The Coalinga plant was designed by Edward Selover as an efficient tool for conducting individual tube experiments. Harry Baldwin obtained all the data reported on the Coalinga plant, which he operates. T h e city officials of Coalinga have been most cooperative, in particular Glenn Marcussen, City Manager, and Reginald Phelps, Director of Public Works. Thanks are expressed to Harry Lonsdale of General Atomics for appropriate suggestions on the inclusion of salt flux and the salt permeability Coefficient in the development of the equations.
water permeability coefficient, cc./sq. cm. sec. atm. salt permeability coefficient, cm./sec. cB salt concentration in bulk brine on saline side of membrane, grams/cc. cg = salt concentration in desalinized water from membrane, grams/cc. cw = salt concentration at interface between membrane and saline solution, grams/cc. D = membrane tube internal diameter, cm. D , = desalination ratiio, C B / C D D , = average molecular diffusion coefficient of salt in brine, sq. cm./sec. f = friction factor F1 = water flux, cc./aq. cm. sec. Used interchangeably with total flux, F = salt flux, grams/’sq. cm. sec. F1 j , = Chilton-Colburn mass transfer factor, koNsoO 6 7 / u B . Determined in this paper from j g = f / 2 , where f is function of iVRegiven by Drew, Koo, and McAdams (2) ko = mass transfer coefficient, cm./sec. ATR, = Reynolds number, D U B / V Nsc = Schmidt number, Y / D S
Downloaded by CENTRAL MICHIGAN UNIV on September 12, 2015 | http://pubs.acs.org Publication Date: January 1, 1967 | doi: 10.1021/i260021a022
B
ug
K Y
?TD AW
hydraulic pressure drop across membrane, atm. interfacial salt rejection, 1 - c ~ / c w bulk brine velocity, cm./sec. concentration polarization exponent, F~Ns,O.G~/UB~O kinematic viscosity, sq. cm./sec. osmotic pressure in bulk brine on saline side of membrane, atm. = osmotic pressure in desalinized water from membrane, atm. = osmotic pressure in brine a t interface between membrane and saline solution, atm. =
= = = = =
Literature Cited
Nomenclature
A
AP
R
= = =
(1) Brian, P. L. T., “Influence of Concentration Polarization on Reverse Osmosis System Design,” First International Symposium on Water Desalination, Washington, D. C., Oct. 3-9, 1965. (2) Drew. T. B.. Koo. E. C..’ McAdams. W. H.. Trans. Am. Znst. ’ Chem. En.. 28,‘56 (1933). (3) Loeb, S., Desalination 1, No. 1, 35 (April 1966). (4) Loeb, S., Sourirajan, S., Advan. Chem. Ser., No. 38, 117 (1962). (5) Lonsdale, H. K., Merten,. U.,. Riley, . . R. L., J . Abbl. .. Polymer kci. 9, 1341’(1965).’ (6) Manjikian, S., Loeb, S., McCutchan, J. W., “Improvement in Fabrication Techniques for Reverse Osmosis Desalination Membranes,” First International Symposium on Water Desalination, Washington, D. C., Oct. 3-9, 1965. ( 7 ) Merten, U., Lonsdale, H. K., Riley, R. L., Znd. Eng. Chem. Fundamentals 3, 210 (1964). (8) Michaels, A. S., Bixler, H. J., Hodges, R. M., Jr., J . Colloid Sci. 20. 1034 (1965). ( 9 ) Sherwood, T. K.,’ Brian, P. L. T., Fisher, R. E., Dresner, L., Znd. Eng. Chem. Fundamentals4, 113 (1965). (10) Sherwood, T. K., Brian, P. L. T., Sarofim, A. F., “Research on Saline Water Conversion,” Dept. Chem. Engr., M.I.T. Rept. 295-8 (Dec. 21, 1965).
-
RECEIVED for review April 18, 1966 ACCEPTED August 5, 1966
HEAT TRANSFER TO AGITATED, TWO-PHASE
LIQUIDS IN JACKETED VESSELS $5.
W.
BODMAN AND D. H. CORTEZ
Xchool of Chemical Engineering Practice, Massachusetts Institute of Technology, American Cyanamid Go., Bound Brook, N . J .
