562
Ind. Eng. Chem. Res. 1991,30,562-569
Dahlquist, G.; Bjbrck, A. Numerical Methods; Prentice-Hall: Englewood Cliffs, NJ, 1974;pp 146-147, 152-157. Deen, W. M.; Bridges, C. R.; Brenner, B. M. Biophysical Basis of Glomerular Permselectivity. J. Membr. Biol. 1983, 71, 1-10. Dudukovic, M. P.; Mills, P. L. A Correction Factor for Mass Transfer Coefficients for Transport to Partially Impenetrable or Nonadsorbing Surfaces. AlChE J. 1985,31,491-493. Finlayson, B. A. Nonlinear Analysis in Chemical Engineering; McGraw-Hill: New York, 1980; pp 291-307. Gueshi, T.; Tokuda, K.; Matsuda, H. Voltammetry at Partially Covered Electrodes: Part I. Chronopotentiometry and Chronoamperometry at Model Electrodes. J.Electroad. Chem. 1978, 89,247-260. Herskowitz, M.; Carbonell, R. G.; Smith, J. M. Effectiveness Factors and Mass Transfer in Trickle-Bed Reactors. AIChE J. 1979,25, 272-282. Holmes, J. T.; Wilke, C. R.; Olander, D. R. Convective Mass Transfer in a Diaphragm Diffusion Cell. J. Phys. Chem. 1963, 67, 1469-1472. Hume, E. C.; Deen, W. M.; Brown, R. A. Mass Transfer Analysis of Electrodeposition Through Polymeric Masks. J. Electrochem. SOC. 1984,131,1251-1258. Keh, H. J. Diffusion of Rigid Brownian Spheres Through Pores of Finite Length. PCH, PhysicoChem. Hydrodynam. 1986, 7, 281-295. Keller, K. H.; Stein, T. R. A Two-Dimensional Analysis of Porous Membrane Transport. Math. Biosci. 1967,1,421-437. Kelman, R. B. Steady-State Diffusion Through a Finite Pore into an Infmite Reaervoir: An Exact Solution. Bull. Math. Biophys. 1965, 27,57-65. Kuan, D.-Y.; Davis, H. T.; Aris, R. Effectiveness of Catalytic Archipelagos-I. Regular Arrays of Regular Islands. Chem. Eng. Sci. 1983a,38,719-732. Kuan, D.-Y.; Aris, R.; Davis, H. T. Effectiveness of Catalytic Archipelagos-11. Random Arrays of Random Islands. Chem. Eng. Sci. 1983b,38,1569-1579. Malone, D. M.; Anderson, J. L. Diffusional Boundary-Layer Resistance for Membranes with Low Porosity. AIChE J. 1977,23, 177-184.
Monteith, J. L. Principles of Environmental Physics; Eleevier: New York, 1973;pp 134-149. Nanis, L.; Kesselman, W. Engineering Applications of Current and Potential Distributions in Disk Electrode Systems. J. Electrochem. SOC. 1971,118,454-461. Prager, S.; Frisch, H. L. Interaction Between Penetration Sites in Diffusion Through Thin Membranes. J. Chem. Phys. 1975,62, 89-91. Reller, H.; Kirowa-Eisner, E.; Gileadi, E. Ensembles of Microelectrodes: A Digital Simulation. J. Electroanal. Chem. 1982,138, 65-77. Scattergood, E. M.; Lightfoot, E. N. Diffusional Interaction in an Ion-Exchange Membrane. Trans. Faraday SOC.1968, 64, 1135-1146. Scheller, F.; Muller, S.; Landsberg, R.; Spitzer, H.-J. Gesetzmiissigkeit fur den Diffusionsgrenzstrom an teilweise blockierten Modellelektroden. J. Electroanal. Chem. 1968,19, 187-198. Scheller, F.;Landsberg, R.; Miiller, S. Zur R~rabhangigkeitdes Grenzstromes an teilweise bedeckten rotierenden Scheibenelektroden bei relativ grossen Umdrehungszahlen. J. Electroanal. Chem. 1969,20,375-381. Scheller, F.; Landsberg, R.; Wolf, H. Uber Kriterien fur das heterogene Verhalten von Elektrodenoberflachen. 2.Phys. Chem. 1970,243,345-355. Smythe, W. R. Current Flow in Cylinders. J. Appl. Phys. 1953,24, 70-73. Solomon, A. K. Characterization of Biological Membranes by Equivalent Pores. J. Gen. Physiol. 1968,51,335s-364s. Wakeham, W.A.; Mason, E. A. Diffusion Through Multiperforate Laminae. Ind. Eng. Chem. Fundam. 1979,18,301-305. Whelan, M. E.; MacHattie, L. E.; Goodings, A. C.; Turl, L. H.The Diffusion of Water Vapor Through Laminae with Particular Reference to Textile Fabrics. Text. Res. J. 1955,25, 197-223. Received for review June 7, 1990 Revised manuscript received October 5,1990 Accepted October 12, 1990
Boiling Incipience in a Reboiler Tube Hamid Ali* and S. S. Alam Department of Chemical Engineering, Aligarh Muslim University, Aligarh 202 002,India
The heating surface and liquid temperature distributions were experimentally obtained to identify the boiling incipience conditions in a single vertical tube thermosiphon reboiler with water, acetone, ethanol, and ethylene glycol as test liquids. The test section was an electrically heated stainless steel tube of 25.56-mm i.d. and 1900 mm long. The uniform heat flux values were used in the range of 3800-40000 W/m2, while inlet liquid subcooling were varied from 0.2 to 45.5 "C. The liquid submergence was maintained around 100,75,50 and 30%. All the data were generated at 1-atm pressure. The maximum superheats attained around boiling incipience were taken from the wall temperature distributions and correlated with heat flux and physical properties of liquids using the expression of Yin and Abdelmessih. The heated sections required for onset of fully developed boiling with net vapor generation were determined assuming a thermal equilibrium model. A dimensionless correlation relating these values with heat flux, liquid subcooling, and submergence was proposed. Introduction Vertical tube thermosiphon reboiler system finds wide and increaRing application in the chemical and petrochemical industry as vaporizer, evaporator, reboiler, and similar other unita because of mechanical simplicity, low manufacturing cost, and operation in the nucleate boiling region. Apart from the above conventional applications it provides a potential means of heat transfer in diverse situations requiring high heat flux and induced flow conditions as encountered in power planta, nuclear reactors, and solar energy transportation.
