concentration of sodium acetate in liquid phase a t equilibrium = diffusion coefficient for bulk diffusion of species 1 in a multicomponent mixture, sq. cm./sec.= diameter of particle, cm. = mean particle diameter, microns = diameter of a n individual particle, microns = acceleration due to gravity, cm./sec.2 = observed reaction rate constant, liters/sec. = intrinsic reaction rate constant, cc./sec. g.-mole = intrinsic reaction rate constant, cm./sec. = mass transfer coefficient, cm./sec. = mass-transfer coefficient for free settling, cm./sec. = number of i particles = rate of absorption and reaction in slurry, g.-moles/ sec. cc. liquid = intrinsic homogeneous rate of reaction, g.-moles/sec. cc. = temperature, ’K . = fluid velocity, cm./sec. = fraction of unconverted alkyl chloride (free hydrocarbon basis) =
T U
X
GREEKLETTERS 0 ps p~
P
reaction time, hours density of solid, g./cc. = density of fluid, g./cc. = viscosity, g./sec. cm. = =
literature Cited Bieber, H., Gaden, E. L., A.1.Ch.E. meeting, Los Angeles, Calif., Feb. 7, 1962. Friedlander, S.K., A.I.Ch.E. J . 7, 347 (1961). Hauser, E. A , , “Colloidal Phenomena,” pp. 16, 20, McGrawHill. New York. 1939. Heilman, E. A., Spray Dryer Division, Nichols Engineering Co., personal communication, 1966. Hougen, 0. A., Watson, K. M., “Chemical Process Principles,” p. 908, Wiley, New York, 1947. Polinski, L., personal observation, 1964. Satterfield, C. N., Sherwood, T. K., “The Role of Diffusion in Catalysis,” Addison-Wesley, Reading, Mass., 1963. Smith, H. A,, Fuzek, J. F., J . A m . Chem. Soc. 68,229 (1946).
RECEIVED for review November 17, 1966 ACCEPTED June 8, 1967
OXIDATION OF M E T H A N E TO FORMALDEHYDE IN A FLUIDIZED BED REACTOR B. H. M C C O N K E Y A N D P. R. W l L K l N S O N Central Research Laboratories, Imperial Chemical Industries of Australia and ,Vew Zealand, Ltd., Ascot Vale, Victoria, Australia
Production of formaldehyde b y high temperature free radical oxidation of methane with air and homogeneous initiators has been studied in a reactor employing a fluidized bed as heat transfer medium. The ratio of rate constants for radical attack on formaldehyde and methane was found to b e 2 1 f 4 a t 670”C., and as a result only relatively small concentrations of formaldehyde have been produced. Evidence i s presented that hydroxy radicals are the prime reactive species. Theoretically and experimentally it appears that high yields are possible only at low methane conversions; hence appreciable concentrations of formaldehyde in the effluent gases cannot b e achieved. HE partial oxidation of methane a t high temperature has T b e e n studied exhaustively, principally in static systems, and the mechanism has been reviewed in detail (Semenov, 1959; Shtern, 1964). Formaldehyde and traces of methanol have been the organic products isolated, and, as the main intermediate product, the conversion to formaldehyde reaches a maximum as reaction proceeds. For many years this maximum conversion to formaldehyde has been reported as up to about 3% of the methane present, but in recent patents (Huttenwerke Oberhausen, 1961, 1962, 1963) pass conversions of up to 60% have been claimed. T h e present work was intended to establish whether high concentrations of formaldehyde in the product were possible, perhaps by introducing selectivity into the branching chain radical reaction by the use of reactive surfaces and solid quenching agents. T h e kinetics of the reaction in a flow system have also been studied.