Unsteady-state heat transfer experiments were carried out in a jacketed, agitated, glass-lined vessel using as heat transfer media both single-phase and two-phase fluids: water, toluene, lubricating oil, watertoluene mixtures, and ,water-lubricating oil mixtures. Data were first obtained for the single-phase fluids and were found to agree with those of previous investigators. The rate of heat transfer to two-phase, agitated fluids was then measured and compared with the results for single-phase heat transfer. Several correlation techniques for the two-phase heat transfer results were attempted; these differed in the methods used to compute the physical properties of the two-phase mixtures. The use of bulk, volume-average properties yielded the most consistent correlation of the data. Gravitational effects at low agitator speed are discussed in some detail.
LAss-lined, jacketed kettles have been in common use for
6 many years throughout the chemical process industry. During this time, several investigators have studied heat transfer rates to single-phase liquids in jacketed, agitated vessels (7-7, 9). Results of these investigations are in reasonable agreement and they are summarized in a comprehensive
review by Uhl and Gray (72). However, the rate of heat transfer to two-phase mixtures in agitated vessels has received only cursory examination. Cummings and West (7) measured heat transfer rates for water-mineral oil mixtures in an agitated kettle equipped with a cooling coil. Because of the limited amount of two-phase data which were obtained by Cummings VOL. 6
NO. 1
JANUARY 1967
127
and West (7), only a qualitative interpretation of these data was possible. Many chemical operations require the processing of twophase liquid mixtures in agitated kettles. Therefore, knowledge of the effect of a second liquid phase on the rate of heat transfer in a jacketed kettle can be important. The purpose of the present investigation was to obtain and correlate data which accurately describe the rate of heat transfer to agitated, two-phase mixtures. For turbulent agitation of a single-phase fluid, previous workers have presented their data in the following form:
Downloaded by CENTRAL MICHIGAN UNIV on September 12, 2015 | http://pubs.acs.org Publication Date: January 1, 1967 | doi: 10.1021/i260021a022
There is good agreement as to the value of the exponents on the Reynolds number, the Prandtl number, and the SiederTate ratio. The value of C varies significantly and is thought to be a strong function of vessel geometry. The only correlation reported specifically for glass-lined equipment and the one believed most pertinent to the present investigation is the correlation of Ackley (7) :
N N , = 0.33 NRea/aNpr1/aNVi~J4
(2)
The applicability of Equations 1 and 2 has never been tested quantitatively for two-phase liquid mixtures. In the present study, data were obtained and correlated for heat transfer to single-phase liquids. Heat transfer rates to two-phase mixtures were then measured and these data were correlated in a manner similar to that used for the single-phase results. Theoretical
T o determine the rate of heat transfer to a liquid being heated in an agitated, jacketed kettle, an energy balance is written on the contents of the vessel. Assuming that the power input of the impeller is small, the folloiving equation may be written:
(3) T h e last term in Equation 3 represents the rate of heat loss from the kettle to the surroundings. Assuming that C,, U, and K are constant, the solution to Equation 3 is readily found to be:
Differentiating Equation 4 with respect to time, rearranging, and assuming that heat losses are negligible, one obtains:
(5)
-
A plot of In( T , T ) us. time permits the direct calculation of U. Assuming equal external and internal areas of the jacketed surface, the total resistance to heat transfer may be expressed as the sum of the individual resistances:
-1 - -1+ - 1+ - xs+ -
xg
U
kg
ha
hi
ks
Since hi is proportional to N 2 l 8 ,a plot of 1/U us. 1/N2/3 should give a straight line with I$ = l/ho x,/ks xJk, as its intercept. This is the well-known Wilson plot method for the determination of wall and external film resistance (73).
