Kinetics of Reaction between Methane and Sulfur Va R . A. FISHER1 AXD J . 3%. SRlITH Purdue University, Lafayette, Ind.
T
Preheating of the methT h e kinetics of the homogeneous reaction between HE availability and ane and sulfur separately low cost of natural gas methane and sulfur vapor were studied in a stainless steel is difficult because of thc and sulfur has stimulated reactor at temperatures from 550' to 625" C. and varying heat absorbed when t'he reactants ratios and space velocities. l h e data were the investigation of the sulfur vapor is diluted. analyzed on the basis of the assumption that the rate of production of carbon disulUnless good heat transfer is available where the gases fide by the reaction of dissociation of SS and s6 to SZ is fast with respect to the are mixed the temperature methane and sulfur. The rate of the reaction with methane. A second order reacof the gases will fall condevelopment of a satisfaction between methane and the S2 species of sulfur offers siderably. The heat abtory commercial process has a satisfactory kinetic interpretation of the experimental sorbed when 1 mole of Sx been underway for some results. The reaction velocity constant (milliliter per dissociates to Sg and S; is approximately 10,000 and years in the petroleum ingram mole-hour) is given by the equation: 95,000 calories, respectively. dustry. The first published -34,400 The most, serious experi____ results were those of D e mental difficulty was tmhe IC = 4.9 x 1016e RT Simo ( 4 )who found that the control and measurement of small sulfur rates. The reaction was possible in the Kinetic equations postulating that s6 or Sg is the reactive unusual viscosity effects vapor phase a t e l e v a t e d species of sulfur vapor do not agree with the observed data. hinder the conventional t e m D e r a t u r e s 1800' t o liquid rate measurements. 900" C.) and was catalyzed A method based upon pasaing the sulfur vapor through a heated capillary tube was found by metallic sulfides. Later Thacker and Miller ( 7 ) showed that, t o offer the best solution. a reasonable rate could be obtained a t lower temperatures (500 ' The continuous flow system used in this investigation is shoaii to 700" C.) with catalysts of the clay type. Bacon and Boe ( 1 ) in Figure 1. The reactor consisted of st,andard 1-inch stainless have recently corroborated these results and also determined steel pipe, 6 inches long, capped a t both ends, and with leads t o the caps at either end. The reactor was maintained a t the desired approximately the extent of the homogeneous reaction. The temperature level by placing it in the vertical hollow core (2.5construction of the first commercial plant for carbon disulfide by inch inside diameter, 19 inches long) of an electrical furnace. this process was reported in 1949. A second furnace directly below the first (Figure 1) served to heat While the previous work uncovered effective catalysts for the the sulfur capillary and preheat the mixture of reactants. The temperature measurements were made with 3 Chromel-Alumel reaction and determined the general conversion levels, no attempt thermocouples, two located on the outside surface of the reactor had been made to investigate the mechanism of the process. and one inside the reactor at, the midpoint. One of the surface This problem-is of particular significance because of the partial thermocouples was placed at the same height as the inside thermodissociation of sulfur in the vapor phase. I n the neighborhood of the normal boiling point, sulfur vapor consists of approximately --3 equal amounts of s6 and SSa t equilibrium, but these species disI I sociate to a significant extent with an increase in temperature, or CONDENSER with dilution, to 86 and Sz. At atmospheric pressure the SI form does not exist in appreciable concentration below 1000 ' C. D R Y ICE ACETONE On the other hand, S6 and Sz are the predominant species in the temperature range where the carbon disulfide reaction is commercially feasible. The purpose of this investigation was to determine, if possible, the species of sulfur vapor which takes the predominant part in the homogeneous combination with methane and also to study the kinetics of the reaction as a whole. Since the homogeneous reaction rate is significant, any investigation of the mechanism of the catalytic process must be preceded by a HEATERS knowledge of the kinetics in the gas phase. Accordingly, this preliminary work is concerned only with the homogeneous gas phase reaction. CAPILLARY
-
VAPORIZER
EQUIPMENT AND EXPERIMENTAL PROCEDURE
The problems in constructing and operating the experimental equipment arose primarily from the behavior and properties of sulfur a t high temperatures. The vapors are extraordinarily corrosive and will attack platinum thermocouple leads a t temperatures near 1000" C. I n the neighborhood of 600" C., stainlese steel is corroded, but at rates which permit a reasonably long life for a reactor made of this material. Because silica gel was found by Thacker and Miller ( 7 ) to be an effective catalyst, it did not appear desirable to use quartz. For these reasons the reactor was constructed of stainless steel. 1
Present address, University of
T e x a s , Austin,
AIR
U Figure 1.
