Znd. Eng. Chem. Res. 1991,30,536-543
536
acentric factor, was established for the interaction parameter between COz and the bitumen component for both equations of state studied. The specific gravities and viscosities of the bitumen samples were determined experimentally, and the critical properties were estimated by established correlations. The trend in interaction parameters was similar to that observed for the interaction parameters of heavy hydrocarbons with COz. Acknowledgment We acknowledge the financial support provided by the Mobil Research and Development Corporation through a grant from the Mobil Foundation. Nomenclature K = Watson characterization factor n = number of points SG = specific gravity at 60 O F x = liquid-phase mole fraction y = vapor-phase mole fraction d = interaction parameter w = acentric factor Subsripts and Superscripts
b = boiling point
br = reduced boiling point c = critical; pressure or temperature cal = calculated, using the EOS exp = experimental 1 = for component i j = for component j i j = for the binary system of components i and j r = reduced; pressure or temperature Registry No. C02, 124-38-9. Literature Cited Bunger, J. W. Techniques of Analysis of Tar Sand Bitumen. Division of Petroleum Chemistry Preprints; American Chemical So-
ciety: Washington, DC, 1977; p 716. Cavett. R. H. Phvsical Data for Distillation Calculations-VawrLiquid EquiliGria. Proceedings of the 27th APZ Meeting,-San Francisco; 1962; p 351. Deo, M. D.; Nutakki, R.; Orr, F. M., Jr. Schmidt-Wenzel and Peng-Robinson Equations of State for C02-Hydrocarbon Mixtures: Binary Interaction Parameters and Volume Translation Factors. SPE 18796. Proceedings of the SPE Califomia Regional Meeting, 1989; p 485. Holm, L. W.; Josendal, V. A. Mechanism of Oil Displacement by Carbon Dioxide. J. Pet. Technol. 1974,26, 1427. Hougen, 0. A,; Wataon, K. M.; Ragatz, R. A. In Chemical Process Principles, Part I. Material and Energy Balances, 2nd ed.; Wiley New York, 1959; p 406. IP Standards for Petroleum and Its Products, Part 1, Section 2, 35th ed.; The Institute of Petroleum: London, 1976; p 837. Kesler, M. G.; Lee, B. I. Improved Prediction of Enthalpy of Fractions. Hydrocarbon Process. 1976,55 (3,153. Klins, M. A.; Farouq Ali, S. M. Heavy Oil Production by Carbon Dioxide Injection. Can. J . Pet. Technol. 1982, Sept.-Oct., 64. Mulliken, C. A.; Sandler, S. I. The Prediction of COz Solubility and Swelling Factors for Enhanced Oil Recovery. Znd. Eng. Chem. Process Des. Deu. 1980, 19,709. Mungan, N. Carbon Dioxide Flooding-Fundament. Can. J. Pet. Technol. 1981, Jan-Feb, 87. Peng, D. Y.; Robinson D. B. A New Two Constant Equation of State. Znd. Eng. Chem. Fundam. 1976,15,59. Riazi, M. R.; Daubert, T. E. Characterization parameters for Petroleum Fractions. Znd. Eng. Chem. Res. 1987,26, 755. Ritzma, H. R. 'Oil Impregnated Rock Deposita of Utah". Utah Geological and Mineral Survey, 1979, Map 47. Schmidt, G.; Wenzel, H. A Modified van der Waals Equation of State. Chem. Eng. Sci. 1980,&5,1503-1512. Simon, R.; Graue, D. J. Generalized Correlations for Predicting Solubility, Swelling and Viscosity Behavior of C02-Crude Oil Systems. J. Pet. Technol. 1966,17,102. Syncrude Research. Syncrude Analytical Methods for Oil Sand and Bitumen Processing; AOSTRA: Edmonton, Alberta, Canada, 1979; p 46.
