INDUSTRIAL AND ENGINEERING CHEMISTRY
November, 1924
1157
Rate of Absorption and Equilibrium of Carbon Dioxide in Alkaline Solutions'" By R. V. Williamson and J. H. Mathews UNIVERSITY
N THE commercial production of carbon dioxide, less than one-half the total gas can be saved economically for market purposes. The purpose of this investigation was to study the factors influencing the rate of absorption of carbon dioxide in alkaline solutions, in order to determine the possibility of increasing the efficiency of commercial production.
I
APPARATUS
O F WISCONSlN, M A D I S O N , WIS.
The eflect on the rate of absorption of increasing the rate of liquid flow under conditions of liquid surface oarying f r o m a perfectly smooth surface to a oery turbulent one, and the result of increasing the rate of gas flow when a slight excess is already passing through the tower have been studied. The rate of absorption of carbon dioxide in potassium carbonate solutions is practically independent of the concentration of potassium carbonate. It increases with a rise in temperature u p to a maximum oj 70' or 75 ' C. and then decreases as the temperature is increased. With the apparatus used, a 48 per cent decrease i n the loss of carbon dioxide escaping f r o m the tower and a decrease of 26 per cent in the time of operation were obtained under a gioen set of conditions by carrying on the absorption at 70" C. instead of 25a C., prooided the absorption was stopped when a saturation of 65 per cent was obtained. A n equation has been developed for calculating the rate of absorption of carbon dioxide in alh.aline solutions. A method is gioen f o r determining equilibrium conditions for K:CO,, KHCO3, and COz at diflerent temperatures with a minimum amount of experimental data.
A n a p p a r a t u s was develooed on the counterflow prinhple, as shown in Fig. 1. The tower and reservoir were made from 7.62-cm. cast-iron pipe and t h e i r c o m b i n e d height was 182 cm. The solution used as the absorbing agent was pumped from the reservoir T by the pump B, and by regulating the overflow valve F the solution could be forced into the top of the tower through t h e sprinkler G a t any desirable rate. The rate of liquid flow was measured by the mercury-filled flowmeter C. The solution flowed over the baffles W , as i t descended into the reservoir, and in so doing absorbed the carbon dioxide which was circulating in the opposite direction as i t passed from the gas entrance to the c.xit D. The composition of the gas mixture as well as its rate of flow through the apparatus was regulated by the valves Q and Q". One valve controlled the air supply and the other the carbon dioxide. By means of the cylinder X, a constant gas pressure was maintained. The flowmeters R and R' served t o determine the amount of each constituent of the gas mixture which entered the apparatus; R" was a calibrated gas meter used for determining the total amount of gas passed through the apparatus and also for calibrating the flowmeters for maintaining a gas mixture of definite composi- G tion; T' was a water manometer for measuring the pressure of t h e gas; A', A"' was a n electrical heating circuit for controlling the temperature of the entering gas; iM was a valve for controlling t h e pressure of the gas in t h e tower; S was a water-filled flowmeter for , measuring t h e rate at which excess gas escaped from t h e tower; S' was a gas meter for measuring the amount of gas which was not absorbed; A , A ', A was a n electrical heating circuit for controlling the temperature of t h e solution; V was a cork which floated on the surface of t h e solution to prevent absorption of carbon dioxide while the air was being blown out of the
LIQUIDFLOW Three types of absorption chamber were used in the study of theeffect of therate of liquid flow on the rate of a b s o r p t i o n-namely, (1) the baffled tower shown in Fig. 1; (2) the same tower packed with approximately round pebbles, 2.5 em. in diameter; (3) a specially constructed absorption box in which the surface of the liquid Was as nearly level as possible and without movement in any particular direction, although the , liquid beneath the surface was flowing a t the rate of 10 em. per second. F~~an increaseof per cent in the rate of liquid flow, after the surface over which the solution flowed was completely wet, the following increases in rate of absorption were obtained:
Received November 19, 1925. This paper constitutes the major part of a thesis submitted by R. V. Williamson in partial fulfilment of the requirements for the degree of Doctor 1
2
of Philosophy at the University or Wisconsin.
tower previous to starting experiment; a t E was placed a wire screen t o prevent the cork float from becoming misplaced in the reservoir when the solution was withU was a stopcock drawn. for draining the apparatus and also For removing samples f o r a n a l y s i s t o check the metered results or, in cases of high temperatures, as the means of following the course of the experiment.
