I n d . Eng. Chem. Res. 1987,26, 107-112
coming liquid, leaving no energy left to boil off vapor. The values of the heat given up by the condensing steam (AH*V,) and the sensible heat demand ( ~ N L N- hN+&N+1) of the laet stage are shown in Table VI. One can see a gradual trend of decreasing available heat supply as the stages increase. The sensible head demand in the last stage also increases as the stages increase, because hN+lLN+l (the feed enthalpy flow) is constant and small relative to hNLN. The quantity hN is constant, because T N and X N are specified. As the stages increase the liquid leaving the last stage (LN)increases also. Thus, sensible heat demand in the last stage must increase with the number of stages. When the heat supply drops below the sensible heat demand, as in stage ll, the vapor flow (VN)becomes negative. Because the heat balance is forced to agree in the equation-solving procedure, VNmust become negative when not enough heat is available to meet the sensible heat demand. The boiling point rise failure is illustrated back in Table V, a few lines below the sensible heat demand failure. After a three-stage series, the area per stage can be seen to increase as the number of stages increases, because the temperature driving force available for heat transfer is shrinking (due to the increasing sum of the boiling point rises), and the overall heat-transfer coefficients are not changing much from stage to adjacent stage or case to case. Thus, the area must increase to maintain the heat transfer. When the temperature driving force for heat transfer goes negative as in a boiling point rise failure, the area must also become negative to maintain the sign on the heat transferred (to satisfy the heat balance equations). Thus, the area becomes negative in Table V when the AT
107
available for heat transfer becomes negative.
Conclusions 1. The LJK method has very favorable convergence and stability characteristics relative to other types of computer methods for solving the evaporator series problem, including generalized nonlinear methods. 2. The LJK method shows remarkable insensitivity to starting values, where nonlinear methods fail to converge. 3. Physical limitations on N-effect evaporator series exist from two causes: where the sum of the boiling point rises exceeds the overall temperature driving force for heat transfer (a physically imposed boundary condition) and where the incoming steam to a stage cannot supply the heat required to raise the temperature of liquid entering that stage to its boiling point. 4. In the multiple-effect evaporator system, an arbitrarily large number of stages cannot exist for backwardfeed systems or for forward-feed systems with a boiling point rise. Literature Cited ZMSL Library Reference Manual, 9.2 ed.: IMSL: Houston, 1984; 4 Vols., Chapter 'Z. Lambert, R. N.; Joye, D. D.; Koko, F. W. Znd. Eng. Chem. Process Des. Dev., preceding paper in this issue. McCabe, W. L.; Smith, J. C.; Harriott, P. Unit Operations of Chemical Engineering, 4th ed.; McGraw-Hill: New York, 1985. Seader, J. D. Chem. Eng. Educ. 1985,19(2),88-103. Received for review February 26, 1986 Accepted J u n e 30, 1986
Two Models of Vapor Pressure along the Saturation Curve J. David Chase Celanese Chemical Company, Inc., Technical Center, Corpus Christi, Texas 78469
Linear correlations of vapor pressure data can be quite precise and yet violate the experimentally observed behavior of the saturation curve. Thus, both factors should be considered and balanced. Observed behavior of the saturation curve has been previously generalized and may be expressed by a number of quantitative parameters. Three of these were used by Ambrose et al. for the model developed at the U.K. National Physical Laboratory (NPL). An alternate model, developed in Germany by Plank and Riedel, uses a single parameter that is unique to that model. These two alternate models were compared for oxygenated organics; they are qualitatively equivalent for the upper range of the saturation curve. Riedel's development may be used to predict point values for all of the existing saturation curve parameters that apply above the normal boiling point. A regular progression of parameter values within each homologous series of compounds results. However, the quantitative correctness of the predicted values remains to be proven. For vapor pressure data