+
128
I&EC PROCESS DESIGN
+
A N D DEVELOPMENT
Once 4 is known, hi can be calculated for each experimental run to be made. Experimental Equipment
Unsteady-state heat transfer experiments were carried out in a 20-gallon, glass-lined jacketed vessel. The kettle, including the baffle and agitator drive, was manufactured by Glasscote Products, Inc., Cleveland, Ohio. The wall of the vessel was constructed of 3/8-inch pressed steel. The thickness of the glass coating was specified to be in the range from 0.05 to 0.07 inch. The kettle had an inside diameter of 18 inches and was equipped with a IO-inch diameter, three-bladed (retreating type) glass-coated impeller. The heating jacket covered the bottom of the vessel and the sides of the vessel to a height of 163/8 inches above the dished bottom. This height corresponds to 7.2 sq. feet of heat transfer area. A variable-speed drive assembly permitting agitator speeds of 43 to 228 r.p.m. was mounted above the center of the kettle. One vertical 3-inch baffle was located in a stationary position approximately perpendicular to the wall of the vessel. TWO temperature-measuring devices were fixed in the equipment. A pressure thermometer, connected to a Minneapolis Honeywell recorder, measured the bulk temperature of the agitated liquid. The pressure thermometer lead ran through a well in the center of the baffle, its tip being located at the base of the baffle. A thermocouple, installed a t the top of the jacket to measure the temperature of the jacket steam, was connected to a gage on the control panel. The temperature-measuring devices were calibrated by comparing their readings with those from an iron-constantan thermocouple. During three trials, the thermocouple probe was also used to measure bulk temperatures at various locations in the kettle; these measurements were then compared with the pressure thermometer reading. The results of these calibration experiments indicated that the temperature measurements were accurate to within 1' F. Moreover, the temperature of the bulk liquid was found to be uniform to within 1' F. The lags in the temperature-measuring devices were found to be sufficiently small to have no significant effect upon the experimental results. Experimental Procedure
Thirty-two trials were conducted in a 20-gallon kettle. Each trial consisted of heating 15 gallons of liquid of known composition to a desired temperature, allowing the temperature to peak without further heat application, and then cooling to the desired temperature. The liquid was agitated at constant impeller speed throughout the trial. Temperatures of the bulk liquid and jacket steam were measured and recorded a t 1-minute intervals. The agitator speed was adjusted and maintained to within 1 r.p.m. prior to turning on the steam. High pressure steam was admitted to the top of the jacket and the jacket drain was left open to the atmosphere to allow condensate to drain. The steam inlet valve was adjusted to maintain the jacket steam temperature between 100' and 102' C. The steam was left on until the temperature of the liquid in the kettle reached the desired temperature, which was 70' C. for most trials. The steam inlet valve was then closed and the liquid was agitated for an additional 5 minutes. Cooling water was then circulated through the jacket in order to bring the contents of the vessel back to room temperature and to allow for the start of the next run. Electrical conductivity experiments were performed to determine the continuous phase for the toluene-water and lubricating oil-water mixtures. When two components differ greatly in electrical conductivity, a plot of electrical conductivity us. volume per cent will show a sharp break at the point where the shift in continuous phase takes place. A pH meter was used for this purpose. The p H of mixtures of varying compositions was measured for both types of two-phase mixtures studied in the present work. In the experimental program, chemically pure grade toluene was used. The lubricating oil used was Esstic 50, a high grade lubricating oil manufactured by the Humble Oil and Refining Co. The 15 gallons of fluid used in each run corresponded to 7.2 sq. feet of heat transfer area.
then calculated from Equation 6 . The results and a summary of calculated values are shown in Table I. Measurements of electrical conductivity with a p H meter indicated the continuous phase. For mixtures containing more than 40% toluene in water, toluene was the continuous phase. This checks the critical value of 44% toluene as reported by Davies and Rideal (8). Similarly, for the lubricating oil-water system, water was found to be the continuous phase for mixtures containing more than 28% water.
Results
Over-all heat transfer coefficients can be determined from Equation 5 if the assumptions in the derivation of this equation can be verified. T h e first assumption, that of negligible heat losses, was justified by observing the change in bulk liquid temperature for an extended period of time after the steam had been turned off. I t was found that the maximum rate of heat loss was less than 1% of the minimum rate of heat transfer through the jacket wall. The assumption of constant U and C, was tested by conT ) us. time. These plots resulted in structing plots of In( T , straight lines, indicating the constancy of the quantity C,/U. Experimental values of U were then obtained by multiplying the slope of In( T , T ) us. time plots by mC,/At. For each liquid and mixture of liquids tested, Wilson plots were constructed to determine the wall resistance. The average value of @ was found to be 0.0095 (B.t.u./hr. sq. ft. O F.)-l with an average absolute deviation of 0.0005 (B.t.u./hr. sq. ft. O F.)-l. Experimental values of hi for each run were
Treatment of Data
-
In order to compare the experimental results with Equation 2, a plot of the Colburn j-factor for heat transfer us. the Reynolds number was desired. From Equation 2 one can write
Downloaded by CENTRAL MICHIGAN UNIV on September 12, 2015 | http://pubs.acs.org Publication Date: January 1, 1967 | doi: 10.1021/i260021a022
-
Table 1.
