December 1951 =
=
INDUSTRIAL AND ENGINEERING CHEMISTRY
Lrn + + Lrn + q(L
e@ - j - b3u
u)e-juP(L q(L
u)e-blum,(L
u)P(L
+ u)ekudL
+ u)m,(L + u)d(L+ u )
The integral is practically equal to the constant
JI;"
for P practically vanishes for the small values of the argument between o and u. Hence
where a2 and bs are constants. Now y depends on the distribution curve m(L) in such a manner that for a series of successive equally spaced curves, approximately equally spaced values of y will result if the range covered is not too great. Moreover, the way in which y depends on the distribution will not involve any sudden changes which would severely restrict this range. Since equally spaced rn curves mean equally spaced values of 21 and also equally spaced corresponding values of u, u is a linear function of y and hence
-9 = aze-b2cs(y dt
- vo)
= ase-bsv
which the particles of a given L were identical, and then show that the contribution of each species to the change of y was linear in In t, and hence that the sum total change of 21 was linear in In t. It is simpler, and appears sufficient for the present, to replace the actual size descriptive variable L in the preceding argument by
L' = qPmodL,
(8)
which has been shown to be equivalent to the empirical law y = - b In t. Although it was assumed to simplify the preceding discussion that all particles of the same size L are identical, it is not necessary to do so. One way of generalizing the theory might be to divide the particles into separate species within any one of
a
2897
1
In P/al so that particles of bi
a given L' will all have the
same P,but will have the size L' only on the average, individuals varying in L. If it is assumed that this spread of L about the average L' does not prevent y from depending in a smooth and regular way upon the distribution curves, now m(L') instead of m(L), then the preceding argument still holds for the real case where the particles are not completely described by a single size variable. ACKNOWLEDGMENT
The authors gratefully acknowledge data obtained from G. F. Green, Fiberboard Products, Inc., Port Angeles, Wash., on experimental ball mill testa of selected wood pulp types. LITERATURE CITED
(1) Farrington and Birdsall, Oil Gas J., 45, No. 46, 268 (1947). (2) McFarlane, Inst. Spokesman, 6, No. 12 (1943). (3) McLennan and Smith, ASTM Bull., No. 152, 71 (1948). (4) Morris and Schnurman, Nature, 160, 674 (1947). (5) Sohroeter, Congr. mondial pbtrole, 11,434 (1933). ( 6 ) Simha, J.Applied Phys., 13, 147 (1942). (7) Stross and Abrams, J . Am. Chem. SOC.,73, 2825 (1951). (8) Tech. Assoc. Pulp Paper Ind.,Standard Testing Methods, Designation T-224 sm-45. (9) Vold, Hattiangdi, and Vold, IND. ENC.CHEM.,41, 2539 (1949). RECEIVEDSeptember 19, 1950. Presented before the Division of Colloid CHEMICAL SOCIETY, ChiChemistry at the 118th Meeting of the AMERICAN cago, Ill.
Corrosion of Steel in Molten
Sulfur ANDREW DRAVNIEKS Engineering Research Department, Standard Oil Co. (Indiana), Chicago, Ill. Corrosion of steel vessels by hot sulfur-bearing media causes constant difficulties in many industrial processes. Little is known about the basic corrosion reactions involved. The simplest ease of this type is studied in the present work. Between 300" and 450" C. the corrosion of steel in sulfur is limited by two processes, one chemical and another mechanical. A thin film consisting principally of ferrous sulfide grows by diffusion of reactants, presumably iron ions, through the film. The rate of corrosion is inversely proportional to the thickness of the film. With increasing thickness, mechanical strains produce film rupture followed by temporary local acceleration of attack. Kinetic constants of the reaction are given, and the film structure is described. The paper clarifies the fundamental mechanisms in sulfide formation on steel in molten sulfur. This instance of corrosion falls into the type of film-growth reactions complicated by a cracking-heating process.
S
ULFUR compounds attack most of the metals and alloys
used in chemical engineering. With the greater use of oils with high sulfur content in the petroleum industry, sulfur corrosion increases considerably in importance. The corrosion products usually are sulfides, and even in the corrosion of alloy steels in sulfur dioxide-containing flue gases, the sulfides often are reaction intermediates. However, little is known as to the mechanism and the rate law for the corrosion of metals with sulfide formation, even in liquid sulfur. The behavior of
metals in this medium must be understood before studies in even more complicated media are undertaken. LITERATURE
Hackerman and Shock (6,11) foundonly a slight discoloration of steel held in contact with dry sulfur for 3 hours at 130' C. However, theyreported enormous corrosion ratesof several inches per year if water was present simultaneously and the steel coupons were in contact with both sulfur and water. West (14) reports a corrosion rate of steel in sulfur of 0.025 mm. or 0.001 inch per year at the melting point of sulfur, 115' C., and 12.5 mm. or 0.5 inch per year at the boiling point, 445' C. Gel'd and Esin (5) suggest that the sulfide scale grows by iron diffusion outwards, in an analogy to Pfeil's (8) picture of oxide scale growth on iron. The change of the reaction rate with time and temperature has not been studied systematically in the iron-sulfur system.
