Ind. Eng. Chem. Res. 1987,26, 1323-1329
(ii) For I., > D-/2. The dimensionless foulant volume V(j,h) can be calculated by
2(i - l)Ah)2 F(D) dD -
2iAh
- 2iAh)2F(D) dD)]
(A-6)
+
where m = ((Dmin/2)/Ah) 1 and n = h/Ah. Equation A-6 can be further transformed as
2h)
F(D) dD) dh] (A-7)
Equation A-7 is equivalent to eq 5 quoted by Androutsopoulos and Mann (1978). Registry No. COO,1307-96-6; Moo3, 1313-27-5; C, 7440-44-0; Ni, 7440-02-0; V, 7440-62-2.
Literature Cited Ammus, J.; Androutsopoulos, G. P. Ind. Eng. Chem. Res. 1987,26, 494. Ammus, J. Ph.D. Thesis, National Technical University of Athens, 1985. Androutsopoulos, G. P.; Mann, R. Chem. Eng. Sci. 1978, 33, 673. Beuther, H.; Schmidt, B. K. Presented a t the 6th World Petroleum Congress, Frankfurt/Main, 1963; May 19-26, Section 111, Paper 20-PD7. Butt, J.; Billimoria, R. M. "Catalyst Deactivation" Chemical Reaction Engineering Review-Houston, in ACS Symp. Ser. 1972, 72, 1. Cir, J.; Cirova, A. Int. Chem. Eng. 1979, 19(4), 671.
1323
De Beer, V. H. J.; Bevelander, C.; Van Sint Fiet, T. M. M.; Werter, P. G. A. J.; Amberg, C. H. J. Phys. Chem. 1976,43,68. de Grange, P. Catal. Rev. Sci. Eng. 1980,21(1), 135-181. Froment, G. F.; Bischoff, K. B. Chemical Reactor Analysis and Design; Wiley: New York, 1979. Furimsky, E. Ind. Eng. Chem. Prod. Res. Deu. 1978, 17(4), 329. Furimsky, E. AIChE J. 1979a, 25(2), 306. Furimsky, E. Ind. Eng. Chem. Prod. Res. Dev. 1979b, 18(3), 206. Hirotsugu, N.; Yasuo, S.; Yutaka, 0. J.Jpn. Petrol. Inst. 1980,23(5), 321. Hirotsugu, N.; Hisahiro, S.; Yasuo, S.; Yutaka, 0. J. Jpn. Petrol. Inst. 1981, 24(4), 253. Johnathon, E. W.; Howard, F. R. Znd. Eng. Chem. Prod. Res. Dev. 1982, 21(4), 555. Inogouchi, M. Shokubai 1976,18(3), 78. Kodama, S.; Haruhiko, N.; Tohru, T.; Tohru, Y. J. Jpn. Petrol. Inst. 1980, 23(5), 310. Masso, I.; Satoshi, S.; Yoshihito, S.; Kiyohiko, I.; Jarumi, K.; Kazuhito, T.; Takehiko, M.; Reijiro, N.; Tamotsu, N.; Saburo, 0. Bull. Jpn. Petrol. Inst. 1972, 14(2), 153. Newson, E. J. Prepr.-Am. Chem. SOC., Diu. Petrol. Chem. Chicago, Sept. 1970, 15(4), A141. Ohutsuka, T. Catal. Rev. Sci. Eng. 1977, 16(2), 291. Ocampo, A.; Schrodt, J. T.; Kovach, S. M. Znd. Eng. Chem. Prod. Res. Dev. 1978, 17(1), 50. Papayannakos, N.; Marangozis, J. J. Chem. Eng. Sci. 1984, 39(6), 1051. Pazos, J. M.; Gonzales, J. C.; Salazar, A. J. Ind. Eng. Chem. Process. Des. Dev. 1983, 22(4), 653. Ripperger, W.; Saw, W. J . Less-Common Met. 1977,54, 534. Schuit, G. C. A,; Gates, B. C. AIChE J . 1973, 19(3), 417. Shah, Y. T.; Paraskos, J. A. Ind. Eng. Chem. Process Des. Dev. 1975, 14(4), 368. Soon-Jai, Khang; Mosby, J. F. Ind. Eng. Chem. Process Des. Dev. 1986, 25, 437. Tamm, P. W.; Harnsberger, H. P.; Bridge, A. G. Ind. Eng. Chem. Process Des. Dev. 1981, 20(2), 262. Ternan, M.; Furimsky, E.; Parsons, B. I. Fuel Oil Technol. 1979,2, 45.
