Experimental and Mathematical Modelling of. Ultrasonic Treatments for Breaking. Oil-Water Emulsions. M.R. Islam, R Genyk, Q. Malik. University of Regina.
PAPER 2000-87
Experimental and Mathematical Modelling of Ultrasonic Treatments for Breaking Oil-Water Emulsions M.R. Islam, R Genyk, Q. Malik University of Regina This paper is to be presented at the Petroleum Society’s Canadian International Petroleum Conference 2000, Calgary, Alberta, Canada, June 4 – 8, 2000. Discussion of this paper is invited and may be presented at the meeting if filed in writing with the technical program chairman prior to the conclusion of the meeting. This paper and any discussion filed will be considered for publication in Petroleum Society journals. Publication rights are reserved. This is a pre-print and subject to correction.
ABSTRACT Stable oil-in-water emulsions are very difficult to break and constitute one of the most difficult problems encountered during oil production. The emulsion viscosity is much higher than that of the segregated phases and, therefore, accounts of high pressure drop in the wellbore as well as low recovery in the reservoir. A laboratory investigation on the use of ultrasonic energy for enhancing the separation of suspended oil phase from aqueous media was carried out in this study. This paper investigates the effect of ultrasonic energy on separation of oil and water from a stable oil-in-water emulsion. It was found that concentration of oil phase, composition of oil phase, ultrasonic intensity, and temperature are key factors in emulsion coalescence, which occurs after a relatively short time upon exposure to ultrasonic treatment. Also, clumping of oil droplets with higher oil phase compositions (10%, 35%), a possible explanation for reduced residual oil observed in past research efforts. Numerous microphotographs of the dynamic process of the coalescence were taken and changes in average droplet sizes noted. This led to the development of a mathematical model for the coalescence rate as a function of ultrasonic frequency, oil phase concentration, and other variables. These models are theoretically sound and easy to use. A comparison
between mathematical model predictions experimental results provided excellent agreement.
and
It was observed that, for the cases studied, ultrasonic treatment at the optimal energy level outperforms some chemical flocculants in terms of enhancing liquid-liquid separation. This technology could also be applied to postproduction emulsion separation as well as in situ wellbore treatment.
INTRODUCTION Oil-in-water emulsions are important in various phases of drilling, completion and production of petroleum wells. Oil-water emulsions are present whether it be in the oil reservoir itself or is formed as a result of the extraction process. These emulsions add considerably to the cost of transportation and refining and, in fact, to wellbore and reservoir problems. Emulsions are conventionally thought of as an irreversible yet integral stage of oil production. The most important properties of these emulsions include particle size and distribution, viscosity, density, concentration, oil and carbon content, sound velocity, pH, zeta-potential, and surface charge, etc. Depending on the values of these parameters, emulsions can form or break. In most cases in petroleum engineering applications, however, these oilin-water emulsions need to be broken.