Run 2 3 4 5 6 7 8 9 10 11
12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32
Composition, Vol. ?& Water Water Water Water Water Toluene Toluene Toluene Toluene 90y0 toluene l O ~ ,water 907, toluene 10% water 90% toluene lOyc water 90% toluene 107, water 757, toluene 257, water 757, toluene 257, water 75y0 toluene 257, water 757, toluene 2.57, water 2570 toluene 75y0 water 2570 toluene 7570 water 257, toluene 75y0 water :25yo toluene ‘757, water 50yc toluene 507, water 1 5 0 7toluene ~ !50% water !50yotoluene !507, water Lube oil Lube oil Lube oil 757, lube oil 25’3, water 757, lube oil ‘2!570water 25% lube oil 7‘5570 water 25Yc lube oil 757, water
N , R.P.M. 215 150 112 68 43 44 66 146 210 210 ~~~
(7) where Ns, and N,, are special forms of the Stanton number and Reynolds number as applied to agitated vessels. Single-phase Heat Transfer. For runs 2 through 9, in which pure toluene and water were used, experimental values
Experimental Results hi, B.T.U./Hr. Sq. Ft. F. Sq. Ft. F. 93.9 825 90.5 633 552 86.2 400 83.5 292 77.6 42.5 71.5 48.2 89 62.1 152 71 .O 218 78.5 304
U,B.T.?./Hr.
jrr ( X IOa) 3.86 4.25 4.96 5.93 6.83 7.0 5.81 4.49 4.48 5.5
329 200 129 113 174 385 553 477
65
53.7
109.7
6.3
150
146
71.2
219
5.6
332
44
47.6
86.7
7.36
102
66
54.7
113,5
5.1
154
205
77.0
284
4.1
478
146
66.0
175.5
3.56
340
46
52.5
105
6.76
108
45
67.2
184.5
6.27
108
217
91.4
680
4.8
521
148
81.5
368
3.8
356
67
70.0
208
4.75
161
148
82.9
389
5.5
351
208
92.4
753
7.56
493
66
70.9
21 6
6.85
156
210 146 68 21 1
40.5 35.5 26.4 52.9
66.7 53.4 35.1 106
22.7 25.8 35.8 23.4
6.27 4.36 2.03 8.7
150
50.4
96.5
30.0
6.2
150
68.8
197
18.4
20.6
228
74.1
247
15.2
31.2
VOL. 6
NO. 1
JANUARY 1967
129
Downloaded by CENTRAL MICHIGAN UNIV on September 12, 2015 | http://pubs.acs.org Publication Date: January 1, 1967 | doi: 10.1021/i260021a022
of j , and NRe were calculated. These results are shown in Figure 1 ; as can be seen, the single-phase results compare well with Equation 2. The average absolute deviation between experimental values of j , and those calculated from Equation 2 was 3%. For runs 26 to 28, in which lubricating oil was used as a heat transfer fluid, the values of NRe ranged from 2030 to 6270. Chapman and Holland (5) report that the transition region for heat transfer in an agitated kettle lies in the Reynolds number range of 400 to 10,000. These results confirmed the earlier findings of Uhl ( 7 7 ) . Assuming that the data for pure lubricating oil fall within the transition region, the following correlation for transition region heat transfer was developed in the present study:
Equation 8 fits the pure lubricating oil data with an average absolute deviation of 2%. Two-Phase Heat Transfer. GRAVITATIONAL EFFECTS. For heat transfer to two-phase mixtures, several complications arise. The degree of agitation is an important factor in all these complications. At low agitator speeds, the two phases will tend to separate and “settling” will become important. At high agitator speeds, the discontinuous phase becomes well dispersed in the continuous phase, and gravitational or settling effects can be neglected. T o estimate the importance of settling in an agitated fluid mixture, a dimensionless settling number was developed. This dimensionless group was formulated by taking the ratio of the inertial force to the buoyant force in the agitated, twophase mixture. The settling group is designated as $, and is defined as $ =
g(p1
- PZ) (9)
Values of $ were calculated for an equivolume mixture of
water and toluene over the range of agitator speeds encountered in present work. These values ranged from 0.0157 at the lowest speed of 45 r.p.m. to 0.312 at 210 r.p.m. Evidence obtained during experimentation indicated that good mixing was not achieved during all runs. It was observed by sampling the top and bottom of water-toluene mixtures during agitation that significant settling occurred for agitator speeds less than 100 r.p.m. This corresponds to a $ value of 0.07. Surface tension also has a significant effect on settling as evidenced by the lubricating oil-water system. Good dispersion of the two phases was achieved at all speeds because the water and lubricating oil formed an emulsion. GOOD MIXING. Since in any convective heat transfer process the boundary layer provides the major resistance to the rate of heat transfer, the composition of the boundary layer on the heated wall of a vessel has an important effect on the rate of heat transfer into the vessel. Therefore, the average physical properties of the boundary layer are conventionally used in the correlation of heat transfer data. However, all investigations of agitated kettle heat transfer previous to the present study make use of bulk fluid properties in their data correlations. The boundary layer properties can be calculated in several ways. If the contents of the vessel are well mixed, it may be assumed that the boundary layer consists entirely of the continuous phase. On the other hand, a layer might have the same composition as the bulk liquid, in which case the volumeaverage physical properties should be used. Experimental values of jx and NRe for those runs in which the fluids were well mixed-Le., N > 100 r.p.m.-were calculated using the physical properties of the continuous phase. These results are plotted in Figure 2. For the same runs, experimental values of jx and NRewere calculated using volume-average properties of the bulk liqujd (Figure 3 and Table I). POOR MIXING. The condition of the boundary layer will have an important effect on the rate of heat transfer. For well-mixed liquids, the degree of dispersion of the discontinuous phase in the boundary layer is important. For poorly mixed liquids, the denser of the two phases will settle, and two distinct types of boundary layers will result.
