Ind. Eng. Chem. Res. 1990,29, 1396-1404
1396
Vertical Thermosyphon Reboilers. Maximum Heat Flux and Separation Efficiency Ian A. Furzer Department of Chemical Engineering, University of Sydney, Sydney, New South Wales, Australia 2006
A simplified model of a vertical thermosyphon reboiler near the maximum heat flux shows the pressure balance t o be dominated by two-phase pressure drop, acceleration, and two-phase static pressure drop. These terms can be developed by using the Martinelli parameter t o provide the circulation rate of fluid in the tubes and the heat flux. The maximum heat flux is shown t o be a function of the reduced pressure and gives a global maxima when PR = 0.25 for a wide variety of pure components. The other variables that affect (Q/A)MAXare the vapor fraction a t the tube exit and the tube geometry. A list of 11important characteristics has been obtained to assist in reboiler design. A new reboiler separation efficiency is derived for binary systems, which provides a sound basis for reboiler testing. The boiling of liquids from a metal surface when natural convection dominates has been called pool boiling. A large number of experiments show an increase in the heat flux with temperature difference until a maximum heat flux is obtained. Thereafter, the thermal characteristics show a decline in the heat flux to a minimum and then a further rise when vapor blankets the surface. A photographic study to determine the heat-transfer mechanisms in the three regimes of nucleate, transition, and film boiling is given by Westwater (1956). The maximum heat flux was found to be dependent on the roughness of the surface, the number of nucleation sites, and the degree of agitation of the surrounding liquid. Cichelli and Bonilla (1945) conducted experiments with ethanol, propane, pentane, and benzene over wide pressure ranges and found a global maximum heat flux when the reduced pressure was near 0.35, although there is considerable scatter in the results. Global maximum heat fluxes of over 1MW/m2 were obtained. An important feature of their results is the low value of the maximum heat flux under vacuum conditions and also under conditions approaching the critical temperature and pressure. Thermosyphon reboilers (see Figure 1) with a vertical or horizontal configuration are widely used in the chemical processing industries. The maximum heat flux through the tube surface is an important design and control consideration. Lee et al. (19561, Johnson (1956),Shellene et al. (1968),and Volejnik (1979) obtained extensive thermal data on water, benzene, acetone, cyclohexane, propylene glycol, ethylbenzene, and butane. Maximum heat fluxes of 325 kW/m2 for water were obtained, but the maximum values for the organics was 170 kW/m2. Lee et al. (1956) attempted to correlate the results using tube length and physical properties including the interfacial tension (a) and the absolute temperature ( T I . Lee et al. (1956) note that the maximum heat flux occurred when there was a departure from smooth operation to surging operation and vapor locking was the cause of the problem. The very high heat fluxes obtained in pool boiling could not be observed in the thermosyphon reboiler, and different controlling mechanisms exist in these two different geometries. Lee et al. (1956) also noted low values of the maximum heat flux under vacuum conditions. Weak global maxima were observed near the maximum operating pressures, which corresponded to a reduced pressure of less than 0.2. Various mechanisms and models have been proposed for the maximum heat flux, but most of these studies apply to the important case of water boiling. One important model on a microsde considers the process as the transfer of vapor away from the heated surface in cylinders and the 0888-5885/90/2629-1396502.50/0
inflow of liquid feeding the heated surface. Helmholtz instabilities in the vapor cylinders lead to vapor blanking of the surface and a reduction in the heat flux. Equations from this model contain the interfacial tension (a). Numerous maximum heat flux equations exist, but those of Rohsenow and Griffith and Kutateladze are given by Tong (1965). A global maximum heat flux is obtained near PR = 0.3 and TR = 0.85. Sciance et al. (1967) studied the pool boiling of ethane, propane, and butane over a wide pressure range. Experimental global maximum heat fluxes were obtained near PR= 0.3 with values of 450 kW/m2. Cobb and Park (1969) boiled liquid nitrogen and liquid argon over a wide pressure range and found a global maximum at PR = 0.25 and TR = 0.85. Srinivasan and Krisna Murthy (1986) also obtained results at PR = 0.3 using a corresponding state model for a wide range of cryogenic liquids, halocarbons, water, and C02. Other models of the CHF are based on the breakdown of a liquid film a t the heated surface under convective conditions and the formation of a mist or dispersed phase. A complex mechanism of liquid droplet deposition on the surface and entrainment controls the heat-transfer processes. Hewitt (19781, Whalley et al. (1978), Kitto (1980), and Katto (1981) provide details of the model and the approach to complete vaporization. Kalinin et al. (1987) have reviewed the transition regime of boiling, and correlations for one limit of this regime correspond to the maximum heat flux condition. Katto (1985) provides a thorough and comprehensive review of CHF through a wide range of conditions. There are multiple flow regimes during boiling in reboilers. Liquid moves from a single phase to a two-phase condition and passes through a churn or slug flow regime and annular flow regime with high heat fluxes into a liquid-dispersed or mist flow regime. Martinelli and Nelson (1948) and Lockhart and Martinelli (1949) have used a separated flow model to calculate the two-phase pressure drop from a single-phase pressure drop with the vapor flowing alone in the tube and with a multiplier (@G2). The ratio of the single-phase pressure drops for liquid and vapor flowing alone in the tube provides a value for the Martinelli parameter (Xd.Correlations of @G and X, have been obtained from experimental data and show considerable scatter. Chisholm (1967) has proposed a simple relationship between these variables. Further analysis of annular two-phase flow is provided by Hewitt and Whalley ( 1980). Fair (1963a-c) used the Martinelli relationships for the two-phase pressure drop calculations and the best available heat-transfer correlations for the design of vertical ther0 1990 American Chemical Society
Ind. Eng. Chem. Res., Vol. 29, No. 7, 1990 1397
u N E
.
