Some Aspects of the Homogeneous Kinetics of Sulfite Oxidation Tsung-l Chen and Charles H. Barren* Chemical Engineering Department, University of Virginia, Charlottesville, Vu. 28901
The homogeneous kinetics and catalysis of sodium sulfite oxidation in an aqueous solution were studied b y means of the rapid-mixing method of Hartridge and Roughton. This technique allowed the reaction of already dissolved oxygen, thus eliminating possible errors due to the interphase transfer of oxygen. The manner in which the cobalt ion participates in the reaction sequence was developed. A full reaction sequence describing the chain of events was elaborated. A reaction rate expression derived from this sequence was shown to b e in agreement with the experimental results. The experimental findings showed that: (a) the reaction rate was independent of oxygen concentration; (b) the reaction order was three-halves with respect to sulfite concentration; and (c) the reaction rate was proportional to the square root of the total concentration of cobalt added to the reacting solution.
T h e oxidation of aqueous solutions of sodium sulfite in the presence of cobalt ion catalyst is one of the few suitable reactions for testing the mass transfer characteristics of engineering systems. However, the description and ultimate analysis of such systems requires accurate information on the kinetics of the homogeneous chemical reaction. Although the reaction system has developed quite a history of controversy, the kinetics of the reaction are still not well understood. The literature dealing with this reaction is extensive and i t has been thoroughly reviewed by Danckwerts (1970) and Astarita (1967). More recent mass transfer studies have been published by Linek and Mayrhoferova (1970) and Reith (1968), which clearly illustrate the difficulty of analysis of results taken under conditions involving the transfer of oxygen from the gas phase to the reaction phase. I n this investigation measurements were made of the homogeneous rate of this reaction system by the rapid-mixing continuous flow method of Hartridge and Roughton (1923). This method allows the reaction of already dissolved oxygen and thus eliminates the possible interference by mass-transfer effects. Srivastava, et al. (1968), used the same technique to study this reaction. Their results differ significantly in conclusion; however, it should be noted that their data fit their proposed model of first-order kinetics in oxygen best at sulfite concentrations significantly higher than those used in the present study. Careful examination of their results was not possible since none of the original data were presented in their paper. The only data were already calculated using the assumed rate expression, and i t is apparent from examination of their Figure 2 that this rate expression was not satisfactory a t low concentrations, as evidenced by severe scatter in the value of the specific reaction rate. I n the same sulfite concentration range as the present study, less than 0.06 hf (molarity), several previous workers report zero-order kinetics in oxygen, which is in agreement with the results of the present investigators. These previous results were reported by Volfkovich and Bolopolski (1932), Riccoboni, et al. (1949), Westerterp, et al. (1961), and Astarita, et al. (1964). A reaction sequence is presented herein which leads to a kinetics result t h a t is in compIete agreement with the experimental findings. 466 Ind. Eng. Chem. Fundam., Vol. 1 1 , No. 4, 1972
This sequence is the same as that found to be satisfactory when a copper ion catalyst was used by Barron and O'Hern (1966), and the sequence is essentially that presented originally by Backstrom (1934). Experimental Section
The technique which was used has become almost standard, as described by Roughton (1963). However, some of the details of equipment vary between experiments, and a brief description of the equipmen$ used in this study is necessary. The principle involved is t h a t of measuring the temperature change due to reaction along t h e length of an observation tube in which the reaction occurs in a steady flow configuration. Except for the observation tube, the entire experimental system was thermostated by a water bath maintained a t 25 i 0.01"Cby means of a Hallikainen Resistotrol Temperature Controller, Model 1215-4. The temperature rise along the observation tube due to