Dissolution of Tetragonal Ferrous Sulfide (Mackinawite) in Anoxic Aqueous Systems. 2. Implications for the Cycling of Iron, Sulfur, and Trace Metals James F. Pankow’” and James J. Morgan Environmental Engineering Science, California Institute of Technology, Pasadena, Calif. 9 1125
Both nonoxidative and oxidative mechanisms can play important roles in determining how FeS and associated trace metals are solubilized under different environmental conditions. Models are presented for determining t h e FeS concentration profiles in anoxic sediments experiencing FeS dissolution. Methods for calculating the time required to completely dissolve suspended FeS particles of various sizes in anoxic waters are also presented. The relative rates of oxidative and nonoxidative FeS dissolution are discussed with respect to trace metal release from sewage sludge and sediments and pyritization in sediments. The kinetics of the nonoxidative dissolution of mackinawite have a direct bearing on the rates of several environmentally important phenomena: (1) the nonoxidative release of iron, trace metals, and sulfur from sulfide phases in anoxic sediments and sewage; (2) the oxidative release of these elements from the same systems; and (3) the pyritization of recent sediments. T h e first paper of this series ( I ) described an experimental study of t h e nonoxidative dissolution of mackinawite. We now idiscuss the above phenomena in terms of the results of t h a t study. The dissolution rate law, which pellets pressed from e l - p m particles of mackinawite (FeS) were found ( I ) to obey, is:
F = hl[H+]
+ kp
(1)
where F is the flux of dissolving metal sulfide (mol/(cm2.minj) and [H+]is the hydrogen ion concentration (mol/cm*). At 25 “ C and ionic strength 0.05 M (NaClj, t h e values of the rate constants hl and h2 were found to be 0.18 f 0.06 cm/min and 1.9 f 0.9 X 1 0 V mol/(cm2.min), with energies of actication of 6.8 and 7.3 kcal/mol, respectively. The k p term dominates the rate law a t pH 25.3. Therefore, we assume that F = k2 for most natural water systems of interest. Nonoxidatiiie D~ssolution Nonoxidative dissolution of sulfide phases in natural environments requires that oxygen be absent. This condition is met in t h e same types of environments in which sulfides originally form, Le., anaerobic sewage sludges and anoxic sediments, as well as in the anoxic waters which may lie above these sediments. Sediments. In the case of anoxic sediments t h a t contain either naturally formed or anthropogenic metal sulfides, instability with respect to dissolution would require lowering of t h e aqueous metal and/or sulfide concentration below saturation. Considering the extreme insolubility of most metal sulfides, and barring oxidation reactions, such a lowering would be very difficult to accomplish by a chemical reaction (e.g., precipitation) in t h e pore waters immediately surrounding the metal sulfide. Oxidation by 0 2 of the dissolved sulfide and/or metal in neighboring sediments could, however, lead to the development of concentration gradients through the sediment medium and thereby the diffusive loss of sulfide and metal ions from pore waters that remain free of 01.T h e types of processes that are responsible for such a juxtaposition of oxic and anclxic sediments are: (1) the fall overturn of Present address, Department of Environmental Science, Oregon Graduate Center, 19600 N.W. Walker Road, Beaverton, Oreg. 97006. 0013-936X/80/0914-0183$01 .OO/O @ 1980 American Chemical Societ)
stagnant lakes; (2) dredging; (3) bioturbation; and (4) a reduction in t h e organic carbon loading to a sediment/water interface. T h e undersaturation accompanying the development of such concentration gradients could then initiate the nonoxidative dissolution of solid metal sulfide. Figure 1 presents a schematic diagram of this problem. I n this model, the pores of the sediment are considered to be straight cylinders of radius r. T h e distance variable x is zero a t the interface and is measured positively downward. In sediments t h a t contain substantial amounts (several percent) of organic carbon, t h e position of this interface may remain stationary or move only slowly into the anoxic region: the oxygen diffusing downward from the sediment/water interface is consumed by organics diffusing up toward the interface. (For sediments of lower organic carbon content, the oxic front might advance through the anoxic sediment more quickly than the FeS may be able to dissolve nonoxidatively. In this case, any solubilization of Fe, S, and associated trace metals t h a t occurs will take place according to oxidative reaction mechanisms.) In order to model this problem for FeS dissolution, it is necessary to know how the dissolution rate varies with e, the dissolved metal sulfide concentration. Although this was not studied in our previous paper ( I ) , when the dissolution is taking place in solutions containing no initial sulfide, we know t h a t F = he when c = 0 and also t h a t F = 0 when c = cs, t h e saturation Concentration. For order of magnitude calculations then, it will be assumed that the flux f (mol/(cm2.min))from the sediment pore walls is given by:
This equation obeys the above “boundary conditions” and also takes account of the fact that only a fraction (g) of the exposed pore wall area is FeS. Certain anoxic sediments can contain appreciable amounts of dissolved H&, and the validity of Equation 2 for such sediments is in question. For reasons we will discuss later, it does not appear, however, that their general behavior would he much different from sediments that d o not contain excess H2S. T h e area (pore walls only) and volume elements d a and dl: corresponding to the pore distance element dx are 2 x r dx and x r 2 dx, respectively. T h e area t o volume ratio for these hypothetical pores is therefore equal to 2/r, and the rate of dissolution R (mol/(cm.’.minj) of FeS per unit volume of pore water is given by 2flr. T h e basic differential equation which applies to this onedimensional diffusion problem with a production term R is: ac
a%
-=D,+R at ax-
where D is the appropriate diffusion coefficient. T h e logical choice for boundary conditions is that c = c, when s = and c = 0 when x = 0. The steady-state solution, Le., that which obtains when &/at = 0 a t all x , may be determined analytically. While t h e steady-state condition is never strictly correct for any sediment system, it greatly simplifies the mathematical analysis of such problems. T h e steady-state solution is:
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183
F = @(2gkzD~,/r)l/~ GXIC WATERS
INTERFACE GF SEDIMENT WITH OXIC WATERS OXlC SEDIMENTS
x = o l N _ ~ E ~ F A COF E OXlC WEJHaNOXIC SEDIMENTS
\
XI
rzW ’ 0
GI
x-3
0,NLY ONE
Flgure 1. Schematic diagram of adjacent oxic and anoxic sediments. Diameter of hypothetical pores is 2 r . The variable x is zero at the boundary of the two regions, and increases downward
Large values of g, k z , and x tend to make c close to c,. A large value of D, on the other hand, would tend to lower c below c,, because higher rates of diffusive loss from the pores would be favored. Increasing r would also lower c because large pores have small daldu ratios; there is less reactive surface area per unit volume of pore. Finally, large values of c, tend t o favor greater undersaturation because the absolute magnitude of the diffusive losses from the pores will be large when the concentrations in the pores are large. The rate at which the lost solute can be replaced, however, is limited by the magnitude of k z , and larger undersaturations tend to develop in the pores when c , is large. Even under those conditions that favor disequilibrium in the pores (e.g., large c, and r ) , calculations based on Equation 4 reveal that equilibrium (Le., c = e,) is maintained a t all but small distances from the oxic zone. For example, an upper bound on r for most sediments would be -lo-* cm, the particle size of fine sand. An upper bound on c, in sediments would be -lops mol/cm3, the saturation concentration for FeS a t p H -7.0 in the absence of excess sulfide. A value of -3 X lo-” cm2/min may be taken for D. Berner ( 2 )has found that anaerobic sediments often contain FeS at levels of -0.1%, and so an order of magnitude estimate of g might be Using these values of e,, r, D , and g, and our experimental value of 1.9 X mol/(cm2.min) for k z , a value of -4 cm-1 is calculated for the square root term in Equation 4. Thus at a distance of 0.25 cm from the oxic zone, the c / ~ ratio , would have already climbed to -0.6. We see, therefore, t h a t extensive diffusive transport would not be required for t h e Fez+ concentration to adopt the profile described by Equation 4; such steady-state diagenesis could be set u p very quickly after the introduction of oxygen to the sediments. Moreover, if the anoxic pores contain appreciable dissolved HzS, pore equilibrium with respect to FeS dissolution will still tend to prevail near the oxic interface even if k z is reduced by this H2S since c, will be very low. Although we have shown that the bulk of the anoxic sediments would remain a t equilibrium with respect to FeS dissolution, the rate of dissolution is not without influence on the FeS release rate. The rate of diffusive release of FeS from the anoxic zone per cm2 of the oxidanoxic interface is: (5) F = @Ll($) x = o T h e porosity of the sediment, a, is included in Equation 5 , since only the sediment’s pores are available for diffusion. Therefore: 184
Environmental Science & Technology