Wood, R. E.; Ritzma, H. R. 'Analysis of Oil Deposita in Utah". Utah Geological and Mineral Survey, Special Studies 39, 1972; p 19. Received for review April 2, 1990 Revised manuscript received July 30, 1990 Accepted September 4, 1990
On-Line Monitoring of Drop Size Distributions in Agitated Vessels. 1. Effects of Temperature and Impeller Speed Eleni
G.Chatzi,* Costas J. Boutris, and Costas Kiparissides
Chemical Engineering Department and Chemical Process Engineering Research Institute, Aristotle University of Thessaloniki, P.O. Box 1517, 540 06 University City, Greece
Transient drop size distributions in a batch stirred tank were measured by a laser diffraction technique. Ita short measuring time permitted on-line analysis with minimal possible instrumental, sampling, and dispersion errors. Comparison with the previously used photographic technique showed increased sensitivity in measuring the small diameter drops. In this study, the effecta of temperature and impeller speed were investigated for a system of 1%styrene in water stabilized with 0.1 g/L poly(viny1 alcohol) (PVA)as a suspending agent. The system assumed characteristic bimodal distributions within a very short time. Further stirring only reduced the drop sizes without substantially affecting the shape of their distribution. Increasing the agitation rate caused a shift of both peake to smaller diameters since higher turbulence intensity is more effective in breaking the drops. An increase in temperature resulted in a size reduction and narrowing of the large-size peak of the distribution. Finally, the minimum time required for the system to reach steady state a t different conditions was found to depend on the Weber number of the main flow. An increase of agitation rate or a decrease of interfacial tension caused a reduction of the minimum transition time, thus allowing the system to approach equilibrium much faster. Introduction Stirred tanks are widely used in the chemical induetry. The analysis of flow patterns and mixing mechanisms in
agitated vessels has been the subject of numerous theoretical and experimental investigations. It has been shown that flow and mixing conditions in stirred vessels strongly
0888-6886/91/2630-0636$02.60/0(0 1991 American Chemical Society
Ind. Eng. Chem. Res., Vol. 30, No. 3, 1991 537 vary with the geometry of the vessel and impeller as well as with the physical properties of the mixed phases. These variables determine the relative breakage and coalescence rates that give rise to a distribution of droplet sizes of the dispersed phase. Drop size distributions are an important characteristic of liquid-liquid dispersions. The physical and chemical phenomena taking place in an agitated vessel largely depend upon the size of the dispersed droplets. For proceasea such as suspension polymerization, it is essential that the drops are sized by agitation for a period of time before polymerization begins. An understanding of the factors that affect particle size distribution and its evolution with the stirring time would enable the process engineer to control the particle size and uniformity of the size distribution of the product. A large number of publications dealing with experimental measurements of droplet size in stirred liquidliquid systems have been reported in the literature. However, most investigations refer to the average drop size at steady state and give correlations of the mean drop size, d32,with the vessel geometry and properties of the dispersion system (Mersmann and Grossman, 1982). Only a few measurements of the transient drop size distributions have been reported in the open literature and used to elucidate the dynamic processes related with breakage and coalescence of the dispersed phase. Narsimhan et al. (1984) employed a photographic technique in a two-phase dispersion system with a low dispersed-phase fraction and obtained information about the droplet breakage mechanism. Laso et al. (1987) evaluated the coalescence and breakage rates by suddenly changing the intensity of agitation and recording the evolution of drop size distribution with time. Bajpai et al. (1975) proposed a method for the measurement of the drop interaction frequency by using the moments of the unsteady-state drop size distributions measured by a detergent stabilization method. Hong and Lee (1983,1985) measured photographically the transient drop size distributions for a number of different systems. They correlated changes of the Sauter mean droplet diameter with respect to time and the minimum time required to reach the steady state with the physical propertiea and geometric characteristics of the agitation system. In the present work, a laser diffraction technique is used for the on-line measurement of the drop size distribution in an agitated vessel for a styrene/water dispersion system. The effects of agitation rate and temperature on the transient drop size distribution are investigated.
Experimental Details Msterialr and Procedure. A model system of styrene in water was chosen for our experimental studies. The two-phase system consisted of styrene (Fluka AG) as the dispersed phase and distilled water as the continuous phase. The volume fraction of styrene was 0.01. The continuoue phase contained 0.1 g/L poly(viny1 alcohol) (PVA) as a suspending agent. The PVA had a degree of polymerization of 500 and a hydrolysis ratio of 97.5-99.5 mol % (Fluka AG). The mixing vessel was a capped round-bottomed glass cylinder with 15-cm internal diameter fitted with four vertical, equally spaced stainless steel baffles. The width of each baffle was equal to one-tenth of the tank diameter. A stainless steel six-blade turbine impeller with diameter equal to one-third the tank diameter was connected to a controlled variable-speed power supply. The length of the immersed portion of the impeller was equal to one-third of the total height of the liquid-liquid dispersion, which was always maintained equal to the vessel diameter. The
EXHAUST
I
L-qkzK-r
P R l . 2 Mixing Metering vessel diaphragm pumps
WASTE COLLECT,ON
V I ,2,3,4,5 T v a - w a y bald valves V6,7,8 Three-vag bold v e l v r s S Possible sample collection VIS381 C Mrasurtnq call
Figure 1. Schematic diagram of the sampling system.