reaction was measured by a movable copper-constantan thermocouple. The thermocouple leads were mounted in a stainless steel capillary fixed to a rack and pinion used to adjust the thermocouple position in the observation tube. The thermocouple bead, which was exposed to the reacting solution, was insulated by a thin wax coating over a coating of spar varnish. The wax was a 50: 50 mixture of beeswax and paraffin, and the combined coating was thin enough so that the response time of the thermocouple was less than a fraction of a second. The potential differences of the movable thermocouple were measured mith respect to the constant temperature bath by a Keithley Model 148 Nanovoltmeter, which has a range from 10 nV to 100 mV. Potential readings were recorded by a Keithley Model 370 Recorder. The temperature measuring system was calibrated and the recorder was adjusted to full span by using a Keithley Model 260 Nanovolt Reference Source. The experimental system, and particularly the feed system, is shown schematically in Figure 1. There were two feed tanks, one of which contained the sulfite solution, while the other contained solutions of previously dissolved oxygen. Both of
0 0
0.075-
W
u
50
o
M 0.0278
e e
0.0144 0.000247 0.0094 0.000143
M 6000418
W
LEGEND OXYGEN SATURATOR FOR SOLUTION PREPARATION B SULFITE SOLUTION FEED BOTTLE C OXYGEN SOLUTION FEED BOTTLE D ATMOSPHERIC VENT E,F AUTOMATIC VALUES G OXYGEN SOLUTION TRANSFER TUBE 0 OBSERVATION TUBE S OXYGEN SPARGER T MOVABLE THERMOCOUPLE
A
Figure 1. Schematic diagram of experimental apparatus
0
the feed tanks were 0.5 1. bottles and both of the feed solutions were driven into the mixing chamber by a common source of nitrogen pressure. The flow rates of solution in the observation tube were calibrated a t various driving gas pressures by running distilled water. A velocity of 63.3 cm/sec corresponded to 4 in. of Hg pressure, and this pressure was used for most of this experimentation. The Reynolds number for this flow rate is 2000 and the flow in the observation tube was considered to be turbulent, especially in the light of the initial turbulence induced in the mixing chamber. Each stream flows into the mixing chamber with equal flow rate in the above velocity range. So, the concentration of mixed solution in the reactor tube is half of its original value in the feed tank. The flow was controlled by three electromagnetic valves, indicated in Figure 1. The mixing chamber follows the design given by Berger, et al. (1968). For each stream, there were four jets, 0.5 mm in diameter, arranged semitangentially to the chamber, which was 1 / 6 in. in diameter and 0.45 cm in depth. The solution gets a rotational motion which accelerates mixing. Then the solution flows into the observation tube which is a glass in. inside diameter and which is 4 em long. tube with a Sodium sulfite solution is easily oxidized by air, and caution is necessary in its preparation. It was prepared by adding a specific amount of the salt to distilled water or catalyst solution, just before putting the bottle into the water bath for thermal equilibration. The system was allowed a period of 3 hr to come to thermal equilibrium, and during this time a solution of oxygen was prepared in a 1-1. bottle of distilled water or catalyst solution by slowly bubbling oxygen through a fritted glass, as shown in Figure 1. The oxygen absorber was vented to the atmosphere so that the distilled water was partially saturated under 1 atm of pressure of oxygen. Various oxygen concentrations were obtained by allowing different absorption times. I n this study the highest concentration of oxygen achieved was 0.000418 M ,obtained in 4 hr, and the lowest was 0.000124 M ,obtained in 1 hr. These values may be compared to a value of 0.000637 Ji for a completely saturated solution a t 25°C and 1 atm of pressure. After the desired absorption period elapsed, oxygen solution was transferred to the feed bottle by closing vent tube D so t h a t the solution was driven through plastic tube G into the feed bottle C by the oxygen pressure. The system was ready for operation after the prescribed
I 2 REACTOR TUBE LENGTH, crn
3
Figure 2. Typical temperature profiles along the observation tube