* Correspondence to be addressed to this author. 0888-5885/91/2630-0562$02.50/0
In almost all the above applications, a subcooled liquid entering the tube receives the sensible heat and its temperature rises as it moves upward. Depending upon wall temperature conditions, subcooled boiling may set in at the surface. When the liquid temperature attains saturation value, saturated boiling begins with the existence of net vapor which increases, resulting in bubbly to mist flow. Thus the heat transfer to liquids in the reboiler tube generates a changing two-phase flow with various flow regimes spread along the tube length. The point at which the two-phase flow begins is known as incipient point of boiling (IPB). It corresponds to the conditions of minimum degree of superheat or heat flux required for the formation and detachment of the first vapor bubble from Q 1991 American Chemical Society
Ind. Eng. Chem. Res., Vol. 30, No. 3, 1991 563 the heating surface. Since IPB divides the tube in two distinct regions, nonboiling single phase and boiling two phase with entirely different modes and rates of heat transfer, ita prediction is important in the design of numerous engineering units as referred to above using the thermosiphon reboiler principle. The point of onset of nucleation along the tube length and its required superheat depends upon a number of operating parameters. Studies of this effect on predicting superheat through a semiempirical approach for forced convection boiling in tubes have been reported in the literature. These studies include the effect of various physical parameters: surface roughness by Corty and Foust (19551, size and geometry of nucleation sites by Clark et al. (1959), Griffith and Wallis (19601, Howell and Siege1 (19661, Schultz et al. (1975), and Jemison et al. (1982);and the role of the surface tension and wettability by Harrison and Levine (1957) and Lorentz et al. (1974). Some of the experimental studies have also been reported for the influence of prior boiling and effect of dissolved gases by Murphy and Bergles (1972). Hodgson (19691, Murphy and Bergles (1972), and Yin and Abdelmessih (1974) have shown through experimental studies the presence of two boiling incipience points, depending on the direction (increasing or decreasing) of change in heat flux. The widely accepted approach for the prediction of incipient boiling has been the one which is based on Gibb’s equilibrium theory of bubble in a uniformly superheated liquid and the one-dimensional steady or transient heat conduction equation. It was postulated, that, in the liquid film adjacent to the heating surface, the superheated layer, 6*, must attain a threshold value 80 that the critical bubble nuclei with radius rc can further grow to the point of detachment. The relation between 6* and r, is therefore of primary importance in determining the incipient point of boiling. Zuber (1959) was probably the first to analyze the interrelationship between the local heat flux, the superheated layer, and the diameter of the surface cavity. He employed the data of Clark et al. (1959) and Griffith and Wallis (19601, carried out a series of calculations,and found that the superheated layer thickness is approximately equal to the diameter of the cavity. Hsu (1962) and Hsu and Graham (1961) developed analytical expressions for the size range of active nucleation sites for constant heat flux at the wall. Bergles and Rohsenow (1964) adopted the procedure proposed by Hsu and Graham (1961) to develop a criterion of incipient point for systems that have a wide range of cavity sizes that should be applicable to commercially finished surfaces. They concluded that only a small additional increase in wall temperature is necessary to activate a considerable range of cavity sizes when bubbles originating from cavities of a particular radius start to grow. Jiji and Clark (1962) made a visual observation of incipient subcooled boiling for forced convection flow of pressurized water past a heated surface. Han and Griffith (1965) obtained an analytical formula for the prediction of the incipience of nucleate pool boiling. Sato and Matsumura (1964) proposed an analytical expression equivalent to that of Hsu’s for the prediction of incipient nucleate boiling of water at atmospheric pressure. Davis and Anderson (19661, as an extension of the analysis established by Hsu (1962) and Bergles and Rohsenow (1964), derived an equation for the prediction of subcooled incipient boiling of water in forced convection. They concluded that the criterion used in their analysis appears satisfactory for determining an upper limit of the liquid superheat to initiate nucleate boiling when a wide range of cavity sizes exists. Butterworth and Shock (1982) found
