Meranda, D., Fwter. W. F., A.1.Ch.E. J., 18, 111 (1972). Murti, P. S.,van Winkle, M., J. Chem. fng. Data. 3, 72 (1958). Prausnitz, J. M., Eckert. C. A,, Orye, E. V., O’Connell, J. P., “Computer Calcuhtions for MUkiCOmpOnant Vagoc-Liquid Equilibrium”, Prentice-Hall, En. . glewood Cliffs, N.J., 1967. Ramahlo, R. S.,Tiller, F. M., James, W. J., Bunch, D. W., Ind. fng. Chem., 53,896 (1961). Rowlinson. J. S.,Trans. Faraday Soc., 45, 974 (1949).
Timmermans. J., “Physico-Chemical Constants of Pure Organic Compounds”. Elsevier, New York, N.Y.. 1950. Wilson, G. M.. J. Am. Chem. Soc., 86, 127 (1964).
Received for review February 7,1974 Resubmitted June 16,1975 Accepted October 28,1975
Kinetics of the Reaction between Sulfur Dioxide, Oxygen, and Cupric Oxide in a Tubular, Packed Bed Reactor John G. Yates’ and Robert J. Best Department of ChemicalEngineering, University College London, London WC 1E 7JE, England
In the reacting system described here the copper oxide was dispersed on particles of alumina, and the absorption of SO:! in the presence of oxygen at 350-450 OC was assumed to follow a two-step consecutive mechanism leading via cupric oxysulfate (CUO-CUSO~) to cupric sulfate. The results were fitted to a homogeneous dispersion model described previously in the literature to account for catalyst particle deactivation in packed beds. The rate coefficients of the two reactions were found in terms of the preexponential factors Ai, and the activation energies Ei. Thus: A I = 550.1 s-‘, El = 17.62 kJ/mol, A2 = 36.79 s-’, .E2= 14.54 kJ/mol.
Introduction In recent years a great deal of attention has been given to the problem of reducing the level of atmospheric pollution caused by the sulfur dioxide emissions from electrical power plants fired by fossil fuels, and several processes for the desulfurization of the flue gases from such plants have been developed. In one of these processes (Dautzenberg et al., 1971; McCrea et al., 1970) the flue gas is brought into contact with spheres of cupric oxide-impregnated alumina whereupon the SO2 present at low concentration (<1% v/v) reacts to produce copper sulfate. The reaction takes place at a convenient rate at 400 “C and a not inconsiderable advantage of the process is the readiness with which the copper oxide may be regenerated a t the same temperature with a reducing gas such as hydrogen or a light alkane. By means of this latter reaction a gas stream richer in SO2 than the original flue gas may be produced and used downstream for conversion, via direct oxidation, to sulfuric acid. Such a process clearly lends itself to operation in a system of coupled fluidized bed reactors where by suitable adjustment of the flow of solid between desulfurizer and regenerator a constant level of activity may be maintained in both reactors. We therefore undertook an investigation of the process in a laboratory scale fluidized bed unit, and the results of this work will be presented in the near future. In order to facilitate the interpretation of these results, however, it was first necessary to obtain the kinetic parameters of the cupric oxide-sulfur dioxide-oxygen reaction in a system with less uncertain hydrodynamics than those found in a fluidized bed. A conventional packed bed reactor was chosen for this purpose and in this publication we wish to present our findings from it.