total volume of the dispersion was 2 L. Water from a constant-temperature Neslab RTE-210 bath was steadily circulated through the vessel’s jacket to maintain a desired temperature inside the tank, which was monitored by an RS-2 remote temperature sensor. The same constant-temperature bath was used to maintain a steady temperature in a secondary agitated vessel filled with continuous phase. The solution in the secondary vessel was used for filling and cleaning the sampling lines and for obtaining the background measurement of the continuous phase. In a typical experiment, the vessel was first fded with the required amounts of distilled water and concentrated PVA solution and the impeller speed was adjusted to the desired setting. The temperature of the mixture was raised to the specified temperature value. Subsequently, the organic phase was added into the continuous phase. A schematic diagram of the sampling system is shown in Figure 1. At prespecified time intervals, samples were withdrawn from the bottom of the vessel (Rl) and directed through a continuous sampling line first to the measuring flow cell (C)and through a metering diaphragm pump (Pl) back to the reactor. The recirculation of each sample lasted for about 3 min during which two consecutive measurements of the drop size distribution were obtained for comparison reasons. The circulation was then stopped, the sampling system (tubing and measuring cell) was thoroughly cleaned with the continuous phase through the metering diaphragm pump P2 to the collection vessel S, and a new background measurement was taken before the next sample analysis. Pumping and circulation were shown to have a negligible effect on the drop size distribution. This was evidenced by measuring for several minutes the drop size distribution of a sample that was continuously recirculated through a closed-loop system. In this case, after a typical measurement the direction of the three-way valve V7 was changed so that the sample withdrawn from the reactor vessel was finally directed to the sample collection vessel S. Subsequently, valves V2 and V6 were closed and valve V4 opened, so that the sample could be continuously recirculated through the closed-loop system Pl-V7-S-V4-C-V&Pl (Figure 1). A typical comparison between the drop size distribution obtained by sample recirculation to the mixing vessel and the distribution measured after 10 min of closed-loop circulation is presented in Figure 2. The absence of any significant dif-
~I
638 Ind. Eng. Chem. Res., Vol. 30,No. 3,1991 7
500
ci~a~a-i~~p clrculatlon
: t 200
1
R~~lr~uletlon
100
L
e
f
6 40
eo
I20
160
200
Drop dlamrtar, pm
6
Raclrculatlon to mfxlng vr8aal
\\
tiomad-loop
sirculetion
200
240
280
Drop d ~ e m a t r r ,pm
Figure 2. Comparison of the diameter and volume density distributions obtained by sample recirculation to the mixing vessel and by closed-loop circulation for 10 min.
ferences shows that the pumping ayd circulation effects are negligible for the sampling time dnd measuring system used in this work. Nevertheless, in all experiments, care was taken to minimize frequent sampling and external circulation of the two-phase system. For the measurement of the drop size distribution, a Malvern laser diffraction particle sizer Model 2605c interfaced with an Olivetti M24 microcomputer was used. The particle size analyzer was equipped with a continuous flow cell. A lens with focal length 300 mm and dynamic range 1W1was attached to the optical measurement unit. The analyzer was capable of detecting particles and droplets in the size range of 5.8-564 pm with an accuracy of &4% on volume median diameter. The primary output of the instrument was the relative volume size distribution stored in 32 size classes uniformly spaced on a logarithmic scale. Drop Size Measurements by Laser Diffraction. Determination of the droplet size is typically carried out by indirect methods, which measure the variation of some physical parameter of the suspension with size. In the literature, drop sizes have been measured by a number of tachniquea including photography, microphotography, light transmission, electronic counting, encapsulation, sedimentation, and detergent stabilization (Mlynek and Rsshnick, 1972;Fernandes and Sharma, 1967;Tavlarides and Stamatoudis, 1981;Sprow, 1967;Bajpai and Prokop, 1974). Laser diffraction is a more recent technique and is based on the measurement and interpretation of the angular distribution of light diffracted by the droplets using the Fraunhofer diffraction theory. It is an extremely flexible measurement technique that does not require calibration and can be used equally well for liquid and solid dispersions. A typical measurement is completed within seconds, thus making the technique suitable for on-line size analysis
(Biirkholz and Polke, 1984). The instrument uses a low-power laser transmitter to produce a parallel, monochromatic beam of light that illuminates the droplets or particles flowing in an appropriate sample cell. The incident light is diffracted by the illuminated particles, resulting in a stationary diffraction pattern regardless of particle movement. As particles flow through the illuminated area, the evolving diffraction pattern reflects the instantaneous size distribution in this area. Thus, by using a continuous flux of particles through the illuminated area and by integrating over a suitable time period, the final measured diffraction pattern is representative of the bulk sample of the particles. A Fourier transform lens focuses the diffraction pattern onto a multielement photoelectric detector, which produces an analogue signal proportional to the incident light intensity. The detector consists