Model Reactor Studies of the Hydrogen Cyanide Synthesis from Methane and Ammonia Edgar Koberstein Physical-Chemical Research Department, Degussa Wolfgang, 646 H a n a u , Germany
+
+
+
The highly endothermic reaction NH3 CHI = HCN 3Hz 60 kcal, which i s technically realized in tube reactors with wall catalysis, i s investigated. With the a i d of special quartz probes, concentration profiles as function of the tube length and the tube radius are determined at different throughputs, together with the temperature distribution along the tube axis. Flow type, heat and mass transfer, as well as a macrokinetic model, are estimated. Concentration curves calculated with those data for extreme conditions "envelope" the measured concentration profiles. The parameters limiting the overall reaction are elucidated.
H y d r o g e n cyanide is industrially produced according t o the so called "B1I.A process," using ceramic tubes of 2000 mm length and 20 mm diameter with a platinum-containing catalyst layer on the inner wall as reaction units (Endter, 1958, 1959). The highly endothermic reaction
CH,
+ KH3 = HCK + 3H2 + 60 kea1
(1)
takes place a t temperatures between 1200 and 1300' T o obtain information about the macrokinetics and reaction mechanism, measurements of the radial and axial concentration profiles and of the temperature distribution were made in an electrically heated model reactor with reaction tubes of 1500 mni length, but otherwise identical with those used in the technical reactor (for experimental set up see Endter, 1958,1959). Experimental Section
Apparatus. Quart'z probes as shown in Figure 1, which could be shifted into definite positions along t h e t u b e axis during t'he reaction, were used t'o extract small gas samples near the wall and in the center of the tube simultaneously. A t times the probes (having, except for the sampling tips, the same dimeiisioiis as the thermocouple wells) replaced one of the thermocouple wells which were accessible from the inlet aiid outlet ends of the reaction tube. The out'er walls of those probes were coated, in t h e same way as the tliermocouple wells, with catalyst t'o avoid disturbances of the reaction as far as possible. During preliminary experiments it was found t'hat the reaction proceeds only very slowly on quartz surfaces; therefore, the inside walls of the probes secured a rapid iiiterruption of the reaction during sampling. FThen the total system had reached steady-state conditions, small gas samples were d r a w l by means of a mechanical pump. During warm up t'he probes were flushed with hydrogen. Two probes were used, each reaching to the middle of the reaction tube, from the inlet and outlet ends, respectively. During the experiments, one probe and one therniocouple well were combined, e.g., lower half, probe; upper half, thermocouple well, and vice versa. The probes were moved from the center to the end of the reaction tube a t intervals of 50 mm, samples being drawn with a flow rate corresponding t,othe ai-erage f l o rate ~ within the react'ion tube. 444
Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 4, 1973
Analysis. By means of Hg-filled gas burets, control samples (ident.ica1 amounts from both lines simultaneously) were drawn out of the sampling gas stream via a T piece for rapid approximatire gas analytic determiiiations (thereis a systematic error). For more exact analysis, the total sampliiig gas stream was bubbled t'hrough H2SOI and S a O H solutiolis for about 20 min, and the absorbed amount of S H a and H C S were determined titrimetrically. The residual gas n-as collected in a gasometer. Volume, temperature, and pressure were recorded. The gas composition (mol yo)was calculated as follows ?2R =
(B
% HCS
=
bi - by)V:/RT
(2)
l 0 0 n ~ cZn~
(-1)
The performance of the reactor tube without probes was checked before aiid after the measurements. Results