lo-
.
3
-
2i 7.5 h
B I
Figure 1. Vertical thermosyphon reboiler.
mosyphon reboilers. The pressure balance around the thermosyphon is critical in the design. Fair (1963a), using the data of Pope (1959),has correlated the transition from annular flow to mist flow with the Martineli parameter. The correlation is not dimensionless and may be influenced by the system geometry. The correlation indicates that the mass flux (C) in the tubes varies from 200 to 1000 kg/(m2s). Palen et al. (1982) confirm and extend the Fair correlation with G values varying from 70 to 700 kg/(m2 s). Operation in the mist flow regime offers the possibility of tube fouling and should be avoided. The experiments of Palen et al. (1982) were obtained with a valve in the thermosyphon line, whereby the added resistance could reduce the mass flux and force the thermosyphon to enter the mist flow regime. The design procedures, including the two-phase pressure drop and heat transfer, have been given for vertical and horizontal reboilers by Holland et al. (1974), Ludwig (1983), Fair and Klip (1983), and Smith (1986). Fair and Klip (1983) refer to a computer program written by Pauls, which was the basis of the earlier Fair (1963b) publication. Other programs are described by Sarma et al. (1973), Behan (1980, Zinemanas et al. (1984), and Yilmaz (1978a,b). There are numerous codes for water in pressurized water reactors that have similar thermalhydraulic characteristics. The notable programs are ATHOSP, CAFCA, and TRIGEVE as given by Wazzan et al. (1988). There are very few details provided of the thermosyphon reboiler codes, which give an overview of the reboiler characteristics. Of particular importance are the algorithms used when the heat flux approaches the maximum heat flux. There is a need for an improved understanding of the output from these programs and the development of simpler models based on this output that provide insight into the principal reboiler characteristics.
Simulation Models Figure 1 shows a vertical thermosyphon reboiler which can be considered as stage N of a distillatioil column. Liquid from the lowest plate in the column (N- 1)mixes with recycle liquid ( L R ) in a mixing junction. This stream is partly withdrawn as bottoms (B), and the remainder ( L I N ) enters the vertical riser where it is heated to its bubble-point temperature, followed by vapor generation (VN) and liquid recycle (LR). The recycle ratio L R / L N ; I is an important design variable. Unless a flowmeter is installed after the liquid mixing junction, the flow rate (LIN) is unknown, and this is the principal difficulty in the design. From L I N , the mass flux (G)and the velocity in the tubes could be obtained. From G, the single-phase
,
I
5
2.5
,
I
7.5
I
I
,
10
I
I
12.5
U(Expt) kw/m2 K Figure 2. Computer simulated results and experimental data from Lee et al. (1956).
201
0
10
I
I
20
30
40
Q/A Heat Flux kw/m2
Figure 3. Pressure drops in thermosyphon reboiler: Benzene at P = 100 kPa, TP = two-phase flow pressure drop, A = acceleration pressure drop, T P static = two-phase static pressure drop, exit = pressure drop in exit pipework, total = sum of all pressure drops.