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
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The most recent critical compilation of data on the phase diagram of the ironsulfur system was published by Lundquist ( 7 ) and is reproduced in Figure 1. The marcasite form of iron disulfide is not shown in this diagram, as marcasite forms only hydrothermal I y and has not been found in iron-sulfur mixtureswhich m-ere held at temperature until equilibrium obtained.
corrosion, but for a correct estimate of the absolute thickness of metal consumed, it is necessary to continue the experiment until the strip specimen is totally corroded. The moment is readily detected, for at that time there is a more or less sudden change
', LIQ. + V A P .
LIQ.
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Vol. 43, No. 12
-12
-11 410
,e ATOMIC PER CENT SULFUR
Figure 1. Iron-Sulfur Equilibrium Diagram by Lundquist 1, 2, S, 4..
F
Modifications of iron
.>. Superlattice phase of FeS
6. FeS phase with B8 structure 7 . YIonoclinic deformed FeS phase 8 . Cuhic FeSn phase 9 , 1 0 , !I, 12. Modifications of sulfur
EXPERIMENTAL
The corrosion experiments \+ereconducted in the device shown in Figure 2. Molten sulfur of commercial purity was kept in a 125-ml. Erlenmeyer flask maintained within 1" C. of the prescribed temperature by a thermostated aluminum block. Before use, sulfur was boiled for several hours to remove volatile impurities-e.g., traces of sulfuric acid. A Brown Pyrovane controller in combination with an Xactline regulator served to control the temperature. The specimens were cut from 25-micron or 125-micron nominal thickness steel shim stock in the form shown in Figure 2. The specimen proper had long striplike ends extending through the tubes, B , and forming four connecting leads, H . The progress of corroeion was recorded conductometrically ( 1 ) by passing a small, 0.1- to 0.3-ampere current from a storage battery through the specimen hy means of two leads, and recording the potential drop along the specimen on a multipoint recording Brown Electronik potentiometer. As corrosion occurs, the metal is converted to corrosion products of lower conductivity; so, from the potential drop changes, the changes in the cross section of the specimen can be calculated and thuc; the progress of corrosion can be followed over a range of time. The analyses of the steels xeie a i follows: Steel Thickness, R Inch Carbon 0 001 0 00:
0 08 0 06
%
%
nese
phorus
Sulfur
Silicon
Copper
SicRel
0 44
0 030 0 018
0 036 0 031
0 002 0 002
0 003 0 02
0.004 0 06
Manpa0 37
Phos-
'Z
%
%
7
To provide an independent check, weight-loss tests were made concurrently with the conductometric experiments. Samples of steel sheet of 125-micron thickness were cut into 8 X 45 mm. pieces and immersed, in triplicate, in liquid sulfur for various lengths of time. To determine the weight loss, the corrosion product was removed by fii st clcaning the specimen mechanically and then pickling with thiourea-inhibited 10% sulfuiic acid. Samples of the sulfide scales fc rined in corrosion vere collected and subjected to micrcscopic and x-ray examination.
Figure 2. Schematic Representation of Experimental Setup Specimen Silica double-hore tubes Sulfur D . Aluminum block E . Aluminum stopper F . Glas-col heater 6. Thermocouple €I. Specimen connecting leads A.
B. C.
in the slope of the conductivity-time curve. To make this change sharper, small specimens-e.g., 1.5 X 9 mm.-are used so that the rate of corrosion over the specimen is more uniform. Another way to estimate the correct absolute amount of corrosion is by means of weight-loss tests. Once the correction factor, which compensates for the conductivity of the sulfide, is established, the conductivity data may be easily converted in order to express the corrosion in terms of penetration depth. Tin % Iron % The conductivity of the sulfidic corrosion Remainder product immediately after disappearance 0:025 Remainder of the metal phase is 0.25 to 0.30 of the conductivity of the steel strip at the same
1.0
,
i
EVALUATION OF RESULTS
If the electrical conductivity of the corrosion product is negligible compared to the conductivity of the corroding metal, the fraction of the initial cross section left intact at any moment is equal to the fraction of the initial conductivity left. However, since most sulfides have a specific conductivity comparable to that of metals, the specimen is stili conducting even after conversion to the sulfide is completed. Therefore, the plot of the conductivity change with time will reproduce the time law of
0
1
4
9
16
a0
36
49
64
TIME. EOURB
Figure 3. Corrosion of 25-Micron Thick Steel Strip in Sulfur
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
December 1951
temperature. There is little change of this ratio with temperature. The corrosion data obtained conductometrically are most easily handled if the corrosion is essentially uniform. In cases of pronounced pitting, the method still retains certain advantages, but the curves are less easily interpretable. I n the case of the sulfur-steel reaction, the attack was basically uniform.
