Environ. Sci. Technol. 1991, 25, 2071-2075
Kinetic Study of SO2 Reaction with Dolomite Sanjeev Tambe,t K. La1 Gauri,"*tSuhan Ll,+ and W. Geoffrey Cobournt Department of Geology and Department of Mechanical Engineering, University of Louisville, Louisville, Kentucky 40292
w In today's industrialized environments, sulfur dioxide, to the exclusion of other pollutant gases, is the main cause of chemical deterioration of building materials such as marble, limestone, and dolomite. This paper gives the results of an experimental study of the reaction of laurel dolomite, a coarsely crystalline variety of dolomite, with sulfur dioxide. With the progress of reaction it was found that a gypsum-epsomite crust grows outward due to a continuous supply of Ca and Mg ions from an increasingly greater depth inside the stone. Therefore, the rate data were analyzed by following a shrinking unreacted core model using first- and fractional-order (0.5) kinetic rate constants. These two reaction orders fit the experimental data equally well for the initial phase of the reaction, but the fractional rate constant, 0.19 mmoP5 ~ 1 1 1 - O .h-l, ~ gives the best fit to the overall experimental data. Introduction
The deterioration of building stone due to the air pollutants sulfur and nitrogen oxides is of increasing concern because these pollutants adversely affect the appearance and life of building materials. SOz and NOz react with carbonate rocks to form sulfates and nitrates, which, due to their solubility in water, may be drained away or, if protected from the rain, may form unsightly crusts that eventually exfoliate. The analysis of crusts upon naturally weathered carbonate rocks and experimental studies on combined SOz and NOz reactions reveal that the crusts are largely made of sulfates while only trace quantities of nitrate are present (1-3). A substantial amount of literature on the reactivity and kinetics of the reaction of SOz with carbonate rocks is available (4-9). Recently, Kulshreshtha et al. (10) and Gauri et al. (11)conducted experimental studies involving the exposure of different types of marble to 10 and 300 ppm SOz atmospheres. The rate constants thus determined have proved useful in estimating the extent of damage to marble in ambient SOz concentrations found in industrial environments. The damage was expressed as the thickness of the product crust (CaSO4.2HZ0)at the surfaces of structures protected from rain or for surfaces exposed to rain as the amount of erosion. In this paper we describe the results of experiments on SOz reaction with a dolomite [CaMg(CO,),], laurel dolomite, which is a coarsely crystalline and highly porous variety of dolomite rock. Further, this dolomite is stoichiometrically balanced; i.e., the proportions of Ca and Mg are nearly equal (12). However, this dolomite has certain occluded minerals, including gypsum in the amount of nearly 1% by weight. This quantity of gypsum was subtracted from the reaction rate calculations. X-ray diffraction analysis of a 120-year-oldsample of dolomite from Louisville and that of samples reacted in the laboratory reveals that the reaction of SOz with dolomite takes place according to the equation
H,O,O,
CaMg(C03)z+ 2S02 CaS04.2Hz0 + MgSO4-7HZO+ 2C02 (1) 'Department of Geology. 1 Department of Mechanical Engineering. 0013-936X/91/0925-2071$02.50/0
Experiments were conducted employing sulfur dioxide concentrations in the range 8-21 ppm. The kinetics of the reaction was established by fitting the shrinking unreacted core model (13-15) to the rate data. Also, analytical solutions for model equations for the reacted mass of dolomite and the crust thickness were obtained. E x p e r i m e n t a l M e t h o d s a n d Materials
Dolomite slabs were exposed to humid atmospheres containing SOz. The details of the experimental setup used in the present study are given in Kulshreshtha et al. (10). Dolomite slabs (2.8 cm X 1.6 cm X 0.3 cm) were cut, uniformly polished with 400-grit silicon-carbide powder, cleaned in an ultrasonic bath, and exposed to a given test atmosphere. The dimensions of the slab were measured accurately with a vernier caliper. An atmosphere containing SOz was generated by passing air through a humidifier and then over a permeation tube. The airflow rates were adjusted properly so as to obtain the desired SOz concentration in the reaction chamber, where the specimens under study were suspended. T o maintain 100% relative humidity, a prerequisite to the performance of rapid reaction, water was placed a t the bottom of the reaction chamber, a modified 10-L desiccator. This simulates a frequently occurring condition outdoor, where the stone is coated with a thin film of condensed moisture. Prior to exposing the dolomite samples to SOz, the water a t the bottom of the chamber was equilibrated with the partial pressure of SOz in the test atmosphere. At any