of a concentric array of 32 semicircular photodiodes, each representing a certain size band (Malvern Instruments Ltd.,1987). Once the diffraction pattern of a sample has been obtained, the particle size data are extracted by performing an iterative nonlinear least-squares calculation. An initial size distribution, divided into 32 size bands, is assumed either from raw data (model independent) or from some particular form of distribution, e.g., Rosin-Rammler. A set of 32 corresponding light intensity values is calculated, and the sum of the squares of the differences between the calculated and measured intensity values is minimized by successively refining the assumed size distribution. The software supplied by Malvern Instruments Ltd. (1987) allows the user to specify the type of size distribution as a Rosin-Rammler, normal or log-normal. Alternatively, a model-independent analysis can be selected. In the latter case, multimodal particle size distributions can be identified with high resolution (Burkholz and Polke, 1984). The on-line capability of the laser diffraction instrument is especially desired for measurement of transient drop size distributions. The samples can be scanned as they are pumped through the flow cell, and a number of sweeps of the detector are collected for data averaging (typically 200) in order to obtain representative and statistically meaningful drop size distributions. The sizes being measured for each lens cover a range of 1801. In case a sample contains particles smaller than the lowest size band of the lens, a subsize measurement compensation is automatically performed with high accuracy when less than 20% of the material is in the subsize class (Malvern Instruments La., 1987). On the contrary, at the upper limit of each lens, the coarse fraction leads to measurement error, particularly in the final two size channels (Biirkholz and Polke, 1984). On the other hand, the laser diffraction technique has a certain range of acceptable scattering intensities over which the accuracy of the system can be preserved. Since scattering intensity is a function of particle size and concentration, the sample concentration limits depend on the size of the material. A t the lower concentrations, poor signal level and large random errors exist, while at high concentrations multiple scattering effects may introduce systematic errors. It has been shown that measurements are independent of sample concentration if the fraction of diffracted light is within 5-50% (Malvern Instruments Ltd., 1987). Typical results generated by the instrument include cumulative size distribution, volume fraction within each size band, and a listing of the main parametera of the distribution including the volume mean, median, and Sauter mean diameters (Malvern Instruments Ltd.,1987). A computer program has been written for the mathe-
Ind. Eng. Chem. Res., Vol. 30, No. 3, 1991 139
z 2ool L
1
:100-
II
6 eo
I20 Drop dlamrtrr. pm
40
r
1
i
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,
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li0
,
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f
100
r dlftracllon, 3 k
50
j
:
..
c
f
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Ob
'
120 160 200 DTop dlrmatar, pm
240
260
Figure 3. Reproducibility of the laser diffraction measurements.
matical transformation of the measufed volume frequency distribution to corresponding volume,density and diameter density distributions. The discrete distribution can be transformed into a continuous one by the use of the quasi-cubic Hermite splines method. Various characteristic moments and averages of the discrete distribution such as expected drop diameter, surface and arithmetic means, and maximum diameter as well as the total number of drops in the vessel can be calculated from the measured volume frequency data. The validity and reproducibility of the laser diffraction method was tested by carrying out consecutive measurementa as the sample was recirculated through the flow cell (Figure 3). Furthermore, it was found that the location of sample withdrawal had no significant effect on the measured drop size distribution. This was expected for the particular system and the experimental conditions employed since the degree of inhomogeneity of the vessel contents was quite low (Chatzi et al., 1989). The experimental diameter and volume density distributions obtained by photography and laser diffraction are compared in Figure 4 for 1% styrene in water at tem. perature 25 O C and agitation rate 200 rpm. It can be seen that the volume frequency distributions are in close agreement in the region of larger size drops. The observed differences in the small-size range appear to be more significant in the diameter density distributions. These differences can be explained in view of the accuracy of each technique in measuring the small-size portion of the drops and their inherent measurement errors. In the laser diffraction technique, the size range is discretized on a logarithmic diameter scale, which places more weight on the small-size droplets. On the other hand, the actual determination of drop sizes by photography may result in significant errors (Mlynek and Reshnick, 1972; Chatzi et al., 1989), especially for small drops that cannot be distinguished very clearly. ABa result, the error associated with the measurement of small drops is higher than that for the large drops. This discrepancy becomes less obvious in the volume distribution since the fraction of small drops rep-
60
120 160 200 Drop dlamrtrr. pm
240
Figure 4. Comparison of the laser diffraction and photographic techniques for a system of 1% styrene in water at 25 O C and 200 rpm.