Received for review December 11, 1985 Revised manuscript received March 16, 1987 Accepted April 18, 1987
Study of the Chlorine-Alkaline Hydrogen Peroxide Reaction A s h w a n i K u m a r a n d R i c h a r d J. McCluskey* Department of Chemical Engineering, Clarkson University, Potsdam, N e w York 13676
The reaction of chlorine with hydrogen peroxide solutions approximately 3 M in potassium hydroxide was studied in an unstirred, cylindrical Pyrex reactor. Batch reactions were performed with initial chlorine partial pressures ranging from 6 to 58 P a . The extent of reaction was measured for reaction times of 1, 3, and 6 min with two different peroxide solutions each having a distinctly different rate of disproportionation. Experimental results are compared to those predicted by penetration theory and by a one-parameter film theory model. The rates of disproportionation of several alkaline hydrogen peroxide solutions were also measured. Considerable interest has recently been shown in singlet oxygen [02('A)], molecular oxygen in its lowest excited electronic state. This is due in part to increased recognition of singlet oxygen as an important oxidant (Frimer, 1985; Wassermann and Murray, 1978) and in part to its use in oxygen-iodine chemical lasers (McDermott et al., 1978; Benard et al., 1979). Lengyel et al. (1981) investigated the generation of singlet oxygen by reaction of chlorine, bromine, and iodine with hydrogen peroxide in acidic, neutral, and alkaline solutions. They found the generation rate to be highest in alkaline media and to 0888-58851 871 2626-1323$01.50/0
increase with the type of halogen in the order iodine < bromine < chlorine. Richardson et al. (1981a) carried out static bulb experiments in which gaseous chlorine reacted with solutions of base, hydrogen peroxide, and alkaline hydrogen peroxide. The performance of the chlorine-alkaline peroxide reaction in various types of reactor configurations, such as spray nozzles, sparged tanks, and wetted-wall columns has also been described (Richardson et al., 1981b). A detailed discussion of the chlorine-alkaline peroxide reaction mechanism has been presented recently by Storch 0 1987 American Chemical Society
1324 Ind. Eng. Chem. Res., Vol. 26, No. 7, 1987
et al. (1983). The perhydroxyl anion, HOz-, is present in high concentration in alkaline peroxide solution, and the initial step is the reaction of absorbed chlorine with perhydroxyl anion. The overall reaction can be expressed as Cl2
+ 2H02-
+
OZ('A)
+ HzOz + 2C1-
1
(1)
To vacuum pump
Perhydroxyl anion concentrations can be determined from the total peroxide and base concentrations and a knowledge of the equilibrium constant for the reaction
HZOz
+ OH-
HOZ-
+ H2O
(2)
This equilibrium has been examined by Balej and Spalek (1979) and also by Keyser (1980). Because the lifetime of singlet oxygen in solution is only a few microseconds (Merkel and Kearns, 1972) in order for high yields of singlet oxygen to be observed, reaction 1must take place a t or very near the gas-liquid interface. However, details of the reaction kinetics are poorly understood. The reaction system is complicated by a number of factors: the rapidity of the reaction, a gas-phase resistance to chlorine transport, and the instability of basic hydrogen peroxide solutions. Useful information about the chlorine-basic hydrogen peroxide reaction can be inferred from a very similar chemical system, chlorine absorption and reaction in concentrated sodium hydroxide solutions. This system has been well studied (Richardson et al., 1981a; Sandall et al., 1981; Hikita et al., 1973; Takahashi et al., 1967). Experimental conditions for both Takahashi's and Hikita's research groups were 30 "C, atmospheric pressure, and 0.05-0.30 M base concentrations. They employed a stopcock absorber and liquid jet apparatuses, respectively, and found the average absorption flux varied as the exposure time to the --I/? power. This functional dependence, which held for exposure times from 1to 20000 s, is the theoretical relationship for absorption with instantaneous reaction (Danckwerts, 1970, p 38; Astarita, 1967, p 56). Sandall et al. used a roller drum reactor at 0 "C, pressures below 0.27 kPa, and 6 M base concentration. On the basis of a surface renewal model, they estimated the pseudo-first-order rate constant to be 3 X lo7 m3 kg-mol-l s-l. Design of efficient gas-liquid contactors for singlet oxygen generation hinges on the trade-off between maximizing liquid reactant utilization and minimizing singlet oxygen deactivation. As a first step in understanding liquid-phase mass transfer in this system, we have studied the reaction of chlorine with alkaline hydrogen peroxide using a simple, unstirred batch reactor. Specific objectives were to measure the extent of chlorine absorption and reaction over various fixed time intervals for different alkaline peroxide solutions and to explore the suitability of penetration theory for modeling the experimental chlorine absorption and reaction data. Disproportionation Reaction. A major side reaction in alkaline hydrogen peroxide solutions is the exothermic disproportionation reaction, H202 + Hog-
+
H2O
+ 02 + OH-
(3)
In concentrated hydrogen peroxide solutions, the rate of disproportionation is first order in hydrogen peroxide concentration. But in alkaline solutions, the reaction mechanism changes and the rate of reaction is a complicated function of peroxide, perhydroxyl anion, and impurity concentrations (Schumb et al., 1955; Legenchenko and Stupichenko, 1977, 1981). In this work, we have experimentally measured the disproportionation rate of alkaline peroxide solutions of various compositions and studied its effect on the extent
Figure 1. Experimental setup. (1,2) Needle valves, (3-8) rotaflo valves, (C) cold trap, (F) flow meter, (R) reactor, and (T)thermometer.