Texas.
704
x Flow System
THERMOCOUPLE JUNCTIONS
April 1950
INDUSTRIAL AND ENGINEERING CHEMISTRY
705
of the disulfide condenses.
METHANE ARM
CAPILLARY TC. PROBE
RESERVOIR
I
E L E C T R IC
-
a
BATH
Figure 2.
I
1
Sulfur Vapor Generator
couple t o permit measurement of the radial temperature gradient, while the other was placed near the bottom of the reactor in order t o observe axial temperature gradients. The inside thermocouple was contained in a quartz probe about 0.125 inch in diameter. T o ensure maximum heat transfer ca acity, the reactor was packed with approximately 7-mesh roc{ salt. Some of the preheating of the charged gases extends into a shallow layer of the packing at the bottom, as found by preliminary tests. The most successful solution of the problem of joining the quartz tubing t o the reactor consisted of a packing gland which held the quartz leads in a packing of asbestos cord. The method did not permit fine adjustments of position in making the connections, but this difficulty was avoided by introducing a ground joint in the quartz leads a t a short distance from the gland, and making the adjustments a t this position. The use of these joints also facilitated the introduction of the quartz thermocouple probe. The glands are leakproof if they are not subjected t o extreme heating and cooling cycles. The sulfur metering system is illustrated in Figure 2. Liquid sulfur is maintained at a constant pressure in a reservoir by application of controlled air pressure. Liquid sulfur is forced upward from the reservoir through a tube by the regulated air pressure, The reservoir and tube are of glass and make connection with the quartz capillary section through a standard taper joint in the delivery tube. The uartz tube is wound closely with Nichrome wire for a length of &out 0.5 inch as indicated in Figure 2. The sulfur vaporizes a t this point at a constant pressure. At a short distance above the heater, .the entrance end of the capillary hangs free in the v a or section. The capillary itself is suspended from a rin seal a\ &e exit end. With .a constant pressure on the sulfur cofumn rising into t h e vaporizer, the liquid-vapor interface tends to be stabilized. Variations in the interface level are reduced automatically by the differences in rates of heat transfer t o liquid and gaseous sulfur. If the liquid level tends t o rise, the additional surface covered by the liquid increases the heat transfer, and the sulfur is evaporated more rapidly. Similarly, if the level falls, more of the surface in the vaporizing section is exposed t o sulfur vapor. and the heat transfer rate goes down permitting the liquid level t o return to its original position. The vapor temperature is measured with the aid of a thermocouple probe protruding into the vapor space below the capillary. Hence, small changes in the temperatures of the vapors, which may result from changes in the vaporizer heat input, are detectable. With proper dimensions of the capillary an essentially linear relation between pressure drop and rate of flow is obtained, and reproducibility of flow rates within 0.5% of the average value is possible. After passing through the reactor, the mixture of gases goes through the sulfur condenser, where unreacted sulfur is removed. Finely-divided sulfur is then removed by glass wool filters before the mixture passes into the carbon disulfide condenser. I n view of the results shown by Thacker and Miller (7), who found t h a t side reactions are not significant, the product gases were analyzed for carbon disulfide only. Carbon disulfide was continuously extracted from the product gases in the condenser by cooling them t o -60" C., a t which temperature essentially all
The remainder in the gas was estimated from the vapor pressure of carbon disulfide at -60" C. This choice of temperature minimized the condensation of hydrogen sulfide. The condensate was analyzed for carbon disulfide according t o the xanthate oxidation method of Bell and Agruss ( 2 ) which permits the selective determination of carbon disulfide in the presence of all the possible sulfides. The reactor system and sulfur metering system were maintained within =t1' C. during operation. I n the final set of runs (53 t o 79) the radial temperature difference between the inside and outside of the reactor was never larger than 2" C., while the axial change in temperature from bottom t o top of the reactor was less than 5' C. I n view of the sensitivity of the quartz-steel glands t o leakage, it was desirable t o minimize the gage pressure in the reactor. All runs were made at reactor pressures of the order of 0.5 inch of water. Leakage was tested before each run by noting the change in pressure of the system as a whole with time. When not in use the system was flushed and filled with nitrogen gas. RESULTS