2899
of corrosion (8). As the film thickens, it may occasionally break or crack (4). A new film then starts to form at the place of failure. The corrosion-retarding action of the sulfide film would be strongest if the film never failed. Mechanical and geometrical
RESULTS AND DISCUSSION
I n the corrosion of steel KINETICS OF SULFIDE FORXATION. by liquid sulfur, the rate of attack decreased with time. The reaction may be classified as one of the scale-growth type which has been described by Pilling and Bedworth (9) and by others (3, 12, 15). In the simplest case the rate of attack is inversely propcrtional to the thickness of the scale preaent at a given moment, or
I 1
or 1.0
,
i
s 4 I e TIME, SOUR8
a
i a e ~ o
Figure 5. Effect of Failures in Sulfide Scale on Conductivity of Steel Strip Corroding in Sulfur at 445' C.
factors as well as temperature changes tend to promote cracking and therefore to accelerate corrosion. If the corrosion per year is calculated from thin film experiments and the parabolic law is used as a basis for extrapolation, the figure thus obtained would represent the slowest possible corrosion rate under given conditions. Figure 6 shows how the corrosion for the first year depends, theoretically, on the frequency of breaks in the film. It has been assumed that these are full breaks always occurring in the same location. Using Equation 2, the parabolic rate constants can be calculated. Figure 7 contains the constante compiled on a conventional activation energy plot. Only short-time weight-loss 1
4
9
18
26
96
49
64
81
100
TIME, BOWRE
Figure 4. Corrosion of 125-Micron Thick. Steel Strip in Sulfur
where y is thickness of the scale, t is the time since beginning of reaction, and L and kl are parabolic rate constants. According to the last equation, the conductivity of the strip specimen plotted against the square root of time will give a curve which is straight if the parabolic law is obeyed. I n Figure 3 such plots are shown for steel specimens with a thickness of 25 microns at several temperatures. The parabolic relationship is essentially obeyed. Similar curves, obtained for 125-micron thick specimens, are shown in Figure 4. The breaks indicated by the arrows are due to a complete conversion of metal to sulfide. After the break, there is still a slow continuous change in the conductivity, caused by further transformations in the sulfide. These changes are discussed later. Thus, it may be concluded that the reaction of steel with sulfur proceeds according to the parabolic law and hence is controlled by diffusion of metal through the sulfide scale. This conclusion, however, holds only for thin sulfide layers. The curves of Figure 4 were obtained on specimens of especially small size. If larger specimens are used, cracking of the sulfide scale is observed, accompanied by a rapid increase in the rate of corrosion with a subsequent decrease in the rate as the crack heals. A curve of this type is reproduced in Figure 5 . On the basis of these experiments, the corrosion of large size steel specimens in molten sulfur is controlled by two mechanisms. The rate of corrosion depends initially on the rate of diffusion of iron ions through thin films of sulfide formed in the process
NUMBER OF FILM FRACTURES PER DAY
Figure 6. Corrosion of LOW Carbon Steel Strip in Boiling Sulfur at 445' C. as a Function of Film Fractures
tests were used to obtain the constants so as to exclude the complications arising from cracking of the scale. Only those conductivity curves were used which did not show any breaks because of scale cracking. The activation energy represented by the slope of the line is approximately 41 kg.-cal. per mole. Diffusionrate generally depends on the gradient of the chemical potential, the absolute concentration, and the absolute mobility of the diffusing particles. On the basis of available information it is not possible to resolve the observed activation energy into terms corresponding to each of the-e factors.
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INDUSTRIAL %ND ENGINEERING CHEMISTRY
Vol. 43, No. 12
ioma-
1,ow
-
100
-
10
-
c
d
o250 t
300
350
spo
490
4qO
1.4
1.6
t
1.8
spoec 1.7
1.8
x 10s
450
400
TBMPERATURE.
OC.