Reynolds number can be obtained, and then the rate of heat transfer and the pressure drop readily follow. However, the transition plane from single- to two-phase flow has not been located, so the extent of the single-phase region is unknown. In addition, the total vessel pressure is constant at the entry to the liquid downcomer and oli the exit of the vertical riser. Programs that solve the thermal-hydraulic equations must close the iteration loops on all these considerations. Operating experiencewith the program by Behan (1981) shows excellent agreement between the calculated U values and the experimental data of Lee et al. (1956), as shown in Figure 2. However, numerical difficulties are encountered at high heat fluxes, which have not been previously reported. The origin of this difficulty is the problem of closing the pressure balances around the thermosyphon loop. Figure 3 shows the pressure drops of various components of the loop for the boiling of benzene at 100 kPa. Figure 3 shows the rising contribution due to the two-phase pressure drop, the pressure drop due to acceleration in the riser, and the two-phase static pressure loss with increases in the heat
1398 Ind. Eng. Chem. Res., Vol. 29, No. 7, 1990 0 75
i
j 0.65
.-
04
2 0
c 2 0.55
a
-co c)
045
.-C 0 e
k 0.35
I '
T w
TIN
C
T
.-
I
Figure 4. Thermodynamic path on a
2 V
P-T diagram.
0.25
2 / / I C
10
20
30
40
Q/A Heat Flux kw/m2
Figure 6. Effect of heat flux on phase transition point: various total pressures.
mk-
d'
'
0:
/
I
/
I
15
,
/
I
I
25
I
3
L Tube Length m Figure 5. Temperature profiles in a thermosyphon reboiler: various heat fluxes.
flux ( Q I A ) . The dominance of these three terms in the pressure balance strongly indicates that pressure drop considerations are more important than microscale phenomena in determining the maximum heat flux in thermosyphon reboilers. A simplified model of the pressure balance would be
Figure 7. Effect of heat flux on mass fraction vaporized: various total pressures.
= apTP + + (1) where APs is the static pressure available from the downcomer. It is useful to consider a single pure comonent in its passage through the reboiler. If the total pressure is Po at the top of the downcomer and the liquid is at its boiling point temperature (TIN),then this can be shown on the P-T diagram for the fluid in Figure 4. As the liquid proceeds down downcomer path a, the pressure rises to PIN, the entry pressure to the vertical riser. Under these conditions, the fluid is subcooled. On entry to the vertical riser as a single-phase liquid, it is heated on path b and the temperature rises to T- on the saturated vapor pressure line. The slope of path b depends on the single-liquidphase heat-transfer characteristics and the single-phase pressure drop. Vapor begins to be generated at the end of this path a t the transition plane between single- and two-phase flow. If the two-phase mixture is in equilibrium in the two-phase region, then path c returns the fluid to its original temperature (TIN)and pressure (Po). The principal thermal characteristics of the thermosyphon reboiler are a rising temperature in the single-liquid-phase region, a maximum temperature at the transition plane,
and a falling temperature in the two-phase region. There is a pinch temperature condition a t the transition plane. Figure 5 shows the computed temperature profiles for benzene at Po= 100 P a at various heat fluxes. With high heat fluxes, there are corresponding large temperature gradients in the single-liquid-phase region. Also at high heat fluxes, a large fraction of the tube length contains a heated two-phase mixture. This suppression of the transition plane toward the inlet of the vertical riser a t high heat fluxes is an important reboiler characteristic. Figure 6 shows the fraction of the tube length in the single-phase region at various heat fluxes. Similar characteristics are generated at column pressures of 150 and 200 kPa. A simplified model of this process is difficult, as large temperature gradients are required in this small single-phase region a t high heat fluxes. The mass fraction of vapor (xo) at the exit of the vertical riser increases with heat flux ( Q / A ) as shown on Figure 7 for benzene a t total pressures of 100,150, and 200 kPa. Figure 8 shows the calculated mass flux ( G ) in the tube and its decrease with the heat flux ( Q / A ) at various total pressures. This declining characteristic is an important feature of thermosyphon reboilers. It is tempting to project
Ind. Eng. Chem. Res., Vol. 29, NO. 7 , 1990 1399 From eq 4 and 5,
700
1-XPV x,, = -
x
PL
(7)
The Martinelli parameter goes to zero for complete vaporization. The two-phase pressure gradient can be obtained from the single-phase vapor-alone pressure gradient and the multiplier @G2:
It can be shown from Chisholm (1967) that @G2
=1
+ 20Xa + xt:
(9)
From eq 7,
300
o 10
20
30
40
Q/A Heat Flux kw/m2 Figure 8. G mass flux in tubes in a thermosyphon reboiler: various total pressures.
these curves to the heat flux when G = 0; however, this would require calculation in the mist flow regime. If G was reduced to near zero, then there is the possibility of hydraulic instabilities and reverse flow. At high heat fluxes, we have a situation where the two-phase region occupies most of the tube; the mass fraction vaporized is increasing and the mass flux in the tube is decreasing rapidly. It is in this region that numerical problems have been observed in the computer program.