The ammoilia and liydrogeii cyanide conceiitrntioris as a function of the length coordinate for a throughput of 6 and 12 mol/ hr are shown in Table I (see paragraph a t eud of paper regarding supplenieiitary material) and plotted in Figures 2 and 3. Figure 4 (Table I) shon-s the corresponding teniperature plots, measured bj- shifting the thermocouples in the thermocouple wells accordingly. Energy input \\-as adjusted to attain a masinium temperature of about 1200". Tables I1 and I11 (supplementary material) aiid corresponding Figures 5 and 6 slion- the ammoilia conversion as a fuiiction of residence time (throughput 6 and 12 niol lir). Residence time was calculated as 7 = Ll'v for each seetioil of 50 mm length. These data indicate that most of t,he conversion takes place in a coniparatirelj- small 5ection and a t coriiliaratively short reaction times (e.g., for 6 mol hr throughput, more than 90% of the total amount is converted in a sectioii 450 mni long in about 150 niaec). Balancing the analj-tical data for each of the t50-nim sections, one can locate the ammonia decompositiori, although the analytical data for the small nmnioriia deficiriicy S ~ O W comparatively large deviatioiis. -1 statistical evaluation indicated that the average ammonia decomposition definitely
Gmole/hr HCN OC
probe1
probe I1
35
Figure 1 . Quartz probes for sampling
105
75
cm Figure 4. Temperature distribution cm Y N H ~ ~
O C
800 25 20,513 \Throughput 1
,
I
980 LO .0,40
1005: 45-0.30/ I
1 1040. 50 1070. 55.0,20,
,
-_
1130 6510,101 I
15 3!5 55 75 cm
----tube and p r o b & . . L
1210_9510 I
95 115 135
50
0
100- 150 200
T msec
Figure 2. Csoncentration profiles for NH3
Figure 5. NH3 conversion vs. residence time (throughput 6 mol/hr HCN)
25~
O c cm Y"3 lo20 880 L5 30/0.50 o , ~
Throughput
~ 12rnole/hr o , HCN d probe l
1OCO1 501
' 1
1060 55-0,30 1 070 601o,20
':
11001 70J 10.1 0 1180~100/ I
I5 35
55 75 95 cm
115 135
0
's
50
100
'I; m s e t
150 200
Figure 6. NH3 conversion vs. residence time (throughput 12 mol/hr HCN)
Figure 3. Concentration profiles for HCN
increased within the sections from 200 t o 500 mm with a statistical certainty of more than 95%. As Table Is' indicates, a separation of t h e gas components occurs a t the outlet end of the reaction t'ube. Discussion
For obtaining a theoretical reaction model which could he compared with measured data, the flow type, heat and mass transfer: mid macrokinetics are discussed and finally comhied. Flow Type. Reynold numbers Re = nd;?
'.,
(5)
were calcu!ated for the follo\~-ingexbreme conditions: (a) tube section 100 mm, conversion 0, temperature 500'; (b) tube section 100 mm, coilversion loo%, temperature 1 2 0 0 O .
Viscosity data not available in literature ryere calculated according t o Andrussow (1952, 1953). A11 Reynolds iiumbers are well below 2300. Therefore, we can assume laminar flow during the m r m - u p section and, despite some dist'urbaiice near the wall, ayprosimately in the reaction zone also (see concentration gradients bet,ween center and wall, Table IV). H e a t Transfer. It is obvious t h a t due to the high endothermic reaction heat and the high reaction temperature, heat transfer has to play ail important part. In providing a sufficiently high temperature on the outer tube wall! the thermal coriductioii through the ceramic material arid the heat traiisfer from iiiiier vial1 to gas could be limiting factors. The heat conduction through a cyliiidrical tube wall is calculated according to the forniula
Q
=
X 2 ~ L ~ ? i T t (~r l, n' T i )
Ind. Eng. Chem. Process Des. Develop., Vol. 12,
(6) No. 4, 1973
445
Table IV. HCN concn, % Probe Probe centera WOlP
Throughput, mol of HCN/hr
0
6 23.9 26.4 6 23.3 25.7 12 22.3 24.5 12 21.5 26.0 Located 12 cm from the outlet end.
Difference,
5 = 0,99
%
1
= 0,9 = 0.7 = 0,5 5 = 0,3
2.5 2.4 2.2 3 5
5=0,1 Q[kcall
SCO.
th.5.S
i
/
5000.