2x
10-2,
I
I V A
i JH
c
16‘
I
1
1
A
COntinUOUS Phase Properties
JH
o Pure Water b.
Pure Toluene
i
:
L 2x
lo5
Figure 1. 130
10%WATER 2 5 % WATER 50% WATER 75% WATER
NRe
Single-phase heat transfer correlation
I h E C PROCESS D E S I G N A N D DEVELOPMENT
106
I
I o5
I
I
I
!
I
d 106
NRI
Figure 2. Two-phase heat transfer correlation using areaaverage and continuous phase properties
1
Downloaded by CENTRAL MICHIGAN UNIV on September 12, 2015 | http://pubs.acs.org Publication Date: January 1, 1967 | doi: 10.1021/i260021a022
I
1
0 2 5 % Water P 5 0 % Water 7 5 % Water
IO6
105
NR.
Figure 3. Two-phose heat transfer volume-average properties
correlation using
Since in the present work the bulk temperature was measured only at the base of the baffle, it is possible that an undetected temperature difference existed between the settled phases. T o analyze for a possible temperature difference, a model was postulated whereby toluene and water were visualized in a jacketed vessel with all of the water settled a t the bottom of the vessel. During heating, constant over-all heat transfer coefficients, LrT and Uw,were assumed for the toluene and water phases, respectively. Similarly, it was assumed that a constant over-all heat transfer coefficient, V I ,could be ascribed to a planar interface between the two-liquid phases. Writing an energy balance on each phase, and assuming negligible heat losses amd power input, there can be written:
1.8 sq. feet were assumed. During agitation, the interfacial heat transfer coefficient is probably at least as great as the coefficient at the wall. I n addition, the interfacial area is probably not planar and, therefore, is greater than 1.8 sq. feet. Thus, it was assumed that for settled mixtures containing greater than 25% water there was no significant temperature difference between phases. The larger temperature difference which was computed for low water compositions is due mainly to the dished shape of the vessel bottom. At low percentages of water, the percentage of heat transfer area covered by water is large relative to the amount of water present. Experimental values ofj, and N R e for toluene-water mixtures were calculated for the cases in which settling was believed significant-Le., N < 100 r.p.m. I n these cases, the physical properties were weighted according to the fraction of heat transfer area covered by each phase. These results are shown in Figure 2. Runs 12 and 14 are not shown in Figure 2 because the calculated temperature difference between settled phases was considered too great, because of the low agitator speed and low water content. The water-lubricating oil runs were not considered in this analysis because an emulsion was formed and no settling was observed. Experimental values of j , and N,, were also calculated for the poor-mixing runs using bulk, volume-average physical properties (Figure 3). Correlating Errors
I n summary, Figure 2 shows the experimental values of j a and NRe for water-toluene mixtures which were calculated using either the continuous phase properties for well mixed liquids or area-average properties for poorly mixed liquids. The absolute average deviation of these results from those predicted by Equation 2 is 54%. Experimental values of j , and N R e were also calculated for water-toluene mixtures using bulk, volume-average properties. These results are shown in Figure 3; these data have an absolute average deviation of 18.7YGwhen they are compared with Equation 2. Figure 4 shows the results when volume-average properties are used for all runs including lubricating oil-water mixtures. In this case, the average deviation is 14.8%. If only the turbulent region is considered, the average deviation is 16%.