correlation, the N P L constrained correlation approach appears to be a superior strategy, by comparison to simple linear fitting of experimental data, for producing accurate (both statistically and phenomenologically) wide-range correlations. The practical quantitative modeling of the vapor pressure (t-P) saturation curve, which began about two generations ago, may now be considered reasonably complete. Along the way, there have been a number of high points. (1)In 1950, Thodos detailed experimental confirmation of the general definition of the saturation curve (shallow "S"on a In P - 1/T plot). (2) In 1954, Waring stated general requirements for the analytical representation of the saturation curve, based on (AHlAZ) - T plot considerations. 0888-5885/87/2626-0l07$01.50/0
(3) In 1974 and 1976, King detailed advantages of using thermal data (especially at low temperatures) when evaluating the coefficients of t-P correlations. (4) In 1975-1978, Ambrose and his U.K. National Physical Laboratory (NPL) co-workers further defined the saturation curve between T,= 0.7 and 1.0. (5) In 1978, Hicks published strategy and a computer program for constrained correlation of t-P data. (6) In 1983, McGarry correlates and amplifies constraint ranges. 0 1987 American Chemical Society
108 Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987
The result of the NPL work may be thought of as the English model, with the NPL Constrained Correlation strategy as the prime example of its practical application. The NPL model uses a Wagner equation form for analytical representation: In P = In P,
+ (T,/T)[AT + B
P
+ CT3 + D P ]
(1)
where
T = (1- T / T , ) Three constraints are applied during the correlation of data. (1)The derived (AH/AZ) - T curve has a minimum, Tmr, within a specified range of TI values (Waring’s criterion). This has been expressed alternately as the requirement that there be an inflection point (at Tior Ti) in the In P - 1/T curve; Tmrand Til are one in the same. (2) In (P/P3Tr=o,9,-a deviation constraint (Ambrose’s criterion)-falls within a specified range (at TI = 0.95). In P‘is defined by a straight line on a In P - 1 / T plot, where P’ = P a t TI = 0.7 and 1.0. (3) The derived AH/U values approximate AHv(latent heat of vaporization) a t low reduced temperatures. The first two constraints apply to the upper end of the t-P curve, Le., between the normal boiling point (n-bp, Tb, or Tb) and the critical point (T,);the latter applies from the triple point to slightly below T b (typically, to T I = 0.6). Development of another model began in Germany about 1948 and reached its zenith in 1954 (Plank and Riedel, 1948, 1949; Riedel, 1954). This model was a brilliant application of the Principle of Corresponding States, based on a single criterion (the Riedel criterion) deduced from ”a curves” ( a vs. T I ) ,where a = d(ln PI)/d(ln T I ) . The Riedel criterion (da/dT, = 0 at T, = 1.0) thus related vapor pressure for any compound to a single factor. The Riedel model uses the Plank-Riedel equation form In PI = A -B/TI
+ C l n T, + DT,6
( 2)
for the analytical representation of the t-P curve. The coefficients A , B, C, and D may be estimated from the value of a, (Reid et al., 1977). Of the three criteria that apply above Tb,Riedel’s and Waring’s have enjoyed the most success. In particular, Riedel’s criterion has been used in most of the vapor pressure prediction techniques developed in the last 20 years.
t - P Data Correlation Qualitatively, it would seem that the constrained correlation strategy should be superior to linear correlation of t-P data, if one is to achieve state of the art; correlations that do not match the observed behavior of the saturation curve might be particularly misleading when derived quantities are desired (e.g., dP/dT values for estimating latent heat of evaporation). Alternately, one might choose to determine the coefficients of the Plank-Riedel equation from a,. This, too, may have its drawbacks. (1) The Riedel development has not been proven equivalent, either qualitatively or quantitatively, to the other two upper saturation curve criteria; it is only assumed to be. (2) As a prediction technique, the Riedel procedure is known to give poor results below Tb,with increasing error as the temperature decreases (Reid et al., 1977; Gupte et al., 1982). (3) No controls are provided for the lower part of the saturation curve.