given time no more than 30 samples were present in the chamber. Each dolomite sample was weighed before exposure. At irregular intervals, two or three samples were removed from the chamber and immediately immersed in 100 mL of deionized water to dissolve the reaction product. For long exposures, the slabs were washed two to three times to ensure that the entire reaction product had been removed. These washings were analyzed for calcium, magnesium, and sulfate ions. The amounts of Ca and Mg were determined by atomic absorption spectrophotometry, and the amount of sulfate was determined by a turbidimetric method using UV/vis spectroscopy. The permeation tube was weighed before and after the end of each run to estimate the total amount of SOz passed through the reaction chamber. The amount of SOz was also monitored by a sulfur dioxide analyzer manufactured by Columbia Scientific Instruments. For the calculation of the reaction rate, 20 samples were selected from a total of 50 exposed. The selection was based upon a close match of mass of the reaction product [gypsum (CaS04.2H20) and epsomite (MgSO4.7Hz0)] calculated through various methods, namely, from Ca Mg ions, from SO4 ions, and from the gravimetric weight loss of the leached samples. For the selected samples, the mean and standard deviation values fall in the ranges of 3.46-508.77 and 0.27-12.62 mg, respectively; higher standard deviation values (>5) were encountered for only two samples with long exposure times (>400 h).
+
M e c h a n i s m of Formation a n d M e a s u r e m e n t of T h i c k n e s s of Crust Figure 1 shows the profile of a reacted sample in cross
section. Three horizons, namely, crust, leached zone, and
@ 1991 American Chemical Society
Environ. Sci. Technol., Vol. 25, No. 12, 1991 2071
C
A
a-
-b
Figure 1. Profile of a sectioned dolomite specimen exposed to 14.05 ppm SO, atmosphere lor 410 h. showing crust (a).leached zone (b).
and unreacted dolomite core (c).
-C
the unaltered dolomite, are seen. The crust, a continuous layer of gypsum crystals, lies above the original slab surface. Underlying the crust is the cavernous leached zone, which must have provided the Ca and Mg ions that reacted with SOza t the surface to form the gypsum and epsomite. Epsomite is absent from the crust due to its deliquescent property. Figure 2 shows schematically the mechanism of formation of crust upon dolomite. Skoulikidis and Charalambous (16),in their studies on the sulfur dioxide reaction with calcite (CaCOJ, found that the calcium ions near the solid surface diffuse outward and react with SO,. They explained this phenomenon on the combined hasis of a galvanic cell model and solid-state diffusion. Our studies on dolomite corroborate that explanation. The thickness of the reacted dolomite (dd) was calculated by dividing the reacted volume, obtained from the weight loss of reacted sample when immersed in deionized water, by the surface area of the sample. This thickness was converted to equivalent product crust thickness (5,) by multiplying it by the ratio of the molar volume of product (gypsum plus epsomite) to that of dolomite. The following equation summarizes this calculation: 5, =
(WI A.Pd
wz)MpJ’d MdPp
Application of the Shrinking Unreacted Core Model to the Decay of Dolomite T h e shrinking unreacted core model is directly applicable to the dolomite-SOZ reaction. In this model, the reaction front, in terms of the supply of Ca and Mg ions (thereby the mass loss of parent dolomite) uniformly moves inside the solid with progress of reaction. This results in the reduction of the unreacted part of the solid. T h e presented model assumes that the pore diffusion resistance is negligible. This assumption is based upon the fact that the observed reaction rate is small due to the low reaction temperature (17). Also, the reaction rate remains Environ. Sci. TechnOl., VoI. 25. No.
12. 1991
essentially constant throughout the reaction period, indicating that the pore diffusional resistance was not operative. In the event that the progress of reaction is affected hy chemical reaction and external mass-transfer resistances, the contributions of these processes must he simultaneously considered. Consequently, the overall reaction rate, assuming pseudo steady state, is equal to the interfacial chemical reaction and to that of external mass transfer. The mass balance equation can then be written as (13-15) (I/A,)(fld/dt)
= bk,C.P =
(2)
Where W,, W,,and A, denote the sample weight before exposure, sample weight after the reaction product is leached, and external surface area, respectively. pd and p,,denote densities of dolomite (2.6593 g/mL as determined by pycnometer and mercury porosimeter) and reaction products, respectively. The term Mppd!Mdpp represents the ratio of the molar volumes of reaction product CaS0,.2Hz0 + MgS04.7.Hz0 and dolomite and has a value of 3.187.