elapsed time to reach thermal equilibrium. The reactant solutions were driven by nitrogen pressure past valves E and F into the mixing chamber, and hence down the observation tube. As the reaction proceeds, temperature rises along the observation tube, and this rise was measured by the movable Cu-Cn thermocouple a t the desired locations. The potential differences were measured by the nanovoltmeter and recorded automatically. Reaction rates were calculated from the data thus obtained. The concentration of sodium sulfite was measured analytically by means of a n oxidation-reduction titration. Some of the sulfite solution remained after the rate measurement, and 10 or 20 cm3 of this solution was added to an excess of 0.2 N of iodine-iodide standard solution, which was then back-titrated with 0.1 N of sodium thiosulfate standard solution using a 0.2% starch solution as indicator, as indicated in standard reference books on analytical chemistry. The oxygen concentration was calculated rather than using an analytical measurement. This procedure was justified by results in agreement with analytical measurements made earlier by Barron (1962). The oxidation of sulfite is a n exothermic reaction with a standard enthalpy of reaction of 131.6 kcal per g-mole of oxygen reacted. I n the present experiments, the oxygen was completely consumed, as evidenced by the plateau reached in the temperature profile along the observation tube. The energy liberated by reaction raised the temperature of solution and the total temperature rise was measured. The oxygen concentration, 11,was determined by the energy balance AHR X Ji = AT X Cp.The mean heat capacity, C p , of the solution was approximated as that of water, since the sulfite concentration was low, e.g., the range was from 0.005 to 0.03 Ai. The experimental data were obtained as potential differences along the observation tube with respect to a reference junction in the water bath. Plotting potential difference us. distance indicated various straight lines rising to a plateau. The rate of oxygen consumption was calculated from the slope of such lines. The details of these calculations, as well as the full set of data, are given by Chen (1970). Ind. Eng. Chem. Fundam., Vol. 1 1 , No. 4, 1972
467
I
' (L
OO
0.01
0.02
0.04
TIME, sec
I
0
0.03
I
0.C
I
2
3
REACTOR TUBE LENGTH, cm
0
I I1
0.003
CATALYST
IN OXYGEN FEED SOLUTION
o CATALYST IN SULFITE FEED SOLUTlOh
'
I
I
'
0.006
l
l
I
0.01
0.02
l
I
I
0.04
AVERAGE SULFITE CONCENTRATION,
Figure 4. Effect of sulfite concentration on the rate of oxygen consumption
Figure 3. Temperature profiles along the observation tube which demonstrate the effect of oxygen concentration Results
Typical temperature profiles along the observation tube are shown in Figure 2. Such plots always showed straight lines with different slopes and heights of plateau. Obviously, the oxygen reacted until it was consumed completely. When the sulfite concentration was fixed, while the concentration of oxygen was varied from run to run, the data indicated, as shown in Figure 3, a common slope with a changing plateau that directly corresponded to the intentionally varied oxygen concentration. Such results clearly indicate, a t this level of sulfite concentration, that the reaction system is zero order in oxygen. This result is in agreement with the rate expression which is derived subsequently and with the results of previous investigators cited earlier. The oxygen concentration in the reacting solution was always small compared to the sulfite concentration, of the order of 0.01 to 0.04 in magnitude. Hence, the sulfite concentration can be taken as constant in any experiment and its value calculated as the average of the inlet and, outlet concentrations. A number of experiments were performed a t various sulfite concentrations to demonstrate this effect on the rate of reaction. The rate of oxygen consumption is shown as a function of average sulfite concentration in Figure 4. This plot clearly indicates t h a t the reaction is three-halves order with respect to sulfite concentration over the range considered. Since, over this same concentration range, the value of the pH of sulfite solutions will increase from 9.0 at a sulfite concentration of 0.005 -11 to 9.7 a t 0.05 .TI, there is reason to question whether the effect of pH, as discussed by Linek and hIayrhoferova (1970) and Sawicki (1971), would account for the observed dependence. This is not the case, since both studies indicated that over this range of pH the rate would increase by less than a factor of 2 and the observed change reported here corresponds to a factor on the reaction rate of greater than 30. It is believed that the p H effect reported in heterogeneous reaction systems such as those 468