The conversion to carbon disulfide was measured at 4 temperatures, 550", 575", 600°, and 625" C., with a methane t o sulfur (as Sz) reactants molal ratio of 1 to 2, and for space velocities from 27 t o 373 reciprocal hours. At 600" C. additional data were obtained at reactants ratios of 2 t o 1and 1to 1. The methane mass flow rates ranged from 0.03 t o 0.42 gram mole per hour. Most of the results reported in Table I were measured in the reactor completely packed (bed depth 6.25 inches) with 7-mesh rock salt. To test the homogeneity of the reaction, some preliminary data were obtained with the reactor packed t o a depth of only 1.25 inches. These results are also included in Table I. HOMOGENEITY OF REACTION
As a preliminary test of the homogeneity of the reaction, the data of runs 25 t o 46 were compared. I n runs 25 through 36 the surface of the rock salt exposed t o the reactants was relatively small, while in runs 37 t o 46 the reactor was packed to its full depth of 6.25 inches. The inert character of the surface is revealed in t h a t the molal yield of carbon disulfide per hour changes in proportion to the reactor void volume rather than t o the surface area available. Thus the yield for runs 37 to 46 is less than that for runs 25 t o 37 at the same temperature and space velocity. This would be expected if the reaction were homogeneous, because the void volume is smaller in the fully packed reactor (runs 37 t o 46). COMPOSITION OF REACTANTS
The development of the kinetics of the reaction is complicated by the partial dissociation of sulfur vapor The gas consist8 of Ss, Sa, and Sz in appreciable quantities a t 550 O to 625 C., and i t is necessary t o relate the concentration of these species to the degree of conversion in examining the reaction rate behavior. The problem has been approached by setting up two simultaneous equations: (1) a material balance between reactants and products involving the degree of conversion and (2) an expression governing the equilibrium existing among the 3 species of sulfur vapor. The equations are solved by trial and error and the results are used to plot what will be referred to as the "conversion map," showing the amount of each constituent as a function of conversion. This information may then be used t o study the kinetics of the reaction. The term (Sp) will be used to denote a hypothetical gas which results from the complete dissociation of a mixture of SS, Sg, and S p ;and will be used to denote the moles of this hypothetical gas. The moles of the individual species Sz, Se, and SS present at any time will be designated as p , w, and II, respectively. Then n; = p 3n 411 (1)
ni
+ +
According to the reaction CHI ~ ( S Z---t ) CSz
+
+ 2HzS
INDUSTRIAL AND ENGINEERING CHEMISTRY
706
Vol. 42, No. 4
where the equilibrium constaiits A and B are given by l'reunor and Schupp as a function of temperature. Combining thmc cquations and expressing the partial pressure as the product of the mole fraction ailti the total pressurc (essentially- 1 at,inosphere in this investigation), loads to the followii~grelationship between 7r and 11.
15quationa 5 and 8 can be solved for T mtl 11 for given valucs of t,he total number of moles present, n, and the original react:tri;i: ratio (which determines A ) . Then fi can h(3 ihterniineti from 1,:quation 6 and -a from Iikluation 4. The imults of the calculations are shox-n in Figures 3 and 4, T h e number of niolcs of a I
cs, Clt
OO
1.0
1.0
0
CONVERSION
u Run Tenip., So.
Figure 3. Effect of Temperature a t Fixed Reactant Ratio of 1 &Tole of Methane to 2 Moles of ( S p )
+ p + r + rI +
01
+2O1
=
I 1 2 0 1 $- fi + 7 r
+ I1 ( 2 )
If, instead of t,he stoichiometric quaiitit),. 1 moles of mrthaiii~ are present in excess originally:
n= A+l+Z-a+p+7i+II
(3)
Since the stoichionietric amount of (8,) mole of methane is 2 moles, the conversion 01 in terms of the ( S p )piezeiit at an)- point in the reactor by the equation :
Substituting Equation 4 in 3 gives an expression d a t i n g thc total moles and the moles of SS and Ss umractctl. R =
a
+ 3 - (2T + 3rl)
Reactants, Molal Ratio, zCHa:y(Sp)
k, C.; hlole/Hr, CFIa
(Sz)
CJSp
Convcrsion, a
Reactor Was E m p t y Except for Preheater Bcd of 10- to l 4 - I I e ~ l Salt, i 1.25 In. Deep. Temperature Recorded Is at Point Just helow the 'To)) Surface arid a t the Xxii of t h e Bed. React,or Condition Is Ilesianated as Parking C. Yoid Volume of Reactor, T-R, was 67.0 MI.