Figure 8. Longest Number of Days a Steel Thickness of 125 Microns Could Withstand Molten Sulfur at Various Temperatures
Figure 7. Activation Energy Plot for Steel-Sulfur Reaction
An experiment was conducted to ascertain if hydrogen sulfide gas might accelerate the steel-sulfur reaction. The gas was bubbled through boiling sulfur in which the steel specimen was immersed. No change in reaction rate as compared with plain boiling sulfur was detected. Figure 8 s h o m the longest times steel with a thickness of 126 microns might ever withstand molten sulfur at various temperaturcs, assuming that the sulfide scale would never crack. REACTION PRODUCTS
Both pyrite (FeS2)and pyrrhotite (FeS) were detected in the reaction product by using x-ray techniques. At the beginning of the reaction the patterns were somewhat Figure 9. blurred, but a t later stages the lines beSchematic came sharper, and the match with the Represen t a purest available pyrrhotite and pyrite, tion of Sulfide as well as with x-ray index card data, was Scale Layers on Steel satisfactory. Additional microscopic and magnetic 1. P y r r h o t i t e non(FeS), studies revealed more details of the remagnetic 2. P y r r h o t i t e action product structure. The sulfide (FeS), magscale consisted of three layers shown schenetic 3. Pyrite (FeSd, matically in Figure 9. The two outer magnetic? layers, 3 and 2, were dark gray and coherent. The outermost was identified as pyrite, the middle layer as pyrrhotite. A positive complete physical separation of the two layers was impossible, but as far as it could be judged from the behavior of separate particles in vicinity of a strong magnet, they both were ferromagnetic. Since pyrite is nonmagnetic, the outer layer might be pyrrhotite interpenetrated by pyrite. The layer next to the steel, 1, consisted of a loose grayish powder, easily removed by a needle. The x-ray pattern of this powder corresponded to that of pyrrhotite. Some samples of the powder were nonmagnetic, some very slightly magnetic. Since pyrrhotite with a composition between FeS and FeSl.15 is not ferromagnetic (IO), the thin powdery layer next to the steel should be within these composition limits. The bulk of the scale consists of ferromagnetic sulfide, FeSl 15 to FeSl 8 and higher. During the initial stages of the reaction, when the sulfide scale
was no more than a few microns thick, both sulfides were detected in the scale. I n a few cases, this scale was apparently nonmagnetic; it may be that here the scale contained only pyrite and the nonmagnetic pyrrhotite of low sulfur content. This point was not pursued further, After all the metal was consumed, the scale consisted of both sulfides. The middle of such specimens was hollow, indicating that the mode of growth of the scale is at least partly outward. The inner pyrrhotite core was enveloped by pyrite. If the specimen was left in molten sulfur, the reaction continued. The fraction of pyrrhotite gradually decreased, by conversion to pyrite. However, this reaction wa8 extremely slow. A steel strip 125 microns thick was all converted to scale after 20 hours in boiling sulfur; after a further 220-hour exposure, the sample was still strongly ferromagnetic, and the x-ray pattern demonstrated that it still consisted mainly of pyrrhotite. The function of the loose powdery pyrrhotite layer may be understood if one considers that a ferrous sulfide layer grows principally by diffusion of iron ions toward the pyrite-pyrrhotite interface The metal phase remains in contact with the bulk pyrrhotite by means of loosely packed columns and aggregates of pyrrhotite. The columns serve as conduits to maintain iron ion flow to the scale. The mechanisms by which these columns can extend into the zone of metal consumption have been discussed elsewhere (f?, 8). It is probable that the dissociation of sulfide on the rnetal side is one of participating mechanisms. As the metal boundary moves away, the loose powdery material recrystallizes and becomes integral with the bulk of the scale. LITERATURE CITED
(1) Dravnieks, A,, J. Am. Chem. Soc., 72, 3761 (1950). (2) Dravnieks, A., and McDonald, H. J., J . Electrochem. Soc., 94,
139 (1948). (3) Evans, U. R., Trans. Electrochem. Soc., 83, 335 (1943). (4)Ihid.,91,547 (1947). ( 6 ) Gel’d, P. V., and Esin, 0. A , J . A p p l i e d Chem. (U.S.S.R.), 19, 678 (1946). (6) Hackerman, IS., and Shook, D. A., Corrosion, 6 , 195 (1950). (7) Lundquist, D., Arkiv Kemi, Mineral. Geol., 24A, No. 22 (1947). (8) Pfeil, L. B., J . Iron Steel Inst. (London), 119, 501, 559 (1929). (9) Pilling, N. B., and Bedworth, R. E., J. Inst. Metals, 29, 529 (1923). (10) Selwood, P. W., “Magnetoohemistzy,” pp. 246, 247, New York, Interscience Publishers, 1943. (11)Shock, D. A.,and Hackerman, N., IND.ENG.CHEM.,41, 1974 (1949). (12) Tammann, G., and Koster, W., 2.anorg. u. allgem. Chem., 123, 196 (1922). (13) Wagner, C., 2. physik. Chem., B21,25 (1933). (14) West, J. R., Chem. Eng., 53, No. 10, 225 (1946). RECEIVBD March 14, 1951.