Experimental T h e reactor was constructed of stainless steel tubing 1 inch in diameter and 15 inches long. A 4-inch section containing the fluidized bed (resting volume between 10 and 40 ml.) was heated electrically and above this was placed a 1-inch water jacket for quenching purposes. Air and nitrogen were preheated to 800’ C . and passed straight into the reactor below the fluidized bed, where they were mixed with methane and nitric oxide which entered a t room temperature. The result436
I&EC
PROCESS DESIGN A N D DEVELOPMENT
ant gas mixture, at atmospheric pressure and a little below the reaction temperature, was rapidly heated in the fluidized bed where reaction was initiated. Some reaction occurred at the hotter reactor walls, particularly when the air supply was insufficiently preheated, in which case heat transfer across the bed was inefficient. Temperatures were measured by thermocouples placed in the center and on the inner and outer walls of the reactor. I n general, it was possible to operate the reactor so that the temperature measured at the center of the bed was not more than 15’ lower than that measured on the wall. Furnace temperatures were generally some 50’ to 100’ higher. After leaving the reactor, the gas stream was split and passed through heated tubing to the gas injection ports of the gas chromatograph. Formaldehyde, methanol, and carbon oxides were separated on a ?-foot column of 20 w./\v.% Ethofat 60/25 on Columnpak T (Bombaugh and Bull, 1962) a t 130’ C. using a hydrogen-nitrogen mixture as carrier gas, methane and carbon oxides being measured together on this column. The effluent from the column was passed through a 5-inch bed of Ni-Tho*-kieselguhr methanating catalyst which enabled all the components including formaldehyde to be measured in a flame ionization detector. Methane was separated from carbon oxides on a 3-foot column of molecular sieve 5A, also at 130’ C. Carbon oxides were thus measured by difference only. No attempt has been made to measure the ratio of C O to COZ,since all previous workers have found this to be high. In agreement with all previous reports, methanol has been found to be only a trace product; consequently we have ignored it in all considerations regarding mechanism and kinetics.
All gases except nitric oxide were pure grades, used directly from cylinders. Nitric oxide was generated by dripping 1 volume slightly diluted nitric acid (5 volumes of 7 0 7 , acid of water) onto granular copper, and was dried by passing through a tower of calcium chloride. All gas flow rates were measured by calibrated rotameters, total flow rates varying between 2 and 5 liters per minute at S.T.P. Solid phases used were obtained from a variety of sources. Particle sizes were chosen in ranges bet\veen 0.7 and 2.4 mm.
+
- 100
10.0-
I
I' a
3
ln ln w
6.0J
ic Ia Results
Effect of Temperature. I t was necessary to work a t concentrations outside the explosive limits: At temperatures above 650' C. and linear flow rates in the ranges 600 to 1200 cm. per second, these corresponded to partial pressures of methane in air of less than 11 and more than 152 mm. of Hg. I n addition, it was necessary to ensure that severe thermal gradients did not exist across the bed. T h e effect of temperature upon the oxidation is shown in Figure 1. T h e partial pressure of formaldehyde increases rapidly above some threshold temperature to reach a maximum, whereas the total conversion of methane increases monotonically. T h e partial pressure of formaldehyde, after it has reached its maximum, is relatively insensitive to temperature. 'Thus result,s obtained over a range of 20' C. are within the experimental accuracy and can be used for kinetic analysis; methane conversions, however, correspond to a specific temperature only. Effect of Residence 'Time. For a homogeneous free radical reaction (contrast a heterogeneous reaction) the residence time, 7, in the free volume of the heated zone is the significant parameter. Values of 7 have been based on flow rates a t S.T.P., since the range of temperatures employed (see Figure 1) was not wide enough to cause a significant error in comparing results. Residence times have been altered by varying flow rates and particle sizes, and also the volume of the solid used. Changes of partial pressures of methane and formaldehyde with residence time are shown in Figures 2 and 3. I n a manner typical of a n intermediate in a consecutive series of reactions, the partial pressure of formaldehyde increases to a maximum, a t which point the residence time is about 0.5 second. T h e methane conversion appears to increase linearly. Figures 1 to 3, and Table 111, show that a t the highest formaldehyde concentrations in the product the yield of formaldehyde is always less than 40% (which corresponds to conversions of methane to formaldehyde of only 4%). Hence, further oxidation is rapid. Furthermore, the decreased partial pressures of formaldehyde a t longer residence times confirm that its rate of oxidation depends directly upon its concentration. Kinetic Dependences. Figures 4 to 6 present the effect of varying the partial pressures of the various reactants. From the data, pressure dependences have been established (Table I). As shown in Figure '6, the reaction is close to first order in both methane and oxygen. (The d a t a of Figure 3 suggest that the conversion of inethane should be zero-order but this is a fortuitous result of the presence of a branching chain reaction.) T h e apparent orders with respect to nitric oxide are not of quantitative significance. They show that, as expected, nitric oxide does act EIS a n initiator, not only for methane oxidation but also for further formaldehyde oxidation. Hence the apparent dependence on nitric oxide pressure in the case of methane oxidation is indicative of the over-all kinetic chain length.
