at the venturi throat (B and A0 then refer to venturi throat instead of orifice) and C, is unity. The Effect of Non-Newtonian Properties. Emulsions are Newtonian only at low to moderate concentrations of dispersed phase. At high dispersed-phase concentrations, emulsions generally exhibit non-Newtonian pseudoplastic behavior and the viscosity decreases with an increase in the shear rate. The power-law model is often used to describe the shear stress/shear rate behavior of the emulsions: 7"K.j."
(1)
where A0 is the orifice area, hp is the difference in pressure between the upstream and downstream pressure taps (orifice meters are frequently used with D and D / 2 pressure tappings, where D is the pipe diameter), p is the fluid density, C, is the contraction coefficient defined as the ratio of fluid jet area at the downstream pressure tap location to the area of the orifice, and 6 is the orifice to pipe diameter ratio. To account for the frictional losses and nonuniform velocity profiles, the above equation is
(3)
Here a1 and a2 are kinetic energy correction factors due to nonuniform velocity profiles and m is the number of velocity heads lost due to friction. The various factors in (3)are functions of Reynolds number and j3. Consequently,
Analytical Considerations Emulsions can be considered as pseudohomogeneous fluids as the dispersed droplets are generally small and are well-dispersed. Consequently, one can apply the usual single-phaseflow equations to emulsion flow with averaged fluid properties. The volumetricdischarge rate (8)for steady,frictionless, single-phase flow through the orifice meters is given by
(2)
(5)
where T is the shear stress, is the shear rate, and K and n are power-law constants. Thus, the pressure drop across the orifice or the venturi will depend upon K and n in addition to DO,D,VO,and p (DOis the orifice or venturi throat diameter, VOis the average velocity at the orifice or venturi throat): hp= f(DoP,R),P&,n)
(6) The dimensional analysis of the above relationship gives the following dimensionless groups: (pV:/AP);
(pVOhD,,"/K); (8); and (n)
According to (21, the dimensionless group ( p V o 2 / W can be replaced by another dimensionless group, Le., (cD/(1 - j34)1/2). Also,the groups ( ~ V O ~ ~ D O and V (Kn)) may be combined to obtain the well-known generalized Reynolds number (Metzner and Reed, 1955):
0888-5885/93/2632-1212$04.00/00 1993 American Chemical Society
(a)
ACRYLIC PftEssUpE Tw
S.S.PLI ORIFICE TE?
r
Ind. Eng. Chem. Res., Vol. 32, No. 6, 1993 1213 SOUARE EDGE
ORIFICE
ACRYLIC -& / SURE
TAP
FLOW
S.S. PIPE
U N I T S :m m
L T O PRESSURE TRANSDUCER
LTRPiNSDUCER PR&& J
WITH
"0''RING UNITS
:rnm
Figure 1. Schematic diagrams and various dimensions of orifice and venturi meters.
NRBp = 8[n/(6n + ~ ) I " [ P V ~ - ~ D ~ / K I (7) Consequently, we have four independent dimensionless groups: CD,Nb,n,j3, and n. This implies that For geometrically similar meters where j3 is constant CD = fWk,n,n)
(9) Thus, in general CD will be a function of Nh,,, and n for a given flowmeter. It is interesting to note that an analogous relationship exists in turbulent pipeline flow of non-Newtonian fluids where the friction factor is a complicated function of Nb,,, and n and one obtains a family of friction factor versus N R ~curves , ~ with n as a parameter (Dodge and Metzner, 1959). By analogy, therefore, one may expect to obtain a family of CDversus Nb,n curves with n as a parameter.