Reaction Mechanism The kinetics and mechanism of the reaction under consideration appear, from the open literature, to have received scant attention. The reverse process, however, the
thermal decomposition of copper sulfate, has been extensively studied and its thermodynamic and kinetic features are well understood (Ingraham, 1965; Ingraham and Marier, 1965; Lorant, 1966). A t temperatures in excess of about 600 “C anhydrous copper sulfate begins to decompose in two distinct stages, first to cupric oxysulfate and sulfur trioxide 2 c u s o 4 = CUO * c u s o 4
the cupric oxysulfate then breaking down to give cupric oxide and more SO3 CUO * c u s o 4 = 2 c u o
Below 875 “C sulfur trioxide is thermally stable (Kelley, 1937) and a t 400 “C the equilibrium is strongly to the right of reaction 3
SO2 + %02 SO3
It would thus seem to be a reasonable assumption that the reaction between cupric oxide, sulfur dioxide, and oxygen proceeds in two stages according to (4)and (5). Both reactions are thermodynamically favorable at the temperatures under consideration, i.e., 300-450 “C (Ingraham, 1965). 2cuo
+ so2 + 1/202 = CUO - c u s o 4 + so2 + lhO2 = 2 c u s o 4
CUO c u s o 4
Kinetic Model Consider a packed bed of particles through which gas passes in plug flow and assume that the inlet concentration CAIof reactant gas A is so low that any reduction in its concentration causes a negligible change in the overall volume flowrate, F . Assume further that reaction occurs by a twostep consecutive mechanism of the form represented by eq 4 and 5, and that the “concentrations” of the solid reactant R and solid intermediate S are little changed by the pasInd. Eng. Chem., Process Des. Dev., Vol. 15, No. 2, 1976
sage of an element of gas through the reactor. This latter assumption will only be valid for a low reactant gas concentration, slow reaction kinetics, and a relatively short bed, conditions which seem to pertain in the system under consideration; the reasonableness of this picture is attested to by the early breakthrough of SO2 found to occur experimentally. On the basis of this assumption we may use an average value for the surface coverage of each solid reactant, R and S, and with the gas in plug flow the design equation for the system becomes
be pursued further. Equations 10, 13, and 14 may be combined thus = exp CAi
k l exp -(kRt)
Now from the stoichiometry and boundary conditions of the system (see Appendix), it can be shown that
kR = We will now deal with the solution of this equation for the consecutive reactions 4 and 5 considering their rates to be proportional to the concentration of SO2 in the gas phase and to the fraction of unreacted solid. The reaction mechanism may be reduced to the following scheme ki
A+S-+T where A represents SO2 and RCuO-CuO; S is the intermediate CuO.CuSO4 and T is the final product CuSO&uSO4. The concentration of oxygen, in large excess in the system studied experimentally, is taken to be constant throughout and is conveniently included in the rate coefficients. The approach to the solution of (6) is similar to that used by Levenspiel in his treatment of deactivating catalyst particles (Levenspiel, 1972) since the system under consideration is formally similar to that in which a gas-solid catalytic reaction leads to the formation of a nonvolatile product. Let X R = fraction of R converted to S and T, X s = fraction of surface covered by S, and X T = fraction of surface covered by T. The rate of disappearance of A is given by the sum of the rates of the two reactions of eq 7. rA = k i C A ( 1 - X R )
which on substitution into (6) gives
This may be integrated to g&O
= exp - jj [k1(1 - X R ) + k p x s ] )
The rates of consumption of the solid reactants, R and S, can be expressed as dXR -- kR (1- X R ) dt
and (12) where the coefficients kR and k s are functions of k l , k z , V , and F . Equations 11 and 12 are ordinary differential equations which can be solved simultaneously in the usual manner to give 1 - XR = exp -(kRt)
provided kR # k s , a most unlikely situation which will not 240
Ind. Eng. Chem., Process Des. Dev., Vol. 15,No. 2, 1976
[ 1 - exp -
thus by measuring the gas breakthrough from a suitable (differential) fixed bed reactor it is possible for this particular reaction mechanism to determine values of the rate coefficients kl and kz. Owing to the complexity of these equations, however, the determination cannot be accomplished analytically and it is necessary to use a numerical procedure, such as the Rosenbrock hill-climbing technique (Keuster and Mise, 1973). By this means, values of the two ,unknowns k l , kz were calculated to minimize
where f; is the value of (CAJCAJ calculated from eq 15, 16 and 17 for a time t;, F; is the corresponding experimental value, and ne is the number of experimental points, (F;, t;). By this means, the sum, S E ~of, the squares of the errors, ej2, between the theoretical and experimental points on the breakthrough curve was reduced to below for each breakthrough curve: this represents a standard error of observation of less than f0.02 in all cases.