0.5 0.55
0.60
0.65
0.70
0.75
Reduced Temperature at n-bp,Tb,
Figure 1. Critical properties of oxygenated organics (Ambrose, 1980): oxygenated organics (except alcohols), (-) alcohols (except methanol); ( 0 )alcohols,).( heterocyclics, (A) ethers, ( 0 ) acids, (0) esters, (0)phenols, (0)ketones, and (A)aromatic ethers. (-e)
In either case, within the context of this study, correlation for the entire lower range of the saturation curve (i.e., to the triple point) is not a major concern for two reasons: (1)the typical lower limit of experimental vapor pressure data (1-10 kPa) is usually adequate for engineering applications; (2) precise vapor pressure data at lower pressures are often unavailable or inaccurate (Ambrose and Davies, 1980). Comparison of Criteria The equivalency, or not, of the Riedel criterion to the other two criteria (Waring and Ambrose criteria) for the upper range of the saturation curve is an interesting question. That is, does it “naturally” express the observed phenomenology of the other two? When the criteria of Waring and of Ambrose are related to their expression via the Plank-Riedel equation, both become functions of cy, 3.52a, a, - 13.229
I””
In (P/P1T,=o.95 = 0.0058334~~~ - 0.050194
(3)
(4)
and may be predicted. However, to draw conclusions, these predictions must be related to available evidence. Such is typically a function of Tb,not a, (McGarry, 1983). In addition, we must further relate Tb,Tb,,and P, to find QC*
These latter quantities may be generalized, in this study for oxygenated organics, as shown in Figure 1. As demonstrated earlier by both Ambrose and McGarry, and shown again here, alcohols are a special class of oxygenated organics. If we take In P, (in MPa) = 8.6910 - 10.814Tb, (5) as a general representation of all oxygenated organics except alcohols, and for alcohols (except methanol) (6) In P, (in MPa) = 17.391 - 22.900Tbr
Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987 109
9.5
0.92
E‘ 0.90
-
9 -
I-
$
.-
c
I
0.88
8.5
0
f
L
0
+
e!
c
0.86
$ -
a
e
e
.LL
a
E b
8
U 01
0.84
75
0.82
7
Q U
B a
o’80 0.78
A
6
6.5
7
7.5
8
8.5
6.5
6
9.5
9
4
Pl/ 2
I
0
2
-2
II
c’
0.70
0.75
0.80
Reduced Temperature at the n-bp, Tb,
Figure 2. Riedel model predictions for the minimum in the (AH/AZ) - T curve: (a)parameter ranges from McGarry (1983); (0) parameter ranges from Ambrose et al. (1975).
rT)
0.65
0.60
Riedel Factor,ac
-4
c
+ -6
$
Figure 4. Riedel factors for oxygenated organics
We may conclude from these comparisons that Reidel’s criterion is at least qualitatively representative of the other two criteria for most oxygenated organics.
Homologous Series Criteria The preceeding crude analysis suggests that there may be a definate progression of predicted Tmrand In (PI P’)Tr=o.95 values for the various homologous series of oxygenated organics. Thus, even though experimental data may be insufficient to define the suspected relationships, predicted values could serve as a guideline for expected parameter values. For this purpose, the following additional critical point correlations were developed from Figure 1:
C
1 -8
heterocyclics and ethers
h-J
0,
In P, (in MPa) = 8.6360 - ll.llOTb,
-10
(7)
ketones and esters
-12
In P, (in MPa) = 8.6700 - ~ ~ . o o o T b ~ (8) -14
phenols 6
6.5
7
7.5
8
8.5
9
9.5
Riedel Factor , a,
Figure 3. Riedel model predictions for In (P/P? at T,= 0.95: ( 8 ) parameter ranges from McGarry (1983); (0) parameter ranges from Ambrose et al. (1975).
we may then calculate the Riedel factors for each group of compounds. Tmrand In (P/P3Tr=o.95 values predicted via the Riedel procedure (eq 3 and 4) are compared to other evidence in Figures 2 and 3, respectively. For the alcohols, the observed parameter ranges were as follows: Tm 10$n
(P/P’)T,=O.SSI
Ambrose et al., 1975
McGarry, 1983
0.87-0.97 -3-14
0.90-0.98 7-40
Thus, the predicted parameter values match the evidence of Ambrose et al. better than they do those of McGarry.
