Absorption of Sulfur Dioxide in Water F. FT. ADAMIS, Massachusetts Institute of Technology, Cambridge, Mass.
EWIS and Whitman have
shown ( 2 ) that in the absorption of a very slightly soluble gas from air by water or in the absorption of a pure gas in water, the rate of absorption is controlled by the resistance of a film of liquid a t the liquid-gas int e r f a c e . On the other hand, where a very soluble gas is being absorbed from air by water, the resistance of the gas film a t this interface controls. With sulfur dioxide and water we have a n intermediate case which is rendered complex by the fact that i t may or may not come under either of these classifications. Here the t y p e of absorbing e q u i p m e n t may exert a controlling effect on the mechanism of absorption. This i n v e s t i g a t i o n reports a study of the effect of l i q u o r velocity, gas velocity, and temperature on the rate of absorption of s u l f u r d i o x i d e f r o m sulfur-burner gas by water in a spiral-tile packed tower ( 3 ) .
The absorption of sulfur dioxide in water in a spiral-tile packed tower is studied with relation to the effects of liquor relocity, gas velocity, and temperature on the mechanism of absorption. Data suitable for the design of absorption equipment are obtained in the practical operating range of these zwiables. The ocer-all resistance to the absorption of sulfur dioxide comprises both gas and liquid film resistances, although the latter is generally of major importance. Resistance to its absorption m a y be reduced by increasing liquor f!elocity, temperalure, and gas velocity, the magnitude qf the effect being in the order named. Ouer-all resistance (RL) is inz!ersely proportional to the 0.89 power of liquor velocity. The effect of temperature on over-all resistance ut low gas and liquor celocities is similar to its effect in a wetted-wall tower; at high liquor velocity, the effect is much greater. Gas eelocity affects the resistance to absorption at higher liquor velocity, but is unimportant at l o x 1iquor velocity.
EXPERIJIEKTAL PROCEDURE An experimental tower was constructed of 18-inch tile pipe which was packed with 3-inch spiral, acid-proof tile. Provision was made for controlling liquor velocity, gas velocity, and temperature in the tower. Gas for absorption was obtained by tapping off from a main through which commercial burner gas was flowing. An orifice in the line gave a rough measure, suitable for control purposes, of the amount of gas flowing. After passing through the tower, the inert gases with the residual sulfur dioxide were exhausted by a vacuum pump. Water was fed to a constant-head box in which was immersed a steam coil to facilitate temperature control. Variation of liquor velocity was obtained by means of a hand-controlled valve between the head box and the distributing device in the top of the tower. The liquor a t the base of the tower was maintained a t a constant level to insure that the liquor exit was always sealed and to prevent sealing of the gas inlet. The acid produced was measured in barrels, samples for analysis being taken in the discharge pipe from the tower. Gas analyses for sulfur dioxide were made by means of a n Orsat apparatus a t the entrance and exit of the tower. Temperatures of entering and leaving gas and liquor were obtained with thermometers. The operating conditions were maintained uniform for a sufficient period of time before and after a run so that there was no chance of accumulation or depletion in the system during the run. Between series, the tower was cleaned and repacked and, in some cases, modification of the liquor distributing head was made.
states that the rate of absorption (dW/dO) is e q u a l t o t h e product of the specific r a t e of a b s o r p t i o n (ka),the volume of absorption apparatus (dT?), a n d a d r i v i n g f o r c e (Acj, which in this equation has been taken as the difference in conc e n t r a t i o n of solute between gas and liquor. The equation m a y be w r i t t e n i n t e r m s of diffusional resistance (TI,), crosssectional area (A), and height ( d l ) of tower dTT' - i l d l i c d% rL
This equations holds for diffusion through a liquid film and may be used a l s o w h e r e tlie major resistance to absorption ih the resistance of the liquid film. 4 similar equation:
applies to gas film diffusion, or where the major resistance to absorption is encountered in the gas film. I n intermediate cases, where both gas and liquid films offer substantial resistance to diffusion, individual film resistances cannot be determined directly. If the system follows Henry'.< law, the equations may be integrated readily to yield an over-all resistance t o absorption ( R ) . Thus,
where (Acja,.. and ( A P ) ~ ~are . the logarithmic mean driving forces through the tower expressed as concentration difference and pressure difference, respectively. I n the absorption of sulfur dioxide, Henry's law does not hold, so that the values of RL and R G have been obtained by graphical integration (see Methods of Calculation) of Equations 2 and 3, expressing the results as over-all resistances. The diffusional resistance, R L , is composed of t\vo resistances in series, that of the gay film and t,liat of the liquid film, through which the solute must diffuse:
DISCUSSIOK OF RESULTS
= rL =
RL = Hro -k rL (6) resistance of gas film resistance of liquid film, both expressed in concentration units, and €I being the solubility coefficient of sulfur dioxide in water and used here for converting from pressure units to concentration units.