of chlorine absorption and reaction. Experimental Section A sketch of the experimental apparatus is given in Figure 1. The cylindrical glass reactor (2.9 cm X 40 cm) contains a removable, vacuum-tight O-ring joint that permits transfer of solutions to and from the reactor and a side-arm for a PTFE-coated thermometer. The thermometer is adjusted so that the bulb is fully immersed in alkaline peroxide solution which is cooled by an ice bath surrounding the lower part of the reactor. The reactor is connected to chlorine and nitrogen feed lines, a manometer, and two cold traps in series with a mechanical vacuum pump. All solid surfaces that contact the reactants are either Pyrex glass or PTFE (Teflon). O-rings are of PTFE, and all valves are glass-PTFE (Rotaflo). A PTFE tube connects the reactor to the manometer. The manometer fluid is mercury, covered with a layer of silicone oil to minimize reaction with chlorine or singlet oxygen. The system was periodically leak checked. An initially evacuated system always showed less than a l-kPa pressure buildup over 60 min. All experiments were completed in less than 10 min. Alkaline hydrogen peroxide solutions were prepared by adding a known volume of 30% hydrogen peroxide to a conical flask chilled in an ice bath. Prescribed amounts of 5 N KOH were then added dropwise while the solution was agitated with a PTFE stirring bar. After transferring this solution to the reactor, its temperature was maintained a t 10 f 1 "C by a surrounding ice bath. Vacuum was drawn on the reactor until vigorous bubbling in the solution was observed. This typically resulted in ambient pressures of under 6 kPa. Disproportionation Experiments. Preliminary experiments measured the rate of disproportion of four different alkaline hydrogen peroxide solutions by following pressure increase with time (due to oxygen evolution in reaction 3). Two solutions, having similar perhydroxyl anion concentration but showing greater than an order of magnitude difference in the rate of disproportionation, were chosen for subsequent experiments involving reaction with chlorine. Chlorine-Alkaline Peroxide Experiments. In these experiments, the solution temperature was first brought to 8 "C. Chlorine gas was introduced into the reactor and the initial chlorine partial pressure recorded. On addition of chlorine to the reactor, there was an immediate rise in solution temperature, which was held at 10 f 1 "C by controlling the surrounding ice bath. A t the end of the desired reaction time, the final pressure was recorded and the gases in the reactor were evacuated through the cold traps. The system was vented to atmospheric pressure,
Ind. Eng. Chem. Res., Vol. 26, No. 7, 1987 1325 Table I. Alkaline Hydrogen Peroxide Solutions-Species Concentrations and Disproportionation Rates solution A B C D 15 40 25 30 Voi 5 N KOH,cm3 10 25 30 vol 30% H202, cm3 20 0.18 4.24 1.47 HzOa M 1.69 48.1 48.3 46.5 HzO, M 48.0 K+,M 2.88 3.88 1.94 2.96 2.27 1.89 2.73 OzH-,M 2.67 1.61 0.05 0.23 OH-,M 0.21 0.10 1.27 3.23 [dno,/dt]106, g-mol/s 2.56
and the solution was poured into a clean beaker and immediately neutralized. For each of the two solutions chosen, initial chlorine partial pressures ranging from 6 to 58 kPa were examined for reaction times of 1, 3, and 6 min. The chloride ion concentration in the reacted solution was determined using an Orion 701 ion analyzer with an Orion 94-17 chloride ion specific electrode and an Orion 900 double-junction reference electrode. Prior to analysis, solutions were neutralized with nitric acid, received 1cm3 of ionic strength adjustor (5 M NaN03), and were then brought to 22 f 2 "C. Calibration curves were prepared using identical alkaline solution similarly neutralized prior to chloride ion addition. All neutralized solutions showed no sign of oxygen evolution (due to reaction 3). On a weekly basis, the calibration curves were checked and electrode filling solutions were replaced. Unreacted chlorine was first condensed in cold traps immersed in liquid nitrogen. The traps were then connected to a scrubbing unit consisting of two 1/2-galtanks of 5% NaOH solution. Nitrogen purge gas swept the chlorine out of the warming traps into the caustic scrubber. Chemicals Employed. The chemicals used in our experiments were Baker Analyzed, reagent grade 30% hydrogen peroxide; Baker Analyzed, reagent grade potassium hydroxide pellets; Matheson, research grade chlorine (99.96% purity); Baker Analyzed, reagent grade sodium chloride crystals (99.7 % purity); and VWR Scientific, reagent grade 70% nitric acid. Safety. All standard safety precautions for handling chlorine, alkali, and hydrogen peroxide solutions were exercised. Exposure to chlorine and direct contact with hydrogen peroxide was avoided. Venting of chlorine gas to the atmosphere was circumventedby neutralizing it with sodium hydroxide solution. The temperatures of alkaline peroxide solutions were closely monitored to maintain control over the rate of the exothermic disproportionation reaction. All alkaline peroxide solutions were used immediately after preparation.