Experimental Section Apparatus. Emulsions were prepared in a large tank (capacity = 1m3) equipped with two high shear mixers. The emulsion from the tank was circulated to a metering test section by a centrifugal pump. The metering test section consisted of a straight pipe section (S.S.-316, seamless with i.d. = 26.92 mm) which contained a square-edged orifice meter and a venturi meter (both designed according to British Standards B.S. 1042 (1964)). Figure 1gives the schematic diagrams andvarious dimensions of the two meters. The orifice plate was made from S.S.-316 and had an orifice of 16-mm diameter. The upstream pressure tap was placed a distance D (internal diameter of pipe) from the orifice plate, and the downstream pressure tap was placed a distance D/2 from the plate. The meter was installed about 500 downstream from the entrance to the metering section. The venturi meter was made by machining a solid cylindrical block of S.S.-316. The diameter of the throat was kept as 16mm. The upstream pressure tap was located at a distance of 50.93 mm upstream from the center of the
throat and the downstream pressure tap was located at the center of the throat, as shown in Figure 1. The meter was installed about 500 downstream of the orifice plate. The pressure drops across the orifice and venturi were measured by means of the variable reluctance type pressure transducers. The output signals from the pressure transducers were recorded by a microcomputer data-acquisition system. The flow rates were measured by diverting the flow outside the flow loop intoa weighing tank (the weight collected over a measured period of time gave the mass flow rate). Emulsion Preparation. Two different sets of emulsions were prepared. In one set, no chemical emulsifier was added so that the emulsions produced were unstable with respect to coalescence (emulsions readily separated into oil and water phases if left unstirred for some time). In the other set, a nonionic emulsifier was added, and consequently, the emulsions produced were very stable with regards to coalescence. For the unstable emulsions, the concentration of oil was varied from 0 to 84.32 vol %. The emulsions were oilin-water type (oil droplets dispersed in a continuum of water phase) until the inversion point (77.53 vol % oil) where the oil-in-water emulsion inverted to a water-in-oil type (water droplets dispersed in oil phase). The stable emulsions were prepared by the agent-inwater method; i.e., the emulsifier was dissolved in water (tap water). The emulsifier concentration in the water was kept as 1w t 5%. The known amounts of oil and aqueous surfactant solution were sheared together to produce an oil-in-water emulsion of known dispersed-phase (oil) concentration. The higher concentration oil-in-water emulsions were prepared by adding more oil to an already existing lower concentration emulsion and then carrying out the required mixing. In this way, the highest dispersed phase (oil) concentration reached was 72.21 vol %. No inversion of oil-in-water to water-in-oil emulsion occurred in the present case. The oil used in the experiments was Bayol-35 supplied by Esso Petroleum Canada. This is a refined white mineral oil having a density of 780 kg/m3 and a viscosity of 2.41 mPa-s at 25 "C. The emulsifier used was Triton X-100, which is a nonionic water-soluble emulsifier. The chemical name of Triton X-100 is (isoocty1phenoxy)polyethoxyethanol. It has a density of 1065 kg/m3 and a viscosity of 240 mPa-s at 25 "C. Throughout the experiments, the temperature was maintained constant at 25 "C with the help of a temperature controller. Rheological Characterization. For the stable emulsions, rheological measurements were carried out in a coaxial cylinder viscometer. Two different gap-width rotor/bob combinations were used (gap widths were 0.117 and 0.614 cm, respectively); this enabled us to check for wall effects, if any. The shear rates in the viscometer were calculated according to the methods recommended for the Newtonian/non-Newtonian fluids. The droplet sizes of the stable emulsions were measured by taking photomicrographs of the emulsion samples using a Zeiss optical microscope equipped with a camera. The unstable emulsions could not be characterized with the coaxial cylinder viscometer. The samples of these emulsions separated into oil and water phases when removed from the flow loop (in the flow loop emulsions remained well-dispersed because of the agitation due to mixers and pump). Therefore, use was made of the online pipe viscometers installed in the flow metering apparatus. The pressure drop/flow rate data were collected from three different diameter horizontal pipelines.
1214 Ind. Eng. Chem. loo0
p?
L
Res., Vol. 32,No. 6,1993 Stable O/W emulsions
(a)
1
100
0
a E v F
10
1 E4
h
m loo0
zE
-
v
Figures. Typicalphotomicmsrapbstoratableoil-iPlat (oil concentration is 44.41 vol %).
loo
10
I
1 1
10
loo
lo00
9 (9-1) Figure 2. A p ~ n t v i s c a s i t y v s n a h ~ r a t s d a t a f o r ~ o ~ a ~ h l e oil-in-wataremulsiona. The internal diameters of the pipelines were 8.9.12.6, and 15.8 mm,respectively. The L/D ratios of these pipeline viscometers were 377,218,and 164,respectively (note that Lis the length of the pipeline test section over which the pressure drop was measured). Results and Dincussion Rheological Characteristics. Figure 2a shows the flow curves for the stable oil-in-water emulsions. The emulsions are Newtonian up to an oil concentration of 55.14 vol % . A t higher values of the dispersed-phase (oil) concentration, emulsions exhibit pseudoplastic non-Newtonian behavior in that the viscosity decreases with an increase in the shear rate. The flow curves of viscosity versus shear rate are linear (on a log-log scale) for the non-Newtonian emulsionsindicatingthat these emulsions follow the power-law model (5). The power-law index (n) for the non-Newtonian emulsions were as follows: n = 0.96 for 59.61 vol 7% oil, n = 0.90 for 65.15 vol 7% oil, and n = 0.36 for 72.21 vol % oil concentration. Figure 2b compares viscosity data obtained from two different gapwidth rotor/bob combinations for the same emulsions. The datashow excellent agreement indicating the absence of 'wall effects". It may he mentioned that "wall effects" generally become important when the dispersed particle sizes are significant relative to the gap width; in the present study, the droplet sizes of the stable emulsions were all smaller than 12 pm (see Figure 3 for typical photomicrographs) whereas the minimum gap widthwas 1170pm (almost 1OOtimesthemaximumdroplet size). Thus, wall effects are expected to be negligible.