Ind. Eng. Chem. Fundam., Vol. 1 1 , No. 4, 1972
mentioned above is actually a result of the influence of pH on the kinetics of the initiator oxidation step, the production of the Co(II1) complex from Co(I1). This effect is explored in greater detail by Sawicki (1971). Another observation follows from these results: the reaction rate is seen to be about twice as fast when the cobaltous sulfate is added to the oxygen feed solution as when it is added to the sulfite feed solution. This effect will be discussed in somewhat greater detail later, but for the present it clearly supports the hypothesis that the initiation reaction involves the cobalt ion in a higher oxidation state than is normally present in sulfite solution. All of the data shown in Figure 4 correspond to a total cobalt concentration in the reacting solution of 10-6 -11. The oxidation of sulfite ions in aqueous solution is a typical chain reaction and, as such, its rate depends markedly on both catalyst properties, as shown above, and on catalyst concentration. To clarify this dependence a series of experiments was performed a t approximately constant sulfite concentration of 0.0094 JI, using intentionally varied cobalt concentrations between lo-' .If and 3 X 10-6 J1.The maximum level of impurity which acted as a n initiator in this system was in the range of a n equivalent cobalt concentration of 10-8 M. The results of these experiments are shown in Figure 5. The reaction rate is proportional to the square root of the total cobalt concentration. This result agrees with data obtained by Linek and Mayrhoferova (1970) in the range of cobalt concentration from 5 X X to l o w 4-11. The onehalf order dependence on the cobalt concentration is also confirmed by the rate expression derived from the reaction sequence, which is discussed below. Discussion
The experimental results presented have shown that the rate of oxidation of sulfite ions in the presence of cobalt ion catalysts is independent of oxygen concentration and that the reaction rate is three-halves order in sulfite concentration and proportional to the square root of total cobalt concentration.
A reaction sequence will be presented from which a rate expression can be derived which agrees with all of these results. A reaction sequence for the oxidation of sulfite ions was developed by Backstrom (1934) and this sequence is adapted below to include the cobaltic hexqaquo complex ion as the initiator. SOB’- f CO(Hz0)6’+
-% CO(Hz0)6’+ + .SOBkz
(2)
.so6- + 503’- -% sob2-+ .so3-
(3)
+ s0s2-kr_ 2s04’-
+ .SO,- inert products .SO3- + .so5--+ inert products .SO5- + *sob-+inert products .SO3-
ka
(5) (6) (7)
8
and =
c
(4)
The above steps represent a typical chain reaction. The first reaction is a n initiation step in which cobaltic hexaaquo complex ions abstract a n electron from sulfite ions and produce active centers .SOs-. The next two propagation steps produce another active center, SO5-, and the strong oxidizing agent SO5*- which reacts with sulfite t o produce sulfate ions. There are three possible termination steps involving recombination reactions of the two active centers, reactions 5, 6, and 7. All of the steps in the sequence are fast; however, in the light of the experimental findings, it is reasonable to assume t h a t since the rate of reaction is independent of oxygen Concentration, the second step is faster t h a n any other propagation step. So the active center .SO?is present in low concentration compared to . SOs-. This relative reactivity of the transient species was independently confirmed by Hayon, et al. (1972), who measured the kinetics of t h e recombination reactions 5 and 7 by means of transient ultraviolet absorption spectra. These authors further proposed to modify the reaction sequence to include the effect of ’Sod-; however, in the present study there was no evidence to suggest the need for including this species. I n fact, they also report no direct evidence for the role played by the.SO4- in the chain reaction. Using the terminology of Boudart (1968), the active center .SOs- is rate limiting and it follows t h a t the only significant termination step is reaction 7. Using the stationarystate approximation for both of the active centers, the following rate expression can be derived.