Simplified Model at (&/A )MAX The basic assumptions in the simplified model are as follows. 1. Turbulent flow occurs in both phases in two-phase flow. 2. A linear relationship occurs between mass fraction vapor ( x ) and the length (1) along the tube in the two-phase region. 3. The average volume fraction vapor (a)in the tube is high at 0.9. 4. The pressure balance is dominated by the two-phase pressure drop, the acceleration, and the two-phase static pressure losses as given by eq 1. The pressure gradient due to liquid flow alone in the two-phase region is given by dl d If G is the mass flux of both liquid and gas, then G(1- x ) is the mass flux of the liquid:
G
= -(1 - x ) PL
Similarly, with the vapor phase alone,
-x = - xo LTP
From eq 11, we have
The overall two-phase pressure drop over the tube is given by
Let a=
2f -dpL - - -pLuL2
UL
When the vaporization is linear in the two-phase region of length LTp,
1 ::
1-20-+--
(3)
The pressure gradient due to acceleration is given by
The Martinelli parameter is given by
(21)
From eq 12, 20, and 21,
1400 Ind. Eng. Chem. Res., Vol. 29, No. 7, 1990 200,
When the average volume fraction vapor (a)in the twophase region is 0.9, the pressure difference between the single- and two-phase regions is given by (23) - f l ~ p s= P L ~ L T P-(pv/PL)O.g ~ From eq 1,
(
pLgL*p 1 - pL 0.9 = pv) ~
[axo2
+ bxo + c]2f-LTp + d
I
( ")
1- - x PL
PLPV(1 - PV/PL)
(0.9gL*p)1/2
+
[axo2 bx,
+ c,2@d + (1 -
(24) Pv
:)xol
I
025
I 0.5
I
0 75
Pr Reduced Pressure Figure 9. Maximum heat flux: benzene. Various mass fractions vaporized.
(25) Equation 25 is important, as it provides the mass flux (G ) in terms of the physical properties (pL and pv), the mass fraction vapor at the exit (x,), a , and the geometric term (LTP). The average heat flux over the full tube length (L) is given by
From eq 25,
I
L
[axo2+ bx,
+ c l 2LTP f7-
Let
I
I
I
0 2s
0.5
0 75
Pr Reduced Pressure
K = axo2+ bxo + c
(28)
Figure 10. Normalized maximum heat flux: benzene. Various ma98 fractions vaporized.
In SI units with g = 9.80 m/s2,
r
The dimensions L = 3.0 m and d = 0.025 m correspond to the Lee et al. (1956) equipment. As the length of the two-phase region was a large fraction of the total tube length, then a typical value is given by L*p = 0.95L
(29) Equation 29 provides a value for the heat flux in terms of the physical properties pL, pv, and AHv, the value of xo, and the geometric terms L, d , and LTp.
Maximum Heat Flux If the conditions at the maximum heat flux correspond to the dominance of the pressure drop terms due to twophase friction, acceleration, and two-phase static losses, the Q/A term from eq 29 can be considered to be the maximum heat flux. The maximum heat flux can be expressed as
The physical properties were calculated from the Physical Properties Data Service package, PPDS (1986).
(31)
Figure 9 shows a computer output for benzene for eq 30 for various values of xo. The values of (Q/A)MX are strongly dependent on the reduced pressure (PR,and show a global maximum near PR = 0.25. The magnitude of the global maximum of 100-200 kW/mz is similar to values obtained experimentally. If these results are normalized to PR = 0.25, then a single curve is obtained over the range of xo as shown in Figure 10. If xo is held constant at xo = 0.4 and the tube length varied from 1 to 7 m, then the normalized values of (Q/A)MAXare shown on Figure 11. The position of the maximum heat flux is somewhat removed from PR = 0.25 for shorter tube lengths. These results indicate higher fluxes with shorter tubes. The effect of changing the pure component is shown on Figure 12 for hydrocarbons from C3 to Cg. The higher when hydrocarbons provide the larger value of (Q/A)x = 0.4 and L = 3.0 m. The global maxima are near PR
Ind. Eng. Chem. Res., Vol. 29,No. 7, 1990 1401
c3
1 0
I
I
I
0.25
0.5
0.75
Y1
Pr Reduced Pressure Figure 11. Normalized heat flux: effect of tube length, benzene.
"0
0.25
0.5
0
I
I
0.5
0.25
I
0.75
I
Pr Reduced Pressure Figure 12. Normalized maximum heat flux: hydrocarbons. C3 = propane, CB= nonane.