FIG 1
RATE O F
Pebble-packed tower Baffled tower Speclal absorption box (floor level)
Per cent 66 50 25
These data show a substantial increase in the rate of absorption when the rate of liquid flow is increased, although there may be no disturbance of the surface. The greatest effect is produced, however, under conditions of greatest turbulence. RATEOF GASFLOW With constant pressure, an increase of 100 per cent in the rate of gas flow, when a slight excess of carbon dioxide was passing through the tower, caused an increase of 40 per cent in the rate of absorption and a loss of slightly over 60 per cent of the increased flow of carbon dioxide. This means that the percentage loss was multiplied many times by doubling the rate of gas flow when a slight excess was already passing through the
1158
INDUSTRIAL AND ENGINEERING CHEMISTRY
tower. In commercial practice, the rate of flow would be governed by the amount of gas that could be economically allowed to pass out of the tower. CONCENTRATION OF SOLUTION Preliminary experiments on the effect of concentration of potassium carbonate on the rate of absorption of carbon dioxide in a solution of potassium carbonate indicated that the rate of absorption was independent of the concentration of the salt. Some experiments were then conducted on the rate of absorption of carbon dioxide in solutions of potassium hydroxide of different concentrations. The results of these experiments are shown graphically in Fig. 2. At the first break in Curves I and 11, indicated by the arrows, enough carbon dioxide had been absorbed to convert all the potassium hydroxide to potassium carbonate. At the second break enough additional carbon dioxide had been absorbed to convert the potassium carbonate to bicarbonate. The remainder of these curves represents the saturation of the solution of bicarbonate. I n the case shown by Curve I11 no bicarbonate is formed and there is no break in the curve as in the case of the potassium hydroxide. From these curves it is apparent that the rate of absorption is very greatly increased by increasing the concentration of potassium hydroxide, but is almost independent of the concentration of potassium carbonate. It also appears that the initial rate of absorption in distilled water is almost the same as in potassium carbonate solution^.^ A study of these curves showed that the rate of absorption in either a potas-
Vol. 16, No. 11
tional to the amount of hydroxide and inversely proportional to the amount of bicarbonate present. Assuming the rate of absorption of carbon dioxide in water for this particular apparatus to be 2.4 liters per minute, the rate of absorption can be expressed in liters for any solution for this apparatus, as follows: Rate =
+
(K X COH)- (K'X C H C O ~ ) 2.4
The concentration of HC03ions is proportional to the concentration of hydrogen ions so that the equation may be written: Rate
=
(K X COH)- ( K " X CH)
+ 2.4
I n Fig. 3 is shown graphically the rate of absorption of a 0.6 N solution of potassium hydroxide plotted against the normality of potassium hydroxide on the z axis to the left of the middle of the figure and against the concentration of potassium carbonate to the right of the middle of the figure. The results of the application of the equation as compared with experimental results are shown by the circles on Fig. 3. The discrepancy a t the lower end of the curve is due to the experimental difficulty of determining the hydrogen-ion concentration of a solution of potassium bicarbonate. The equation may also be used for predicting the rate of absorption of carbon dioxide in any water solution if the hydrogen-ion concentration is known. The hydrogen-ion concentration of 0.5 N solutions of trisodium phosphate, sodium carbonate, and disodium phosphate were determined and from these data the hydroxyl-ion concentrations were calfi9 3. Curve8 sbowm9 rdofion of rote of absorpt/on fo the
re/ohve concenfrof/ons of KOH KcCOs XHCO3
p's 11.32 040
$
B::
2-p:
030
g 849
k
8 s
0./0
2.83
NormoMy K'CO,
sium hydroxide or carbonate solution was equal to the absorption in distilled water plus an amount which was propor8 The work of Ledig and Weaver [J.A m . Chem. S O L . ,46, 650 (1924)1, published since this work was done, shows that when carbon dioxide is bubbled through a n absorbing liquid the rate of absorption per square centimeter is greater in distilled water than in sodium carbonate solutions. This would not be apparent in a large apparatus of the tower type, because t h e absorption gradient between the top and the bottom of the tower would be abnormally great with water as compared t o alkaline solutions, owing t o the marked decrease in the absorption rate for water when a small amount of carbon dioxide is present.
culated. The values for the hydrogen and hydroxyl-ion concentrations were then substituted in the formula and the rates calculated. A comparison of the calculated and experimentally determined rates is given in Table I. TABLE I -RATE Solution NaaPOa NazCOa NazHP04
OF ABSORPTION---
Experimental Liters/Min.