that the Davis and Anderson (1966) equation did not predict the incipience of subcooled boiling satisfactorily for higher values of r, for some fluids and conditions. They recommended the Bergles and Rohsenow (1964) equation for water at 0.1 X loe to 13.6 X 106 Pa and the Davis and Anderson (1966) equation for water at pressure less than 0.1 X lo6Pa for organic liquids including refrigerants and cryogenic liquids for r, less than 0.50 pm. Frost and Dzakowic (1967) extended the analysis of Davis and Anderson (1966) and derived an equation for the prediction of incipience of boiling for a variety of different liquids. They considered their equation to be applicable to both forced and natural convection systems. Tong (1972) studied the existing nucleate and film boiling correlations and recommended the Davis-Anderson equation for the prediction of incipient nucleate boiling in subcooled flow boiling of water. Fiore and Ricque (1964) made an analysis for the prediction of the incipience of nucleation under forced convection conditions of high boiling point multicomponent organic liquids. The analysis was also extended to the condition of degassing. Murphy and Bergles (1972) obtained a relation for the prediction of incipient flow boiling of Freon-113under chemical potential equilibrium. They noted that their analysis satisfactorily predicted the point where nucleation dies and that it is not capable of predicting the traverse nucleation behavior encountered on the increasing heat flux traverse. Abdelmessih et al. (1973) demonstrated that only a few data of Bergles and Rohsenow (1964) have predicted the degree of superheating at the incipient point of boiling during the subcooled nucleate flow boiling of water. Unal(l976) obtained a correlation to determine the maximum bubble diameter at the incipient point of boiling of a subcooled nucleate flow boiling of water. Yin and Abdelmessih (1977), on the basis of the existing theories, developed an analytical method for predicting points of boiling incipience. They also generated experimental data with Freon-11 as test liquid for both cases of increasing and decreasing heat flux conditions. Using the analytical expression and experimental data, two correlations were proposed for computing the incipient boiling superheats. Unal(l977) determined the incipient point of boiling for subcooled nucleate flow boiling of water with high-speed photography. He correlated his data and those available in the literature covering ranges of pressure, mass velocity, hydraulic radius, heat flux, and subcooling for plate, circular tube, and annulus with stainless steel and nickel surfaces. He also modified his own equation developed in 1976 for maximum bubble diameter at the incipient point of boiling. Maximum bubble diameters at the incipient point of boiling were measured and correlated along with the data of Abdelmessih et al. (1972). Almost all the studies mentioned above have been conducted for forced convection boiling of liquids. In spite of the industrial importance of natural circulation boiling of liquids in vertical tubes where flow and heat transfer strongly interact with each other, studies on thermosiphon boiling of liquids in vertical tubes have been reported only by Golovchenko and Fokin (1979), Agarwal (1980), Ali (1989), and Ali and Alam (1988). In the present experimental investigation an attempt has been made to identify the conditions of boiling incipience experimentally and relate them to the relevant parameters such as heat flux, liquid submergence, and subcooling during nucleate boiling of liquids in a vertical tube of a thermosiphon reboiler. Experimentation The experimental reboiler was made of two vertical
564 Ind. Eng. Chem. Res., Vol. 30,No. 3, 1991 cc
Table I. Range of Experimental Parameters avstem a. W/mZ AT.,,k, "C 599639949 0.2-45.5 water 3800-15115 1.0-16.3 acetone 3800-21884 1.1-21.6 ethanol 15115-33654 3.2-15.8 ethylene glycol ~~
a:: J
1 Test section
2 Copper chmps 3 Mew port for inlet liquid b G b s tube section 5 Vapour- liquid separator 6 P r i m r y condenser 7 Spiral coil 8 Secondary condenser 9 Liquid down-flow pipe IOCooling pcket 11 won thcrmocoupks 12 Liquid thermocouple p m b a 13 L'Quid bvel indicator 14Condenvr down flow pipe 1 5 R e m b l e screwd cap v1-v3, Control wkes
c 1 - C ~ Drain cock mtves
Figure 1. Schematic diagram of experimental setup.