I
m
1.2
Ol
0.75
Pr Reduced Pressure Figure 13. Normalized maximum heat fluxes: alcohols. C1 = methanol, C3 = propanol.
I
I
I
0.25
0.5
0.75
I
Pr Reduced Pressure Figure 14. Normalized maximum heat flux: water.
= 0.25. The normalized values provide little scatter in the moderate pressure regions. The effect of changing to alcohols from C1to C3is shown on Figure 13. Water is known to have a high maximum heat flux, and this is shown normalized in Figure 14. The complete set of data for benzene, hydrocarbons, alcohols, and water is normalized and shown in Figure 15. This result shows surprisingly little scatter for this wide variety of structurally different components,and the global maximum heat flux is near PR = 0.25. Palen et al. (1974)provide a correlation of the maximum heat flux by
(Q/A)Mm = 350(d2/L)0~36~~o~61P~0Ro.25(1 - PR) (32) The global maximum heat flux from this correlation occurs when
i
"0
(33) and
PR
=
0.33
(34)
0.25
0.5
0.75
t
I
Pr Reduced Pressure Figure 15. Generalized normalized maximum heat flux. All pure components.
Yilmaz (1987a,b) for horizontal reboilers provides a correlation whereby
1402 Ind. Eng. Chem. Res., Vol. 29, No. 7, 1990
(35)
A t the global maximum heat flux, P R = 0.28
60
(36)
I
There appears to be reasonable agreement on the value of the reduced pressure at the global maximum heat flux between the pressure balance model and the published correlations. There are very little published data on reboiler performance a t high pressure. Palan et al. (1974) provides data for pentane at high pressure and shows the significant decrease in the heat flux with increasing pressure when PRexceeds a value near 0.25.
Reboiler Characteristics The principal characteristics of a vertical thermosyphon reboiler near the maximum heat flux are summarized as follows. (1)The temperature of the fluid in and out of the reboiler are equal. (2) There is a temperature pinch condition near the tube entry. (3) There is a fluid maximum temperature at the temperature pinch condition. (4) There is a large temperature gradient in the single-phase region near the tube entry. (5) The fraction of the tube length in the single-phase region is small. (6) The mass flux ( G ) in the tubes decreases with increasing heat flux. (7) A numerical study of the pressure balance analysis shows a global maximum heat flux when the reduced pressure is near 0.25. (8) Low values of the heat flux are obtained under vacuum conditions. (9) Low values of the heat flux are obtained under conditions approaching the critical pressure. (10) The important physical properties that control the thermosyphon reboiler are pL, pv, and A H V . (11)Normalized maximum heat fluxes could be correlated together for a wide range of pure components including water, benzene, hydrocarbons, and alcohols. The extension of this analysis to binary component and multicomponent systems is complicated by the changes in the critical pressure for mixtures a t high pressure. Rowlinson and Swinton (1982) show the classification of binary mixtures at high pressures. The type I mixture can provide a critical locus which exceeds the critical pressure of the pure components. The calculated reduced pressures for the mixture may be considerably lower than values based on the pure components. Further experimental data on high-pressure mixtures are needed to verify if the global maximum heat flux is at PR= 0.25. Further complications in high-pressure equilibria are with type I1 systems when a second liquid phase is present. This may cause operational problems if the two liquid phases have widely different physical properties. Shah (1979) reports on the presence of water in a hydrocarbon system and the disturbances that can appear in the reboiler. Further experimental data are required for these two liquid systems, particularly a t high pressure. Reboiler Separation Efficiencies The inclusion of a reboiler in the standard PonchonSavarit method is given by Furzer (1986). The construction on an H-x diagram leads to the reboiler providing another ideal stage. A more accurate description of the process when liquid recycle is present is given here, showing the maximum separation improvement that could be obtained. Figure 1shows the reboiler with recycle. As there is no vapor entry into a reboiler, it is not possible to define a Murphree or thermodynamic vapor-phase efficiency. The streams leaving the reboiler ( VN and L R ) are considered in equilibrium and are shown as a tie line on Figure 16. The recycle stream ( L R ) mixes with the liquid (LN-1) from
0
0 2 1
06
04
08
10
X,Y
A
Figure 16. Thermosyphon reboiler on a H-x diagram. Separation efficiency.