Similarly, but using pressure units,
The basic absorption equation
I N D U S T R I A L A N D E N G I N E E R I S G C H E AI I S T R Y
The effect of liquor velocity on the over-all resistance is shown in Table I, where liquor velocity varies between 2.50 and 56.2 pounds per per square foot Of tower Cross section. Gas velocity was maintained reasonably constant a t '.j8 pounds per IninUte per 'quare foot, and the liquor constant around 760 F' Inspection sho'vs temperature 100 80
200 RL = Lo.ag
In order to study the gas film, i t is desirable that runs be liquor velocity, so that the resistance of the lllade at a liquid filln may be reduced. Table 11 shows the results of a series of runs a t an average liquor velocity of 41.6 poullds per minute per square foot and an average temperature of 58" F. On the basis that RL varies inversely as the 0.89 power of liquor velocity, the values of RL have been corrected to the average liquor velocity for this series in the sixth column of Table 11. Plotting the corrected resiqtance us. gas velocity on logarithmic paper (Figure a),TT-e find a slope of -0.57. The fact that this slope falls conqiderably below the slope to be expected if gas film resistance were controlling, can be explained by appreciable resistance to absorption in the liquid film. I t has been shon-n ( 1 ) that the resistance of the ga* film is inversely proportional to the 0.8 power of the gai velocity. Thus:
H GO 8
liL = -
8 0 100
that a large yariatioii in RL is obtained, although it i- not quite inversely proportional to the change in liquor velocity. This decrease in resistance with an increase in liquor velocity may be caused by a n increased area of absorption or by increased turbulence, causing a thinning of the liquid film through which diffusion is taking place. Since the liquor flow was unifornily distributed a t the top of the toner, the change in the resistance due to changing area of interface is undoubtedly small. The large effect of liquor wlocity shows that either the liquid film offers the major resistance to absorption or t h a t a n increase in liquor velocity has the qame effect on the film thicknesses of both gas and liquid, the latter being extremely improbable.
This enables plotting RL vs. 1 G1 to obtain the apparent resistance of tlie liquid film (Figure 3). This apparent liquid filni resistance varies between 19 and 33 per cent of the total resistance in this series of run%.
POUNDS PER UIN PER SQ FT
F I G I ~ 1. ~ ~ EFFECT E OF LIQUORVELOCITI RESIST4NCE Rr.
T ~ B LI1 E
B1 I32 B3 H4
I36 I37 B8 I39 '/ G
Lb./nkn./sq. /1. F. 0.98 42.3 62 7.87 7.99 620 1.016 0.99 47.0 61 6.65 7.40 465 1.008 1.38 42.0 62 6.i6 6.81 595 0.797 1.37 38.8 61 6.70 6.30 570 0.778 1.84 38.8 54 6.02 460 0.615 5.66 1.94 39.4 54 5,Ql 5.64 455 0.589 2.03 43.0 3'; 4.36 4.49 395 0.568 2.19 43.9 JJ 4.il 4.64 370 0,5:34 2.30 41.8 55 4.87 4.89 385 0.513 gas velocity, Ib./min./sq. i t . : L = liquor veliicity, Ib./rnin./sq.Et.