Figure 4. Pipeline viseomstsr data for the unstable emuhiom. Figure 4 shows the pipeline data for the unstable emulsions (not all emulsions studied are shown in Figure 4). The viscoeity of emulsions is determined from the well-known Hagen-Poiseuille Law:
= (AP/L)=D'l128Q (10) The viscosity is plotted as a function of N h ,which is defmed aa IJ
Ind. Eng. Chem. Res., Vol. 32, No. 6,1993 1215 Viscosity data f o r
0.8
30
I
I _
0 water 0 16.53% O f W V 30.4% O/W 0 44.41% O/W A 49.85% O/W V 55.14% O/W
0.5
0.0
0.2
0.6
0.4
0.8
1.0
Oil Conc.
Figure 5. Viscosity variation with oil concentration (unstable emulsions).
Comparison of experimental discharge coefficients with t h e literature values
0.8 Stable O/W (+-lo *-1)
0.5
1
- Experimental ---- Litera tu re
0.4
1
20
100
1000
1 E4
1 E5
NRl3,"
0.0
0.2
0.4
0.6
0.8
1.0
@ Figure 6. Comparison of Viscosity data for the stable and unstable oil-in-water emulsions.
where qc is the continuous-phaseviscosity. Provided that the emulsion behaves as a Newtonian fluid and that the flow regime is laminar, one would expect the viscosity values calculated from (10) to be constant independent of NRe,C. For the non-Newtonian pseudoplastic emulsions (assuming laminar regime), the viscosity is expected to decrease with an increase in the Nr(d,C.As the HagenPoiseuille law (10) is inapplicable in the turbulent regime, the values of q calculated from this law in the turbulent regime will be much higher than the true viscosity of the emulsion. From the plots of q versus Nh,cshown in Figure 4, one can clearly see the transition from laminar to turbulent flow. Also, in the laminar regime, the viscosity is nearly constant with respect to NR,,,~for all the emulsions, indicating Newtonian behavior. It should further be noted that the viscosity (laminar) increases with an increase in the oil concentration for the oil-in-water type emulsions. Upon inversion of oil-in-water emulsion to water-in-oil emulsion, a sudden drop in viscosity occurs; this can be seen more clearly in Figure 5. Figure 6 compares the viscosity data for stable and unstable oil-in-wateremulsions (asthe highly concentrated stable emulsions, 4 1 59.61 % ,were non-Newtonian,their viscosities were calculated at a shear rate of 10 8-9. The viscosities for the stable and unstable emulsions hardly differ from each other when 4 I 0.60. At larger values of 4, the stable emulsions have higher viscosities and the difference increases with an increase in the value of 4. The unstable oil-in-water emulsions exhibit lower viscosities because deformation and internal circulation are
Figure 7. Orifice discharge coefficient data for the stable oil-inwater emulsions.