1 mole of methane and 2 moles of (8,)coristitutc the stoicliiometric quantities of reactants. The t,olal number of molrr present a t a point in the reactor where 01 moles of mvthanr: hax-c been converted will be: 72 = ( 1 - - a )
C.
Space Velocityn
i.5
The relationship between the quantity of (?achspecies ol sulfui, present depends also upon the rate OC dissociation of the sulfur vapor. Reinhold and Schinitt (fi) traced the change in thermal conductivity in an unstable inisturc of sulfur vapor and fouiid that the half-life of the attainment o f equilibrium was about 1 minute at 2 5 0 " to 4 5 0 " C. The partiiwlar species of sulfur causing this slow change was not k n o ~ v n . Ihaune and Petcr (5)measured the time necessary for Ss to reach equilibrium an\l found that only a fraction of a second was required at 250" C. They also pointed out, that Reinhold and Schmitt, dealt. with systems in which the SI species may have been responsible for thc slow change in thermal conduct,ivity. Although more data would be desirable, the results of Braurie and Peter indicatc: that the rate of dissociation is very rapid at teniperatures from 550" to 625" C. Accordingly, it was assumed that the dissociation process was fast in comparison with the reaction nit11 methane. With this assumption the equilibrium data of Preuner and Schupp ( 5 )may be used to relate the moles of SSand SSo c c u i ~ i n g in Equation 5. Their results are expressed in the forms:
25 26 27 28
29 30 31 32 33 34 35 36
600 600 600 550 550 550 572 57,) 575 626 62.5 G25
213 373 106 7 106 7 213 373 373 213 106.7 373 213 106 7
1:2 1:2 1:2
1:2 1:2 1:2 1:2 1:2 1:2 1:2 1:2 1:2
0.238 0.417 0.11'3 0,119 0.238 0.417 0 417 0.238 0.119 0.417 0,238 0.119
0,476 0 834 0.238 0 238 0.476 0.834 0 . 83-1 0.476 0.238 0.834 0 . 476 0.238
0 0 0 0 0 0
0251 0J14
0214 0048 0058 0033 n 01 1.; 0 0097 0 0114 0 0531 0 0391 0 0312
0 10:
0.07; 0.180
0 . 040 0,024 0.013 0.028 0 041 0 096 0 127 0.164 0.262
Reactor Was Disassenibled and Packing C Was Replaced n.itir 1'ac:king D , a Bed of Approximately 7-lies11 R o c k Salt Completely I.'illing t h e Reactor (8.23 In. Deep). and of \-aid Volume Equal t o 35.2 111. Teinpeiatiire Refers t o Middle of Parliing
37 88
39 40
62.5 625 626 625
373 213 106.7 160
1:2 1:2 1:2 1:2
0.417 0.238 0.119 0.1785
0.834 0.476 0.238 0.337
0.0178 0.0179 0.0204 0 0220
0.043 0 07.5 0.171 0.123
I'ackinp7D Wan Replaced by- Packing E , a Reproduction of the Conditions in D . I e t n r ~ e r a t u r eIs Again Measured a t the Axis, a t the APid-Deilth of Bed 41 625 373 1:2 0.417 0.834 n.0188 0.045 1 : ~ 0.238 0 . 4 7 6 n . 0 1 ~ 2 0.081 42 625 213 43 625 160 1 : ~ 0.1785 n . 3 . x n.020:1 0.114 44 625 106.7 1:2 0 , 1 1 9 0.238 11.0212 0 178 106.7 1:2 0.119 0 238 0.0224 0.188 45 62;7 106.7 1:2 0.119 0 . 2 3 8 0.0213 46 62.5 0.179 I'low R a t e Range of Sulfnr-hletering System \Vat Altered to I'eriiiit 1.on.er Rates. 'I'enil)eratiire a t Capillary Was Also Depressed. l'ackinx Condit,inn Remained Unclianged 1:2 0.119 0.238 0.0026 0.021 53 106,7 1:2 0.476 0.002!i 0.012 0.238 213 1:2 26.6 0 , 0 2 9 7 2 0.0595 0.007!> 0.268 1:2 0.476 o.no5rJ 0,025 0.238 213 56 1:2 27 0 . 2 3 8 0.0076 0.066 0.119 106.7 1:2 0,0595 0.119 0.0086 0.141 53.3 .!8 106.7 0.110 0.238 0.0072 0.060 1:2 59 1:2 0 . 2 3 8 0.0160 0.135 0.119 106,7 GO 1:2 0.476 0.0161 0.068 213 0,238 61 53.3 1:2 0.279 0.0595 0.119 0.0166 62 26.6 1:2 0.0298 0.0595 0.0136 0.457 63 0 . 4 7 6 0.0015 213 1:2 0.238 0.006 64 0.119 1:2 0.238 0.0018 0.015 106.7 65 53.3 1:2 0,0595 0.119 0.0024 0.040 66 1:2 0,02976 0.0595 0.0025 0.084 26.6 67 0.027 1:2 106.7 0.119 0.238 0.0032 68 1:2 0.012 213 0.238 0 . 