resents only a minor portion of the dispersed phase. Operational Conditions and Physical Properties. The experiments were carried out at atmospheric pressure and temperatures 25, 30, 50, and 60 O C . Two impeller speeds were investigated, namely, 200 and 300 rpm. Both speeds were above the minimum impeller speed for complete liquid-liquid dispersion. The maximum impeller speed of 300 rpm was just below the level at which air entertainment occurred. The amount of PVA used was sufficient for saturation of the total droplet interfacial area generated under different experimental conditions. The interfacial tension was measured with a KRUSS surface tensiometer Model K10 using the Wilhelmy plate method. For PVA concentrations less than 10 g/L, the physical properties of the continuous phase do not significantly vary from those of pure water, Therefore, the average density and viscosity of the dispersion were calculated as weighted averages of the corresponding values of the dispersed and continuous phases.
Results and Discussion Particle Size Distribution and Agitation Time. Figure 5 shows transient drop size distributions obtained at 60 OC and 300 rpm for stirring times 7,15,45, and 120 min. The distributions are clearly bimodal, with the large-size peak shifting from 80 to 60 pm and the small-size peak from 35 to 30 pm as the agitation time increases. A similar behavior is observed at 60 OC and 200 rpm, as illustrated in Figure 6. However, a more gradual reduction of drop size is experienced at the lower agitation rate, especially during the initial period. In this case, the large-size peak shifts from 140 to 85 pm and the small-size peak from 60 to 35 pm as the agitation time increases. A similar tendency is also observed for all other experiments. For both agitation levels, the system assumes its characteristic bimodal shape of the size distribution in less than 5 min. Further stirring reduces only the drop sizes without
540 Ind. Eng. Chem. Res., Vol. 30, No. 3, 1991
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Figure 5. Transient diameter and volume density distributiona for a system of 1% styrene in water at 60 "C and 300 rpm and for agitation times 7, 15,45,and 180 min.
b 5001 f
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Figure 6. Transient diameter and volume density distributions for a system of 1% styrene in water at 60 O C and 200 rpm and for agitation times 7, 30,45,and 160 min.
substantially altering the shape of the distribution. The almost instantaneous initial breakdown of the dispersed phase into a large number of drops has been also recognized by Bajpai et al. (1976). This process is termed as the primary phase of a breakdown and is followed by a secondary phase during which the droplet dispersion phenomena occur at a much slower rate. During the
secondary breakage process, the number of drops remains essentially constant with time. The size distribution, however, continues to change gradually until a dynamic balance is achieved. Bimodal distributions have been scarsely reported in the literature (Ward and Knudsen, 1967;Hong and Lee, 1985;Laso et al., 1987). This may be attributed to the method of measuring the drop size distributions (i.e., photography), which does not allow accurate interpretation of this type of data. Ward and Knudsen (1967)obtained drop size distributions characterized by two peaks from photographs of a flowing dispersion. ks circulation proceeded, the position of the peaks remained relatively constant with respect to diameter but their relative frequency changed. Their experiments showed that the peak corresponding to the large diameter drops decreased while the peak of the small diameter drops increased. They recognized that the shape of the distribution curve depended on the concentration as well as on the physical properties of the two liquids making up the dispersion. It was found that the median volume of the low-diameter peak was only from 0.03% up to 4% of the median volume of the high-diameter peak. As a result, they suggested that drop breakage was of an erosive type according to which a droplet breaks off a much larger drop, leaving it virtually unchanged. Hong and Lee (1983)observed bimodal distributions by a microphotographic technique. The multimodality was more pronounced at short agitation times, and the peaks exhibited a shift to smaller diameters as the agitation time increased. Laso et al. (1987)comment on the tendency of the observer to preferentially count larger drops while neglecting smaller ones. The same investigators employed a photographic technique and observed bimodal transient distributions for a slow-coalescing system. The time variation of drop size and the total number of drops as well as the corresponding values at steady state for low-coalescing systems are determined by the breakage process. This is in turn affected by the physical properties of the system and agitation rate. Figure 7 depicts the relation of agitation time with the Sauter mean diameter, dg2,and the total number of drops in the dispersion, N w At lower impeller speeds (200 rpm), the approach to equilibrium is gradual and requires a total agitation time
Ind. Eng. Chem. Res., Vol. 30,No.3, 1991 641
300
: t
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40 Drop dlameter, pm
7!