USE OF ULTRASOUND ENERGY AND EMULSIONS The breaking of emulsions, which is the demulsification process, involves the coalescence of small oil droplets to form larger ones. For accelerating the coalescence process for the enhancement of oil recovery, some additional forces are needed. There exists several techniques for enhancing demulsification. The typical ones found in the literature are the addition of chemical demulsifiers, pH adjustments, gravity or centrifugal settling, filtration, heat treatment and electrostatic demulsification1. The ultrasonic technique has the ability to rapidly break emulsions. This technique can actually be used to analyse emulsions non-destructively2. The same can be used for breaking emulsions to enhance oil recovery and increase the oil production many folds. Schoeppel and Howard3 studied the effect of ultrasonic irradiation on coalescence and separation of crude oil-water emulsions. They investigated experimentally and found that the combined effect of ultrasonic and chemical treatment greatly increased the separation efficiency over chemical treatment exposed only to low frequency mechanical agitation. They concluded that the ultrasonic treatment technique offers a potentially practical method of improving natural oilwater coalescence and separation while simultaneously decreasing chemical requirements. However, they did not investigate what ultrasonic irradiation itself can produce. Experimentation with vibro-energy is rare. However, a few papers have reported encouraging results. Cherskii et al.4 applied a 200-800 Hz frequency to an oil-in-water system. He found surface tension to decrease by a factor of 2.6. Van den Tempel(5-7) performed some of the earliest studies on emulsion flocculation and coalescence. His first paper estimated the strength of the electrical double layer on oil droplets in soaps from surface tension data using the Gibbs equation. Later, van den Tempel developed a model for flocculation and coalescence. His flocculation model was as follows,
1 1 − = at ............................................................... (1) n no where no is the number of droplets at to, n is the number of droplets at t, and a is the flocculation constant, approximately 1011 cm3sec-1. However, he found that if the rate of flocculation was rapid compared to the rate of coalescence, the equation takes the following form,
n=
n o [1 − exp(− Kt )] .............................................. (2) Kt
where K is the constant rate of coalescence, with units sec-1. Also, Van den Tempel7 made the following observations about emulsion behaviour: 1. In emulsions with a wide range of droplet size, gravitational motion enhances collision rates (orthokinetic flocculation). 2. Microscopic droplets have a net attraction force at large distances. The University of Guelf8 has published extensive data on oil-in-water emulsions, and have used Stoke’s Law to determine the rate of separation:
d 2 (ρ o − ρ w )rw 2 V= ............................................ (3) 18µ w V = particle velocity d = particle diameter ρo, ρw = oil and water density r = separation radius from axis of rotation w = angular velocity Kouznetsov et al9 performed laboratory and field tests studying the effect of vibro-energy on oil recovery. This study was done after making observations in oil reservoirs subjected to natural seismic activities. It is very common for oil production to increases in reservoirs near earthquake epicenters immediately after seismic activity. In Kouznetsov’s study, a surface based seismic source was used to induce vibration in the oil reservoir. They found that low-frequency vibrations, when applied to an oil reservoir, decreased the water cut and increased oil production three fold. He concluded that vibro-energy reduces the interfacial tension leading to coalescence, and that it increases the relative permeability of the oil. He also relates accelerations of the oil and water phases with the following equation,
ρ o ∂ 2 xo ∂ 2 xw ⋅ = ................................................. (4) ρ w ∂t 2 ∂t 2 where ρo is oil density, ρw is water density, and x is the distance traveled by the respective components. Because oil density is less than water density, the oil droplets will be excited more than the water. This in turn causes the coalescence of the oil droplets. Periodic movements of the oil and water in pore throats and variable pressure gradient caused by the applied vibro-energy lead to the destruction of water films blocking fluid flow through narrow pore throats. This leads to a general increase of the relative permeability both to oil and to water. The molecules of oil are much larger than those of water. Therefore, destruction of water films sealing pore throats and increasing the size of the