3.40 2.55 1.87
Calculated LiterdMin. 3.60
2.58
1.81
COH
2
x
10-2
2 . 7 X 10-8 8 . 7 X 10-6
INDUBTRIAL A N D ENGINEERIhrG CHEMISTRY
November, 1924
1159
MECHANISM OF ABSORPTION OF CARBON DIOXIDE I N ALKALINE rate of absorption will reach a maximum valueif the other variSOLUTIONS Whitman and Keats* have pointed out that the diffusion of a gas into a liquid in cases where there is no chemical reaction between the gas and the liquid obeys the laws of heat transfer. They picture the diffusion as taking place across a two-film resistance; one film is a stationary liquid film and the other a stationary gas film a t the liquid-gas
ables are kept constant. This was experimentally verified by measuring the rate of absorption for increasing concentrations of potassium hydroxide solutions. The equation also shows that if the quantity r is reduced, the rate of absorption should be increased. Stefan5has shown that the diffusion of carbon dioxide into alcohol is nearly double the rate of its diffusion into water. If this is due to the lower value of the liquid film resistance of alcohql or the value r in the equation, the result should be an increased rate of absorption in an alcoholic solution of potassium hydroxide over that of a water solution of the same concentration. This was also verified experimentally, and the results of the experiments on the rate of absorption in both the water solutions of potassium hydroxide of varying concentration and of alcoholic solutions are given in Table 11. Normality of solution
TABLE I1
5 5 2 0
1 0 0.6
Rate of absorptiona 9 6
9 6 3 4
0 0 3 8
0 6 alcoholic solution (95%) a Expressed in cubic centimeters of normal potassium hydroxide neutralized per minute in a sample of 20 cm. of solution.
These data show that increasing the concentration of potassium hydroxide above 2 N had very little effect on the rate of absorption; that is, the rate of absorption approaches a maximum at a concentration of about 2 N , which is in accordance with the predicted results. The alcoholic solution absorbed very much faster than the water solution of the same concentration, which is also in accordance with the predicted results.
junction. The rate of diffusion is directly proportional to the differencc: in the driving force between the two films and inversely proportional to the film resistance. I n the case of a gas diffusing into a liquid, the driving force will be the difference in pressure between the gas in the liquid film and in the gas film. The writers' experiments are compatible with this idea if it is assumed that the function of the hydroxyl ions is to decrease the pressure or concentration of the carbon dioxide in Ihe liquid surface film. This increases the potential drop or driving force between the two films and thus increases the rate of diffusion. The rate of absorption can be expressed by the equation: - P K X pR f r where P equals pressure in gas phase; p,. pressure in liquid Rate
=
phase; E , gas film resistance; r , liquid film resistance. Any factors influencing the variables in this equation will influence the rate of absorption. For example, stirring the liquid will cause a more rapid diffusionof the carbon dioxide, combined or uncombined, from the surface film into the main body of the solution and thus reduce the value of p in the equation. Likewise, an increase in the concentration of hydroxyl ions will cause reaction with the carbon dioxide and thus reduce the value of p . It is apparent from the equation that if sufficient hydroxyl ions are added to reduce the value of p to such a small quantity that it becomes negligible, the 4
THISJOURNAL, 14, 189 (1922).
EFFECTOF TEMPERATURE ON RATEOF ABSORPTION IN POTASSIUM CARBONATE SOLUTIONS The effect of temperature on the rate of absorption of carbon dioxide in potassium carbonate solutions of 0.1 and 0.5 N concentrations a t temperatures ranging from Oo to 90" C. 6
Chem. Zentr., 49, 369 (1878).