Rearranging, simplifying, and integrating, there result :
y =
Aerl'
x = .&rit
+ Berzt + Ferzr
(1 2) (1 3)
T o determine if a significant temperature difference exists between settled phases, values of UT and Uw as found in the single-phase experiments at 66 r.p.m. were assumed to apply to the two-phase case. For a UT value of 48.1 and a Uw value of 81.7 B.t.u./hr. sq. ft. ' F. maximum values of the temperature difference between phases were calculated for various mixtures of toluene and water. Since no experimental data were available on heat transfer rates between two immiscible liquid phases, values for U1 had to be assumed. For toluene-water mixtures containing 50, 75, and 90% water, maximum temperature differences of 2.8', 5.3', and 6.4' F., respectively, were calculated for the case when Ul equals zero (the case when the greatest error would be caused). For the case of 25YGwater, a maximum temperature difference of 4.7' F. was computed when an interfacial coefficient of 500 B.t.u./hr. sq. ft. ' F. and a smooth interfacial surface area of
Io'2 Correlation Ackley (I) o
f
J
'
w
j
0 Pure W d e r 0 Pure Toluene
A 10% Water x 2 5 % Water
v 50% Water 4 7 5 % Water
-- 90% Toluene 7 5 % Toluene
4
-
5 0 % Toluene 2 5 % Toluene Lubricating Oil A 2 5 % Water 7 5 % Lube O i l T 7 5 % Water 25 %Lube O i l
0
t I
VOL. 6 NO. 1
I
I
I / , l I l
JANUARY 1967
131
Downloaded by CENTRAL MICHIGAN UNIV on September 12, 2015 | http://pubs.acs.org Publication Date: January 1, 1967 | doi: 10.1021/i260021a022
Discussion
The results of the single-phase heat transfer experiments compare well with the results of Ackley ( I ) . Equation 2 correlates the turbulent, single-phase results to within 3% accuracy. The lubricating oil runs fell into the transition region as defined by Chapman and Holland ( 5 ) . Equation 8 was developed for the transition region and fits the data to within 2%. Previous investigators (2-7) found that a single equation could be used to correlate heat transfer data over a wide range of Reynolds numbers from laminar to turbulent flow. Although Equation 8 works well for the three runs conducted in the transition region, enough data were not taken to determine if a separate correlation should be used. A comparison of Figures 2 and 3 clearly indicates that the use of bulk, volume-average properties rather than area-average and continuous phase properties gives a more consistent and useful correlation of the data. The poor correlation achieved by using the properties of the continuous phase is in marked disagreement with the results of Cummings and West (7),who investigated the mineral oil-water system. They found that for both 25% and 7570 water mixtures, the film coefficient was closer to that for pure water. Cummings and West concluded that the water phase preferentially wetted the surface of the heat transfer surface. The results of the present experiments indicate that the condition of the boundary layer in a two-phase mixture is not well understood. Although unexpected, it seems apparent that the use of area-average properties for poorly mixed liquids and continuous phase properties for well-mixed liquids does not represent the true conditions of the boundary layer. The fact that the use of volume-average bulk properties results in the best correlation indicates that a volume average comes closer to describing the actual boundary layer composition than the other methods tried. Considerable experimental error can be attributed to the high wall resistance. Use of the Wilson plot technique indicated the value of $ to be 0.0095 (B.t.u./hr. sq. ft. ' F.)-I. This compares well with the value of 0.0093 (B.t.u./hr. sq. ft. O F.)-l calculated from the approximate steel and glass thicknesses and thermal conductivities as specified by the equipment manufacturer. The jacket side coefficient is estimated to be of the order of 1000 to 3000 B.t.u./hr. sq. ft. F. (70). The value of $ is known to within 5%; however, since the wall resistance is high, an error of 5% can have considerable effect on the value of h f as computed from the experimental data. I n order to analyze for experimental error, the probable errors associated with experimental values of hf were calculated. The probable error as predicted by the error analysis increased with increasing values of h,; the uncertainties in the wall resistance, 6, became more important at the high values of hf. The probable error associated with a film coefficient of 100 B.t.u./hr. sq. ft. O F. was calculated to be 11%, while an hi of 600 B.t.u./hr. sq. ft. O F. had an associated probable error of 43%. The average probable experimental error was found to be 19%. This value compares very well with the average deviation of 16% which was observed when the experimental data were compared with the values predicted by Equation 2 (see Figure 4). Such agreement lends a good deal of confidence to the experimental technique and indicates strongly that the major sources of error have been recognized and taken into account. Settling occurred at a value of approximately 0.07. However, since the degree of settling could not be observed directly, it is not known over what range of IC. settling occurred. More 132