133 OC
300
500
AT
Figure 7. Thermal conduction
Thermal conductivity coefficients h for sintercorundum in the literature (Gerdien, 1933; Perry, 1963; Torkar, 1956) differ between 2.9 and 5.3 kcal/mol hr degree. Figure 7 shows a plot of the amount of heat which can be conducted through a tube section of 100 mm length as function of the temperature differences with h as parameter. Using h = 4.0 as the moet probable value and a temperature difference of, e.g., loo', a t most 870 kea1 can be transferred providing the necessary endothermic heat to form 12 mol,/hr H C S in a section of 100 mm length. Therefore the heat conduction through the ceramic material should not' be a limiting fact'or. This is also confirmed by the fact that the conversion curves for 6 and 12 molihr throughput, with t,he same heating system, are nearly parallel, the 12-mol curye only shifted nearer to the outlet tube end. This shift is caused by a n enlarged warm-up zone, indicating a limiting influence of the comparatively smaller amount of heat to be t'ransferred from the n-all to the gas in order to warm it up. The rapid increase of heat transfer after the reaction has started can be explained by a boundary layer disturbance (volume increase) and by the fact t h a t t h e endothermic reaction heat is transferred to molecules adsorbed on the wall. M a s s Transfer. Gas Diffusion. T o estimate mass t,raiisfer phenomena, diffusion coefficients of the ratedetermining component into the residual gas mixture are necessary. Since they are iiot available in literature for the present case, the diffusion coefficients of ammonia were calculated according t o -1ndrussow (1950, 1953) for seven different conversion rates and in temperature steps of 50' betn-een io0 and 1200'. The results are shown in Figure 8 and in Table L7 (supplementary material available). The diffusion coefficients of methane are similar, lyhich means that the results n-ould iiot be changed essentially if methane diffusion should he the rate-determining factor. 446
Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 4, 1973
Figure 8. Diffusion coefficients of NHa into residual gas
Thermal Diffusion. Regarding thermal diffusion, t h e reaction under investigation shows two pecularities. (a) During the reaction the mass ratio of the gas components changes greatly, from 17/16 t o 2/27. (b) There appear high-temperature gradients and heating is applied only through the reactor tube wall. T o get an idea of whether thermal diffusion could be responsible for the gas separation found experimentally a t the outlet side of the reaction tube, it seems useful to estimate the temperature gradients necessary to produce the separations found. From the basic differential equations (Westphal, 1952) we get (7) As most probable value for a(Hz/HCX), a(H2/N2)'v 0.3 was used (Westphal, 1952). The results are y1 = 0.25, yz = 450'. 0.24, T2 - Ti LV 250'; yl = 0.25, y2 = 0.23, T1 - TI Such gradients are to be expected bet'weeii the wall and gas temperature at the cooled outlet tube end. Macrokinetics. The reaction is practically isobaric, but iiot isothermal. Furthermore, a volume increase is involved. The only parallel reaction is ammonia decomposition which is very small with the catalyst used. There are no consecutive reactions. llicrokinetic data are not available, therefore the following assumptions concerning the surface react'ion had to be made. Considering the molecular st'ructure and the reaction bemperature, a rate-determining methane activation and a Rideal mechanism suggest itself. Methane activat'ion on a platinum catalyst follows a first-order kinetics (Sch\vab, 1926). As long as ammonia decomposition is to be neglected, the rate equation becomes =
- 7 i ? j ~ ~=
*~'FccH,(~)
~ H C N
(8)
I t is obvious that with increasing temperature, mass-transfer phenomena will become rate determining. With laminar diffusion we may assume an approximately linear concentration gradient ct(diff) =
DiF(ci
- ct(W))/s
(9)
For steady-state conditions, expressions 8 and 9 can be equated
-E:
1 1.00’
12 mole/ hr HCN
= 0,5
10 5 I 5
ko = 5 ko = 10 ko = 50
35 Figure 9. kef*’ vs. temperature
fiHCX = - h N H s