Results Disproportionation Reaction Rates. Table I lists the recipes and species concentrations of the four basic peroxide solutions for which disproportionation rates were measured. All concentrations are based on an equilibrium constant for reaction 2 of 368.7 at 10 "C. This value was obtained from the data of Balej and Spalek (1979) by using the van't Hoff relation. Also given in Table I is the molar rate of oxygen evolution (dno,/dt), determined from the pressure vs. time data of Figure 2. Over the time span of any experiment (Le., several minutes), the extent of disproportionation is never sufficient to reduce significantly the concentrations of peroxide or perhydroxyl anion. The disproportionation reaction can proceed via both homogeneous and heterogeneous pathways, and the observed reaction rates are not proportional to any simple
TIME ELASPED ( 8 )
Figure 2. Disproportionation rate data for solutions A (A),B C ( O ) , and D (0).
(X),
INITIAL C12 PARTIAL PRESSURE (kPa)
Figure 3. Chlorine reaction data for solution A for reaction times 3 (A),and 6 min (0). of 1 (O),
4'
0.0
13
28
38
52
1
INITIAL Clp PARTIAL PRESSURE (kPa)
Figure 4. Chlorine reaction data for solution B for reaction times of 1 ( O ) , 3 (A),and 6 min (0).
combination of species concentrations. The marked difference in the rate of disproportionation between solutions A and B is consistent with their qualitatively observed rates of bubble formation. Chlorine-Alkaline Hydrogen Peroxide Reaction. Chlorine reaction data are presented in Figures 3 and 4 for solutions A and B, respectively, as plots of the moles of chlorine converted to chloride ion vs. initial partial
1326 Ind. Eng. Chem. Res., Vol. 26, No. 7, 1987 Table 11. Comparison of Experimental and Calculated Results for Chlorine Absorption per Unit Area (g-mol/cm2 X 10') reaction time 1 min 3 min 6 min L, cm sum of squares error Solution A 4.85 0.21 5.12 f 0.12 5.22 f 0.10 Q exptl 1.85 0.76 1.31 Q penetration (eq 6) 5.16 0.685 0.026 4.98 5.05 Q (eq 9) well-mixed 5.14 0.686 0.030 4.99 5.05 Q (eq 9) quiescent
*
Solution B
Q exptl Q penetration (eq 6) Q (eq 9) well-mixed Q (eq 9) quiescent
4.61 f 0.10 1.02 4.73 4.74
4.97 f 0.11 1.76 4.86 4.86
pressure of chlorine. The initial chlorine partial pressure was found from the change in manometer reading on addition of chlorine. Data for reaction times of 1,3, and 6 min are shown on each plot, as is a solid line corresponding to complete conversion of all charged chlorine. The extent of reaction data parallel this line for low initial partial pressures of chlorine but take on constant values at high initial partial pressures. A t low partial pressures, the results for 1-min reaction time with solution A essentially lie on the solid line, indicating complete conversion to chloride ion of all chlorine charged. Data points lying above the solid line indicate an experimental error. The 6-min reaction time results show the greatest degree of error. All data sets were performed sequentially. The 6-min experiments were those last performed, while the 1-min experiments with solution A were the first. The chloride ion concentration measurements are well reproducible, as judged from the asymtotic values at high pressure, and, because of the recalibration procedures, should show no time variation. We believe the experimental error is associated with the mercury manometer. The accuracy with which the manometer could be read by eye was never better than a few torr, and the manometer fluid was subject to contamination over time by both oxygen and chlorine. The magnitude of the error is shown by how far the plotted points lie above the complete conversion line at low partial pressures. Partial pressure measurements are employed only in a qualitative sense in the analysis that follows.