In P, (in MPa) = 8.9167 - 10.930Tbr
(9)
These relationships were used to predict .a shown in Figure 4, and may be used with Figures 2 and 3 to obtain a t least qualitatively correct point values of Tm,and In (P/P? for various oxygenated organics. Reasonable limits may then be established around these point values. The value of Figure 4 is that the predicted regular progression of a, within any homologous series is easily appreciated. One possible implication is that other parameters (such as the accentric factor, w ) , as well as sets of vapor pressure correlation coefficients, should also show such regularity. If the predicted parameter values are plotted directly as a function of Tb,as shown in Figure 5 , a similar (if more difficult to follow) regularity is shown.
Qualification of t - P Correlations Details of qualification criteria for vapor pressure correlations have been covered earlier (Chase, 1984). Briefly,
110 Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987
LQ
0
2 /I
I -
+
-2
h R
-‘
+
b
C
v
C -6
9
1
I
L
X
0.4
-
-8
0.1
0.9
1.0
Figure 6. (AH/ AZ)for water as a function of reduced temperature (Waring, 1954).
a
-.
0.7
0.6
t.
4
3-10
0.1
a
J
a
- 12
.. 24 0
320
400
480
Normal Boiling Point, Tb/K
Figure 5. Riedel model predicted parameters for oxygenated organics: (-.) alcohols; ( 0 )alcohols,).( heterocyclics, (A)ethers, ( 0 ) acids, (0) esters, (0) phenols, ( 0 )ketones, and (A)aromatic ethers.
the depth of a specific qualification should be consistent with both the intended usage of the correlation and the precision of the data. Thus, in many cases, correlation to the Antoine or other similar equation form is both appropriate and all that is justified. However, if the goal is to produce qualified wide-range correlations, then all qualification criteria should ideally be satisfied. In addition to those discussed above, these include the following: (1) screening criteria, (a) the “Sign rule” (Waring, 1954) and (b) the ”Line rule” (Chase, 1984); (2) detailed criteria, (a) calculated normal boiling point deviation (ATb 6 h0.5
K) .
The Line rule may also be used to form judgments on individual t-P data points and to define valid t-P data fields within which the critical point (TC,P,) must lie. A modified form of the Line rule is used in Germany for wide-range vapor pressure correlations from scant data (Schonberg, 1985). In that case, a straight line is connected, on a In P - 1/T plot, between 10 mmHgA (1.3 P a ) and 760 mmHgA (101.325 kPa). Then, the correlation must lie above the modified Line rule line between the anchor points. Otherwise, the correlation must lie below the modified Line rule line. Basically, there are three ways to produce fully qualified wide-range vapor pressure correlations: (1) linear correlation of precise wide-range t-P data, (2) linear correlation of limited experimental t-P data combined with supplemental (predicted) data, and (3) constrained correlation. The first and third alternates are illustrated and compared in the following sections. Examples of Vapor Pressure Correlation For these examples, it was convenient to use the nonreduced form of the Plank-Riedel equation In P = A
+ B/T + Cln T + D F
(10)
in addition to a Wagner form cited earlier (eq 1). Methanol. The first example is for methanol, which is typical of compounds for which there are good wide-
Temperature
Figure 7. Methanol (case 2) AH/AZ correlation.