2001
c
+
i
,,300
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ii
i
Drop dlomstsr, pm
Figure 8. Effect of impeller speed on the steadystate diameter and volume density distribution for a system of 1% styrene in water at 60 O C .
of about 3 h. On the other hand, at an agitation level of 300 rpm, the system reaches steady state after 1 h. As shown in Figure 7, an increase in temperature causes a decrease in the average drop size and a corresponding increase in the total number of drops. These effects become more significant at 200 rpm for the 25-30 "C temperature increase and at 300 rpm for the 30-60 OC temperature change. Furthermore, the effect of impeller speed is larger at 25 and 60 O C than at 30 OC. The steady-state drop size distributions are compared in Figure 8 for temperature 60 O C and impeller speeds of 200 and 300 rpm. In figure 8, the steady-state drop size distributions are plotted for two impeller speeds (200and 300 rpm) at 60 O C . As the agitation rate increases, both peaks of the distribution exhibit a shift to smaller sizes. For constant drop surface energy, Le., constant temperature, droplet breakage is promoted by higher impeller speeds since the turbulent kinetic energy associated with breaking the drops is increased. Therefore, higher speeds result in smaller drops. Details on the influence of temperature on the shape of the steady-state drop size distribution are shown in Figure 9 for a stirring speed of 200 rpm. A rather pronounced shift of 30 pm is observed for the large-size peak of the distribution when the temperature increases from 25 to 30 O C . A further increase in temperature causes only a narrowing of this particular peak. The shifts of the small-size peak can be explained by examining the dependence of the breakage mechanism on the physical properties of the two-phase system. To examine the effects of initial state of the system on the steady-state distribution, a number of experiments involving step changes in the agitation rate were carried out. Figurea 10 and 11depict the variation of Sauter mean diameter versus time at temperature8 30 and 25 O C , respectively. In Figure 10, a step increase in the agitation rate (from 200 to 300 rpm) is introduced after the system has reached steady state. Ae can be seen, the Sauter mean diameter quickly decreases to a new value, which corre-
I20 160 Drop dtamotar, pm
200
Drop dlamoter, pm
Figure 9. Effect of temperature on the steady-state diameter and volume density distribution for a system of 1%styrene in water at agitation rate 200 rpm. 0.018
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sponds to the Sauter mean diameter at 300 rpm. In Figure 11,the results obtained for positive and negative step changes in agitation rate are shown. In both
542 Ind. Eng. Chem. Res., Vol. 30, No. 3, 1991 Table I. Exmrimental Conditions N*, rpm T,OC (NWe)T 200 23 269 300 25 604 200 30 273 300 30 614 200 50 291 200 60 301 300 60 678
-2.5
(NdT
20635 30953 23 004 34506 33 285 38845 58 267
Q
d32/DI = b(1 + cd)(NW&T4"
Photography
-
N
n
n c c
(1)
(2)
Alternatively, by assuming that the drop sizes are determined by the coalescence process, they obtained eq 3: k(~~I)4'.376(NW,)T~'3's
Laaer D i f f r a c t i o n
0
c.
where (NWe)T = pe(N*)2Dt/u is the Weber number of the main flow. The term 1 + cd reflects the influence of the dispersed phase in damping down the overall level of turbulence. The Weber number represents the effects of turbulence intensity and physicochemical properties of the system. Shinnar and Church (1960) and Shinnar (1961) used Kolmogoroff's theory of universal equilibrium under the local isotropy assumption to derive the following equation for the break-up process as the dominant mechanism: &/DI = k(NWe)T4'8
-2.7
A
e
cases,the system reaches a steady-state distribution, which is independent of its previous agitation history. In fact, the final distribution corresponds to the distribution obtained under constant agitation conditions. In the 200-300 rpm step change, the system quickly attains ita new steady state in about 90 min. This transition is mainly accomplished by a drop breakage process. On the other hand, in the 300-200 rpm step change, the system reaches a new steady state in about 9 h. This is due to a slow coalescence rate of the drops, which requires a1 longer equilibration period. In the latter case, the drops exhibit an initial size reduction followed by an increase up to the final steady state. This might be due to the small contribution of immediate coalescence at 300 rpm. Immediate coalescence occurs when the velocity of approach along the center-line of two colliding drops exceeds a critical value (Howarth, 1964). Therefore, it is more pronounced at higher impeller speeds. At moderate agitation conditions, coalescence takes place by drainage of the intervening film between two adhering drops (Shinnarand Church, 1960). Following the initial drop size reduction, coalescence by film drainage becomes the dominant process in the control of drop size. As a result, a gradual increase in drop sizes is observed. This justifies our initial consideration of a low-coalescing system since the coalescence time is much longer from the time required for drop breakage (9 h vs 90 min). A similar behavior has been reported (Nishikawa et al., 1987) for a system of 1.5% wax in water. Correlations for the Steady-StateMean Drop Size. The most common correlation of the Sauter mean drop diameter to the vessel geometry and physical properties of the dispersion system is given by the following equation (Brown and Pitt, 1970):
d32/DI
I
(3)
The numerical values of the Weber and Reynolds numbers in relation to our experimental conditions are shown in Table I. The Reynolds number of the main flow is defined as (N& = N*D?/v, and is always larger than 20 OOO. This value is well above the limit of 10 OOO proposed be Ruehton et al. (1950) for local isotropy. At high
-2.9 -3.0
2 4
2 6
2 8
3 0
3 2
log(N w e ) T
Figure 12. Comparison between Sauter mean diameters obtained by the laser diffraction and photographic techniques.