I&EC PROCESS DESIGN A N D DEVELOPMENT
information would be helpful on the degree of settling as a function of agitator speed and liquid properties. Although the settling number will be important in determining the effect of settling in an agitated, two-phase mixture, it will not be the only important factor. As can be seen by the lubricating oilwater system, the effects of surface interactions should also be considered in any future work on this problem. Conclusions
The effect of the second phase on heat transfer rates to twophase mixtures depends largely on the condition of the boundary layer which is established adjacent to the heat transfer surface. The use of bulk, volume-average properties appears to approximate most closely the actual boundary layer composition. When estimating heat transfer rates for twophase mixtures in jacketed kettles, correlations developed specifically for single-phase liquids may be used satisfactorily if bulk, volume-average physical properties are used. A settling number has been postulated to serve as an index of the importance of settling in agitated, two-phase mixtures. Acknowledgment
The authors express their appreciation to G. N. Gagliardi and G. F. Lewenczuk of the American Cyanamid Co. for their valuable advice and assistance during the course of this work, The efforts of J. Moslen, E. P. Eich, and H. Yanagioka in obtaining and analyzing the experimental data are gratefully acknowledged. The cooperation of Vincent Uhl in supplying information from his forthcoming publication was of great value in the present study. Nomenclature a
= --(UIAI
-I- U v A w ) / m w C p w ,hr.+
-f)/(rz
- -
- r l ) d [xo/c (72 f) yo], constant in Equation 12, F. A , , A w , AT, A I = heat transfer area for vessel, water phase, toluene phase, and liquid-liquid phase interface, respectively, sq. ft. b = U I A ~ / m W C p hr.-l w, B = yo - A , constant in Equation 12, F. C = UIAl/m&pT, hr.-l C = constant in Equation 1 C,, C,, Cpw= heat capacity of bulk liquid, toluene, and water, respectively, B.t.u./lb. F. d = differential operator = diameter of impeller, ft. Df = inside diameter of kettle, ft. Dt E = c A / ( r 1 - f), constant in Equation 13, F. f = ( U T A T -I- UIAl)/m,C,,,, hr.+ F = cB/(rz - f),constant in Equation 13, F. g = gravitational acceleration, 32.2 ft./sec.2 hf = internal film coefficient, B.t.u./hr. sq. ft. O F. ho = external steam film coefficient, B.t.u./hr. sq. ft. O F. = NBth'P:/3N~,is-0.14, Colburn j-factor for heat transfer in agitated vessels, dimensionless = thermal conductivity of bulk liquid, steel and glass, respectively, B.t.u./hr. ft. F. = constant defined in Equation 3, B.t.u./hr. O F. = mass of bulk liquid, toluene phase and water phase, respectively, lb. = agitator speed, revolutions per minute N = Froude number for agitated vessels, N z D f / g , NFr dimensionless, consistent units = Nusselt number for agitated vessels, hfD,/k, dimensionless, consistent units = Prandtl number, C,h/k, dimensionless, consistent units A
= [(ri
-
= Reynolds number for agitated vessels, ND?p/p,
NR~
dimensionless, consistent units = Stanton number for heat transfer in agitated NE t vessels, (h,/pD,NC,) ( D , / D i ) , dimensionless, consistent units = Sieder-Tate viscosity ratio, ~ / p dimensionless ~ , Nv,s TI = (a f) d ( a - f)’ 4 bc, constant in Equations 12 and 13, hr. rz = (a f) d ( a - f)’ 4 bc, constant in Equations 12 and 13, hr.-I T,T,,T,,TT,Tw -- temperature of bulk liquid, ambient air, jacket steam, bulk toluene phase, and bulk water phase, respectively, ” F. = temperature of bulk liquid at t = m , = (UA,T, T,
-+ + -+
+ +
+ KTa)/(UAt+ K ) , ” F.
= time, hr.
t
U, V I ,UT,Uw = over-all heat transfer coefficient for vessel, two-phase interface, toluene phase, and water phase, B.t.u./hr. sq. ft. F. = wall thickness for steel and glass, respectively, ft. = temperature difference between bulk toluene phase and jacket steam, at any time and at t = 0, respectively, = T r- T,, ” F. = temperature difference between bulk water phase and jacket steam, at any time and t = 0, recspectively, = Tu. - T,, O F.