range data. Three data sets (Hirata and Suda, 1967; Ambrose et al., 1975; Gibbard and Creek, 1974) were correlated; the results are summarized in Table I. Predicted constraint parameters for methanol, based on LY,estimated from the normal boiling point, Tb = 337.664 K (Gibbard and Creek, 1974), and T , = 512.64 K and P, = 8.092 MPa (Ambrose, 1980) were as follows: Tmr= 0.888 In (P/P’)T,=0,95 = -0.0009 As mentioned earlier, the intent is to emphasize the alternate correlations from the lower data range and up and not between the lower range of the experimental data and the triple point. Thus, none of the Table I correlations produce a very accurate calculated triple point pressure, compared to an experimental value of about 1.83 X kPa (Miller, 1964). As typically viewed (i.e., based on just correlation precision statistics), linear correlation would be judged adequate for methanol, and the two linear correlations (cases 1 and 2) would be considered equivalent. Otherwise, the predicted constraint criteria (ATb, T,, and In (P/P’)T=o.95) are reasonably well matched, except for the calcuiated values, which are somewhat high (-0.005 In (P/P’)Tr=o,95 and -0.006 for cases 1 and 2, respectively, vs. a predicted value of -0.0009). There is also a nonobvious shortcoming to the case 2 correlation; its (AH/AZ) - T curve violates observed behavior. Figure 6 (Waring, 1954), for water, illustrates
Ind. Eng. Chem. Res. Vol. 26, No. 1, 1987 111 Table I. ComDarison of Some Methanol Vapor Pressure Correlations case ~~
~
correlation type eq formn deviation constraints usedd ATb, K In ( P / P ? T ~ - o ~ ~
1 linear NRR 11.9*
2 same W 11.7b
0.028 -0.005 0.88 8080 1.74
0.031 -0.006 0.88 8092 2.38
3A' constrained NRR 0.0066' G -0.051 -0.002 0.85 8162 1.47
3Bf same NRR 0.045lC P -0.532 -0.001 0.90 8075 0.42
4 same W 0.0063' P 0.038 -0.002 0.89 8092 1.32
NRR = nonreduced Plank-Riedel; W = Wagner. Root-mean-square deviation in pressure. Root-mean-square deviation in In P. G = general constraint ranges per Hicks (1978): In (P/P? = -0,002 to -0.010; T,, = 0.8-0.9. P = constraint ranges based on Riedel predictions: In (Pip') = -0.002-0.002; Tmr= 0.86-0.90. e First-guess coefficients were based on the normal boiling point plus the three NPL constraints. fFirst-guess coefficients were based on the Riedel factor (estimated from the normal boiling point; cy, = 8.5).
Table 11. Comparison of Some Ethyl Acetate Vapor Pressure Correlations case 1 2 3Ae 3B' correlation type linear same constrained same eq form" NRR W NRR same deviation 0.287b 0.331b 0.0417c 0.0645' constraints usedd G P ATb, K 0.19 0.20 -0.33 -0.06 In (P/P?T,=0.95 0.004 -0.009 -0.004 -0.035 0.92 0.86 Tmr 0.96 0.87 3830 3854 (Pc)calcdr kPa 3625 3848 1.85 1.20 (Pt)caled, kPa x lo3 1.87 1.06
4Af same same 0.0496'
4Bf same same 0.0496'
5A same W 0.0264'
G
P
G
-0.82 -0.007 0.87 3826 1.86
-0.83 -0.007 0.87 3826 1.86
0.40 .-0.002 0.88 3830 1.24
5B same same 0.0253' P 0.30 -0.004 0.88 3830 1.61
NRR = nonreduced Plank-Riedel (eq 10); W = Wagner (eq 1). bRoot-mean-square deviation in pressure. CRoot-mean-squaredeviation in In P. d G = general constraint ranges per Hicks (1978); In (P/P') = -0.002 to -0.010; Tm,= 0.8-0.9. P = constraint ranges based on Riedel predictions (a,= 7.56); In (P/P') = -0.004 to -0.008; Tmr= 0.86-0.88. eFirst-guess coefficients were based on the normal boiling point plus the three NPL constraints. fFirst-guess coefficients were based on the normal Riedel factor (estimated from the normal boiling; ( a , = 7.56).
accepted phenomenology. Figure 7 derived from the case 2 correlation has, by comparison, an unrealistic inflection in the lower temperature range. Cases 3 and 4 for methanol illustrate the fact that there will usually be some degree of degradation of correlation error statistics with constrained correlation (the rootmean-square deviation in In P is about 0.006 for unconstrained correlation with NPL-based software). Thus, phenomenological accuracy must be balanced against the precision of the correlation. Perhaps the best working viewpoint here is the concept of a maximum acceptable root-mean deviation (MAD). If one accepts a normal boiling point deviation (ATb)of f0.5 K as minimally acceptable, then a MAD of about 0.04 (in In P) seems appropriate (case 3B). For the nonreduced Riedel equation (lo), there are two alternate ways of estimating the first guess at the equation coefficients for constrained correlation: (1)the NPL approach, using a matrix of the three constraints (see earlier discussion) plus the first t-P data point and (2) coefficient estimation from the Riedel factor (Reid et al., 1977). In this comparison, the NPL approach to the first guess of the correlation coefficients (case 3A) produced a better correlation than the Riedel factor approach (case 3B). Other experience has shown that the opposite may sometimes be the outcome. Selection of the best constrained correlation, between case 3A and case 4, would depend upon one's emphasis of the various qualification criteria. Overall, correlation to a Wagner equation form (case 4) is better: AT, is less (0.038 vs. -0.051), Tm,matches the predicted value better (0.89 vs. 0.888 predicted), and the calculated In (P/p?T,=o.g~ is equivalent for the two cases (-0.002 vs. -0.0009 predicted). However, either correlation would be adequate for most engineering applications.