Returning t o the initial assumption that the liquid film reoist'ance is coiit'rolliiig the diffusion of sulfur dioxide, it' is paradoxical that even a t this high liquor velocity the niajor resistance should appear to occur in the gas film. This may be explained by assuming that, in a tile-packed tower a t tlie TABLEI. EFFECTOF LIQUORVELOCITYo s DIFFL-SIOYAL liquor rat'es employed, passage of tlie gas stream causes violent RESISTASCE tiirbulence in t'he liquor. Thus the liquid film resistance map LIQCOR GAB LIQCOR be reduced by increasing the liquor flow rate or by inciting RCN 1-ELOCITY YELOCITT TEMP. RL" RGi' greater turbulence due to higher gas velocit'y. The latter P o i k n d s / m z ~ i . / s q ..it. F. A1
.13 .14 A5 .16
A7 A8 .I9
2.50 5,18 6.85 7.71 9.09 14,08 25.6 28.1 56.2
2.34 0.82 1.89 1,28 1.19 1.62 1.79 1.52 1.75
77 75 7% 81 75 77 72
89.0 47.0 19.9 34.1 23.6 17.0 8.25 9.7' 5.94
11580 5980 2400 4330 3040 2320 996 1175 624
1 = Ib/rnin./cu. f t . / [ l b . / c u . i t . ) b R G = 1 Ib./miri./cu. ft./rnm. of Hp
The data of Table I are plotted in Figure 1 on a logarithmic scale, showing the relation between resistance t o absorption ( R L )and liquor velocity ( L ) ; the data points falling on a straight line. Further indication of a relatively small gas film resistance is brought out in this plot, where the solid points represent runs in which the gas velocity was abol-e the average, and the circles represent runs of lower gas velocity. If gas film resistance were of importance, the solid points would fall well below the straight line, the circles well above. KOsuch effect is noticed. The slope of the line is -0.89, yielding the equation:
; 9 6
CAS VCLOCITI POUNDS PER MIH.PLR $%IN.
FIGURE2 . EFFECTOF GAS VELOCITY OY D I F F U S I O Y l L RESISTANCE
nieclianism is less violent than the former, so that its effect is not noticed in the first series of runs a t varying liquor rates, but in this series a t constant high-liquor velocity and varying gas velocity it plays a inajor part in reducing liquid film resistance. To present the other side of the picture, t,lie correlation between Ro and gas velocity is also shown in Table I1 and Figure 4. They do not fall in together as well as the values of R L corrected to a constant liquor velocity. Figure 5 S ~ O T V SRG plot,ted against' 1,'Go.*. The intercept of
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Vol. 25, No. 4
Series E and F (Table 111) were run a t higher liquor velocities, giving lower over-all resistances than in the previous series. The proportion of total resistance due to the liquid film is larger in these series, causing a more pronounced temperature effect than before. At the high liquor velocities a t which series B, E, and F were run, it is probable that the gas is bubbling through the stream of liquid as in a bubble-cap column, yielding low gas-film resistance. This would account
FIGURE3. OF APPARENT DIFFUSIONAL RESISTANCE, rL, OF LIQUID FILMON CONCENTRATION BASIS the line with the axis corroborates the results shown in Figure 3. Further proof that liquid film resistance controls the rate of diffusion of sulfur dioxide into water in this type of apparatus is afforded by a study of the effect of varying temperature. Table I11 presents the results of four series of runs a t temperature between 38" and 127" F. The effect of temperature over this range is about equal to a fourfold increase in liquor velocity. Previous investigators ( I ) , studying absorption in a wetted-wall tower, have found that an increase in temperature causes an increase in gas film resistance and a decrease in liquid film resistance. Figure 6 shows the effect of temperature on the over-all resistance, plotted on semi-logarithmic paper to facilitate comparison. I n series C (Table 111) the decrease in liquid film resistance ( T L ) is greater than the increase in gas film resistance (HTQ),with a consequent reduction in the over-all resistance (RL) as temperature
increases. Series D was made a t practically the same liquor velocity as series C, so that the decrease in liquid film resistance with temperature should be about the same in each. The gas velocity in series D was nearly 2.5 times as great as in C, resulting in a much smaller gas film resistance a t any temperature and consequently less effect of gas film on the over-all resistance. Therefore, there is a greater proportional decrease in the over-all resistance in series D for the same temperature rise, as indicated by the relative slopes of curves C and D in Figure 6.