the plate above in the mixing junction to give a stream ( L M ) . The mass and enthalpy balances are L R + LN-1 = L M (37) L R h R + LN-1hN-I = L M h M (38) or R -L LN-1
- hN-l hR - hM
- hM
(39)
R = LR/LN-1 (40) where R is the recycle ratio. The mixed stream (LM) is split into L I N and B, as shown on Figure 1. Streams L M , L I N , and B all have the same liquid enthalpy and can be located by eq 39 or the lever rule on Figure 16. This construction allows for the calculation of the composition and enthalpy of the liquid stream (LIN)entering the riser. It should be noted that the lowest composition in this reboiler system is L R and the bottoms stream (B) is withdrawn at a higher composition identical with L I N . Mass and enthalpy balances over the reboiler only, to include streams L I N , VN, and L R , are given by (41) LIN = VN + L R (42) L I N h I N = vNHN + L R h R - LIN(?IN where (?IN = Q R B / ~ N (43) or _ LR - HN - ( h I N + (?IN) (44) IN
HN - hR
The nonadiabatic process is represented on Figure 16 by moving the enthalpy of LINto hIN qINso that L R , the new L I N , and VN are on the tie line and the ratio L R I L I N can be obtained from eq 44 or by the lever rule. Overall mass and enthalpy balances to include streams LN-1, VN, and B give LN-1 = V N + B (45) LN-lhN-1 = V N H N B h B + Bqg (46) where q B = QRB/B (47) or
+
+
(48) The composition of B (xB) has the same composition as LIN and the bottom difference point (A") is located a distance qB below hg, the enthalpy of B,and Lm The lever
Ind. Eng. Chem. Res., Vol. 29, No. 7, 1990 1403 rule or eq 48 places A”, LN-1, and VN on a straight line, and the lever rule can be used directly on the figure to obtain LN-l/B. When the recycle ratio ( R ) is large, the construction moves point LIN toward LR, and the normal PonchonSavarit construction is valid. When R is small, near the maximum heat flux, the construction shown on Figure 16 must be used. In this case, the bottoms composition (xB) is at a high composition than stream LR, and the reboiler is not performing as an ideal stage. It is possible to define a reboiler efficiency as the change in liquid composition to the maximum change that would occur a t an infinite R: (49)
The lever rule can be used on Figure 16 to obtain Em and in the example gives E R B = 0.60.
Discussion Values of the maximum heat flux in pool boiling provide the global maximum of the CHF when the reduced pressure is from 0.25 to 0.30. Attempts to correlate the results using dimensionless analysis lead to the introduction of an interfacial tension term, eq 6. The magnitudes of the global maxima are considerably higher than the limited reported data in vertical thermosyphon reboilers. The simplified model proposed on a pressure balance analysis leads to a global maximum heat flux at PR= 0.25 for a wide range of pure components. The only physical properties required are pL,pv, and AH,. It should be noted that the interfacial term is absent. An important feature of the results is the low value of the maximum heat flux under vacuum conditions and under conditions approaching the critical pressure. The thermal-hydraulic model provides the temperature profile along the tube and shows that the transition plane between single- and two-phase flow is near the entry position to the tube. Large temperature gradients are required in the single-phase region so that the maximum temperture at the transition plane can be achieved. Heat-transfer rates in this region of the tube are not particularly favorable due to the accumulation of condensate. A large temperature difference between the steam and the single-phase fluid is necessary to achieve the required temperture gradients. There may be complicated stability problems originating from this phenomena. Smith (1974) notes the need to efficiently remove condensate and the presence of a temperture pinch on the tubes. The model also shows a decreasing mass flux (G) in the tubes as the heat flux is increased. There is obviously a limit to this decrease in G before unstable conditions are encountered. If there are disturbances affecting the reboiler from the liquid entry or from the steam supply, then with small values of G and the close approach of the transition plane to the riser entry, there is the possibility of many unstable conditions. One such condition might force the transition plane to move rapidly out of the tube, leading to momentarily backflow, surging, and periodic flow oscillations. Experiments on a reboiler with special attention to the tube entry may provide some valuable insight into these instability problems. Nomenclature a = parameter b = parameter c = parameter CHF = critical heat flux, W/m2 d = diameter of tube, m