Discussion Figures 3 and 4 indicate that the amount of reaction in any specified time period is directly proportional to the amount of chlorine charged up to initial chlorine partial pressures of about 20 kPa. A t higher initial partial pressures, the increase in reaction per unit of chlorine charged drops rapidly, and beyond initial chlorine partial pressures of 30 kPa, no increment is noticed in the amount of reaction during any specified time period. The high conversion of chlorine at low initial partial pressures is consistent with a rapid reaction between chlorine and perhydroxyl anion occurring near the gas-liquid interface. The decrease in incremental amount of reaction per unit of chlorine charged is explicable in terms of an increasing mass-transfer limitation on the reaction rate. Since liquid-phase diffusivities are several orders of magnitude less than those in low-pressure gases, the dominant transport resistance should lie in the liquid phase. Once the interfacial region becomes depleted of perhydroxyl anions, reaction will occur only within the liquid phase, and the rate of reaction will be limited by the rate of liquid-phase transport of reactants to the reaction zone. We consider reaction 1 to be an instantaneous, irreversible reaction. This assumption is reasonable in light of the high values estimated for the liquid-phase reaction
5.05 f 0.11 2.49 5.06 5.02
0.479 0.481
0.021 0.025
rate constant, e.g., lo7 m3 kg-mol-l s-l (Richardson et al., 1981a; Sandal1 et al., 1981). We also assume that equilibrium via reaction 2 is maintained throughout the liquid phase. This means the perhydroxyl anion concentration will fall to zero only in regions where the chloride ion concentration increases to that of the potassium ion. For absorption of a gas having constant partial pressure into a quiescent medium followed by instantaneous reaction, the amount of absorption per unit interfacial area, Q, is given by (Danckwerts, 1970, p 38) Q = 2EiA*(DAt/r)'I2
(4)
where E,, the enhancement factor, is the ratio of absorption with reaction per unit time to the amount of absorption per unit time that would occur without reaction, A* is the constant interfacial equilibrium concentration of dissolved gas, DA is the liquid diffusivjty of the dissolved gas, and t is time after the interfacial concentration of liquid-phase reactant falls to zero. A procedure for estimating A* is presented in Appendix A. When the equilibrium concentration of dissolved gas is small relative to the initial concentration of liquid-phase reactant (Danckwerts, 1970, P 39), Ei = (DA/DB)'l2 + (Dg/DA)1/2Bo/~A* (5) where Bo is the initial concentration of reactive anion (the sum of the initial concentrations of perhydroxyl and hydroxyl anions), DB is the effective diffusivity of the reactive anion, and z is the number of moles of liquid-phase reactant that react with 1 mol of dissolved chlorine. Values of the diffusivities are estimated in Appendix B. For the conditions of our experiments, the magnitude of (DA/DB)'/* is less than 1, while Bo/zA* is greater than 20, and eq 4 can be written as
Q = (DBt/a)'/22B0/z
(6)
Equation 6 predicts the absorption per unit area to be independent of chlorine partial pressure and to increase as the square root of time. This is a common result for absorption with reaction when BO/zA* is large. The extent of absorption is limited by the rate at which the liquidphase reactant can reach the reaction zone. For each set of experimental conditions for solutions A and B, Table I1 presents the average chlorine absorption per unit area for conditions where Q is independent of chlorine partial pressure. The corresponding 95% confidence limits are also given. Each average is based on the three highest pressure data points with 35 kPa as the lowest partial pressure considered. The amount of chlorine absorbed calculated from eq 6 is also listed in Table I1 (Q penetration). These were calculated using the independent hydroxide ion diffusivity, i.e., a maximum estimate for Dg. Even so, these results are less than half of the experimental values. This indi-
Ind. Eng. Chem. Res., Vol. 26, No. 7, 1987 1327
GAS
I
Chlorine absorption at any time t is
LIQUID
Q(t) = Qo
+ S t0( D B B ( L ) / z Y dt' )
(9)
where B ( L ) is the reactive anion concentration at depth L. The value of B(L) depends on the bulk liquid behavior. There are two cases we will consider: (i) the liquid phase beyond the stagnant film is treated as well mixed, in which case B(L) = Bo at all times, and (ii) the liquid phase is quiescent beneath depth L, for which (Carslaw and Jaeger, 1959, p 71)
B ( L ) = Bo eXp(DB2t/&o~)(1 - erf (DB(t/DBo)"'/ Y)) (10) Figure 5. Concentration profiles for chlorine (A) and reactive anions (B)in the stagnant film.