dominant factors in these emulsions. Also, the droplet sizes of the unstable emulsions (although not directly measured) are expected to be much larger. Furthermore, aggregation (flocculation) of droplets is expected to be of less importance in the unstable emulsions because of the coalescence phenomenon. Orifice Results. Figure 7a shows the orifice discharge coefficient data for various differently concentrated stable oil-in-water emulsions. The data are plotted as discharge coefficient versus Reynolds number (based on orifice conditions). For the Newtonian emulsions, conventional Reynolds number is used. In the case of the nonNewtonian emulsions, the generalized Reynolds number (Nkp)isused. Interestingly, the experimental data follow a single curve, independent of the power-law index, n. This indicates that the orifice calibration curve obtained from single-phase Newtonian fluids is valid for the stable emulsions, both Newtonian as well as non-Newtonian, except that one should use the generalized Reynolds number in the latter case. However, it may be mentioned that, in the case of the highly nonlinear (non-Newtonian) 72.21% oil-in-water emulsion, the data extend up to a Reynoldsnumber of about 2000. We assume that nothing irregular happens at higher Reynolds numbers. The orifice discharge coefficient data of Figure 7a can be described adequately by the following polynomial expression (solid curve shown in Figure 7a is from this polynomial fit):
where A0 = -6.3986 X le1, AI = 1.516, Az = -5.7292 X 10-l,As = 8.7787 X 10-2, and Ad = -4.7686 X 10s. Figure 7b compares the literature values for the discharge
1216 Ind. Eng. Chem. Res., Vol. 32, No. 6, 1993 0.9
1.1
Unstable emulsions
Stable O/W emulsions
0.8
x
Experimental fit Literature values
'.O
F t
0.7
0 0.6
0.8
0
0
water
16.53% O/W
V
water 15.65% O/W A 28.76%0/W 0 44.98%0/W 55.07% O / W A 64.87%0/W
0
72.31XO)W 15.68%W/O
0.7
22.4731:W)O
0.4 100
1000
1 E4
1 E5
0.6 100
i-3
where A0 = 6.8205 X lO-l, A1 = 4.0239 X A2 = -2.1477 X and AB = 2.1397 X Venturi Results. The venturi meter results for the stable oil-in-water emulsions are given in Figure 9. The discharge coefficient is plotted as a function of the Reynolds number (based on venturi throat conditions). For the Newtonian emulsions, conventional Reynolds number is used, whereas for the non-Newtonianemulsions, the generalized Reynolds number is used. Like the orifice data, the venturi discharge coefficient data follow a single curve, independent of the power-law index, n. Thus, the venturi and orifice calibration curves obtained from singlephase Newtonian fluids are valid for the stable emulsions, both Newtonian and non-Newtonian (in the latter case, one needs to use the generalized Reynolds number). This is indeed a significant finding. The venturi discharge coefficient data can be described adequately by the following polynomial expression (solid curve in Figure 9a): i=A
where Ao = -2.5679, A1 = 2.8754, A2 = -8.9188 X lO-l, A3 = 1.2368 X lO-l, and A4 = -6.4135 X 10-3. Figure 9b compares this expression with the literature values for the single-phaseNewtonian fluids (Greenkorn and Kessler, 1972). The agreement is reasonably good.
1 E4
1 E5
NRe,n
Re Figure 8. Orifice discharge coefficient data for the unstable emulsions.
coefficients (Miller, 1983; Stearns et al., 1951) with the above polynomial expression. Clearly, there is a close agreement. Figure 8 shows the orifice discharge coefficient data for the unstable emulsions. Data for the inverted emulsions are also included (note that inversion of oil-in-water to water-in-oil emulsion occurred at an oil concentration of 77.53 vol % ' 1. A t high Reynolds number, the experimental discharge coefficients agree well with the literature values for the single-phase Newtonian fluids, but the deviation At low N b , the orifice becomes important at low discharge coefficients for the unstable emulsions tend to be significantly lower. While the exact cause for this behavior is not clear at this point, it may be due to coalescence and breakup of emulsion droplets. The dischargecoefficientdata for the unstable emulsions can be described adequately by the following polynomial expression (solid curve in Figure 8):
1000
1 .o
0.9
I
Comparison of experimental discharge coefficients with the literature v c ' , ' - -
I
2 ; 0.8 I.
0.7
---
E I'
0.6 100
1000
1
Literature
1 E4
1 1 E5
NRe,n Figure 9. Venturi discharge coefficient data for the stable oil-inwater emulsions.
Figure 10 shows the venturi discharge coefficient data for the unstable emulsions (including inverted emulsions). At high Reynolds number, the experimental values compare well with the literature values for the single-phase Newtonian fluids. However, at low NR,the experimental discharge Coefficients tend to be somewhat higher than the literaturevalues. Again, this may be due to coalescence and breakup of emulsion dropleta although the exact cause is not clear. The experimental data of Figure 10can further be described adequately by the following polynomial expression (solid curve in Figure 10is from this expression): i=3
where A0 = 1.424 X l t l ,A1 = 4.517 X l t l , AB= -8.3982 X 1p2, and A3 5.2574 X 103. Finally, it may be mentioned that the discharge coefficient correlations proposed above for the orifice and venturi meters are accurate to within *5%. The goodness of fit of the correlations is shown in Figure 11. Conclusions The major conclusions of this study are as follows: 1. Orifice and venturi meters are feasible flow metering devices for oil/water emulsions. 2. The orifice and venturi calibration curves (discharge coefficient versus Reynolds number), obtained from any single-phase Newtonian fluid, are applicable to surfactantstabilized emulsions. The same calibration curve is valid for both Newtonian and non-Newtonian emulsions. However, in the latter case one needs to replace the conventional Reynolds number with the generalized one.