open part of pore throats should produce a larger effect on the relative permeability of the rock to oil than to water. The relative permeability to oil also increases due to reduction in the interfacial tension and contact angle between oil and water on application of vibro-energy. Several phenomena occur in a liquid when subjected to ultrasonic irradiation. These result from the molecular transfer of pressure pulses causing a vibrating motion of the material along the direction of wave-propagation. Alternate high and low pressure periods cause corresponding compressions and rarefactions within the liquid with associated changes in density and temperature10,11. Emulsification of immiscible liquids by ultrasonic irradiation occurs when the intensity of ultrasonic irradiations exceeds the cavitation level. Emulsions so generated are more stable than those mixed by mechanical stirring or blending; the stability of the emulsion being a function of the size and distribution of dispersed droplets11,12. With lower intensity irradiations, however, the equilibrium droplet size is sufficiently large that spontaneous coagulation occurs upon interruption of the treatment. Depending on the viscosity of the dispersing phase and the settling distance, a coagulation with separation can be achieved when sound intensities are below that capable of producing emulsions13. Experiments were carried out with an oil-in-water emulsion by Sollner13 and with a water-in-oil emulsion by Summerfrucht14. Their systems consisted of transparent tubes to house the suspensions with a transducer element introduced at one end. After a few minutes of vibration, their suspensions were broken with either the dispersed or the dispersing phase occupying relatively quiescent area near the mid-points of nodes of the standing waves with the other phase concentrating at the antinodes. (If the dispersed phase has a lower density than the continuos phase, collection has been found to occur at the nodes; otherwise, collection occurs at the anti-nodes.)14 Only two field applications involving the use of sonic vibrations as a coagulating force in crude oil-water systems were found in the literature(15-17). One applies continuos-flow treatment to separate oil-water emulsions whereas the other operates in a batch system. In one of the batch field tests16, a magnetostrictor of high-nickel permalloy was used to generate ultrasonic energy. The field scale unit had a 1,900 watt generator with an output frequency of 22.5 kilo-cycle /sec and a 4 inch diameter signal discharge plate. The unit was installed in a 500 barrel vessel. Under normal operating conditions, the unit removed 99.0 to 99.7 per cent of water from the emulsified oil. The unit was claimed to have given efficient operation with a relatively small capital investment and a low electrical energy requirement.
Shortcomings of Previous Research The idea of applying acoustic energy to oil reservoirs to enhance recovery is a relatively new one. There is much to be desired in describing the mechanism associated with the improved oil recovery,
mathematically and physically. Mathematical description of emulsion behaviour is very complex, and there is no existing equation that relates vibro-energy to emulsion behaviour. The closest is Kouznetsov’s studies carried out in 1998, which focussed on wave equation relating density and droplet acceleration (Equation 3). Stoke’s Law (Equation 4) is not time dependent, and therefore the term describing droplet size is constant. This paper focuses on relating this parameter to physical properties of emulsions and acoustic parameters. From past literature, coalescence has occurred from frequencies ranging from 1 Hz to 800 Hz. This research extends this range to ultrasonic frequencies ie to frequencies of approximately 20 MHz. Field tests have been carried out, but a workover is necessary to perform these tests. The extent of increased production due to workover has not been established. To date, how the physical properties of emulsions correlate with applied acoustic energy has not been studied. In this paper, a mathematical correlation will be made based on the Kouznetsov equation (Eq. 4), after subjecting oil-in-water emulsions to ultrasonic stimulation.
EXPERIMENTAL SET- UP AND PROCEDURE These experiments involved applying ultrasonic energy to various homogenized milk emulsions to induce coalescence. Homogenized milk is an acceptable substitute for oil-in-water emulsions due to its oil-inwater nature (University of Guelf, 1999). It also contains solid particles, similar to most reservoir fluids. Milk has stability within the ranges for oilfield emulsions as well. Further data on milk can be found in appendix A. Although further tests should be made using actual reservoir crude, milk is a readily accessible and costeffective alternative which will produce comparable results. Specialized equipment required for Task 1 included a multi-intensity sonic device. The operating frequency of this device was constant at approximately 20 MHz. The samples were placed in a beaker surrounded by a water bath. An immersible sonic transducer was used to apply acoustic energy. Several runs were performed, with variable factors being acoustic intensity, and emulsion composition. Temperatures and the size distribution of coalescing particles were recorded for each run. The different milk emulsions tested included 2%, 10%, and 35% fat concentrations. The density ranged from 0.994 (35%) to 1.033 (2%), at 20oC. To measure the effect of temperature on coalescence, a water bath was added to the experimental setup, and the emulsion was stabilized to 18 oC before starting vibration. Magnified images of the process were taken using a camera mounted on a microscope.