K
49
w >
-
2
-20 I
I
620
640
660
I
I
600
700
720
T *C
Figure 1.
Effect of bed temperature
0
Formaldehyde yield Methane conversion T = 0.5 second Solid. HF-treated silica gel Reactant. 1 9 0 mm. of methane, 7.6 mm. of nitric oxide in air
+
7
Figure 2. tion
SEC.
Effect of residence time on formaldehyde forma-
Mixtures of methane with 7 6 mm. of oxygen, 7.6 mm. of nitric oxide, balance nitrogen
0,. A, A 0,
HF/SiOp-gel, 660-80' C. SiO,-gel, 660-80' C. Pumice, 7 5 0 ' C. Open symbols, 190 mm. of methane Closed symbols, 3 5 0 mm. of methane
The kinetic chain lengths may be calculated from Figures For partial oxidation to formaldehyde the chain length is less than 10, while for complete oxidation it is between 1 5 and 30, assuming complete reaction of the nitric oxide initiator. Homogeneous Initiators. Some gas phase homogeneous intiators have been investigated; the results are presented in Table I1 for mixtures containing 190 mm. of methane and 7.6 mm. of initiator added to air. Maximum formaldehyde partial pressures were obtained for 7 = 0.5 second, and data are quoted a t this point. 4 and 5.
VOL. 6
NO. 4
OCTOBER
1967
437
i
40
/
5
n60W
i i
>
n w
~
30-
c K >
g 20. V
0.25
0
T'
0.50 SEC.
0.75
Iii
L
I .0 1 0
Figure 3. Effect of residence time on over-all methane conversion
U
5
I
I
I
5
IO
15
20
N 0 PARTIAL PRESSURE M.M.
Figure 5. Dependence of methane conversion on partial pressure of nitric oxide
Reactant. 1 9 0 mm. of methane, 7.6 mm. of nitric oxide in air Solid. HF-treated silica g e l Temperature. 6 7 0 ' C.
Reactant. T
1 9 0 mm. of methane in air
= 0.5 second
Temperature. 670' C. Solid. HF-treated silica g e l
10.0
".ot/-
= . 0
2.0 NO
4 0 6.0 8.0 10.0 PARTIAL PRESSURE M.M.
12.0
14.0
Figure 4. Dependence of formaldehyde formation on partial pressure of nitric oxide Reactant: 1 9 0 mm. of methane in air 7 = 0.5 second 0 HF-treated silica gel, 660-80' C. H Pumice, 7 5 0 ' C.