Experimental Section (a) Packed Bed Reactor System. This is shown schematically in Figure 1. Air for the sulfur dioxide absorption runs was supplied from the laboratory 6 bar main via a molecular sieve dryer and a pressure reducing valve. All other gases were supplied from cylinders: nitrogen, CP grade methane, and 99.9% sulfur dioxide for the reactor and calibration gas and air for the analysis system. The mainstream gas (nitrogen or air) was selected by setting the on/off needle valves, V-1 and V-2, and the three position (nitrogen-off-air) valve, V-5. The reactant gas (methane or sulfur dioxide) was selected by setting the on/ off needle valves V-3 and V-4 and the three position (methane-off-sulfur dioxide) valve, V-6. This selection system was provided in order to minimize the risk of accidentally selecting the hazardous mixture, air and methane. Two mainstreams were available and the pure reactant gas stream was connected to one of these. The mainstreams were controlled by diaphragm valves, V-7 and V-8, and metered by variable area flow meters, F-1 and F-2. The reactant gas stream was controlled by a stainless steel (P.T.F.E. diaphragm) differential valve, V-9, and metered through the variable area flow meter, F-3. The reactant gas stream could be isolated from the mainstream by toggle switch valve, V-10. The pressure in each of the mainstreams was measured by Bourdon-type pressure gauges, P-1 and P-2. A reactor by-pass was provided and, by means of the 4-way tap, V-11, either of the mainstreams could be switched, mutually exclusively, through either the by-pass or the reactor. In this way, it was possible to maintain gas flow through the reactor while purging the reactant gas metering system into the by-pass.
Table I. Solid Absorbent Prouerties A1*0, C SiO, Fe,O Na,O TiO,
(a) Chemical Analysis 99.5% 0.4%
0.008% 0.005% 0.004% 0.09%
( b ) Physical Properties Pure alumina
v N2 A I R CHL SO2
Figure 1. Packed bed flow system.
Figure 2. SO2 breakthrough curve; bed length 10 cm, air flow 4 1.1 min (NTP), inlet SO2 concentration 0.475 vol %, temperature 323 “C. The reactor stream gas was heated to the reactor temperature in a 30 cm long, 4 cm diameter coil of 4 m of 6.35 mm outside diameter stainless steel tubing contained within furnace H-1. The pressure a t the reactor outlet was kept slightly above atmospheric pressure by the diaphragm valve, V-12, to enable the gas to be sampled from a point downstream of the reactor. All of the mainstream pipework was of 6.35-mm 0.d. tubing; the pure reactant gas stream pipework was of 3.18-mm 0.d. tubing. The reactor itself was manufactured from two pieces of 12.7-mm 0.d. stainless steel tubing, joined a t the gauze reactant support plate. Its internal diameter was 8.75 mm and its maximum capacity was 8-10 cm3 of solid particles. A fixed thermocouple was provided, placed immediately below the gauze reactant support, and a vertically moveable thermocouple was placed inside the bed, thus allowing the vertical temperature gradient to be monitored. The furnace temperatures were regulated by “SIRECT” proportional temperature controllers. Temperature control in the furnace was within 1 “C over a period of many weeks. Gas Sampling System. The sampling system (Figure 2) was arranged to supply a Grubb-Parsons Model 30 InfraRed Gas Analyser (IRGA). The IRGA requires flow rates of about 1 l./min of dry, dust-free gas for each of its two sample cells: only one cell is used for measurement a t any time; the other is purged with air. The sample gas was dried with about 5 cm3 of type 5A molecular sieve contained in a glass tube in the sample line. The flow was regulated by a needle valve and measured by a variable area flow meter before being passed to the analyzer sample cell. An independent air supply was provided for purging the sample cell and for purging the unused analyzer cell needle valve and flow meter.