tubes joined in a U shape with the upper ends connected to a vapor-liquid separator and total condenser vessels forming a thermosiphon loop as schematically shown in Figure 1. One of the vertical tubes which served as test section was electrically heated. The test liquid boiled in this tube, flowed upward through a glass section, and entered into the separator. The liquid drained down the bottom of the separator, while vapors went to a watercooled condenser. The condensate joined the separator liquid near the top end of the other jacketed vertical tube (downflow pipe) through which the total liquid circulated back to the test section through a view point. The test section was an electrically heated stainless steel tube of 25.56" id., of 28.85o.d., and 1900 mm long. The stabilized power was supplied through a low-voltage, high-current transformer. The energy input to the test section was measured by a calibrated precision-type voltmeter and ammeter. Twenty-one copper constantan thermocouples were spot-welded on the outer surface of the tube at intervals of 50 mm up to a length of 200 mm from the bottom and 100 mm over the remaining length in order to monitor the heat-transfer surface temperatures. The test section was electrically isolated from the rest of the setup by means of specially designed flanges and an upper glass tube section. The lower end of the flanges was connected to a view port through which the liquid coming out of the downflow pipe could be visually observed to ensure the complete absence of any air or vapor bubbles before its entry to the test section. A copper constantan thermocouple probe was provided in the view port to measure the inlet liquid temperature. The visual observation of the boiling liquid emerging out of the test section was made through the upper glass tube section. Another thermocouple probe was inserted in the exit line leading to the vapor-liquid separator. Provisions were also made to measure the flow rates and temperatures in and around
~~~
~
S. % 30-100 30-100 30-100 50-100
the condenser and other strategic locations in the reboiler loop to ensure a reliable computation of circulation rates through the heat balance. A glass tube level indicator was provided with the downflow pipe to indicate the liquid head (submergence) for the reboiler. The entire setup was thoroughly lagged to reduce the heat losses to a negligibly small value. After the assembly and initial testing of the experimental setup, some forced convection data were collected using water to check the heat balance and standardization of the apparatus. The heat-transfer surface was then stabilized for the reproducibility of the experimental data. This was done by boiling distilled water, under the conditions of full submergence and nearly zero inlet degree of subcooling, for several hours followed by aging in order to obtain stable wall nucleating characteristics. A few runs were also conducted to check the overall Peat balance under the conditions of boiling. Care was also taken that, once the tube wall was stabilized, it remained fully submerged with liquid as the dry test surface always entraps a very thin film of air. This air on heating takes the shape of tiny air bubbles, which leave the surface on further heating. Thus, a microconvection sets in near the heattransfer surface in addition to the convections due to density difference. The test liquid was also boiled off at the start of every experiment to drive out the dissolved air completely, which was indicated by the disappearence of the air bubbles in the bubbler. In an experimental run, the desired heat flux was impressed and submergence adjusted by draining/adding the requisite amount of test liquid. The cooling water rate was regulated to give a maximum temperature rise consistent with no loss of vapor due to inadequate condensation. With the layout designed for a closed-system operation and with a stabilized power supply, the unit once chirged and started could be continuously run for sufficient time. When the steady-state condition was established, the readings of electrical input, wall thermocouples, liquid thermocouple probes, and cooling water were recorded. The maximum liquid head used in the present study corresponded to the liquid level equal to the top end of the reboiler tube. This condition has been termed as 100% Submergence. The cold liquid head could be varied independently by maintaining the submergence at 75,50, and 30%. The experimental data were generated with increasing heat flux and 1.0-atm pressure. The range of parameters covered during experimentation on four liquid systems are given in Table I. Results and Discussion In the experimental reboiler, liquid condenser the tube at a temperature below the corresponding saturation temperature. Because of uniform heat-flux distribution, the liquid bulk temperature starts to increase and continues up to the saturation value if all the heat added to the system goes to raise the temperature of the liquid only. After that, the liquid bulk temperature remains constant at the saturation value and all the heat added goes to generate vapor. This is the thermal equilibrium model suggested by Saha and Zuber (1978). On the basis of this model the circulation rates and liquid bulk temperature distribution in the thermosiphon reboiler have been de-
Ind. Eng. Chem. Res., Vol. 30, No. 3,1991 566 I -5-100
1021
1
100
OB
Figure 3. Variation of wall and liquid temperature8 along the heated length for acetone with heat flux as parameter. Z,m Figure 2. Variation of wall and liquid temperatures along the heated length for water with heat flux as parameter.