k
20
(1)
.SOB- f 02 + .so5-
505’-
t
k 3 ( y
This rate expression is in complete agreement with the experimental results and is similar to t h a t obtained by Barron and O’Hern (1966) when copper ions were used as catalyst. Unfortunately, the specific reaction rate, k , cannot be qumerically evaluated without accurate knowledge of the concentration of the cobaltic hexaaquo complex ion. From the results shown in Figure 5, we can conclude t h a t this concentration is directly proportional to the total concentration of cobalt present in the reacting solution. Such a proportionality would be expected if there existed a n equilibrium ratio of cobaltic to cobaltous ions which is not influenced significantly by the sulfite oxidation reactions. Evidence supporting such a n
I
2
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I
I
I
l l l l
I
I
IO 30 TOTAL CONCENTRATION OF COBALT IN REACTING SOLUTION, M x 107 I
4
6
Figure 5. Effect of cobalt concentration on reaction rate
equilibrium ratio also exists in the studies involving the choice of feed solution for the catalyst. The reaction rate was about twice as high wben cobalt was added to the oxygen solution as when it was added via the sulfite solution. If a n equilibrium exists between the cobaltous and cobaltic complex ions, which is likely the case in the salt solutions in question, adding the cobalt via the oxygen solution results in a higher initial concentration of cobal$ic complex ions. This is a n entirely reasonable result-the higher oxidation state for the cobalt ions would be favored in the oxidizing solution, mhereas the lower oxidation state would be favored in the sulfite solution. A more precise analysis of this system will require kinetic information on the oxidation-reduction reactions involving the cobalt complex ions. There is mounting evidence to support the observation t h a t the reaction kinetics measured in a homogeneous experiment such as t h a t reported here are not the same as the results of a heterogeneous experiment such as t h a t of Sawicki (1971) or Linek and Mayrhoferova (1970). I n the present study the activation energy was measured by a series of six experiments over the temperature range from 20 to 30°C and was calculated to have a value of 72.7 X lo6 J/kmole (17.5 kcal/ g-mole). This compares to a value of 47.7 X lo6 J/kmole (11.4 kcal/g-mole) reported by Sawicki (1971) or 53.5 X lo6 J/kmole (12.8 kcal/g-mole) as reported by Linek and Rfayrhoferova (1970). This evidence alone has led us to place less emphasis on the discrepancies between the present conclusions and those of previous authors who used heterogeneous experiments until such time t h a t the kinetics of the initiation system have been clarified. literature Cited
Astarita, G., “Mass Transfer with Chemical Reaction,” American Elsevier, New York, N. Y., 1967. Astarlta, G., Marucci, G., Coleti, L., Chim. Ind. (Milan) 46, 1021 (1964). Backstrom, H. L. J., 2. Phys. Chem. Abt. R 25, 122 (1934). Barron, C. H., D.Sc. dissertation, University of Virginia, Charlottesville, Va., 1962 Barron, C. H., Q’Hern, H. A., Chem. Eng. Sci. 21, 397 (1966). Boudart, &I., “Kinetics of Chemical Processes,” Prentice-Hall, Englewood Cliffs, N. J., 1968. Berger, R. L., Balko, B., Chapman, H. F., Rev. Sci. Instrum. 39, 493 (1968). Chen, T. I., M.S. thesis, University of Virginia, Charlottesville, Va., 1970. Ind. Eng. Chem. Fundam., Vol. 1 1 , No. 4, 1972
469
Danckwerts, P. V., “Gas-Liquid Reactions,” McGraw-Hill, New York, N. Y., 1970. Hartridge, H., Roughton, F. J. W., Proc. Roy. SOC.,Ser. A 104, 376 (1923). Hayon, E., Treinin, A., Wilf, J., J . Amer. Chem. SOC.94, 47 (1972). ,-- I
Linek, V., Mayrhoferova, J., Chem. Eng. Sci. 2 5 , 787 (1970). Reith, T., Dr.Ir, dissertation, Technical University of Delft, The Netherlands, 1968. Riccoboni, L., Foffani, A., Vecchi, E., Gam. Chim. Ital. 79, 418 f1949L --, \ - -
Roughton, F. J. W., “Techniques of Organic Chemistry,” Vol. VIII, Interscience, New York, N. Y . , 1963. Sawicki, J. E., Ph.D. dissertation, University of Virginia, Charlottesville, Va., 1971.