Ethyl Acetate. A second example (Table 11),for ethyl acetate, was developed to illustrate a somewhat more typical data situation. For these cases, the data of Young (1910) between 253 and 373 K were used. Other parameters (Ambrose, 1980) for ethyl acetate are Tb = 350.30 K
T , = 523.2 K
P, = 3.83 MPa
Riedel-predicted constraint parameters, based on a, = 7.56 estimated from the normal boiling point, were In (P/ P3Tr=o,g5= -0.0062 and Tmr= 0.87. The melting point (189.6 K) was assumed equal to the triple point temperature for this example. Results for eight alternate correlations are shown in Table 11. Both of the linear correlations (cases 1and 2) fail on one or more criteria, although the Wagner equation form may be structurally superior in its ability to reproduce the critical pressure and, thus, vapor pressures above the range of the data. All of the constrained correlations to the NRR form equal, or exceed, the MAD and fail one or more qualification criteria. Overall, either of the Wagner correlations, and particularly case 5B, is superior to the NRR correlations. In addition, there was essentially no degradation of correlation precision for either set of constraints with a Wagner equation form. Conclusions Almost no qualified, state-of-the-art wide-range correlations of vapor pressure data, other than those of Ambrose or McGarry, have appeared in the literature. Neither have many studies of vapor pressure prediction techniques explicitly approached the subject. Recognition of this need will no doubt lead to a greater understanding of the area
Ind. Eng. Chem. Res. 1987, 26, 112-116
112
in general, as well as phenomenologically correct correlations and prediction procedures in the future. On the basis of state of the art, two requirements must be ideally met by any analytical representation for vapor pressure along the entire saturation curve. (1)The representation must be prouen suitable for the entire saturation curve. (2) A strategy must be obtained for conforming to experimental evidence of general saturation curve behavior. Use of the Riedel criterion in the development of a new vapor pressure prediction technique will ensure qualitative correctness for the upper range of the curve (Tbto T J ;the developer is still obligated to demonstrate that the representation is accurate for low pressures as well. Constrained correlation, because of its controls, may be the superior strategy for producing qualified (accurate and phenomenologically correct) correlations of vapor pressure data for the foreseeable future. In this regard, Riedelbased predictions of constraint parameters for the upper temperature ranges may be helpful. However, further work will be necessary to fully prove the quantitative validity of such predictions. Literature Cited Ambrose, D. NPL Report Chem. 107, National Physical Laboratory (U.K.), Feb 1980. Ambrose, D.; Davies, R. H. J . Chem. Thermodyn. 1980. 12, 871.