4 7 6 0.0030 69 1:2 0.061 0.0595 0.119 0.0306 53.3 70 1:2 0,02975 0.0595 0 , 0 0 4 8 0.161 26.6 71 1:2 0.238 0 . 4 7 6 0.0134 0.036 213 72 93.3 1:2 0.0595 0.119 0 . 0 0 3 7 0,063 73 03.3 0.0595 0.119 0 . 0 0 4 2 0.070 1:2 74 0.0595 0,119 0.0079 1:2 0.133 53.3 75 0.269 0,02978 0.0595 0.0080 1:2 26.6 76 0.058 0.119 106.7 1:2 0 . 2 3 8 0.0069 77 1:1 n ,0893 0 . 0 8 9 3 0.0087 0 . 193 63.3 78 0 .321 0.0595 0.0096 2 : 1 0.119 5 3 . 3 79
2;
a Space velocity is equal t o \-olumetric flow rate in ml./lir. divided hy total volume of empty reactor in ml. Flow r a t e is based upon all t h e sulfur vapor considered as Sz and is referred t o 0" C. and 1-atm. pressure.
April 1950
INDUSTRIAL AND ENGINEERING CHEMISTRY
707
KINETlCS O F THE REACTION
If it is supposed that the reaction is second order, the rate, r, in gram moles of carbon disulfide produced per hour per unit volume of reactor, is given by the expression:
! I? k
where CCH,and Cs, are the molal concentrations of methane and the particular species of sulfur vapor assumed to take part in the reaction, and k is a reaction velocity constant measured in milliliters per gram mole-hour. If, at the operating pressure of 1 atmosphere, the gases are assumed to behave as a perfect gas mixture,
4
, ---
and
cs, 0
Figure 4.
1.0
-0
1.0
d
d
where i V values represent mole fractions. If the total number of moles of reaction mixture is n,
Effect of Changing Reactant Ratio at 600 ' C.
Substituting Equations 10 t o 12 into Equation 9 and rearranging:
component is represented by the vertical distance between two curves. In other words each component is represented by a region; the lower left-hand region on each chart refers to methane and indicates that at zero conversion there is 1 mole of methane. The quantity of methane decreases linearly with 01 until all has been reacted, a t which point a: equals 1.0. Proceeding vertically upward, the next region refers to carbon disulfide, then hydrogen sulfide, Sz,Sg,and SS. Figure 3 shows the effect of temperature at a fixed reactants ratio of 1 mole of methane to 2 moles of (SZ). Figure 4 depicts the effect of changing the reactants ratio a t 600" C. The dissociation tends to stabilize the amount of S2 present.
I
REACTANTS
I
+ S6
- 30
625'
-& ;/I:
- 20
Figure 5.
b A
sod
C.
+ 556 x cn,: y ISJ
t 550. Cn, :r C&)
-
(&) kde
The development up to this point has been on the basis that the reaction was carried out batchwise with a reaction time, e. I n the actual flow process, d8 is the time required for an element of the gas to pass through a differential volume of reactor, dV,. In equation form:
A x 576
625'C. 600'
x 575. x
dnm2 Nc"s,
/
REACTANTS : CH4+ S,
REACTANTS: CH4+ Se
A 2:l
Nsz RT
= -
A
625'C. Sob
Y
575.
+550' xcn.:r(sd
- 1.5
;\$$$-k
/*
- 1.0 4
/!
Plot of Runs 53 to 79 When Sa, Ss,and
.2:1
SI Are Assumed to Be the Reactive Species of Sulfur Vapor
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
708
where v is the actual flow rate in milliliters per hour. The problem of the variation in 2. and n with conversion can be eliminated by referring them to the corresponding values n' and v', ba.;ed upon considering all the unreacted sulfur as (Sz). Since v' (and n ' ) does not change with conversion, it is the same as the feed rate--Le., v' represents the feed rate measured in milliliters per hour a t the reaction temperatwe and pressure. The relationship between n, v, n', and I ' is:
Conibining Equation I