2.0t
t/
I
Heterogeneous Surfaces. The influence of a variety of surfaces on the free radical reaction is shown in Table I11 for mixtures containing 190 mm. of methane and 7.6 mm. of nitric oxide added to air. T h a t the various surfaces under these conditions were not catalysts per se is shown by the very low conversions obtained in the absence of nitric oxide (Figures 4 and 5). T h e solids are listed in decreasing order of efficiency in promoting the reaction, taking into account the temperature as well as extent of reaction. Untreated silica gel was noticeably more active than other solids (see Figure 2). Insertion of a cooled 40 B.S.S. mesh copper or bronze grid into the downstream part of the reactor (Huttenwerke Oberhausen, 1963) with a quenching bed of silicon carbide did not enhance the formaldehyde pass yield at residence times of 0.12 and 0.50 second. T h e reaction products remained unchanged from those when only the primary reaction bed was used (Table 111). 438
l&EC
PROCESS DESIGN A N D DEVELOPMENT
I
I
IO
30
20 C H I X 0%M.M.1 X
0
Figure 6. Second-order dependence of formaldehyde partial pressure on methane and oxygen Mixtures of methane, oxygen, 7.6 mm. of nitric oxide, balance nitrogen, using HF-treated silica gel a t 660-80' C.
Kinetic Orders for Formaldehyde Yield and Methane Conversion Quantity In CHa In 02 In N O
Table I.
Initial rate Maximum HzCO partial pressure Methane converted at HzCO maximum
1 .o
...
...
1 .o
1.2
0.21
1 .o
1. o
0.63
Table II.
Catalyst
Comparison of Homogeneous Catalysts
Formaldehyde Pressure, M m.
Methane Converted, M m.
Optimum Ttmfi.,
8.4 5.5 6.7
19 9.5 19
670 720 770
NO EiBr
HC1
~
Table 111.
C.
Afiparent Kinetic Order in HzCO Formed 0.21 0.24 0.24
~~~
Comparison of Fluidized Bed Solid Phases
Solid System
Sec
Formaldehyde Pressure, M m.
Si02 gel Cr203/pumice HF-treated Si02 gel HF/Si02 gel grid N.Z. pumice PbO/A1203
0.32 0.45
9.3 8.4
38.0 28.5
670 660
0.513
8.4
19.0
670
0.50 0.40 0.31 0.26 0.51 0.55
8.4 8.2 7.8 7.6 5.7 1.9
19.0 26.6 20.9 11.3 24.7 15.2
670 740 approx. 690 750 650 620 center 800 wall
7,
+
A1203
Si02/A1203 Empty tube
Methane Converted, M m.
Optimum Temp.,
c.
Discussion
I n the postulated mechanism, O H , and HOZ are considered (Semenov, 1959; Shtern, 1964) to be the main chain-carrying radicals. Thus, in initiation these probably appear by the reactions:
+ CH4+
NO or
2N0
and
NOz 0 2
0 2
+
0 2 +2
+ CH4 + HNO. + HNO.
+ CH3.
HNO.
+
NO2
+ CH3. O H . + NO2 HOz. + N O
HNOz
+ +
(11
(2) (3)
(4)
(5)
Methane is oxidized to formaldehyde by:
+ CHI HOz. + CH4 OH.
CHa.'+
+ CHI. HzOz + CH3. HzCO + O H .
+
HzO
+
0 2 +
(6)
(7)
Clearly this ratio is crucial to the yields of formaldehyde. At low conversions, in fact, it approximates the reciprocal of the pass yield. If radical attack ori formaldehyde is relatively kII ,< kI-conversion to formaldehyde will be slow-Le., high, but where the reactivity of R . to formaldehyde is high-i.e., kII sufficiently > kI-only slight amounts of formaldehyde will remain as product. Maximum partial pressures of formaldehyde obtained in the present work varied with the oxygen-methane ratio; the values of kII/kI calculated therefrom fell in the range 14 to 40 a t 670' C. More reliable values of kII/kI have been obtained by considering the whole of the concentration ,- residence time range, rather than merely the point of steady state. A solution leading to k l I / k I for such second-order consecutive reactions was published by McMillan (1957). T h e data such as shown in Figures 2 and 3 have been computed to obtain the values of the rate constant ratios given in Table IV. Within the reproducibility of the experimental data the values of k I I / k I are satisfactorily consistent, over the range of variation of residence time, reactant concentrations, and heterogeneous surfaces. Values a t very short residence times are less reliable, however, since these correspond to very small conversions of methane. I n terms of McMillan's treatment such d a t s lie in a rapidly changing region of the solution for k I I / k I ; hence satisfactory values cannot be obtained in this region because of the relative inaccuracy of measurement. From Table I V , the mean value of k I I / k Iis 21 f 4 a t 670' C . I t is relevant to consider the evidence for the nature of the radical R. From comparison with other work (Table V) we believe that O H , is the active radical. The value of 21 =t 4 for kII/kI corresponds to values of kg/ke derived by previous authors. Further, it has been established (Egerton et al., 1957; Warren, 1952) that with acidic surfaces HOZ. radicals are converted to hydrogen peroxide and hence to O H . , which accounts for the low values of kII/kI found by Blundell et al. (1965) for acid-washed vessels. T h e solids employed in the fluid bed are of acidic character so far as the surface properties are known.