INDUSTRIAL A N D ENGINEERING CHELWISTRY
1160
and for gas mixtures ranging from 4 to 100 per cent carbon dioxide was studied. The temperature of the apparatus was kept constant to within *lo C. The course of the reaction was followed by withdrawing samples of 20 cc. a t definite intervals and titrating the amount of bicarbonate formed by the Winkler method. Titrations were also made for total alkali in each sample to correct for any change of concentration due to evaporation or change in volume with change of temperature of the
Vol. 16, No. 11
I n Fig. 5 is shown the percentage increase in the rate of absorption plotted against the temperature for gas mixtures of 4,25, 50, and 100 per cent carbon dioxide. It is apparent from these curves that an increase of 60 per cent in the initial rate of absorption is obtained by maintaining the solution a t a temperature of 70" or 75" C. instead of 25" C. It will be noted from Fig. 4 that the rate of absorption drops off more rapidly at the higher temperatures than a t 25" C. However, therateof absorption is higher a t 70" than a t 25" C., until 65 per cent of the carbonate has been converted to bicarbonate. It appears, therefore, that the best conditions for the recovery of carbon dioxide by absorption in potassium carbonate solutions and later expulsion from solution by boiling are (1) to cool the weak liquor coming from the boilers to approximately 75" C. and to maintain it a t that temperature; (2) to continue the absorption until 65 per cent of the carbonate solution has been converted to bicarbonate; and (3) return it to the boilers for boiling off the carbon dioxide, thus converting the solution to carbonate again. Experiments with the apparatus used in this research showed a decrease of 48 per cent in the loss of carbon dioxide escaping from the absorption tower when a gas mixture of 4 per cent carbon dioxide was passed through the apparatus a t the rate of 2.83 liters (0.1 cubic foot) per minute and a t a temperature of 75" C. (instead of under the same conditions except a t a temperature of 25" C.), provided the experiment was not carried beyond a conversion of about 65 per cent of the carbonate to bicarbonate. Not only was the loss in carbon dioxide decreased 48 per cent, but the time of operation was decreased 26 per cent.
EFFECT OF PARTIAL PRESSURE % COP /n
gas
m/xfurc
solution. The quantity of alkali necessary for each titration was measured into a flask previous to taking the sample in order to lessen the interval between the time of removing the sample from the apparatus and adding it to the alkali, so as to avoid changes in equilibrium. Previous to taking the sample, the flask and pipet used for sampling were filled with gas of the same composition as that entering the tower, so as to prevent decomposition of the sample due to a difference in the partial pressure of carbon dioxide within the apparatus and that of the atmosphere of the room. This method of following the reaction was necessary because of the difficulty of controlling all the varying factors and reading the gas meters during the experiments. The samples were measured into the alkali solution a t definite intervals during the experiment and titrated after finishing the experiment. From the data thus obtained, the rates of absorptib were calculated when certain fractions of the total carbonate had been converted to bicarbonate. These rates were then plotted against the percentage of carbonate converted to bicarbonate. In Fig. 4 is shown a typical set of curves. It will be noted that the curve a t 25OC. shows more than 100per cent of bicarbonate formed. This is due to the fact that at 25" C. not only is all the carbonate converted to bicarbonate, but the solution dissolves an added amount of carbon dioxide in excess of that necessary to convert the carbonate to bicarbonate. At the higher temperature, however, the carbonate is not completely converted to bicarbonate with the concentration of gas used in this set of experiments. It is apparent from this set of curves that a maximum in the rate of absorption is reached a t about 70" C. Either above or below this temperature the rate of absorption is less. This was found to be true for all gas mixtures from 4 to 100 per cent and for 0.5 and 0.1 N solutions of potasaium carbonate.