cates greater rates of mass transfer than those due solely to molecular diffusion. Evidently, penetration theory is inappropriate for describing this process. The liquid phase is not truly quiescent. Due to the disproportionation reaction, bubbles of oxygen rise intermittently through the liquid phase. Also, it is reasonable to expect that the steep concentration and temperature gradients present at the onset of reaction could of themselves, or through their effect on dissolved oxygen, induce mixing in the interfacial region (Shah and Szeri, 1974), although no disturbance of the gas-liquid interface was observed visually. Film theory can be used to construct a simple one-parameter model that better fits the experimental data. This model assumes a brief period of intense reaction and mixing in the interfacial region which results in a stagnant film of total depth L beneath the gas-liquid interface as shown in Figure 5. This film is made up of two layers: one containing a region of depth X with a linear concentration gradient in dissolved chlorine, and the other of depth Y (or L - X ) with a linear concentration gradient in reactive anion. The absorbed chlorine diffuses from the interface to the reaction plane at depth X , while the reactive anions diffuse from the bulk liquid to the reaction plane. Since the reaction is instantaneous, absorbed chlorine and reactive anions cannot coexist. The governing diffusion equations and the pertinent boundary conditions are well-described in Astarita (1967, p 20). Following standard film theory, the depth X is found from the condition that the flux of chlorine to the reaction plane must be in balance with that of the reactive anion. Since the reactive anions reach the reaction plane z times faster than absorbed chlorine,
X = L/(1
+ zDBBO/DAA*)
(7)
where DA and DB are the effective diffusivities of absorbed chlorine and reactive anions, respectively, for transport in the stagnant film. Under the conditions of our experiments, X is always less than half of 1%of L. This is the reason chlorine absorption becomes independent of chlorine partial pressure and dependent on the extent of transport of liquid-phase reactant. We assume that the rapid initial reaction occurs over a negligible time period with all product chloride ions remaining within the interfacial film of thickness L. Then the extent of initial chlorine absorption per unit area, Qo, is given by the amount of reactant depleted from the region of depth L beneath the interface, Qo = ( X
+ Y/2)B0/z
(8)
where DBO is the effective diffusivity of reactive anions in the bulk liquid. Both DB, the effective diffusivity through the film of thickness Y, and DBO were treated as constants. Because the liquid-phase reactants are ions, their effective diffusivity is concentration dependent (see Appendix B). The interfacial film will have a lower average reactant concentration than the region just below it, causing DBto be slightly greater than DBO. If B(L) varies with time, neither DB nor DBO will be truly constant. However, our calculations show that B(L)/Bonever falls below 0.75 in 6-min time, the longest period of our experiments. Basing the diffusivities on B ( L ) / B o= 0.9 causes the constant diffusivities calculated to be within 5% of their concentration-dependent values for all the time periods considered (see Appendix B). For both well-mixed and quiescent bulk fluids, eq 9 expresses the chlorine absorption per unit area in terms of a single adjustable parameter L, the total interfacial film thickness. The amount of chlorine absorption for both well-mixed and quiescent bulk fluid models are compared with the experimental chlorine absorption in Table 11. The least-squares best fit values for L are shown along with their sum of squares error. There is little difference between the two models since the initial absorption/reaction term Qo dominates in eq 9. Both models are capable of matching the experimental results to within 3%. Since the hypothesized interfacial films are of several millimeters thickness, it is intuitively more appealing to treat the bulk fluid as quiescent rather than well-mixed. However, the well-mixed assumption provides a slightly better fit to the data, as shown by the error terms in Table 11, and is mathematically more facile. The film thicknesses given in Table I1 are equivalent to constant mass-transfer coefficients for transport of liquid-phase reactant of 4.0 X cm/s for solution A and 5.8 X cm/s for solution B. Since both solutions gave chlorine absorptions per unit area and mass-transfer coefficients of similar magnitude, the rate of disproportionation did not seriously influence liquid-phase transport under the conditions of our experiments.
Conclusions When chlorine gas contacts alkaline hydrogen peroxide solution there is an initial period of rapid reaction and interfacial mixing. Penetration theory does not adequately describe chlorine absorption by unstirred alkaline hydrogen peroxide solutions. A model consisting of instantaneous initial reaction followed by absorption through an interfacial film containing all reactant depleted solution was capable of matching experimental data for two solutions of differing reactant concentrations and disproportionation rates.
1328 Ind. Eng. Chem. Res., Vol. 26, No. 7, 1987
Acknowledgment
This work was partially supported by the Air Force Office of Scientific Research under Grant AFOSR-81-0155, 2303/D9. Nomenclature A* = equilibrium concentration of dissolved chlorine at interface, g-mol/cm3 B = concentration of reactive anions, g-mol/cm3 C = concentration, g-mol/cm3 D = diffusivity, cmz/s E, = enhancement factor F = Faraday’s number, coulomb/g-equiv h = ion factors appearing in eq 12, cm3/g-mol H = Henry’s law constant, kPa.cm3/g-mol I = ionic strength, g-mol/cm3 L = total depth of stagnant film beneath the interface, cm q = equivalent ionic conductance, cm2/(ohm.g-equiv) Q = amount of chlorine absorbed per unit area, g-mol/cm2 R = gas constant, J/(g-mo1.K) t = time, s T = temperature, K X = depth of dissolved chlorine layer beneath the interface, cm Y = depth of reactive ion layer beneath the interface, cm z = number of moles of liquid-phase reactant that react with 1 mol of dissolved chlorine z, = ionic charge, g-mol/g-equiv Superscripts * = equilibrium value 0 = bulk value or initial value Subscripts