RESULTS AND DISCUSSION Test 1: Variable Concentration, Constant Acoustic Intensity Results are compared for 2%, 10%, and 35% fat emulsions. A relative intensity of 90% was used for each run. An exponential growth in average bubble size was observed (Figure 1). This exponential growth in coalescence is proportional to fat concentration. As fat concentration increases, there are more collisions, and coalescence increases exponentially. The addition of acoustic energy is correspondent to an increase in temperature (Figure 2). The temperature rise resulting from fat concentration is due to the difference in specific heat values of the oil and of the aqueous phase. While the specific heat of water is 4.18 kJ/kg oC, the oil phase specific heat ranges from 1.04 to ~3 kJ/kg oC. Therefore, as the concentration of fat increases, the average specific heat of the emulsion decreases. This allows greater heat transfer through the emulsion. The rate of temperature increase slows over time, with the first 15 minutes of each run having identical temperature rises. During early stages, when the emulsion is relatively homogeneous, heat is transported through a system of many small fat globules easily because they are in close contact with each other. As the fat globules become larger and disperse, it takes more time for heat transfer. The relationship between coalescence rate and fat concentration is modeled with the following exponential equation: dn = Aekt......................................................................... (5) where dn is normalized average bubble size, A and k are coefficients, and t is time. The coefficients A and k appear to have a logarithmic correlation with concentration (Figure 3). The numerical values of these coefficients can be calculated using: A = 0.3701*ln Ci + 2.7098 ............................................ (6) k = 0.0245*ln Ci + 0.17................................................. (7) where Ci is the initial fraction of fat and relative intensity is 90%. The logarithmic nature of these coefficients is due to the coalescence mechanism. At higher fat concentrations, there are more collisions between fat globules, which increases coalescence.
Test 2: Variable Acoustic Intensity, Constant Concentration Results are compared for 90%, 75%, and 60% relative intensities. A fat concentration of 10% was used for each run. An exponential growth in bubble size was observed (Figure 4). This exponential growth in bubble size is
proportional to relative intensity. As intensity increases, the particle acceleration caused by the acoustic waves increases, there are more collisions, and coalescence increases exponentially. Mathematically,
dn = Bemt ........................................................................ (8) where dn is normalized average bubble size, B and m are coefficients, and t is time (Figure 5). This equation is accurate within +/- 13% for all runs. The values of coefficients B and m appear to have a linear correlation with relative intensity. The numerical values of these coefficients can be calculated using: B=0.0284(I)-0.647 ........................................................ (9) m=0.0013(I)+0.0125................................................... (10) It can be explained that when a wave is imparted on a droplet, it causes the droplet to move. Typically, a compressibility contrast between the continuous phase and the dispersed phase will cause the droplet to pulsate (monopole oscillation), and a density contrast will cause the droplet to oscillate back and forth relative to the surrounding fluid (dipole oscillation) . Depending on the frequency, higher order modes, such as, quadrupole and octupole may be generated18. From Figures 6 and 7, it can be seen that using ultrasonic treatment for breaking oil-in-water emulsions to enhance oil recovery, even at significantly low temperatures coalescence of oil drops occur and the bubble size increases considerably even with a small rise in temperature. The ultrasonic treatment causes a heating effect but the mode of producing the heating effect causes a large change as compared to conventional heating methods. From conventional wisdom, we can say that the bubble size that can be attained at such low a temperature with conventional heating methods is negligible and hence not plotted on the graphs. It can be explained that sound energy is carried through the emulsion by the back-and-forth motion of the molecules along the direction of propagation. This produces alternate adiabatic compressions and rarefactions, together with corresponding changes in density and temperature. The great changes in pressure causes cavitation. With the collapse of the cavitation bubbles, local temperature of several hundred degrees is produced which may be the causative factor21. The relationship between coalescence rate and fat concentration is modeled with the following exponential equation: dn = Bemt ...................................................................... (11)
The temperature rise resulting from intensity level varies with intensity magnitude (Figure 8). As intensity strengthens, more energy is being transferred to the emulsions, corresponding to a steeper temperature rise. Unlike the comparison of varying fat concentrations, the effect of intensity is observed immediately. The reason for this property is that intensity is directly proportional to energy transfer rate.