2261A
5.100
222
termined by making a heat balance on the test section. In order to determine the liquid circulation rate, it was required to know the length of the effective nonboiling or sensible heating region over which the liquid temperature varied linearly. The effective boiling and nonboiling zones over the entire heated length were determined from the amount of net vapor generation. This could be obtained by the vapor condensed in the condenser. A heat balance around the condenser gives
2181
2021
Thus 1981
and ZNB
= L - ZB
(3)
The test liquid temperature distribution along the tube length in the nonboiling section was represented by a linear relationship:
TL = Ti + (T,- Ti)Z/ZNB
(4)
for Z IZNB. The temperature distribution along the boiling section of the tube was taken as constant at its saturation value, ignoring the effect of the hydrostatic head on boiling point. The error introduced due to this assumption was negligibly small as the length of the test section was not large. The wall temperature distribution along the heated length of test section was obtained from the experimentally measured values of surface temperatures at 21 locations on it. The liquid temperatures corresponding to the above-mentioned locations were computed by use of eq 4. The effect of heat flux and liquid submergence levels on theae temperature distributions were studied extensively for each test liquid. The typical representative plots of
..
.
Z,m Figure 4. Variation of wall and liquid temperatures along the heated length for ethylene glycol with heat flux as parameter.
these distributions with heat flux and liquid submergence as parameters are given in Figures 2-6 for water, acetone, ethanol, and ethylene glycol, respectively. The variations of liquid temperatures have been shown corresponding to the lowermost curves of wall temperatures only. The general characteristic behavior of curves may be observed as follows: (a) The wall temperature, T,, rises at a very fast rate along the heated length of the tube from ita inlet (lower) end up to a point beyond which a steep fall seta in showing a maximum. The variation rate of the wall temperature at a distance quite close to the peak points is diminished, resulting in a gradual decrease with Z in the remaining section up to the exit end of the tube. The shape of the curves is almost similar but their relative positions are
566 Ind. Eng. Chem. Res., Vol. 30, No. 3, 1991
I
I 116 114 112 110
16
12
1021
98Ao
i4 . ole
*
i2
1
116
*
I
io
Z,m Figure 5. Variation of wall and liquid temperatures along the heated length for water with submergence as parameter.
lo*l/q
4=15115.0
106L --I
94c
I
0
I
100 1.40 0.11 2
I
.Q
t-
5
90 88
Ic
92
Figure 6. Variation of wall and liquid temperatures along the heated length for ethanol with submergence as parameter.
altered for various heat-flux levels at the same liquid submergence and approximately same value of inlet liquid subcooling as shown in Figures 2-4. However, the curves at higher heat-flux values are shifted to higher wall temperatures. (b) The peak (maximum) value of wall temperature and its location at a fixed value of heat flux and almost the same degree of subcooling are strongly influenced by the liquid submergence. With the fall in its value from full submergence, the peak wall temperature and the distance required to attain this value decreased. The relatively longer horizontal portions of the curves at lower submergence are clearly exhibited by Figures 5 and 6. The fast-rising linear parts of wall temperature distributions are confined to the lower portions of the tube where the nonboiling region exists as indicated by the
I
l
l
l
*
l
~
l
~
l
r
'
'
l
'
'
'
'
Ind. Eng. Chem. Res., Vol. 30, No. 3, 1991 567
-
60
*4 c " 44 *-
100
28
-
12
t , , , , , , , , , , , , l
\
80
60 40 20
20
60
100
80
Calculated ( a x 1 0 0 )
12 0
4
12
8
20
16
q,kW/m
L
24
Figure 8. Variation of 6*/rcwith q for (a) acetone and (b) ethanol.
Q
A
-
32
40
Figure 10. Comparison of calculated (&/L predicted by eq 9.
X
100) and those
the wall heat flux,submergence, and inlet liquid s u b l i n g for a given liquid. In order to correlate the experimentally determined values of (ZOBIL) in terms of the influencing variables expressed as dimensionless groups, the functional relationship developed by Agarwal(1980) was taken in a slightly modified form:
50 1615.4 7 5 6-15.
00 4-6.35
28 -
-
E ' SP24 20
-
16
-
The values of indices nl, n2,nS,and n4 and constant c1 were determined by the regression analysis for various test liquids as tabulated in Table 111. An effort was made to obtain a unified correlation using the experimental data of all the systems together, and the following equation resulted, though with the enhanced maximum deviation:
0
12 12
I
l
16
r
l
20
r
l
24
l
l
r
2 5
l
l
32
l
36,
q, kWlm Figure 9. Variation of P / r , with q for ethylene glycol.