- _- anion + = cation A = chlorine B = reactive anions eff = effective diffusivity Appendix A The solubility of gases in dilute solutions can be estimated from Henry’s law PA = HA* (11) where Pa is the partial pressure of gas A, A* its liquidphase equilibrium concentration, and H is the Henry’s law constant for the solution. The Henry’s law constant for electrolyte solutions is calculated from log ( H / H o ) = (h++ h. + hc,)l (12) where Ho is the Henry’s law constant for water at the same temperature, I is the solution ionic strength, h, and h- are temperature-independent ion factors, and h G is a constant dependent on both temperature and the nature of the gas. Equation 1 2 and the constants h, and h- are listed in Danckwerts (1970, p 19). hGis taken as -53 cm3/g-mol, the average of the values used by Sandal1 et al. (1981) and Hikita et al. (1979). A value of 891 X lo3 kPa.cm3/g-mol of Id“ (Perry and Chilton, 1973) then implies a Henry’s law constant of 1170 X lo3 kPa-cm3/g-mol for solution A and of 1297 X lo3 kPa.cm3/g-mol for solution R. Appendix B The diffusivity of dissolved chlorine, DA, was estimated to be 1.2 X cm2/s by using the Wilke-Chang (1955) correlation. Diffusion of electrolytes is described by the NernstPlanck equation which contains a term proportional to the local electric field. Use of the condition of electroneutrality to eliminate the electric field from the Nernst-Planck
equation results in an effective diffusivity that is concentration dependent. For the case of a single reactive counteranion diffusing with a single product anion, the effective reactant diffusivity at any point can be shown (Brian et al., 1964) to be D,ff = D-/(I. - O.Fi(l - D _ / D c J C _ / C + ) (13) where D- and Dc, are the self-diffusivities of reactive anion and chloride ion, respectively, and C- and C, are the point concentrations of reactive anion and cation, respectively. C,, the potassium ion concentration, is equal to the initial concentration of reactive anion. The ion self-diffusivities are typically expressed as the diffusivity of free ion at infinite dilution (Newman, 1973, p 229),
D- = RTq_/lzilF2
(14)
where q- represents the free ion equivalent conductance, zi is the ionic charge, and F is the Faraday number. The values of q- are tabulated (Weast and Astle, 1982). If the reactive ion is assigned, the conductance of hydroxide ion, D-, is 3.6 X cm2/s. Electroneutrality, Le., the limitation on the hydroxide ion migration by the counterdiffusion of the larger (slower) chloride ion, ensures that the effective diffusivity of eq 13 is never greater than D-. Sherwood and Ryan (1959) have shown that the appropriate average effective diffusivity for transport through a stagnant film is
DB = 2 0 - / ( 1 + SQRT(1 - (1 - q-/qct)CB/C+))
(15)
where the anion has concentration zero at one side of the film and CB at the other. For a well-mixed bulk fluid, CB = C, and DB is 2.76 X cm2/s. As CB/C+ decreases, DB increases slowly. At CB/C+ = 0.9, DB is 2.81 X cmz/s. Registry No. C12, 7782-50-5; H02-, 14691-59-9.
Literature Cited Astarita, G. Mass Transfer with Chemical Reaction; Elsevier: Amsterdam, 1967. Balej, J.; Spalek, 0. Collect. Czech. Chem. Commun. 1979,44, 488. Benard, D. J.; McDermott, W. E.; Pchelkin, N. R.; Bousek, R. R. Appl. Phys. Lett. 1979, 34, 40. Brian, P. L. T.; Baddour, R. F.; Matiatos, D. C. AIChE J . 1964, 10, 727. Carslaw, H. S.; Jaeger, J. C. Conduction of Heat in Solids; Clarendon: Oxford, 1959; p 71. Danckwerts, P. V. Gas-Liquid Reactions; McGraw-Hill: New York, 1970. Frimer, A. A. Singlet Oxygen; CRC: Boca Raton, FL, 1985. Hikita, H.; Asai, S.; Himukashi, Y.; Takatsuka. T. Chem. Eng. J . 1973, 5, 77. Keyser, L. F. J . Phys. Chem. 1980, 84, 1659. Legenchenko, I. A.; Stupichenko, R. N. Russ. J . Phys. Chem. 1977. 51, 1321. Legenchenko, I. A,; Stupichenko, R. N. Russ. J . Phjs. (‘hem. 1981, 55, 1358. Lengyel, A,, et al., Oxid. Commun. 1981, 2, 1. McDermott, W. E.; Pchelkin, N. R.; Benard, D. J . ; Bousek, R. R. A p p l . Phys. Lett. 1978, 32, 469. Merkel, P. B.; Kearns, D. R. J . Am. Chem. Soc. 1972, 94, 7244. Newman, J. S. Electrochemical Systems; Prentice Hall: Englewood Cliffs, NJ, 1973. Perry, R. H.; Chilton, C. H. Chemical Engineers Handbook, 4th ed.: McGraw-Hill: New York, 1973. Richardson, R. J.; Kelley, J. D.; \7iswall, C. E. J . Appl. Phys. 1981a, 52, 1066. Richardson, R. J.; Wiswall, C. E.; Carr, P. A. G.; Hovis, F. E.; Lilenfeld, H. V. J . Appl. Phys. 1981, 52, 4962. Sandall, 0. C.; Goldberg, I. B.; Hurlock, S. C.; Laeger, H. 0.;Wagner, R. I. AIChE J . 1981,27, 856. Schumb, W. C.; Satterfield, C. N.; Wentworth, R. L. HydroPen Peroxide; Reinhold: New York, 1955. Shah, Y. T.; Szeri, A. Z. Chem. Eng. Sci. 1974, 29. 2219.
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Sherwood, T. K.; Ryan, J. M. Chem. Eng. Sci. 1959,Il,81. Storch, D. M.; Dymek, C. J.; Davis, L. P. J. Am. Chem. SOC.1983, 105, 1765.