FIGURE 5. CALCULATION OF APPARENT DIFFUSIONAL RESISTANCE, rL/H, OF LIQUIDFILMON PRESSURE BASIS for the results obtained a t varying gas velocity (series B, Table 11) and for the large effect of temperature in series E and F (Table 111).
TABLE111. EFFECT OF TEMPERATURE ON DIFFUSIONAL RESISTANCE RUN
c1 C2 c3 c4 c5 C6
D2 D3 D4 D5
E2 E3 F1 F2 F3 F4 F5
CAS VELOCITY POUNDS PER UUI.PFR SP.IH
FIGURE 4. EFFECT OF GAS VELOCITY ON DIFFUSIONAL AESISTANCE RQ
LIQFOR LIQUOR GAS TEXP. VELOCITY VELOCITY F. Pounds/min./sq. ft. 38 20.5 0.77 54 23.2 0.69 69 22.6 0.82 83 21.0 0.68 97 20.5 0.67 120 18.8 0.80 39 19.2 1.65 42 21.6 1.41 61 19.8 1.69 80 20.9 1.61 97 20.9 1.81 40 40.6 0.86 80 34.1 0.79 127 36.5 0.57 40 60.1 1.78 59 58.4 1.47 73 60.1 1.56 85 61.2 1.37 95 53.5 1.30
R 11. 18.6 15.9 13.1 12.3 10.1 10.0 16.5 17.1 11.6 10.4 6.4 17.5 7.4 2.5 9.26 6.14 4.18 3.88 2.67
R 0, 955 1160 1310 1620 1790 2500 960 1060 1090 1340 1150 775 760 970 495 420 380 510 440
Since the solubility coefficient ( H ) for sulfur dioxide in water decreases rapidly with increase in temperature, its change may account in part for the decrease in over-all resistance computed on a concentration basis. Consequently, the over-all resistance has been recalculated on a pressure basis and the results are shown in Figure 7 . While the values for series C and D fall on reasonably straight lines, showing an increase in over-all resistance ( R c ) with temperature, series E and F show no definite trend. This is to be expected, since in the latter two series the resistance is largely in the liquid film, Where gas film resistance becomes of more importance, as in series C and D, its effect is noticeable. A comparison of these results with the effect of temperature on the absorption of sulfur dioxide in a wetted-wall tower (1) indicates that over-all resistance on a concentration basis (RL) for a wetted-wall tower falls on a straight line parallel to curve D (Figure 6). Keeping liquor velocity constant and
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increasing the gas velocity lowers the over-all resistance, but yields parallel lines for temperature os. over-all resistance. Of little significance, but possible interest, are the effects of temperature on the viscosity of water and on specific rates of diffusion for gases dissolved in water. overthe temperature range studied here, the viscosity-temperature curve for water
Since s varies between a maximum of 1.008 and 0.987 for the extreme conditions in any of these runs, a mean value of 1.003 has been used. As the highest value of encountered is 1.21, the error introduced by this mean value will be small. Hence: C
Substituting this term in Equation 10 and differentiating:
-d W_ dB
62.6L'.4dc (62.6 - c)'
Equation 2 states that: _ d W= -
For determining the over-all resistance, this may be rewritten:
FIGURE 6. EFFECTOF TEMPERATURE ON
DIFFUSIONAL RESISTANCE RL