Ambrose, D.; Counsell, J. F.; Hicks, C. P. J . Chem. Thermodyn. 1978, 10, 771. Ambrose, D.; Sprake, C. H. S.;Townsend, R. J . Chem. Thermodyn. 1975, 7, 185. Chase, J. D. Chem. Eng. Prog. 1984, 80, 63. Gibbard, H. F.; Creek, J. L. J . Chem. Eng. Data 1974, 19(4), 308. Gupte, P. A.; Daubert, T. E.; Danner, R. P. DIPPR Project 802, Documentation Report 802-3-82, The Pennsylvania State University, 1982. Hicks, C. D. NPL Report Chem. 77, National Physical Laboratory (U.K.), Jan 1978. Hirata, Mitsuho; Seijiro, Suda Kagaku Kogaku 1967, 31(4). 339. King, M. B. Trans. Inst. Chem. Eng. 1976,54, 54. King, M. B.; Al-Najjar, H. Chem. Eng. Sci. 1974, 29, 1003. McGarry, Jack Ind. Eng. Chem. Process Des Del;. 1983, 22, 313. Miller, George A. J . Chem. Eng. Data 1964, 9(3), 418. Plank, R.; Riedel, L. Ing. Archil;. 1948, 16, 255. Plank, R.; Riedel, L. Teras J . Sci. 1949, 1 , 86. Reid, Robert C.; Prausnitz, John M.; Sherwood, Thomas K. The Properties of Gases and Liquids, 3rd ed.; McGraw-Hill: New York, 1977; Chapter 6. Riedel, L. Chem. Ing. Technol. 1954, 26, 83. Schonberg, Manfred Hoechst, personal communication, July 11, 1985. Thodos, George Ind. Eng. Chem. 1950,42, 1514. Wagner, W.; Pentermann, W. J . Chem. Thermodyn. 1976,8, 1049. Waring, Worden Ind. Eng. Chem. 1954, 46(4), 762. 1910, 12, 374. Young, Sidney Sci. Proc. R. Dublin SOC.
Received for review February 7, 1986 Revised manuscript received June 9, 1986 Accepted July 25, 1986
Gas-Liquid Interfacial Area and Liquid-Side Mass-Transfer Coefficient in a Slurry Bubble Column Eizo Sada,* Hidehiro Kumazawa, Choul Ho Lee,+and Hiroaki N a r u k a w a Department of Chemical Engineering, Kyoto University, Kyoto, 606, Japan
Influences of suspended particles upon such parameters as gas holdup, volumetric liquid-side mass-transfer coefficient, and gas-liquid interfacial area in a bubble column were investigated in sodium sulfite/sulfate solutions in which various loadings of coarse nylon particles and fine alumina particles were suspended. The volumetric mass-transfer coefficients and gas holdups were a bit increased by suspending a small amount of fine particles. The gas-liquid interfacial area in a slurry bubble column in which a small amount of fine particles were suspended was found to be higher than that in a two-phase bubble column. The gas-liquid interfacial area in a slurry bubble column with suspended coarse particles was lower than that in a two-phase bubble column, especially when the superficial gas velocity was high. Influences of suspended fine and coarse particles on the liquid-side mass-transfer coefficient were not found to be so significant within the present experimental conditions. The slurry bubble column is a typical three-phase contactor in which the gas phase moves relative to the slurry phase in the form of discrete bubbles. This type of operation is widely employed in industrial practices because of its simple construction, higher heat- and mass-transfer rates, and good controlability of the liquid residence time. Performance of bubble columns is governed by the hydrodynamical conditions prevailing in the column which are closely related to bubble motion through the mean bubble size (Kawagoe et al., 1974; Nakao et al., 1983). Bubbles generated just upon a gas sparger undergo coalescence and/or breakup in the course of rising until they reach an average size which is represented by the
* Author t o whom correspondence should be addressed. Present address: Korea Research Institute of Chemical Technology, Daejeon, Korea.
0888-5885/87/2626-0112$01.50/0
volume-surface (Sauter) mean diameter (dv.J. The rates of these two processes are associated with the generated bubble sizes and the property of surrounding liquid. In a coalescence-promoting liquid such as water and pure organic liquids, the bubbles generated are apt to coalesce and reach an average size within 5 cm from the gas sparger unless very small bubbles of low number density are generated. When a coalescence-hindering liquid such as electrolytes and alcohols is added to an aqueous solution, the initial bubbles generated from the sparger almost do not change the size in the course of rising. Accordingly, higher gas holdup ( e G ) and gas-liquid interfacial area ( a ) than those encountered in a coalescence-promoting liquid can be achieved (Heijnen and van’t Riet, 1984; Hikita et al., 1980). Because the solids capable of bubble breakup are usually hard to be suspended only by bubble motion in the absence of forced liquid flow, this type of mechanism 0 1987 American Chemical Society