(8)
However, the formaddehyde produced may be oxidized further by the same radicals:
+ H2CO HOz. + H2CO OH.
+
+
+ HCO. HzOz + H C O .
HzO
(9) (10)
and more slowly by H2CO
+
0 2 ---t
HCO.
+ HOz.
(11)
T h e principal reactions leading to the formation and disappearance of formaldehyde may be formulated as :
I. 11.
+ C H I 2 RH + C H B . R . + HzCO 2 RH + H C O R.
in which R . may be either OH. or HOZ. I t can be shown from other data (Ingold and Bryce, 1956) that ks is greater than ks or k, (both represented by k I . in the general sense) and hence Reaction I leads. directly to formaldehyde formation with a n over-all rate constant equal to k I . Therefore, it is easily shown that, in the steady state (with respect to HzCO),
Table IV.
Solid and Initiator (Initiator Pressure 7.6 M m . )
Kinetic Analysis
Pressure CHa in Air, Mm.
7, Au. Sec. krilkr hlkIa HF/Si02, N O 0.26 39.52 190 0.46 18.84,19.31,19.23 19.75 0.64 19.76 0.79 21.57 HF/SiO2, N O 0.26 78.69,61.95 350 0.54 18.51 25.74 0.76 32.97 SiOz, N O 0.12 40.99 190 0 32 17 22 17.22 .__ 24151 HF/Si02, HC1 190 0.46 190 0.46 23.35 HF/SiOz, HBr CrZOa/pumice, NO 190 0.46 19.34 190 0 . 5 1 29.45 SiOdAlzOa. N O 13.97 Alpd~N , O. 190 0.26 190 0.30 20.46 PbO/A1203, N O These a Data at short residence times not included in average kII/kI. correspond to very small conversions, hence low experimental accuracy, and lie in a rapidly changing region of the solution for k l I / k I .
VOL. 6 NO. 4 O C T O B E R 1 9 6 7
439
Table V.
k9/k6
km/h
24 (670” C.) 22 (650” C.)
300 (670’ C.)
Rates of Free Radical Attack on Methane and Formaldehyde h/kI
Basis
33 (500’ C . ) 260 (500’ C.) 21 i 4 (670 ’ C.)
Semi-empirical estimation (Semenov, 1959) Initiated by thermal decomposition of H202 to O H . radicals (Hoare et af., 1959, 1966) Slow oxidation of methane in hydrofluoric acid-washed vessels and in boric acid-washed vessels (Blundell et af., 1965) Present work, initiated by N O in presence of HF-washed silica gel
Further corroborative evidence can be derived from activation energy considerations. By combining the values for kII/kI of 33 at 500’ C. (Blundell et al., 1965) and 21 at 650’ C. (this work), a value of 4 kcal. per mole is obtained for EIEII. From the above references (Semenov, 1959; Hoare, 1966), values of Ee-Eg are 6 and 4 kcal. per mole. The sequence of reactions involving the disappearance of HOZ.radicals
use of suitable reacting and quenching surfaces, but such high conversions would require chain lengths of several hundred. However, it is concluded from the results presented above that it is inconceivable on theoretical grounds, because of the more rapid simultaneous rate of radical attack on formaldehyde, to employ free radicals to provide a high conversion to formaldehyde while further oxidation is inhibited. Acknowledgment
HzOz
+
20H.