TABLEIv. EXPERIMENTAL DATAa Av. (SO?PER PRESSURE SO, PRESSURE LIQUOR RUN ACID RATE cu. FT.) Top Bottom Top Bottom TEMP. Cu. ft./min. Lb. M m . Mercury M m . Mercury F. A1 130 74 0.071 0.896 708 116 127 74 A2 0.147 0.812 699 96 108 77 0.194 0.841 693 87 A3 122 75 95 A4 0.745 698 0.218 78 0,745 698 119 0.257 A5 85 124 81 0.700 696 0.398 88 A6 75 0.725 0.775 687 126 A7 67 77 119 59 0.621 691 0.796 A8 72 115 34 0.519 673 1.590 A9 B1 1.200 0.571 724 10.7 140.5 62 5.7 B2 1.333 0.492 726 128.5 61 19.9 131 62 B3 1.191 0.665 731 703 22.4 61 B4 1.100 0.733 128 1.100 27.1 54 124 B5 0.902 696 0.949 29.7 54 708 131 B6 1.117 0.837 27.9 62 1.217 682 116 B7 55 B8 0.955 28.4 1.158 678 116 32.2 55 116 B9 0.948 1.183 666 732 15.0 134 38 0.844 731 C1 0.584 729 17.5 129 54 C2 0.658 0.630 729 C3 0.642 0.643 714 725 35.7 129 69 C4 0.595 0.556 706 731 38.8 130 83 126 97 C5 0.581 0.483 687 728 46.7 134 120 C6 0.533 0.388 728 75.2 632 700 56 129 39 D1 0.545 1.210 670 D2 0.615 721 51 131 42 1.010 719 689 704 71 132 61 D3 0.564 1.003 D4 0.594 0.730 682 716 73 I29 80 D5 0.594 0.632 664 716 81 125 97 96 40 El 1.150 0.348 725 734 8.7 98 80 E2 0.967 0.398 700 711 9.8 127 18.4 110 E3 1.033 0.311 634 640 18.2 131 40 728 735 F1 1.700 0.629 F2 1.650 0.506 720 728 9.2 114 59 F3 1.700 0.435 714 721 9.3 96 73 15 I22 85 F4 1.733 0.460 714 726 16.4 129 95 F5 1.517 0.528 713 718 a Packed volume of tower: series A, B. C, D = 9.75 D U . ft.: series E , F = 10.15 cu. it. Internal diameter of tower = 1.50 ft. Packing: 3 X 3 inch spiral tile, packed in layers, staggered. Feed liquor: water.
The amount of sulfur dioxide absorbed in any section is:
Rearranging and substituting Ac de (62.6
- c)'(c, - C )
The left-hand side of this equation is integrated graphically as follows: 1 vs. c and obtain the area under the 'lot (62.6 - c)'(c, - c) curve between c = 0 and c = CO. The values of c, - c are obtained by plotting the operating line on the x-y diagram 4000
g Y h
FIGURE7. EFFECT OF TEMPERATURE ON DIFFUSIONAL RESISTANCE
RQ following the procedure outlined by Walker, Lewis, and McAdams (5). From this line the data are replotted on the c-p diagram, along with the equilibrium curve for the required temperature. The equilibrium values are taken from data assembled by Sherwood (4). The calculation of
The calculation of RL is as follows:
62.6L'Adc - -AdlAc (62.6 - c)' RL
Equating (13) and (14):
is practically parallel to curve C. Specific rate-of-diffusion data are meager, but such as are available for carbon dioxide in water, calculated as resistances, yield a line parallel to curve C. The products of these specific diffusion resistances by the corresponding viscosities of water give a curve of about the same slope as series E and F. ANALYSISOF ACID
= -A d l a c
RQ is as follows:
Fol1owing:the method outlined above for calculating RL:
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rewritten in terns of over-all resistance: (19)
Differentiating (18) and ccnbining w t h (19):
Vol. 25, No. 4
G' = inert gas velocity, ib./min./sq. it. H = solubility coefficient = c,/p, k = absorption coefficient, lb./min./sq. ft./(lb./cu. ft.) L = liquor velocit,y, lb./min./sq. ft. L' = water velocity, lb./min.jsq. ft. 1 = height of active tower, ft. p = pressure of sulfur dioxide, mm. of Hg P = total pressure of gas, mm. of Hg ?'G = gas film resistance (lb./min./cu. ft./mm. Hg)-l rL = liquid film resistance [lb./rnin./cu. ft./(lb./cu. ft.)]-' RG = over-all diffusional resistance (lb./min./cu. ft./mm. of Hg)-* RL = over-all diffusional resistance [Ib./min./cu. ft./(lh./cu. ft.)]-1 s = ep. gr. of liquor 1' = active (packed) volume of tower, cu. it. W = weight of sulfur dioxide, lb. 2 = liquor concentration, lb. SOz/lb. H20 y = gas concentration, lb. SOz/lb. inert gas b = time, min. Subscripts: o, at bottom of tower; ', at top of tower; at equilibrium.