Flocculation of Fat Globules At higher concentrations, flocculation of smaller globules was observed. The outer phase would only flow around these flocculated particles. This is shown in a microphotograph, Fig. 9. As ultrasonic energy was added, coalescence of fat globules took place and larger fat structures formed. This is evident from Fig. 10.
a
Flocculation constant
d
Particle diameter
dn
Bubble size
k
Co-efficient
m
Co-efficient
n
Number of droplets at time t
no
Number of droplets at time to
r
Separation radius from axis of rotation
t
Time
w
Angular velocity
xo
Distance traveled by oil
xw
Distance traveled by water
Greek letters
CONCLUSIONS
ρo
Density of oil
It was found that a correlation can be made between the physical characteristics of emulsions, applied acoustic energy, and coalescence rate. Stoke’s Equation (Equation 3) can be multiplied by either of the following correction factors:
ρw
Density of water
µw
Viscosity of water
1.
The equation relating normalized bubble size to initial concentration:
dn = [x1Ln(Ci) + y1]ey2tCx2t The variables x1, x2, y1, and y2 are dependent on intensity. 2.
The equation relating normalized bubble size to intensity level:
dn = [u1I +
v1]e(u2I + v2)t
The variables u1, u2, v1, and v2 are dependent on initial fat concentration. Future study should be done to correlate the four coefficients to concentration and intensity, so the two equations can be combined.
ACKNOWLEDGEMENTS Several co-authors received funding from NSERC and other sources at the University of Regina. This funding is gratefully acknowledged.
LIST OF SYMBOLS A
Co-efficient
B
Co-efficient
Ci
Initial fraction of fat
I
Relative Intensity
K
Constant rate of coalescence
REFERENCES 1. Miller, D.J. and Bohm, R., (1993), 'Optical studies of coalescence in crude oil emulsions' , Amsterdam, pp.1 2. Chanamai, R., Coupland, J.N., McClements, D.J., 'Effects of temperature on the ultrasonic properties of oil-in-water emulsions' , Amherst, U.S.A., pp 242 3. Schoeppel, R.J., Howard, A.W., 'Effect of ultrasonic irradiation on coalescence and separation of crude-oil emulsions', SPE of AIME, Texas, U.S.A., pp 1- 6 4. Cherskii, N.V., Tsarev, V.P., Kouznetsov, D.L., (1985), ‘Effect of Seismotectonic Processes on the Origin and Accumulation of Hydrocarbons’, Nauka, Moscow, pp. 222 5. Van den Tempel, M. (1953). Recl Trav. Chim PaysBas Belg. 72, 419-442. 6. Van den Tempel, M. (1957). Proceedings of the 2nd International Congress on Surface Activity, vol.1, p439. 7. Van den Tempel, M. Vol13, p125.
(1958). J. Colloid Science.