Reynolds numbers > 10000),droplet diameters satisfy the condition L >> d >> q , where L and q are the macroscale and microscale of turbulence, respectively. The microscale of turbulence is given by r)
=
(Y,3/41/4
(4)
where t is the average dissipation energy per unit mass and r) can vary from 8 to 18 pm. The macroscale of turbulence, L, is approximated by the width of the impeller blade (Coulaloglou and Tavlarides, 1976) and is equal to 2 cm for our experimental setup. The experimentally measured drop sizes are larger than the microscale and much smaller than the macroscale of turbulence. As was shown in the previous section, the drop size in our system is mainly determined by the breakage process. Therefore, a least-squares algorithm was used to fit experimental results to eq 2: d32 / DI = 0.045(f0.003) (Nwe)T4.' (5) It should be mentioned that the drop sizes measured by the present technique were smaller than those measured by a photographic method (Chatzi et al., 1989) as illustrated in Figure 12. Accordingly, the estimated value of parameter k in eq 5 was closer to the lower limit of the k values (0.051-0.081) reported in the literature. Minimum Transition Time. The minimum transition time required for the system to reach dynamic equilibrium is important for design purposes. As shown in Figure 7, the Sauter mean diameter decreases exponentially during the initial period of mixing, until it reaches an equilibrium drop size, d32*. The minimum transition time, tmh, can be obtained by plotting the dimensionless drop size, (dS2 - d32*)/d32* vs time (Hong and Lee, 1983). The minimum time t&o.l corresponds to a dimensionless diameter value of 0.1 (Hong and Lee, 1985). As a first approximation, the minimum transition time t-,o,l was correlated with the Weber number by a least-squares algorithm: tmin,O.l = 3.19 x 107(~,,),-2.3 (6) where the t,,,hto.l values are expressed in minutes. The correlation indicates that the time required for the system to reach steady state decreases as the Weber number increases. It is well-known that the Weber number is a measure of the ratio of the shear to surface forces. The turbulence introduced into the system is expected to increase the breakup of drops, while the surface force represents the major restoring force promoting coalescence. Consequently, a larger value of the Weber number, either due to higher agitation rate or decreased interfacial tension, reduces the minimum transition period.
543
Ind. Eng. Chem. Res. 1991,30,543-555
Acknowledgment We gratefully acknowledge the EEC and the CPERI for supporting this research under the BRITE Project P-1560.
Literature Cited Bajpai, R. K.; Prokop, A. A new method for measuring drop-size distribution in hydrocarbon fermentations. Biotechnol. Bioeng. 1974, 16 (ll),1557. Bajpai, R. K.; Ramkrishna, D.; Prokop, A. Coalescence frequencies in Waldof-agitated systems. Biotechnol Bioeng. 1975,17 (ll), 1697. Brown,D. E.; Pitt, K. Drop break-up in a stirred liquid-liquid contactor. Proc. Chemeca, Melbourne and Sydney, 1970;p 83. Blirkholz, A.; Polke, R. Laser diffraction spectrometers/experience in particle size analysis. Part. Charact. 1984, 1, 153. Chatzi, E. G.; Gavrielides, A. D.; Kiparissides, C. Generalized model for prediction of the steady-state drop she distributions in batch stirred vessels. Ind. Eng. Chem. Res. 1989,28,1704. Coulaloglou, C. A.; Tavlarides, L. L. Drop size distributions and coalescence frequencies of liquid-liquid dispersions in flow vessels. AZChE J. 1976,22,289. Fernandes, J. B.; Sharma, M. M. Effective interfacial area in agitated liquid-liquid contactors. Chem. Eng. Sci. 1967,22,1267. Hong, P. 0.; Lee, J. M. Unsteady-state liquid-liquid dispersions in agitated vessels. Ind. Eng. Chem. Process Des. Dev. 1983,22,130. Hong, P. 0.; Lee, J. M. Changes of the average drop sizes during the initial period of liquid-liquid dispersions in agitated vessels. Znd. Eng. Chem. Process Des. Dev. 1985,24,868. Howarth, W. J. Coalescenceof d r o p in a turbulent flow field. Chem. Eng. Sei. 1964,19,33.