+ 7C7R)
(12)
n conibiiiation of n i , m transfer resistance TTyuand surface ~ react’ioiiresistaiice T 1 7 where
na
JV-R =
f(T);
T1-D =
g(T,{, a{/dL, bT/br)
(13)
6ince those functioi-,s are partly unknown, an exact’ solution is impossible. Therefore, simplified models were calculated which “wrrouiid” tlie actual reaction, permitting informative c*oiiclusioiis. Starting from the differential equation (Damkohler, 1937)
v dc f r(v,- vc.l/c) = 0 dL
(14)
we call express keff as a‘ function of experimentally determined data (SH;I,or HlCS concentrations)
- 1) x kif’= -v-d((2glo 2L
To get an approximate evaluation, since the reaction is clinracterized by high-temperature gradients, k e f f f bi-as calculated with average values for 50-mm sections. For throughputs of 6 and 9 mol’hr, Figure 9 shows, after a nearly linear steep ascent, n fiat portion indicating an influence of mass transfer plieiiomeiia on the total rate from a certain temperature upvard. The curve even becomes retrogressive in the case of 12 mol hr throughput, n-hich is caused by tlie fact t h a t the reaction i b shifted into the cooling section, where it is stopped abruptly . The differentinl equatious a cj -
at
=
- div (vcj) + div ( D j grad
115
(11)
= jlNHa(diff)
1/(Ii7D
cm
Figure 10. Calculated and experimentally determined conversion curves
From eq 10 we may interpret a total reaction resistance (or reciprocal rate coilstant) kef*’ =
65
c,)
(nv)cj -- D, ( n grad)cj = ~ ~ 1 1 ~
(16)
describe will reactioiis iiicludiiig mass transfer (Damkohler, 1937). With the limiting conditions stated there an approxi-
mate solution has been given by Wicke, et al. (1956), for t h e cylindrically symmetrical tube reactor. I n Figure 1C corresponding concentration curves n-itli keff’ as parameters are calculated and compared with the experimentally determined conceiitration profile. Obviously the reaction passes through steps, which are controlled to a different amount by reaction and diffusion resistance. This caii be further confirmed by calculating the dimensionless expression D , = kod/2D for extreme surface rate constants ko. N h e n D , > 100 diffusion dominates; when D , < 0.1 chemical surface reaction rates dominate; when 100 > D , > 0.1 there is a transition range (Damkohler, 1937): e.g., ko = 0.5, D , = 0.075; ko = 5.102, D , = 7 5 . Conclusion
Summarizing, the overall reaction can be described as follows. (a) Warm-up and Starting Zone. K t h i n a considerable part of the tube, tlie reactants mixture is heated up only. This process is limited by t h e heat transfer from the wall t o the gas, which determines the length of t h a t zone and thereby the maximuni throughput possible. K i t h optimal catalysts, practically no reaction occurs until the gas is warm enough to permit methane activation. Then the reaction starts aiid rapidly increases its rate, perhaps due to boundary layer disturbances causing more rapid warm up. The only parallel reaction, ammonia decomposition, occurs at’ t h e end of section a and a t the beginning of section b. It limits the maximum yield obtainable. It is to be pointed out t h a t this is true only for the system under investigation, since ammonia decomposition depends strongly on t h e catalyst used. (b) Reaction Zone, The chemical react’ioii rat’e increases further with iiicreasiiig temperature until mass transfer beconies rate determining. The main conversion takes place in this transition range between chemically or diffu sion-con. trolled rates in a comparatively short section of tlie reaction tube. If the outer nall temperature is not sufficient (depending on the throughput) the reaction rate may be reduced again by inner wall temperatures becoming too low. (cj Cooling Section. The outlet tube end is cooled through its support, which leads to a large temperature gradient between wall and gas and separation of the gas compoiieiitsoceurs by thermal diffusion. If the reaction zone is shifted into this section, the reaction is stopped abruptly. S o consecutive reactions occur. Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 4, 1973
447
v,
Acknowledgment
The author wishes to thank X r . Schaetzle for his assistance.