2072
B Schematic diagram for unreacted (A) and reacted dolomne specimen (B).showing gas film (a). Crust (b). leached zone (c). and unreacted dolomite core (d).
Figure 2.
hd(Cb - c.)
(34 (3h)
Where A. is the surface area of the sample, Nddenotes the number of millimoles of dolomite reacted in time t (h), b is the ratio of the stoichiometric coefficient of dolomite to SOz (0.5), k. is the surface reaction rate constant, Cb and C, are the bulk and surface concentrations (mmol/cm3) of sulfur dioxide, respectively, p is the reaction order, and hd is the gas-phase mass-transfer coefficient. Equation 3a can be integrated to obtain Nd = bA,k,C,pt
(4)
T o obtain an expression for the thickness, we note that the derivative term of eq 3 can be modified to represent the thickness of the reaction product, i.e., the crust buildup on the slab surface. From eq 2, the reacted number of moles of dolomite (Nd) is given by Nd
= Pdud/Md = P‘dUd
(5)
where Md. P ’ ~ .and ud respectively denote molecular weight, molar density, and reacted volume of dolomite. Since ud/A, is equal to the thickness of dolomite reacted (5d), eq 3a after substitution and rearrangement becomes d&/dt = (Md/Pd)bkaCaP
(6)
Table 1. Mass-Transfer Coefficients and Other Related Datan
equiv diameter kip),cm
run no.
bulk ( c b ) , ppm 14.05 20.88
2.072 2.072 2.072 2.130
1
2 3
4 ONS,,
SO2 conc,
= 1.134; pR = 1.2047 X
SOz conc,
flow rate, mL/min
surface
(CJ, ppm
8.00
11.15 17.19 5.89
14.12
11.18
700 350 800 800
c
In order to apply eq 4 or 7 to obtain k,, it is essential to determine the surface concentration of sulfur dioxide, C,. For this, eq 3b can be rearranged dCd / d t + hdA,Cb
.-
(8)
t
2 8
450
I
1
350
I
300
5
250
5
zoo
IG
2
:
150
100
wherein the mass-transfer coefficient, hd, can be obtained from the definition of the Sherwood number as hd = Da$\r,h/dp (9)
0
The mass-transfer coefficient (hd) for each run was estimated (18) from the knowledge of the binary diffusion coefficient (Dab)of the air-SO2 system, the Sherwood number ( N S h )and , the equivalent diameter (d,) of the dolomite slab (19). The binary diffusion coefficient (0.1336 cm2/s) and Sherwood number were estimated using the Chapman-Enskog equation and the Rantz-Marshall correlation, respectively. The correlation for laminar flow, which is valid over Reynolds number range 0-200, is as follows: NSh = 2.0 4- ~ . ~ N R ~ ~ N s : . ~(10) ~
5
hdA,
wherein NReand N,, denote Reynolds and Schmidt dimensionless numbers. The Reynolds number is proportional to the ratio of inertial to viscous effects and the Schmidt number is the ratio of molecular momentum diffusivity to molecular mass diffusivity. Their values have been obtained using the definitions NSc
= p/Ppab
(11)
The notations G, k , and pg respectively represent linear fluid velocity (cm/s), viscosity, and density of humid air. The value of p as found from the viscosity tables is equal to a 0.000 182 7 (g cm-l s-l) a t 293 K. The values of C, were estimated by fitting the experimental data to eq 8 with utilization of an optimization subroutine. Table I lists the values of the mass-transfer coefficients and surface concentrations thus obtained for each of the conducted runs.
Evaluation of Surface Rate Constant, k , The Nd versus time data for individual runs were interpolated using the Spline interpolation technique, and the reaction rate was calculated using a second-order finite difference approximation. Data consisting of the derivatives and surface concentration of SO2 (obtained from eq 8) for all the runs were combined. This single set of data was fitted to eq 3a using a multivariable regression subroutine to obtain unique values of reaction order with respect to SOz and the rate constant k, (Figure 3a). Their magnitudes are p = 0.498 (-0.5) and k, = 0.19 mmoP5 ~m”3.~ h-l.
I
+-
50
dpGpg/p
549 524 555 541
400
a
=
0.3436 0.1718 0.3927 0.4037
I