(6)
If ka is lowered, perhaps by the action of large concentrations (-ppm levels) of transition metals, the FeS release rate would be reduced accordingly. Another interesting conclusion to be drawn is that ions of the Fe, S, and associated trace metals will remain essentially immobile until the oxic front has been able to advance to within short distances of them. If these elements are to participate in further diagenetic reactions (e.g., adsorption, oxidation, etc.) once they are freed from the FeS, such reactions will have their first opportunity to occur near the oxiclanoxic interface. Consider, for example, the case of a transition metal ion t h a t tends to associate with FeS, but which also has a marked affinity for iron oxides such as goethite (e.g., CU*+,~). As the FeS dissolves then, such a species would probably become adsorbed on the goethite which is forming in the adjacent oxic sediments: it would not have time to migrate out of the area. Particles in Suspension. While naturally occurring FeS is likely to be limited to the sediment phase, particulates containing metal sulfides can be suspended in the water column when anaerobic sewage sludge is discharged to marine or lacustrine receiving waters. If the water is essentially free of oxygen (as would be the case for the discharge of anaerobic sewage sludge into the anoxic marine basins off Southern California ( 3 ) ) ,then the suspended FeS may dissolve nonoxidatively. Depending on the degree of turbulence in t h e receiving water, the dissolution rate may occur with or without some diffusion control. Case 1: No Diffusion Control. For a single particle of mass m (g),.with no diffusion control,
where s is its surface area (cm2)and W is the formula weight (g) of FeS. For an approximately cubic particle of length 1 (cm) and density p (g/cm3), we have: s = 6m213p-213
(8)
After substituting Equation 8 in Equation 7 and integrating, t h e time for complete dissolution t f will be given by:
Plo tf = 2kz W where 10 is the initial particle size. If k2 = 1.9 X (cm2.min) and p = 4.3 g/cm3: tf =
1071~
(9) mol/ (10)
where t f is in minutes and 10 is in centimeters. Figure 2 shows results of the model for no transport control for three different values of kp. Line B ( k z = 1.9 X indicates that a 0.25-mm particle would require on the order of 1year to dissolve, while only 1 day would be required for a 1.0-pm particle. Considering the special conditions required for the synthesis of FeS crystals even as large as -1 p m ( I ) , if this model is correct and if h z is of the order of mol/(cm2.min), it seems very unlikely that sewage sludge FeS particles could be large enough to last more than several hours. A lowering of k2, perhaps through the action of poisoning metal ions, would increase the lifetimes of the particles proportionately. Case 2: Partial Transport Control. If there is partial transport control, F would be less than that given by k z . A form similar to Equation 2 will be assumed for order of magnitude calculations:
F= kP(1-i)
(11)
where c is the concentration at the surface of the particle.
culated using Equations 9 and 15 for the same k ? value are large when k z and/or 10 is large. The deviation between lines B and E becomes very small when the particle size is less than - 2 pm. This analysis has assumed that the dissolving FeS is present as a suspension of free particles, unassociated with other particles or flocs. This may be unreasonable in the case of sewage sludge where there will no doubt be some aggregation of the FeS with other materials, and the dissolution might occur from within loose aggregates of sludge. In this case, the 1 in Equation 14 would be replaced by d , the approximate dimension of the flocs. Since t h e flocs would be primarily organic, they would not be dissolving rapidly, and d would be approximately constant. The integrated form of the resultant equation would be similar to Equation 9, but multiplied by the factor [l - 1/(2Dcs/h2d l)].The errors that accompany the neglection of this factor would be largest for small values of D and e,, and large values of k z and d. For e, = 2 X 10-9 cm'/min, and taking k ? to be 1.9 x 10-8 mol/cm:', D = 3 X rnol/(cm".min) (ten times the experimental value), this factor takes on the values of 0.9,0.4,0.06, and 0.01 for d values of 1, 10, 100, and 1000 pm. respectively. Faisst ( 5 ) has estimated that the particle size distribution for anaerobic sewage sludge peaks a t around 15 pm, with a majority of the part.icles falling in t h e size range 2-30 pm. Therefore, even if our measured value for k:! ( I ) is low by a factor of 10, order of magnitude calculations of tf for sewage sludge FeS would be the same whether or not transport limitation within sludge flocs is considered.