Table 11. Values of Constants in system S AT,"b water 3b100 0.2-45.5 acetone 30-100 1.0-16.3 ethanol 30-100 1.1-21.6 ethylene glycol 50-100 3.2-15.8
Ea 6 lWaq 6-40.0 3.8-15.1 3.621.9 15.1-33.7
(1
26.0 49.7 51.9 42.0
b 0.5 X lo4 0.1 X 0.1 X lo-' 0.7 X
where a and b are constants, characteristic to the liquids. Substituting eq 6 into eq 5 gives
2aT,
(T,- T,)2 = (a - bqp-
kLhhq
(7)
Equation 7 may be used to predict the degree of superheat required for onset of boiling at a given heat flux using the physical properties of liquid and constants a and b. The values of a and b determined for the experimental conditions and different systems are given in Table 11. The length of heated tube, from the inlet, required for the boiling to be effective has been found to depend upon
A plot of predicted values of ZoB/L versus those calculated by using the thermal equilibrium model is shown in Figure 10. The majority of data points of the present study and those of a similar investigation by Agarwal (1980) lie within a maximum error of *40%. The scatter of points and high error may be attributed to the uncertainties associated with locating the point of incipience from wall temperature distribution curves. The properties used in the equations were at the test liquid saturation temperatures. Conclusions An effort has been made to develop equations to predict the wall superheat required for onset of boiling and the length of heated tube required for the boiling to be effective in terms of relevant parameters for systems having widely varying and strongly temperature dependent physical properties which have a strong influence on the boiling process. The data points of the present study and those of an earlier similar investigation are well correlated by eq 9.
568 Ind. Eng. Chem. Res., Vol. 30, No. 3, 1991 Table 111. Values of Constant a n d system C1 nl water 0.605 0.149 acetone 0.644 0.548 0.674 0.425 ethanol ethylene glycol 0.558 0.122
Indices in Es 8 n2 n3 0.415 0.777 0.032 0.178 -0.322 0.32 0.53 0.954
n4 0.362 0.228 0.081 0.504
Nomenclature
C = specific heat, J/(kg "C) C1= heat capacity of cooling water, J/(kg "C) d = inside diameter of heated tube, m
F = condenser flow rate, kg/s k = thermal conductivity, W/(m "C)' L = length of heated tube, m Mv = rate of vapor generation, kg/s q = heat flux, W/m2 r, = radius of cavity, critical condition, m S = submergence, % T = temperature, "C Tl = inlet temperature of cooling water to condenser, "C T2= outlet temperature of cooling water from condenser, "C T, = condensate temperature in the condenser, "C AT = temperature difference (T, - TL), "C AT,,, = degree of subcooling (T, - TL),"C 2 = distance along the test section, m Creek Letters 6* = superheated layer thickness, m X = latent heat of vaporization, J/kg p =
density, kg/m3
1.1 = dynamic viscosity, N s/m2 Y = kinematic viscosity, m2/s
u =
surface tension, N/m
Subscripts B = boiling c = condenser exptl = experimental i = inlet condition L = liquid NB = nonboiling OB = onset boiling pred = predicted s = saturation v = vapor w = wall Dimensionless Groups Kaub = subcooling number (1 + (pL/pv)(AT,ub/T,)) PeB = Peclet number of boiling ((9/X)(pL/pv)(CL/kL)[o/(pL - Pv)11'2) Literature Cited Abdelmessih, A. H.; Hooper, F. C.; Nangia, S. Flow effecte on bubble growth and collapse in surface boiling. Int. J . Heat Mass Transfer 1972, 15, 115-125. Abdelmessih, A. H.; Yin, S. T.; Fakhri, A. Hysteresis effects and hydrodynamic oscillations in incipient boiling of Freon 11. Proceedings of International Meeting on Reactor Heat Transfer, Karlsruhe; 1973, pp 331-350. Agarwal, C. P. Heat Transfer Studies in a Vertical Tube of Closed Loop Thermoeiphon. Ph.D. Thesis in Chemical Engineering, University of Roorkee, Roorkee, India, 1980. Alam, S. S.; Varshney, B. 5.Pool Boiling of Liquid Mixtures. Proceedings of the 2nd National Heat Mass Transfer Conference; Indian Institute of Technology: Kanpur, 1973; p B-6.