f = friction factor g = gravitational acceleration, mz/s G = mass flux in tube, kg/(m2 s) A H V = latent heat of vaporization, J / k g K = parameter 1 = length along the tube, m L = liquid flow rate, kg/s LTp = length of two-phase region, m PA = pressure drop acceleration, Pa P s = pressure drop single-phase static, Pa hpTp= pressure drop two-phase friction, Pa P T p S = pressure drop two-phase static, Pa Po = pressure in reboiler, Pa P = pressure, Pa PR= reduced pressure Q / A = heat flux, W/m2
T = temperature, K TR = reduced temperature x = mass fraction vapor xo = mass fraction vapor at exit X,, = Martinelli parameter Greek Symbols u = interfacial tension, J/m2 pL = liquid density, kg/m3 pv = vapor density, kg/m3 pm = mean density, kg/m3 $G = gas-phase multiplier
Literature Cited Behan, T. J. The Design of Vertical Thermosyphon Reboilers. Undergrad. Thesis, University of Sydney, Australia, 1981. Chisholm, D. A Theoretical Basis for the Lockhart-Martinelli Correlation for Two-Phase Flow. Min. Tech. NEL Rep. 1967,No. 310. Cichelli, M. T.; Bonilla, C. F. Heat Transfer to Liquids Boiling under Pressure. AZChE J. 1945,41, 755. Cobb, C. B.; Park, E. L. Nucleate Boiling: A Maximum Heat Flux Correlation for Corresponding States Liquids. Chem. Eng. Prog., Symp. Ser. 1969,65 (92), 188. Fair, J. R. Vaporizer and Reboiler Design Part I. Chem. Eng. 1963a, 70 (14), 119. Fair, J. R. Vaporizer and Reboiler Design Part 11. Chem. Eng. 1963b,70 (16), 101. Fair, J. R. Design Steam Distillation Reboilers. Hydrocarbon Process. 1963c,42 (2), 159. Fair, J. R.; Klip, A. Thermal Design of Horizontal Reboilers. Chem. Eng. Prog. 1983,79 (3), 86. Furzer, I. A. Distillation for University Students; Furzer, I. A., Publisher; Dept. Chem. Eng., University of Sydney: Australia, 1986. Hewitt, G. F. Critical Heat Flux in Flow Boiling. Proc. Int. Heat Trans. Conf., 6th 1978,6 , 143. Hewitt, G. F.; Whallev. P. B. Annular Two-Phase Flow: Peraamon: New York, 1980. Holland, F. A.; Moores, R. M.; Watson, F. A.; Wilkinson, J. K. Heat Transfer:Heinemann Books: New York. 1974: D 494. Johnson,’ A.’ E. Circulation Rates and Overall Temperture Driving Forces in a Vertical Thermosyphon Reboiler. Chem. Eng. Prog., Symp. Ser. 1956,52 (18), 37. Kalinin, E. K.; Berlin, I. I.; Kostiouk, V. V. Transition Boiling Heat Transfer. Ado. Heat Transfer 1987,18, 241. Katto, Y. On the Relation between Critical Heat Flux and Outlet Flow Pattern of Forced Convection Boiling in Uniformly Heated Vertical Tubes. Int. J. Heat Mass Transfer 1981,24, 541. Katto, Y. Critical Heat Flux. Adv. Heat Transfer 1985,17, 2. Kitto, J. B., Jr. Critical Heat Flux and the Limiting Quality Phenomena. AlChE Symp. Ser. 1980,76 (199),57. Lee, D. C.; Dorsey, J. W.; Moore, G. Z.; Mayfield, F. D. Design Data for Thermosyphon Reboilers. Chem. Eng. Prog. 1956,52(4),160. Lockhart, R. W.; Martinelli, R. C. Proposed Correlation of Data for Isothermal Two-Phase, Two-Component Flow in Pipes. Chem. Eng. Bog. 1949,45 (11, 39. Ludwig, E. I. Applied Process Design, 2nd ed.; Gulf Houston, TX, 1983; Vol. 3. Martinelli, R. C.; Nelson, D. B. Prediction of Pressure Drop during Forced Circulation Boiling of Water. Trans. ASME 1948,70,695.
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Smith, R. A. Vaporisers: Selection, Design and Operation; Longman: New York, 1986. Srinivasan, K.; Krisna Murthy, M. V. Determination of the BulkSaturated Liquid Condition for Maximum Heat Fluxes a t Boiling Crises. Int. J. Heat Mass Transfer 1986,29 (12), 1963. Tong, L. S. Boiling Heat Transfer and Two-Phase Flow; Wiley: New York, 1965. Volejnik, M. An Investigation of Industrial Reboilers. Int. Chem. Eng. 1979, 19 (4), 689. Wazzan, A. R.; Procaccia, H.; David, J.; Fromal, A.; Pitner, P. Thermal-Hydraulic Characteristics of Presswised Water Reactors during Commercial Operation. Nucl. Eng. Des. 1988, 105, 285. Westwater, J. W. Boiling of Liquids. Adv. Chem. Eng. 1956, 1, 2. Whalley, P. B.; Hutchinson, P.; James, P. W. The Calculation of Critical Heat Flux in Complex Situations using an Annular Flow Model. Proc. Inst. Heat Transfer Conf., 6th, 1978,5, 65. Yilmaz, S. B. Horizontal Shellside Thermosyphon Reboilers. AIChE Symp. Ser. 1987,83 (257), 40; Chem. Eng. Bog. 1987,83 (ll),64. Zinemanas, D.; Hasson, D.; Kehat, E. Simulation of Heat Exchangers with Change of Phase. Comput. Chem. Eng. 1984, 8 (6), 367.