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Weast, R. C.; Astle, M. J. CRC Handbook of Chemistry and Physics, 63rd ed.; CRC: Boca Raton, FL, 1982. Wilke, C. R.; Chang, Pin AZChE J . 1955,I , 264. Received for review December 24, 1985 Revised manuscript received January 27, 1987 Accepted February 25, 1987
Solvent Extract Liquefaction of Coal with Fractionated Anthracene Oil and Recycle Solvent Koji Chiba, Hideyuki Tagaya,* Tsunayoshi Kobayashi, and Yuji Shibuya Faculty of Engineering, Yamagata University, Yonezawa, Yamagata 992, J a p a n
T o estimate a solvent ability for coal liquefaction, 26 kinds of anthracene oils with widely ranging characteristics were used for Yallourn and Taiheiyo coal liquefactions. Hydrogen contents of solvents were correlated well with Yallourn coal conversion having a large coefficient of correlation (0.90), whereas less value was obtained for Taiheiyo coal (0.81). The hydrogen donating ability (HDA) defined by the amount of dihydroanthracene produced in the reaction of the solvent with anthracene was correlated well with conversion to TS for both coals (coefficients of correlation were 0.90 and 0.94). Their relationship was applied to recycle solvents; however, smaller conversions than predicted by the regression curve were obtained. Removing n-paraffin from the recycle solvents increased coal conversion. It was considered that the saturates in the recycle solvents were detrimental to coal liquefaction. It has long been known that, in coal liquefaction, the selection of the solvent has a pronounced effect upon the yield of liquid products from coal. In this paper, to quantitatively define the characteristics of a good solvent for coal dissolution, coal liquefaction using 26 kinds of anthracene oils was carried out. Anthracene oil was hydrogenated under three different conditions. Raw anthracene oil and three types of hydrogenated oils were fractionated into 5 or 6 fractions by vacuum distillation, obtaining 26 kinds of anthracene oils. We already reported the results of the liquefaction of Miike coal using other 20 kinds of anthracene oils (Chiba et al., 1984). In this report, two coals (Taiheiyo and Yallourn coals) whose carbon contents were less than that of Miike coal were liquefied using the anthracene oils. The hydrogen distributions of these oils were measured by ‘H NMR. The structural parameters were calculated by using the Brown-Ladner (1960) method. The main constituents of the oils were determined by GC, and the concentrations of acidic and basic compounds were determined by alkali and acid washing. Furthermore, anthracene was hydrogenated in these oils, and the amount of dihydroanthracene produced was defined as the hydrogen-donating ability of the oils. These solvent characteristics were correlated with conversions of Taiheiyo and Yallourn coals. Moreover, the correlation between the hydrogen donating ability and the Taiheiyo coal conversion was applied to recycle solvents provided by the Mitsui Engineering and Shipbuilding Co., Ltd. Literature Survey
Because solvent quality for coal liquefaction is an important factor (Whitehurst et al., 1980; Shah, 1981), many attempts have been made to correlate solvent characteristics with coal conversion efficiency. Curtis et al. (1981) characterized liquefaction solvents by spectroscopic measurements of their hydrogen distribution and determined the optimum solvent parameter ranges for effective coal dissolution. Miller and Silver 0888-5885/87/2626-1329$01,50/0
(1980),and Miller et al. (1982) reported that a Watson-type characterization factor, K,, was shown to be a good indicator of a solvent’s ability to physically dissolve coal fragments. K , values were calculated using the solvent‘s average volumetric boiling point and specific gravity at 298 K. Weight percent hydrogen in a solvent at its maximum liquefaction effectiveness has been shown to be a linear function of K,. They suggested that basic differences exist in the composition of recycle solvents derived from different coals and different processes. Furlong et al. (1976) defined a parameter called solvent quality index that varied with the degree of solvent hydrogenation in an EDS process. Coal conversion decreased significantly when the quality index of the solvent was less than 10. Details of the solvent quality index are proprietary. Curran et al. (1967) first described the results of hydrogen transfer in terms of a free-radical mechanism where the free radicals produced by the decomposition of coal were stabilized by abstraction of a hydrogen from the solvents. According to this mechanism, a solvent’s hydrogen donor ability is very important. Hydrogen shuttling ability is closely related to the hydrogen donor ability because the shuttling reaction contributes to an increase in the amount of transferred hydrogen. Measurements of a solvent’s hydrogen donor ability have been attempted by many investigators. Hydroaromatic compounds such as tetralin are wellknown hydrogen donor solvents (Obara et al., 1983). Although hydroaromaticity of coal-derived liquids was measured by lH and 13Cmagnetic resonance and correlated with liquefaction conversions (Aiura et al., 1984; Curtis et al., 1985), assignments of shift range are still questioned. Uchino et al. (1984) proposed a proton donatable quality index (PDQI) which was calculated from the donatable naphthenic hydrogen content in hydroaromatic species as analyzed by HPLC and GC/MS methods. Methods to measure hydrogen donor ability using coal model compounds were proposed by many investigators because of its ease of measurement. 0 1987 American Chemical Society