Ali, H. Studies of Thermosiphon Reboiler. Ph.D. Thesis in Chemical Engineering, Aligarh Muslim University, Aligarh, 1988. Ali, H.; Alam, S. S. An Experimental Study for the Prediction of Boiling Incipience in a Vertical Tube Thermosiphon Reboiler. Proceedings of 42nd Annual Session of Indian Institute of Chemical Engineers. Trivandrum, India, Dec 15-18,1989; (2-93, pp 295-300. Bergles, A. E.; Rohsenow, W. M. The Determination of Forced Convection Surface-Boiling Heat Transfer. J. Heat Transfer, Trans. ASME Ser. C 1964,86, 365-372. Butterworth, D.; Shock, R. A. W. Flow Boiling. Proceedings of the 7th International Heat Transfer Conference, Washington, 1982; Vol. 1, pp 11-30. Clark, H. B.; Strenge, P. S.; Westwater, J. W. Active Sites for Nucleate Boiling. Chem. Eng. Prog. Symp. Ser. 1959, 55, 29. Corty, C.; Foust, A. S. Surface Variables in Nucleate Boiling. Chem. Eng. Prog. Symp. Ser. 1955, 51 (17), 1-12. Davis, E. J.; Anderson, G. H. The Incipience of Nucleate Boiling in Forced Convection Flow. AZChE J. 1966,12, 774-780. Fiore, A.; Ricque, R. Proprietes thermiques des Polyphenyles determination du debut de lebullition nuclee du terphenyl OMZ en convection forces. EVR. 1964, 2442. Frost, W.; Dzakowic, G. S. An extension of the method of predicting incipient boiling on commercially finished surfaces. Presented at the ASME-AIChE Heat Transfer Conference, Seattle, 1967; paper 67-HT-61. Golovchenko, 0. A.; Fokin V. S. Determination of Dimensions of the Convective Heat Transfer Zone in Evaporators with a Natural Circulation and Boiling of Solutions in Pipes. Teor. Osm. Khim. Tekhnol. 1979, 13 (6), 927. Griffith, P.; Wallis, J. The Role of Surface Conditions in Nucleate Boiling. Chem. Eng. Prog. Symp. Ser. 1960, 56 (30), 49-63. Han, C. Y.; Griffith, P. The Mechanism of Heat Transfer in Nucleate Pool Boiling-Part I. Bubble Initiation, Growth and Departure. Int. J. Heat Mass Transfer Conf. 1965,8,887-904. Harrison, W. B.; Levine, Z. Wetting Effects on Boiling Heat Transfer-The Copper-Stearic Acid System. AIChE-ASME Heat Transfer Conference,State College, PA, 1957; paper 57-HT-29. Hodgson, A. S. Hysteresis Effects in Surface Boiling of Water. J. Heat Transfer 1969,91, 160-162. Howell, J. R.; Siegel, R. Incipience, Growth and Detachment of Boiling Bubbles in Saturated Water from Artificial Nucleation Sites of known Geometry and Size. Proceedings of the 3rd International Heat Transfer Conference, Chicago, 1966; Vol. iv, pp 12-23. Hsu, Y. Y. On the Size Range of Active Nucleation Cavities on a Heating Surface. J. Heat Transfer, Trans. ASME. Ser. C 1962, 84, 207-216. Hsu, Y. Y. Graham, R. W. An Analytical and Experimental Study of the Thermal Boundary Layer and Ebullition Cycle in Nucleate Boiling. NASA, 1961, TN-D-594. Jemison, T. R.; Rivers, R. J.; Cole, R.: Incipient Vapor Nucleation of Methanol from an Artificial Site-Uniform Superheat. J. Heat Transfer 1982, 104, 567-568. Jiji, L. M.; Clark, J. A. Incipient Boiling in Forced Convection Channel Flow. Presented a t the ASME Winter Annual Meeting, New York, 1962; 62-WA-202. Lorentz, J. J.; Mikic, B. B.; Rohsenow, W. M. The Effect of Surface Conditions on Boiling Characteristics. Heat Transfer. Proceedings of 5th International Heat Transfer Conference,Tokyo, 1974; VOl. 4 Murphy, R. W.; Bergles, A. W. Subcooled Flow Boiling of Fluorocarbons-Hysteresis and Dissolved Gas Effects on Heat Transfer. Proceedings of the Heat Transfer and Fluid Mechanics Institute; Stanford University Press: Stanford, CA, 1972; pp 400-416. Saha, P.; Zuber, N. An Analytical Study of the Thermally Induced Two-phase Flow Instabilities including the effect of Thermal Non-equilibrium. Int. J. Heat Mass Transfer 1978,21,415-426. Sato, T.; Matsumura, H. On the Conditions of Incipient SubcooledBoiling and Forced Convection. Bull. JSME 1964, 7 (36), 292-298. Schultz, R. R.; Kasturirangan, S.; Cole, R. Experimental Studies of Incipient Vapor Nucleation. Can. J. Chem. Eng. 1975, 53, 408-4 13. Tong, L. S.Heat Transfer Mechanisms in Nucleate and Film Boiling. Nucl. Eng. Des. 1972, 21, 1-25. Unal, H. C. Maximum bubble diameter, maximum bubble-growth time and bubble growth rate during the subcooled nucleate flow boiling of water upto 1.77 MN/m*. Int. J.Heat Mass Transfer 1976, 19, 643-649.