Mean particle size, mm Bulk density, glml Voidage Pore volume (total), ml/g Pore volhme (pores < 300 A ), ml/g Average pore diameter (pores < 300 A ), A Surface area (pores < 300 A ), mZ/g
0.794 0.740 0.37 0.55 0.51
Impregnated alumina 0.810
90 27 1
All of the sample system pipework was 3.18-mm 0.d. stainless steel large bore tubing. This was cleaned at frequent intervals to minimize contamination by dust and condensation; during regeneration the sample system was disconnected from the mainstream. The drying agent was replaced a t least once in every ten runs. The reactor was operated with a single batch of copper oxide impregnated alumina for a series of absorption-regeneration cycles, the sulfur dioxide output being continuously monitored during each absorption phase. (b) Solid Absorbent Preparation. The support used for the solid reactant was Laporte “Actal” type ‘‘P” I-mm porous alumina spheres, the properties of which are shown in Table I. Before impregnation, the alumina was dried a t 160 “C for 24 h and allowed to cool in a desiccator. A solution of copper(I1) nitrate (Cu(N0&3HzO) in deionized water was prepared. The alumina was immersed in the nitrate solution for 48 h. The concentration of the impregnating solution, required to give the desired copper concentration in the alumina, was calculated on the basis that all of the pores in the particles would be filled with the solution; thus when the particles were removed and dried the copper contained in the pores would be deposited onto the surface of the alumina. The impregnated alumina was removed from the nitrate solution and quickly rinsed to remove any of the solution trapped between the particles. The particles were dried a t 80 “C for 48 h and the dried particles were heated to 450 “ C in an air-fluidized bed for a further 24 h to decompose the copper nitrate to the desired copper oxide. Copper concentrations on the alumina of between 4 and 6% by weight were aimed for. The copper content of the absorbent was determined volumetrically by the iodine-potassium thiosulfate method. Results compared favorably with the values obtained from the sulfur dioxide breakthrough curves. The surface area of the particles a t the end of the impregnation procedure was determined by the B.E.T. method using nitrogen as adsorbent and was found to be 97.5 m2/g. Thus the available surface area of the alumina support (surface area 271 m2/g) had been considerably reduced by the impregnation and there is no doubt that many of the smaller pores had become blocked with copper oxide. Nonetheless an appreciable area of surface was available for reaction with SO2 and the particles could still reasonably be considered to be closely analogous to those of a porous catalyst and to be suitable for the application of the kinetic model previously described. Ind. Eng. Chem., Process Des. Dev., Vol. 15, No. 2, 1976
k2=36 7 9 e x p ( J G A ] RT
Time ( m l n u t e s l
Figure 3. SO2 breakthrough curve; bed length 10 cm, air flow 4 l./ min (NTP), inlet SO2 concentration 0.479 vol %, temperature 366 OC. l
Figure 6. Arrhenius plot of consecutive reaction rate coefficients.
Table 11. Calculated Arrhenius Equation Parameters I
Figure 4. SO2 breakthrough curve; bed length 10 cm, air flow 4 l./ min (NTP), inlet SO2 concentration 0.291 vol %, temperature 415 “C.
A , , s-‘ E , , kJ/mol A , , s-’ E,, kJ/mol
20 30 Time (minutes)
1t m e j m i n u t e s )
Figure 5 . SO2 breakthrough curve; bed length 10 cm, air flow 3 l./ min (NTP), inlet SO2 concentration 0.390 vol %, temperature 421 OC.
Results a n d Discussion The SO2 concentration in the bed output stream was recorded continuously from the start of the run until it reached a constant value at which it was equal to the inlet concentration, the solid absorbent being by then completely converted to copper sulfate. Graphs of the fractional output concentration ( C A ~ I C A are ~ ) termed “breakthrough curves,” some typical examples being shown in Figures 2-5. By fitting the kinetic scheme already elaborated to these results values of the two rate coefficients, k l and k2, and the initial concentrations of copper on the absorbent particles were calculated. Figure 6 shows an Arrhenius plot of the two rate coefficients as a function of temperature. From this the values of the activation energies and preexponential factors for the two reactions were calculated (Table 11). The close similarity of the two E values suggests that both reactions pass through activated complexes which are not very different in structure. The accepted structure of the intermediate copper oxysulfate