8. University of Guelph, Dairy Science and Technology. “Dairy Chemistry and Physics”, Octoeber 25, 1999. http://www.foodsci.uoguelph.ca/dairyedu/chem.html 9. Kouznetsov, O.L., Simkin, E. M., Chilingar, G.V. and Katz, S.A. (1998), ‘Improved Oil Recovery by Application of Vibro-Energy to Waterflooded Sandstones’, Journal of Petroleum Science and Engineering, 19, pp.191-200. 10. Goldman, R., 'Ultrasonic Technology', Reinhold Publishing Corp. N.Y. , 1962
12. Hill, R. A. W. and Knight, J. T., ' A Kinetic Theory of Droplet Coalescence with Application to emulsion stability ', Trans. Faraday Soc., Jan. 1965, 61, 170 13. Sollner, K., ' Colloidal effects of ultrasonics', Chem. Eng, Prog., 1951,47, No.1,28. 14. Summerfrucht, J.N.,' A study of the feasibility and application of ultrasonics to the treatment of crude oil emulsions', Thesis, U. of Oklahoma, Norman, Okla.1962 15. May, R.D , ' System for the sonic treatment of emulsions and for resolving the same into their constituent parts', U.S. Patent 3, 200, 567 ( Oct. 1965)
APPENDIX B 16 Normalized Bubble Size
11. Carlin, B., ' Ultrasonics', McGraw-Hill Book Co., Inc., New York, N.Y., 2nd Ed. 1960
t=1
14 12 10 8 6 4 2 0 0.00
t= 0.10
0.20
0.30
0.40
Fat Concentration
Graph 1: Bubble size vs. concentration for increasing time.
16. Skripnik, E. I., Dolganov, V.I. and Simileiskii< A.Z., et al , ' Demulsification of crude oil by means of ultrasonics ', Neft. Khoz., (July 1963)
18. Weissler, A., ' Physico-chemical effects of ultrasonics ', Ultrasonics - two symposia, AIChE, pp 22
15 Bubble Size
17. Bondy, C.,and Sollner, K., ' Qualitative Experiments of Emulsification by Ultrasonics', Trans., Faraday Society, 1936, 32, 616
t=1
10 5 0 55
65
75
t=
85
95
Relative Intensity
APPENDIX A Chemical Compositon and Physical Properties of Homogenized Milk • 87.3% water (range of 85.5% - 88.7%) • 3.9 % milk fat (range of 2.4% - 5.5%) • 8.8% solids-not-fat (range of 7.9 - 10.0%): • acids 0.18% - citrate, formate, acetate, lactate, oxalate • enzymes - peroxidase, catalase, phosphatase, lipase • gases - oxygen, nitrogen • protein 3.25% (3/4 casein) • lactose 4.6% • minerals 0.65% - Ca, P, citrate, Mg, K, Na, Zn, Cl, Fe, Cu, sulfate, bicarbonate, many others
Graph 2: Bubble size vs. intensity for various times.
35%
15
10%
10
Bubble Size
Average Bubble Size
15
5
2%
10 5
0 0
5
10 Time (min)
15
20
0 0
Figure 1 : Globule size vs. time, variable composition
10
15
20
Time (min)
Figure 4: Globule Size vs. Time, Variable Intensity.
70
35%
60
2
0.14
10%
50
1.8
30 20
0.12 1.6 1.4 0.1
10 0
10
20
30
40
50
Coefficient m
40
Coefficient B
Temperature (deg C)
5
1.2
Time (m in)
1
Figure 2: Temperature vs. time, variable concentration.
0.08
50
60
70
80
90
100
Relative Acoustic Intensity
Fg. 5 Mathematical coefficient of Intensity
2.5
k
0.1
1
30
Bubble Size
0.15 1.5
Coeffiecient k
A
2
Coefficient A
0.2
0.05
0.5
0
0 0%
10%
20%
Concentration
30%
40%
25
I = 60
20
I = 75 I = 90
15 10 5
Figure 3: Mathematical coefficients of concentration.
0 0
10
20
30
Temperature ( deg C )
Figure 6: Bubble size vs. temperature
7
40
50
Bubble Size
30 25
t=5
20
t = 10
15
t = 15 t = 20
10 5 0 0
10
20
30
40
50
Temperature ( deg C )
Fig. 7 Bubble size vs. temperature
50
Temperature
45 40 35 30 25 20
Fig. 10 Fat globules after 14 minutes of ultrasonic treatment (35% fat)
15 0
5
10
15
20
25
Time (min)
Figure 8: Temperature vs. time for variable frequency
Fig. 9. Flocculation of fat globules before ultrasonic treatment. The darker areas are fat globules, lighter areas are water.
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