Srivastava, R. D., McMillan, A. F., Harris, I. J., Can. J . Chem. Eng. 46, 181 (1968). Voflkovich, S. L.. BoloDolski. A. P., J . A .. a d . Chem. USSR 5 , 509 (1932). ’ Westerterp, K. R., Van Dierendonck, L. L., Abspoel-Chufoer, L. A,, De Ing 41, Ch. 79 (1961). RECEIVED for review March 26, 1971 ACCEPTEDJuly 27, 1972 Portions of this work were supported by U. S. Public Health Service through Research Grants FR-07094-03 and FR-07094-04 as subgrants from the University’s XIH Biomedical Sciences Support Grant and through Research Grant 1-ROI-HE1335201-BBCB.
Momentum Transfer in Two-Phase Flow of Gas-Pseudoplastic Liquid Mixtures R. Mahalingam” and Manuel A. Valle Department of Chemical and Nuclear Engineering, Washington State Cniversity, Pullman, Wash. 99163
The two-phase isothermal flow of gas-pseudoplastic liquid mixtures in horizontal pipes is described here. Strong interaction beiween the two phases is shown to exist at the interface by comparing experimental values of pressure drop and flow rate with those predicted from a proposed model for the annular flow region. The measured pressure drop is found to b e higher than that corresponding to the two-phase flow of gasNewtonian liquid mixtures. A sharp decrease in pressure drop is observed in the slug-flow region for gasnon-Newtonian flow. The liquid holdup is seen to increase with increasing pseudoplasticity. Visual studies of the flow patterns in various two-phase systems are also described.
Two-phase flow is often encountered in chemical engineering processes. It occurs in boiling inside tubes, distillation columns, plastics and food processing, and in chemical and nuclear reactors. A clear understanding of the basic mechanisms involved in two-phase flow is important to the efficient and economic design of such equipment. Good understanding does not exist at the moment, however, and twophase flow remains a complex field in fluid mechanics. . I great deal of research has been devoted to the study of the two-phase flow of gas-Newtonian liquid systems, but little work has been done on the tmo-phase flow of gas-non-Newtonian liquid systems. The present investigation is a n attempt to fill this void. Flow patterns are a n important feature of two-phase flow and h a r e been studied by several investigators. Although visual studies have demonstrated the existence of a wide range of fluid behavior, there is little theoretical work done on this feature of two-phase flow. There have been several attempts to correlate these flow patterns and the results obtained by different investigators indicate obvious discrepancies and the correlations presented lack generality (Al-sheik, et al., 1970; Baker, 1954). Liquid holdup is another feature of two-phase flow t h a t has been studied by a number of investigators; however, the degree of agreement among their correlations is rather poor. This follows from the fact that the liquid holdup is influenced rather strongly by the flow patterns, making i t , 470 Ind. Eng. Chem. Fundam., Vol. 1 1 , No. 4, 1972
therefore, necessary to correlate the holdup individually for each flow pattern studied (Richardson and Higson, 1962; Ross, 1961). h correlation has been successfully developed by Hughmark (1965) for the estimation of holdup in horizontal slug flow. RSuch of the research in two-phase flow has been devoted to the study and prediction of pressure drop. Lockhart and Xartinelli (1949) proposed a correlation for the prediction of pressure drop for the two-phase, two-component flow of gas-Sewtonian liquid mixtures. They defined the twophase pressure drop as a function of the pressure drop that would be obtained if either phase were flowing alone in the pipe. The idea was to obtain a correlation for the esperimental data, but a detailed study of the mechanisms involved in two-phase flow was not attempted. Other inrebtigators have proposed empirical correlations for the twophase horizontal flow of gas-Newtonian liquid systems; details can be obtained in the literature (Dukler, et al., 1964; Govier and Orner, 1962). The two-phase vertical flow of gas-Kewtonian liquid systems has been the subject of a more theoretical treatment. Calvert and Williams (1955) presented a model for the annular flow of air-water mixture? in which the liquid was assumed to flow in a thin layer made u p of a laminar and turbulent layer. The gas flow was approsimated by a n empirical analysis of the pressure drop through the gas core. Later, .Inderson and llantzouranis (1960) modified this