(1 3)
means that a branched-chain reaction is involved. This complicates the kinetic picture, and the normal decrease of rate a t longer ,residence times arising from the simple kinetic second-order dependence on methane and oxygen concentration will not be observed. Thus Figure 3 gives an apparently linear dependence of methane converted on residence time, due to compensation by the branching chain reactions a t longer residence times. Thus there appears to be general agreement regarding the relative rates of attack of OH. (and HOs , ) radicals on methane and formaldehyde. Conditions favoring O H . radicals, as in this work, provide optimum concentrations of formaldehyde. Throughout, the methane oxidation reaction is clearly of branching chain type, the chain length with respect to initiators being, from the present results, about 10. I n recent patents (Huttenwerke Oberhausen, 1961,1962,1963) exceptionally high methane conversions to formaldehyde have been claimed by
T h e assistance of V. L. Paul in computer programming is gratefully recorded. literature Cited
Blundell, R. V . , Cook, I\’. G. A., Hoare, D. E., Milne, G. S., Tenth Symposium (International) on Combustion, p. 445, Combustion Institute, Pittsburgh, 1965. Bombaugh, K. J., Bull, W. C., Anal. Chem. 34,1237 (1962). Egerton, A. C., Minkoff, G. J., Salooja, K. C., Combust. Flame 1, 25 (1957). Hoare, D. E., Proc. Roy. SOL.A291, 73 (1966). Hoare, D. E., Peacock, G. B., Proc. Roy. SOC.A291, 85 (1966). Hoare, D. E., Protheroe, J. B., jt‘alsh, A . D., Trans. Faraday SOL.55, 548 (1959). Huttenwerke Oberhausen A.G. (formerly Bergbau A.G.), Brit. Patents 880,873 (1961); 913,581 (1962); 926,889 (1963). Ingold, K. U., Bryce, I V . A , , J . Chem. Phyf. 24, 360 (1956). 79, 4838 (1957). McMillan, i V . G., J . A m . Chem. SOC. Semenov, N. N., “Some Problems of Chemical Kinetics and Reactivitv.” Pewamon Press. Oxford. 1959. Shtern, V. Ya.,- “The Gas Phase O’xidation of Hydrocarbons,” Pcrgamon Press, Oxford, 1964. Warren, D. R., Proc. Roy. Soc. AZ11, 22, 245 (1952). RECEIVED for review January 30, 1967 ACCEPTEDJune 29, 1967
QUALITY OF CONTROL PROBLEM FOR DEADTIME PLANTS T. J .
McAVOY’ AND E. F. JOHNSON
Department of Chemical Engineering, Princeton University, Princeton, N .J .
wo questions have to be considered in designing a control Tsystem: whether or not the control system is stable, and whether or not the quality of the control attained is good. Quality of control involves the ability of the control system to damp out quickly the effect of a disturbance on the plant. Unlike stability, quality is not a well defined concept and many different criteria have been suggested for it. There is no single answer to what constitutes good quality of control. This paper is concerned with the quality of control problem Present address, Department of Chemical Engineering, University of Massachusetts, Amherst, Mass. 440
l & E C PROCESS D E S I G N A N D D E V E L O P M E N T
associated with the selection of regulators-i.e., controllers which hold certain variables a t steady-state values-for plants with dead-time lags. The following synonyms for the term “dead-time lag” have appeared in the literature: delay time, time lag, transportation lag, transport lag, and distance velocity lag (a special case occurring in flow systems). The incorporation of a dead time into a control loop makes the over-all control system more unstable than the corresponding loop without the dead time. I n general, a poorer quality of control is attained on a plant which contains a dead time than on one which does not (Eckman, 1946).