550.1 17.62 36.79 14.54
is sufficiently similar to that of the cupric sulfate to make this likely (Lorant, 1966). However, the accessibility of reaction sites for the second step is probably much less than that for the first and this could account for the marked difference in the two preexponential factors (AlIA2 ei 15). The concentration of copper determined by the application of the kinetic model to the breakthrough curves was found to decrease slightly with increasing numbers of regenerations. The steady-state value attained after some 15 successive regenerations was, however, in good agreement with the value obtained by chemical analysis and served as an independent check on the kinetic model adopted to describe the reaction. The surface area of the particles after their conversion to copper sulfate was measured by the B.E.T. method and was found to have increased to 156 m2/g, a result which indicates that a certain amount of opening-up of previously blocked pores had occurred during reaction. The good agreement between experimental results and the model predictions over a range of operating variables lends support to the model, which although originally devised to be applicable to a catalytic gas-solid reaction, may be seen to be capable of extension to a noncatalytic system. I t should be pointed out, however, that it will not necessarily be generally valid for noncatalytic reactions since the assumption that the solid reactant is little changed by the passage of an element of gas through the reactor will only be true for cases of slow kinetics, short reactors, and, as here, a very dilute reactant gas mixture. It is felt that in the case of low concentration sulfur dioxide reacting with copper oxide supported on porous alumina, the model is sufficiently reliable to provide rate coefficients which may be used with confidence in a system in which the fluid mechanics deviate appreciably from those of simple plug flow. The application of these rate coefficients to a fluidized bed reactor model will be explored in a future publication. Appendix
c u’ O h
Ind. Eng. Chem., Process Des. Dev., Vol. 15, No. 2, 1976
A mass balance over the bed at time t after the start of reaction shows, from the stoichiometry
d t = Xs
Differentiating with respect to time kzksxs] exp
- jj( k l ( 1 - XR)+ k*Xs)]
Hence from (A10) and (A12)
kR2(1- X R ) kRks(1 - XR) - ks2Xs = [ k i k ~ (1 XR) - k z k ~ ( 1 XR) + kzksxs] X ~ X P-
Substituting (A4) in (A2)
[5 ( k i ( 1 - XR)+ kzXs)]
Again, when t = 0, XR = 0, and XS = 0; therefore
k ~ ' k ~ k =s [ k l k ~ k z k R ] exp - [;ki]
Substituting for dXR/dt and dXs/dt from (11)and (12) therefore
-( 1 =2 2kR ) (l-XR)-kR(l-XR) V
= kR(1 - XR)
Substituting (10) in (A6)
- k z ) exp - (
V ~ k l )- k~
Thus k~ and k s are described in terms of k l , k2, V, and F by eq A8 and A15. Nomenclature C = concentration, mol/cm3
F = volumetric gas flow rate, cm3/s h = reaction rate coefficient, cm3/mol-s r = reaction rate, mol/cm3-s V = bulk volume of solid in reactor, cm3 X = fraction of surface
At t = 0, XR = 0 and XS = 0; therefore V
[ 1 - exp - (:hi)]
T o evaluate k s in terms of the parameters, it is necessary to differentiate (A6) with respect to time
Subscripts i = initial or inlet value o = final or outlet value L i t e r a t u r e Cited
Substituting for dXR/dt and dXs/dt from (11)and (12)
-F dCA, - -kR2(1 VCA~ dt
- X R ) + kRks(1 - X R ) - k s 2 X s (A10)
Differentiating (10) with respect to time
Best, R. J., Ph.D. Thesis, University of London, London, England, 1974. Dautzenberg, F. M., Naber. J. E., van Ginneken. A. J. J., Chem. Eng. frog., 67, 86 ( 1 97 1). Ingraham, T. R.. Trans. Met. SOC.A.I.M.E., 233, 359 (1965). Ingraham, T. R., Marier, P., Trans. Met SOC.A.I.M.E., 233, 363 (1965). Kelley, K. K., U.S. Bur. Mines, Bull. No. 406(1937). Levenspiel O., J. Catal., 25, 365 (1972). Lorant, E., Z.Anal. Chem., 219, 256 (1966). McCrea. D. H., Forney, A. J.. Myers, J. G., J. Air Pollut. Control Assoc., 20, 819 (1970). Keuster, J. L., Mise, J. H., "Optimization Techniques". p 386, McGraw-Hill. New York, N.Y , 1973.
Received for review December 16, 1974 Accepted November 14,1975 We would like to thank the Esso Petroleum Co. Ltd. and the Science Research Council for their financial assistance in this work.
Ind. Eng. Chem., Process Des. Dev., Vol. 15, No. 2. 1976