Palen, J. W.; Shih, C. C.; Yarden, A.; Taborek, J. Performance Limitations in a Large Scale Thermosyphon Reboiler. Ind. Heat Transfer Conf., 5th, 1974, 204. Palen, J. W.; Shih, C. C.; Taborek, J. Mist Flow in Thermosyphon Reboilers. Chem. Eng. Prog. 1982, 78 (71, 59. Pope, B. J. An Investigation of Natural Circulation Tube Reboiler Capacity and Performance. Ph.D. Thesis, University of Washington, Pullman, 1959. PPDS Version 10 (1986), The Inst. Chem. Eng., 165/171 Railway Terrace, Rugby CV21 3HQ, England. Rowlinson, J. S.; Swinton, F. L. Liquids and Liquid Mixtures, 3rd ed.; Butterworth: New York, 1982. Sarma, N. V.; Reddy, P. J.; Murti, P. S. A Computer Design Method for Vertical Thermosyphon Reboilers. Ind. Eng. Chem. Process Des. Deu. 1973, 12 (3), 278. Sciance, C. T.; Clover, C. P.; Sliepcevich, C. M. Nucleate Pool Boiling and Burmout of Liquefied Hydrocarbon Gases. Chem. Eng. Prog. Symp. Ser. 1967, 109 (77), 63. Shah, G. C. Troubleshooting- Reboiler Systems. Chem. Enp. - Prog. 1979, 75 (71, 53. Shellene, K. R.; Sternling, C. N.; Church, D. M.; Snyder, N. H. ExDerimental Studvof a Vertical Thermoswhon Reboiler. Chem. Eng. Prog. Symp. ker. 1968,64 (82), 102' Smith, J. V. Improving the Performance of Vertical Thermosyphon Reboilers. Chem. Eng. Prog. 1974, 70 (71, 68.
Received for review May 17, 1989 Revised manuscript received October 24, 1989 Accepted November 14, 1989
GENERALRESEARCH Generalized Viscosity Behavior of Fluids over the Complete Gaseous and Liquid States Huen Lee' and George Thodos* Department of Chemical Engineering, Northwestern University, Euanston, Illinois 60208-3120
Viscosity measurements reported in the literature have been used for the development of a generalized expression capable of predicting this transport property for all state conditions. These include the dilute and dense gaseous states and the saturated and compressed liquid regions. The present development shows that the excess viscosity, p - p*, can be predicted in a generalized manner from the relationship, 105(p - p * ) y = [exp(bg" dgK)]- 1, where b, d , a , and K are universal constants. The complex nature of the parameter g includes, besides density and temperature, the influence of the expansion characteristics of the substance, in the course of freezing, a t the triple point. The viscosity parameter, y = u ~ ~ ~ / ~ / is M unique ~ / ~ toT a~substance ~ / ~ , and for its definition requires triple-point values. Comparison between experimental and predicted viscosities, covering all fluid-state conditions and including the saturated and compressed liquid regions, yields an average absolute deviation of 3.21% (1563 points) for 24 substances examined.
+
Our present knowledge for the satisfactory prediction of transport properties continues to be limited to the dilute and moderately dense gaseous states of substances. Attempts to extend our background to include gases at high pressures and liquids existing at temperatures below their normal boiling point and for conditions approaching their respective triple points have not yet been properly resolved to permit the formulation of a unified approach for the prediction of viscosity. This difficulty stems largely from the complex nature of liquids associated with this state of aggregation and particularly as temperatures in the proximity of the freezing curve are approached. The
* Author t o whom
correspondence should be addressed. Present address: Korea Advanced Institute of Science and Technology, Seoul, Korea. 0888-5885/90/2629-1404$02.50/0
correlation of the viscosity in a generalized manner in this region has not yet been properly resolved, and consequently, the prediction of this transport property continues to prove inadequate over the complete fluid state. The difficulty for treating, in a generalized manner, the complete liquid region is not unexpected because of the complex nature associated with the aggregation of the liquid state existing below the normal boiling point and particularly as the freezing state is approached. While, on one hand, the kinetic theory of gases offers a direct approach for the estimation of properties of substances in the gaseous state, the lattice theory, on the other hand, provides the theoretical background needed for treating the solid state. The liquid state bridges these two extremes. So far, this bridging has proven to be quite formidable. Nonetheless, the proper interpretation of this
62 1990 American Chemical Society