T
= stoichiometrical conversion number for component j, (v = BJ,) =
residence time, T
Nomenclature
B
=
bl b,
= = =
barometric pressure, ML-IT-2 pressure difference in gasometer, JfL-IT-2 vapor pressure of sealing liquid, .ML-'T-2 c concentration, mol L-2 D = diffusion coefficient, L2T-1 d = diameter, L F = surface area, L 2 k' = l i 0 = chemical rate constant (wall reaction, first order), LT-I kef?' = effective rate constant, LT-' L = length, L n = number of moles nR = number of moles in residual gas Q = amount of heat, cal . R = gas constant, cal mol-' r = radius, L Re = Reynolds number T = absolute temoerature. 0 t = time, T 'b = rate of reaction per unit volume, mol L-3T-l V = volume. La v = linear ga's velocity, L T - 1 IV = rate of reaction per surface unit, mol L-T-' y, = mole fraction of component i ylo = inlet mole fraction of component i
GRLCKLETTER CY
6 {
X q
= = = = =
thermal diffusion ratio thickness of boundary layer, L conversion rate thermal conductivity coefficient, cal L - ' T - W ' kinematic viscosity, L2T-1
literature Cited
Andrussow, L., 2.Elektrochem., 54, 566 (1950). Andrussow, L., Z. Elektrochem., 56, 624 (1952). Andrussow, L., Z. Elektrochem., 57, 124 (1953). Andrussow, L., 2.Elektrochem., 57, 376 (1953). Andrussow, L., Z. Phys. Chem., 199, 314 (1952). Damkohler, G., in "Der Chemie-Ingenieur," 111, Akadem. Verlagsges., Leipzig, 1937, p 359. Endter, F., Chem.-lng.-Techn,, 30, 305 (1958). Endter, F., DECHEMA (Deut. Ges. Chem. Apparatewesen) A%f07L0gr., 33, 28 (1959). Endter, F., et al. (to Degussa), German Patent 1,013,636 (Jan 23, 1958).
Gerdien. H.. 2. Elektrochem.. 39. 13 11933).
Beflin, '1952, p 531. " Wicke, E., Rossberg, M., Chem.-Ing.-Techn., 28, 181 (1956). RECEIVED for review October 6, 1972 ACCEPTED May 25, 1973 Supplementary Material Available. Tables 1-111 and V will appear following these pages in the microfilm edition of this volume of the journal. Photocopies of the supplenieiitary material from this paper only or microfiche (105 X 148 mm, 2 0 X reduction, negatives) containing all of the supplementary material for the papers in this issue may be obtained from the Journals Department, American Chemical Society, 1155 Sixteenth St., K.W., Washington, D. C. 20036. Remit check or money order for $3.00 for hotocopy or $2.00 for microfiche, referring t o code number PRBC-73-444.
A Rate Approach to Design of Perforated-Plate Extraction CoIumns A. H. P. Skelland" and W. 1. Conger Department of Chemical Engineering, The University of Kentucky, Lexington, Kentucky 40606
An attempt i s made to integrate some of the many and diverse studies on droplet phenomena into a coherent design procedure for perforated-plate liquid extraction columns. Equations describing mass transfer during droplet formation, rise, and coalescence, and incorporating relevant hydrodynamics, are used to locate a pseudoequilibrium curve. This curve is used in place of the true equilibrium relationship when stepping off the necessary number of actual stages between the pseudoequilibrium and operating curves on the x-y diagram. The provisional procedure i s written in Fortran IV computer language and the printout gives the number of real plates required for a prescribed separation, the number of perforations per plate, the column diameter, and the cross sectional area of the downcorners. Predictions are compared with all appropriate published values and agreement with fully eligible data (group A) i s substantial.
Stagewise columns achieve contact' between two phases in a discontiiiuous maiiner in stages Tvhich may, for example, take the form of bubble-cap plates or perforated plates. Both types of plate are widely used in gas-liquid contacting, such as distillation and gas absorption. I n liquid-liquid extraction the loiyer density difference b e h e e n phases, the higher viscosity of the disperse phase, and the lower iiiterfacial tensions 448
Ind. Eng. Chem. Process Des. Develop., Vol. 12, No. 4, 1973
cause bubble-cap plates to be ineffective, but perforated plates are successful and have been widely used. Skelland and Coriiish (1965) presented a procedure for the design of perforated-plate columns vihich is intended to eliminate the need for experimental determination of stage efficiencies, because these are normally obtained a t substantial cost in time, effort, and money. Furthermore, the applicability