+
LIFETIME OF PARTICLE ( m i n ) Figure 2. Particle size vs. particle lifetime for both non-diffusion- and partial-diffusion-controlledmodels of FeS dissolution. Lines A, B, and C were calculated using Equation 13 with k2 values of 1.9 X lo-*, 1.9 X and 1.9 X mol/(cm2-min),respectively. Lines D, E, and F were calculated using Equation 19 with a c, value of 2 X mol/ 1.9 X and 1.9 X mol/ cm3 and k2 values of 1.9 X (cm2.min), respectively
Oxidatice Dissolution According to Berner ( 4 ) ,when particles dissolve in a relatively quiescent medium, the diffusion boundary layer thickness is given approximately by t h e radius of the particle. T h e diffusive flux would 1,hen be given by: D F = -(C - Cbulk) (12) 1/2 For simplicity, Cbulk will be assumed equal to zero. Such a condition would be met when t h e particles are dissolving in a large body of water low in Fe(I1) and S(-II). At steady state, we may equate 11 and 12. T h e result is:
1 'c, Since d m l d t = .- WsF, by Equations 11 and 13: dm dt
+
- = - Wsks[l - kn/cS(2D/1 kz/c,)]
(14)
Substituting for s and 1 in terms of m, and integrating: tf=-+- d o do2 2k2W BDWC, If k z is 1.9 X l W 9 mol/(cm'.min), and D min: t f = 10710
+ 21O?/C,
-
3X
cm2/ (16)
Equation 15 is similar to 9, but there is the additional term, p202/8DWc,. This term reflects the fact that partial diffusion limitation of t h e rate will increase t h e time required for complete dissolution. Depending upon the values of hp, lo, and c,, this effect may be either small or large. Figure 2 contains plots of Equations 9 and 15 for D = 3 X 10W cm?/min, c, = 2 X 10 -9 mol/cm", and for three values of h?. This e, value would be the approximate saturation value in a medium a t the typical natural water p H of 8 and initially containing no dissolved Fe(I1) or S(-II). T h e differences between the t f values cal-
T h e oxidative dissolution of suspensions of finely divided FeS (particle size -500-4000 A) has been studied in some detail by Nelson ( 6 ) .Under the conditions of pH 7, [O,] = 4 mg/L M, initial FeS "concentration" of 800 mg/L, and strong stirring, the observed FeS oxidative dissolution rate was M min-'. This is a considerably greater rate of oxidation than would be predicted for t h e homogeneous oxidation of either Fe(I1) or S(-11) a t their p H 7 saturation concentrations (-lop5 M). Under these conditions Fe(I1) would be oxidized a t a rate of only 5 X 10-6 M min-' ( 7 ) . Similarly, the data of Chen and Morris (8)indicate that S(-11) at M would be oxidized to higher valence states a t a rate of M min-l. Both of these rates are well below the observed M min-'. Consequently, it must be concluded that this dissolution involved the direct attack of oxygen at the FeS surface. Considering the extremely high FeS surface area available for reaction, however (from -3 X lo4 cm2/L for 4000-A particles to -2 X lo5 cm'/L for 500-A particles) t h e actual rate per cm'? need not have been large. Since both Fe(I1) and S(-11) oxidations are strongly subject to catalysis by certain transition metal ions (7, 8),however. it seems possible t h a t both oxidative and nonoxidative dissolution might play a role in natural oxic environments in which such catalysts are present. In sulfidic sediments that have become oxic. although the dissolution may be largely oxidative upon the introduction of 0 2 to the system, this need not continue to be the case. Consider the case of a sulfidic sediment containing 4 . 1 %by dry weight of mackinawite. If the porosity of the sediment is -3O%, and the density o f the sediment particles -3 g/cm:', then there would be -0.02 mol of FeS/I,, where L refers to liter of sediment. If bioturbation or other mechanisms saturate the pore waters with 0 2 a t a level of -10 mg/L, there would be only 4 X 10-4 equiv of On/L. If t h e FeS is to be oxidized to Fe(II1) and S ( 0 ) ,there would be 0.06 equiv of FeS/L. Since Nelson ( 6 ) found the reactivity of natural mackinawite to he similar to t h a t of the FeS which he synthesized, assuming no transport
-
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185
limitation, this small amount of 0 2 would be expected to last less than 1 min, and the sediment would be quickly made anoxic. The oxidation of the remaining FeS would require the diffusion of oxygen into the sediment. Thus, although the FeS dissolution initially takes place in an oxidative manner, the 0 2 is soon consumed and the rate of nonoxidative dissolution may again become important. Pyritization of Recent Sediments The formation of pyrite in sediments may occur either directly (9) or via the initial formation of mackinawite and subsequent conversion of the FeS to FeS2 (10, 1 1 ) : FeS
+S
-
FeS2
(17)
The elemental sulfur in this reaction might be present as: (1) dissolved S; (2) solid S8; and/or (3) elemental S on the FeS surface. The source of this S would be the oxidation of reduced sulfur compounds such as H2S and FeS. Since pyrite is the major end product of sulfate reduction in sediments, it plays a very important role in the geochemical cycling of Fe, S, and associated trace metals. This fact accounts for our interest in Reaction 17 as regards mackinawite. The amount of FeS which is ultimately converted to pyrite via Equation 17 will depend upon the availability of elemental sulfur as well as upon the relative rates of (1)the diffusion/ oxidation process involving 0 2 and (2) Reaction 17. While approximate rates may be estimated for the first process, little is known about the rate of the latter. Pyrite formed by this reaction has been observed to crystallize on the surfaces of elemental sulfur (10).I t seems possible, then, that the elemental sulfur reacts with solution phase Fe(I1) and S(-11). This would be the final step in a mechanism for Reaction 17. The nonoxidative dissolution of the FeS as well as the transport of the resultant ions to the sulfur surface would precede it. One wonders, therefore, whether the nonoxidative dissolution could be rate determining for Reaction 17. The results of this research in conjunction with those of Berner (10)indicate that this is probably not the case. During one experiment, Berner combined elemental sulfur with suspensions of finely divided FeS (particle size