Ind. Eng. Chem. Res., Vol. 32, No.6,1993 1217
. ......
1.1
0.9 l.O
2
. . ......
I
. .
I
......
,
I
.
Unstable emulsions
1
0.8 1
/
0 15.65% O/W A 28.76%0/W 0 4438%0/W 0 55.07WO/W A 64.87%0/W V water
/ /
0.7 -
+ 22.47% W/O -Experimental fit
72.31% O/W 0 15.68%W/O
-- Uteroture valuer
t 200
1 E4
1000
1 E5
Figure 10. Venturi discharge coefficient data for the unstable emulsions.
Acknowledgment
Unstable emulsions (Orifice data)
Stable O/W emulsions (Orifice data)
Financial support from Natural Sciences and Engineering Research Council (NSERC) of Canada is gratefully appreciated.
1.1
d
\
4
the corresponding literature values for single-phase Newtonian fluids only at high N I (iVm ~ > 5000). At low &, the orifice discharge coefficients tend to be significantly lower whereas the venturi coefficients tend to be higher. These deviations are believed to be due to coalescence and breakup of droplets. 4. Empirical expressions are given for the orifice and venturi discharge coefficients. These expressions may be used to predict the discharge coefficientsfor the emulsions (stable and unstable) when geometrically similar meters are employed. The correlations are accurate to within *5%. 5. The proposed correlationsare based on experimental data from a single orifice and a single venturi. It is recommended that further experimental work be carried out using orificeand venturi metera with different diameter ratios (Le., orificeto pipe diameter ratio and venturi throat to pipe diameter ratio).
1 .o
0"
Literature Cited
8
Bennett, H.; Bishop, J. L.; Wulfinghoff, M. F. Practical emulsions-Applications; Chemical Publishing Co.: New York, 1968. British Standard 1042. Methods for the measurement of fluid flow in pipes-Part 1. Orifice Plates, Nozzle8 and Venturi !Tubes; British Standards Institution: London, 1964. Dodge, D. W.; Metzner, A. B. Turbulent flow of non-Newtonian system. AZCHE J. 1969,5,18+204. Friberg, 5.Food Emulsions; Marcel Dekker: New York, 1976. Greenkorn, R. A.;Kessler, D. P. Transfer Operations; McGraw-Hilk New York, 1972. Liseant, K. J. Emulsions and Emulsion Technology;MarcelDekker: New York, 1974. Metzner, A. B.; Reed,J. C. Flow of non-Newtonianfluids-correlation of laminar, transition and turbulent flowregimes. AZCHEJ. 1966, 1,434-440. Miller, R. W. Flow Measurement Engineering Handbook; McGraw-Hik New York, 1983. Steams, R. F.; Johnson, R. R.; Jackson, R. M.; Larson, C. A. Flow measurement with orifice meters; Van Noetrand Toronto, 1951. Torrey, S. Emulsions and Emulsifier Applications-Recent Developments; Noyes Data Corporation: Park Ridge, NJ, 1984.
100
1000
1E4 NRe,n
1E5
300 1000
Stable O/W emulsions (Venturi data )
--
1.1
\
p
1.0
n
0
0.9
-.-
1
flR
100
V
30.4%O/W
44.41X O/W
A 49.65%O / W l 55.1 4%O/W 58.61%O/WA 65.15%O/W 72.21%O/W
1000
1E4
NRe,n
1E5
1E5
(Venturi data )
* 5%
0 16,53%,:j
. O,,;ter,
1E4
--
+_5%
L,,
Water, , u,l5.65% 044.98%O/W 55.07%O/W A 64.87%O/W 72.31%O/W 4 22.47% w/O 0 15.68%W/O
A 28.76% O/W
w
300 1000
1E4
1
1E5
NRe
Figure 11. Ratio of calculated to measured discharge Coefficients versus Reynolds number.
3. For the unstable emulsions (without any surfactant), the orifice and venturi discharge coefficients agree with
Receiued for review October 13,1992 Reuked manuscript received February 8,1993 Accepted February 25,1993