Laso, M.; Steiner, L.;Hartland, 5.Dynamic simulation of Gtated liquid-liquid dispersions-11. Experimental determination of breakage and coalescence rates in a stirred tank. Chem. Eng. Sci. 1987,42, (lo), 2437. Malvern Instruments Ltd. Particle Sizer Reference Manual. Spring Lane South, Malvern, Worcestarshire, Jihgland, 1987. Mersmann, A.; Grossman, H. Dispersion of immiscible liquids in agitated vessels. Int. Chem. Eng. 1982,22(4),581. Mlynek, Y.;Reshnick, W.Drop sizes in an agitated liquid-liquid system. AZChE J. 1972,18,122. Narsimhan, G.; Nejfelt, G.; Ramkrishna, D. Breakage functions for droplets in agitated liquid-liquid dispersions. AZChE J. 1984,30 (3),457. Nishikawa, M.; Mori, F.; Fujieda, S. Average drop size in a liquidliquid phase mixing vessel. J . Chem. Eng. Jpn. 1987,20(l),82. Rushton, J. H.; Costich, E. W.; Everett, H. J. Power characteristics of mixing impellers. Chem. Eng. h o g . 1950,46,395. Shinnar, R. On the behavior of liquid dispersions in mixing vessels. J. Fluid Mech. 1961,10,259. Shinnar, R.; Church, J. M. Predicting particle size in agitated dispersions. Znd. Eng. Chem. 1960,52(3),253. Sprow, F. B. Distribution of drop sizes produced in turbulent liquid-liquid dispersion. Chem. Eng. Sci. 1967,22, 435. Tavlarides, L. L.; Stamatoudis, M. The analysis of interphase reaction and mass transfer in liquid-liquid dispersions. Adu. Chem. Eng. 1981, 11, 199. Ward, J.P.; Knudsen, J. G. Turbulent flow of unstable liquid-liquid dispersions: Drop sizes and velocity distributions. MChE J. 1967, 13 (2),356.
Received for review May 3, 1990 Accepted August 7, 1990
Model of Vapor-Liquid Equilibria for Aqueous Acid Gas-Alkanolamine Systems. 2. Representation of H2S and C02 Solubility in Aqueous MDEA and C02 Solubility in Aqueous Mixtures of MDEA with MEA or DEAt David M. Austgen and Gary T. Rochelle* Department of Chemical Engineering, The University of Texas at Austin, Austin, Texas 78712
Chau-Chyun Chen Aspen Technology, Inc., 251 Vassar St., Cambridge, Massachusetts 02139
A physicochemical model developed in earlier work for representing Ha and C02solubility in aqueous solutions of monoethanolamine (MEA) and diethanolamine (DEA) was extended to include the mixtures of methyldiethanolamine (MDEA) with MEA or DEA. The framework of the model is based upon both liquid-phase chemical equilibria and vapor-liquid (phase) equilibria. Activity coefficients are represented with the electrolyte-NRTL equation treating both long-range electrostatic interactions and short-range binary interactions. Adjustable binary interaction parameters of the model were fitted on binary and ternary system MDEA data reported in the literature. The solubility of C02 in aqueous mixtures of MDEA with MEA or DEA was measured at 40 and 80 "C over a wide range of C02 partial pressures. Representation of the data by the model is good, especially a t low to moderate acid gas loadings.
Introduction Monoethanolamine(MEA) and diethanolamine (DEA) have been the most widely employed gas-treating alkanolamine solvents during the past several decades. In recent years, methyldiethanolamine (MDEA) has been used an alternative to MEA or DEA in certain gastreating applications. MDEA reacts rapidly with H2Sand 'Presented at the AIChE 1989 Spring National Meeting, Houston, TX, April 2-6, 1989.
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relatively slowly with COS(Astarita et al., 1983). Therefore, it is oft& used for selective removal of HZS from a gas stream both acid gases* However, is also useful for bulk C 0 2 removal because the heat released by the reaction Of co2 with MDEA is low (Kohland Riesenfeld, 1985). Its use as an alternative to MEA or Dm in co2 removal, in a in energy rewired to strip COz from solution. Recent research-(Chakravarty et d.,1985;Critchfield and Rochelle, 1987,1988, Katti and Wolcott, 1987)indicates that a primary or secondary amine, such as MEA or DEA, can 0 1991 American Chemical Society