xs, XP
x,
20
Downloaded by CENTRAL MICHIGAN UNIV on September 12, 2015 | http://pubs.acs.org Publication Date: January 1, 1967 | doi: 10.1021/i260021a022
Y‘YO
GREEK = = = =
CY
P Y $J
constant defined in Eauation 1, dimensionless constant defined in Eqbation 1, dimensionless constant defined in Equation 1, dimensionless l/h, x s / k s x , / k g , (B.t.u./hr. ft.? ” F.)-I
+
P, PW p, pl, p z
P* ic,
viscosity of bulk liquid, and at wall of vessel, respectively, lb./ft. hr. = density of bulk liquid, phase 1 and phase 2, respectively, lb./cu. ft. = density of liquid a t impeller tip, equal to p2)/2 for well agitated, two-phase mixtures = settling number for agitated vessels, [p*(/pl $1 ( D i / D t ) s ( N ~ , dimensionless, ), consistent units =
+
-
literature Cited
(1) Ackley, E. J., Chem. Eng. 66,181 (1959). (2) Brooks, G., Su, G . J., Chem. Eng. Progr. 55, No. 10, 54 (1959). (3) Brown, R. W., Scott, R., Toyne, C., Trans. Znst. Chem. Eng. (London) 25, 181 (1947). (4) Chapman, F. S., Dallenback, H., Holland, F. A., Zbid., 42, 398 (1964). (5) Chapman, F. S., Holland, F. A., Chem. Eng. 72, 175 (1965). (6) Chilton, T. H., Drew, T. B., Jebens, R. H., Ind. Eng. Chem. 36, 510 (1944). (7) Cummings, G. H., West, A. S., Ibid., 42, 2303 (1950). (8) Davies, J. T., Rideal, E. K., “Interfacial Phenomena,” p. 382, Academic Press, New York, 1961. (9) Gordon, M., Ph.D. thesis, University of Minnesota, June 1941. (10) McCabe, W. L., Smith, J. C., “Unit Operations in Chemical Engineering,” p. 439, McGraw-Hill, New York, 1956. (11) Uhl, V. W., Chem. Eng. Progr. Symp. Ser. No. 17, 51, 93 (1955). (12) Uhl, V. W., Gray, J. B., “Mixing. Theory and Practice,” Vol. 1, Academic Press, New York, 1966. Mech. En,e. 37, 546 (1951). (13) Wilson, E. E., Trans. Am. SOC. RECEIVED for review April 18, 1966 ACCEPTED August 11, 1966
+
KINETIC; STUDY OF T H E PYROLYSIS OF A
H IG H-VO LAT I LE BI T U MI N0 US COA L WENDELL H WISER, GEORGE RICHARD HILL, AND NORBERT J. KERTAMuSi Fuels Engineering Department, University 01 Utah, Salt Lake City, Utah Constant temperature data are presented for the pyrolysis of a Utah high-volatile bituminous coal at temperatures ranging from 4 0 9 “ to 497” C. The reactions are approximately second-order for the first 60 minutes, wit19 an activation energy of 36.6 kcal. per mole. This region is followed by a period of approximately 100 minutes, during which the reaction is first-order, with an activation energy of 5.36 kcal, per mole. A zero-order reaction takes place at times above approximately 300 minutes, extending throughout the balance of the observations, in some cases up to 1500 minutes. Apparent entropies of activation, including the unknown factor of reacting surface sites, were calculated to be -63 entropy units for the firstorder region and - 1 2 entropy units for the second-order region. A model which relates the change in reacting sites to entropy change and a model for the pyrolysis of high-volatile bituminous coal are presented.
N RECENT
years experimental data from several laboratories
I have been presented and analyzed in the literature in an
effort to arrive at greater understanding of the processes associated with the pyrolysis of coal. Each presentation has contributed measurably to an increased understanding, both through the inclusion of experimental data and as a result of interpretations of the data. The presentation of experimental data obtained in this laboratory, accompanied by analyses and comparisons with previously reported data, may shed further light upon these very complex processes. There appear in the literature two basic experimental approaches to this problem: heating a coal sample to a predetermined temperature where the decomposition processes are studied at constant temperature, and increasing the tem1 Present address, Phil.ips Petroleum Co., Bartlesville, Okla.
perature of the coal sample at a predetermined constant rate. Among those who have pursued their studies a t constant temperature, some have heated the coal sample under conditions where the normal coking processes may occur, including the fusion of the sample particles, while others have heated the samples to operating temperatures with the coal particles effectively separated, such that the desired temperature was rapidly attained and fusion of particles was essentially avoided. The results of these approaches are necessarily varied, but related. The present study is concerned with constant temperature observations of finely divided coal samples under conditions such that fusion of the coal mass may occur in a manner characteristic of coking operations, and a t temperatures such that the coal samples pass through the plastic state during the course of the observations. VOL. 6
NO. 1
JANUARY 1967
133