LITERaTURE CITED The two integrals on the left of this equation are integrated graphica,lly, following a similar procedure to that employed in solving Equation 17. hTOhIEKCLATURE
sp. area of interface, sq. ft./cu. ft. active tower volume
A = cross-sectional area of tower, sq. ft. B = a constant c = concentration of liquor, lb. SOn/cu. ft. G = gas velocity, lb./min./sq. ft.
(1) Haslam, Hershey, and K e a n , ISD. ESG. CHEM.,16, 1224 (1924). ( 2 ) Lewis and Whitman, I b i d . , 16, 1215 (1924). (3) Mass. Inst. Tech,, School of Chem. Eng. Practice. Unpublished Repts. (4) S h e r w o o d , . I s ~ .ESG. CHmf.,17, 745 (1925). ( 5 ) K a l k e r , Lewis, and Slc;ldams, "Principles of Chemical Engineering," 2nd ed., p. 680, McGraw-Hill, 1927. RECEIVEDNovember 18, 1932. Presented before the meeting of the American Institute of Chemical Engineers, Washington, D. C., December 6 to 9, 1932.
Heat Flow through Bakery Products I. Time-Temperature Relationships Existing during t h e Baking of Bread LAWRENCE E. STOUT. ~ K DFREDDROSTEN, Washington University, St. Louis, &io.
Time-temperature relationships during the mental data in their study for b r e a d h a s become a baking of bread indicate that the baking operafion four k i n d s O f b r e a d a t o v e n temperatures of 230" C. highly specialized indusmay be divided into three general periods. S u m e r o u s other investigat r y , y e t it i s o n e w h i c h is First, there is a rapid rise in temperature Within tors have studied the baking of governed by empirical standards. the loaf. T h i s is followed by a progressipe debread, but t h e i r r e p o r t s seem Oven temperatures and time of subject to criticism as follows: baking are fixed by experience crease in rate of temperature rise which, in turn, B a l l a n d (1) used maximumand the Only test for "baked" precedes the third or final period of consfant temperature thermometers and load of bread is the physical aptemperature. During the Jirst two periods the f o u n d a recorded temperature pearance of the crust. From an rate of rise in femperature varies with the applied of 101" to 102" C. His work engineering standpoint it A T but during the third period the AT has no shows no time-temperature redoubtful that such control of the lationships. G i r a r d ( 2 ) theobaking operation can take care of effect upon the constant temperature registered. the possible variations in condirized concerning t h e w o r k of This third period must be at least 9 minutes long Balland but added no experitions that are likely to arise from lo insure a done loaf of bread. m e n t a l d a t a . M a l l e t t (3) time to time. It would seem that studied the baking of bread using a critical study of the baking of bread might disclose some time-temperature relationship that alum baking powders. Read (6) determined the temperatures attained, the rate of temperature change, and the points would insure a properly baked loaf as a finished product. The literature contains few complete experimental data of change for bread baked one hour in a n oven at 173" C. on the time-temperature relationships during the baking of These last-mentioned baking conditions do not conform to a loaf of bread under ccmmercial temperature conditions. usual oven temperatures, and the thermometers were inserted As previously mentioned, Platt (6) stated that the done loaf when the bread mas put into the oi-en. This means that t h e of bread attained a temperature of 100" C. Tenny ('7) dis- loaf was punctured just before baking and possibly does not cusses the cooling cf bread in a recently published article and represent a normal loaf of bread. Moreover, Read states gives cooling curves to show the time-temperature relation- that the literature contains nothing on the subject. ships existing when bread cools. These readings were obtained b y inserting a thermcmeter within the loaf of bread BAKISG TESTS immediately after its withdraval frcm the oven. He names The experimental attack on this problem consisted of 210' F. (98.9" C.) as the initial ccoling temperature. Keumann a n d Ealecker (4) approach completeness of experi- baking a large number of loaves of bread under controlled HE commercial baking of