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Unal, H. C. Void Fraction and Incipient Point of Boiling during the Subcooled Nucleate Flow Boiling of Water. Int. J. Heat Mass Transfer 1977,20,409-419. Yin, S . T.; Abdelmessih, A. H. Measurements of Liquid Superheat, Hysteresis Effects and Incipient Boiling Oscillations of Freon 11 in Forced Convection Vertical Flow. University of Toronto Mech. Eng. Tech. Pub. Ser. 1974, TP-7401. Yin, S. T.; Abdelmessih, A. H. Prediction of Incipient Flow Boiling
569
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from a Uniformyl Heat Surface. Solar and Nuclear Heat Transfer. AZChE Symp. Ser. 1977, 73 (la), 236-243. Zuber, N. Hydrodynamic Aspects of Boiling Heat Transfer. Ph.D. Thesis, University of California, Loe Angeles, 1959. Received for review August 25,1989 Revised manuscript received August 6 , 1990 Accepted September 20,1990
Partial Molar Volumes of DHA and EPA Esters in Supercritical Fluids K. Keat Liong, Neil R. Foster,* and S. L. Jimmy Yun School of Chemical Engineering and Industrial Chemistry, University of New South Wales, P.O.Box 1, Kensington, NSW, Australia 2033
The critical loci and partial molar volumes at infinite dilution for solutes such as the ethyl and methyl esters of cis-4,7,10,13,16,19-docosahexaenoic acid (DHA) and the methyl ester of cis-5,8,11,14,17eicosapentaenoic acid (EPA) in supercritical carbon dioxide were determined for a limited range of solute concentrations. The limits of miscibility of the esters in supercritical carbon dioxide were approximately 0.7 wt % . The results of the partial molar volume study exhibited large negative values in the highly compressible near-critical region. The Peng-Robinson and Soave-Redlich-Kwong equations of state were used to correlate the experimental data. These equations of state, although providing acceptable qualitative representations of the experimental data, were only semiquantitative in predictions of partial molar volumes.
Introduction The use of supercritical fluids (SCFs) as solvents has been attracting widespread interest in research and commercial applications. However, commercialization of processes involving SCFs has been hindered by the lack of the type of fundamental thermodynamic data in the critical region that is required for process design. Hence, much effort in research has recently been directed to obtaining such information under SCF conditions. The study of partial molar volumes of solutes at infinite dilution in the near-critical region is of considerable fundamental importance, as the data reflects the interactions occurring between the solute and the solvent. The concept of partial molar volumes is also of consequence when predicting phase behavior because it is actually the pressure derivative of the chemical potential (1).
This derivative has been shown to be a fundamental solution property (Chang et al., 1984). Only a small number of studies involving the measurement of partial molar volumes in the highly compressible near-critical region have been reported, probably due to the difficulty of obtaining derivative data (Benson et al., 1953;Ehrlich and Fariss, 1969;Abraham and Ehrlich, 1975;Eckert et al., 1983, 1986;Foster et al. 1989). In this paper the partial molar volumes of DHA and EPA esters at infinite dilution were determined. Although the systems were sufficiently dilute such that a linear relationship occurred between molar volume and concentration (Eckert et al., 1983),a finite amount of the solute was required. The solutes studied are constituents of marine lipids, which are a rich source of long-chain w-3 polyunsaturated fatty acids. Clinical studies have indicated that diets rich in these lipids result in reduced risks of coronary (Kromhout et al., 1985) and inflammatory diseases (Kremer et al., 1986) and inhibit the abnormal proliferation of cells (Davidson and Liebmn, 1986)and the
synthesis of cholesterol (Dyerberg, 1986). Among these fatty acids, DHA and EPA in particular are believed to have beneficial effects on human health (Dyerberg, 1986). DHA has 22 carbons in the chain with 6 double bonds whereas EPA has 20 carbons with 5 double bonds.
Theoretical Background The properties of pure components in a solution play an important role in thermodynamics. These partial molar properties, as they are known, represent molar values of such extensive quantities as enthalpy and entropy. Whereas the solubility of a solute in a SCF is a Gibbs energy effect, the partial molar volume corresponds to an entropy effect. For example, in an ideal solution, the partial molar volume of a component in solution is the same as the molar volume of the pure component at constant pressure and temperature. In reality, however, the partial molar volumes of components in solution are different from the molar volumes of the pure component at the same pressure and temperature. The partial molar volume of a solute at infinite dilution is defined by
Equation 2 is derived by taking the differentiated form of the Gibbs-Duhem equation at the limit x 2 -c 0 at constant pressure and temperature. The partial differential in (2) can be expressed in a pressure explicit form as shown in (3).
(3)
\avh This provides considerable benefit in modeling processes as accurate volumetric data as a function of composition
0888-5885/91/2630-0569$02.50/0 (6 1991 American Chemical Society