From the data obtained in connection with the effect of temperature on the rate of absorption, the rates of the various gas mixtures a t 25" C. were plotted against the partial pressure of the carbon dioxide, as shown in Fig. 6. From this curve it is seen that the rate of absorption is directly proportional to the partial pressure of the carbon dioxide. VARIATION OF RATEOF ABSORPTION WITH TEMPERATURE There are two factors working in opposition to each other which tend to produce changes in the rate of absorption with change of temperature, as shown in Fig. 5. As the temperature is increased the rate of diffusion of the gas into the solution is increased, owing to variations in the resistance of the gas and 4o liquid surface films and 9 to a decrease in the E pressure of the carbon dioxide in the liquid surface film produced by the increased velocity of the reaction between the free alkali and the carbon dioxide. On the other hand, as the temperature is increased the partial presPercentwe Compos/fm'lcn sure of the carbon dioxide is reduced, owing to the increased partial pressures of the water vapor. The effect; of the increased diffusion is greater than the decrease in partial pressure of the carbon dioxide until a temperature of 70 or 75" C. is reached. At this point the decrease in partial pressure of the carbon dioxide more than counterbalances the increase in diffusion; therefore, the rate of absorption decreases with a continued increase of temperature. I
O
November, __ - _. 1924 _ I
~
_ _ INDUSTRIAL A N D ENGINEERING CHEMISTRY
EVOLUTION OF COSFROM A BOILING SOLUTIONOF KHCOl
As is well known, the amount of bicarbonate in equilibrium with the carbonate in a solution of the alkali carbonates decreases very rapidly with rise of temperature, especially above 75" or 80" C. At the boiling point the decomposition proceeds very rapidly for a short time and then becomes slower and slower as the proportion of carbonate to bicarbon4te increase?. I n the manufacture of carbon dioxide it is desirable t o convert the bicarbonate to carbonate in as short a time as possible. Some experiments were performed to determine the effect of raising the boiling point of the solution by increasing the pressure on the system. This was accomplished by fitting two flasks containing 200 cc. of 0.5 N potassium bicarbonate solution with rubber stoppers carrying a thermometer and 6-mm. exit tube bent so the exit could be dipped into a cylinder containing mercury. One of the flasks was arranged so that the exit was 50 mm. below the surface of mercury in a glass cylinder, while the other was open to the atmosphere. The solutions were heated so that distillation took place a t practically the same rate in each. Five cubic centimeter samples were removed a t measured intervals and titrated to determine the change in concentration. The data are shown in Table 111.
'
1161
By determining the equilibrium conditions for a given partial pressure of carbon dioxide a t the limits of the temperature range desired and plotting the results as a straightline function of the temperature, the ratio of carbonate and bicarbonate can be determined for any other temperature within those limits. By use of the modified McCoy and Smith equation
* Pcoz
= partial pressure of carbon dioxide in the gas phase.
the ratio of carbonate to bicarbonate can be calculated for any other partial pressure of carbon dioxide. I n Fig. 7 are given graphical data showing the relation of the partial pressure of carbon dioxide to the percentage composition of
TABLE111-CHANOE IN CONCENTRATION O F CARBONATE AND BICARBONATE WHEN A 0.5 N SOLUTION OF KHCOa IS BOILEDUNDER DIFFERENT PRESSURES Time interval Temperature Cc. 0.5 N KHCOa Total alkali in 5 cc. Minutes c. 5-cc. sample in terms 0.5 N HCI Atmospheric pressuw QQ 7
0 26 30 57 61 91 96
Almospheric pressure plus 55 m m . inercury 104.9 105.0 105.0 105.0 105.0 105.0 105.0
The results of these experiments indicate that there is no advantage in raising the temperature of the boiling solution by increasing the pressure on the system. The data show that after the ratio of the concentration of bicarbonate to carbonate becomes approximately 1 to 3.3, the concentration of the bicarbonate remains approximately constant while the concentration of the carbonate increases steadily as evaporation takes place. I n other words, after the first few minutes of boiling the rate of decrease in concentration of carbon dioxide is directly proportional to the rate of increase in concentration of potassium carbonate. Since the rate of increase in concentration of potassium carbonate is determined by the rate of distillation, the rate of decrease in concentration of carbon dioxide is also determined by the rate of distillation.
EFFECTOF TEMPERATURE ON EQUILIBRIUM OF SOLUTION OF KzC03, KHCOs,
AND
co,
As shown in Fig. 8, the change in equilibrium of a solution of potassium carbonate and potassium bicarbonate, for a given partial pressure of carbon dioxide and for the temperature range indicated, is a straight-line function of the temperature. This fact taken in connection with a modification of McCoy -and Smith's6 equation for the equilibrium for a given tempera.ture makes it possible to calculate the amount of carbonate and bicarbonate in any such solution for any temperature and parAial pressure of carbon dioxide within the limits of these experiments, by two equilibrium measurements.
..,'
