Article pubs.acs.org/EF
Kinetics of the Dehydroxylation of Serpentine Kimia Alizadehhesari,† Suzanne D. Golding,‡ and Suresh K. Bhatia*,† †
School of Chemical Engineering, and ‡School of Earth Sciences, The University of Queensland, St. Lucia, Queensland 4072, Australia ABSTRACT: There has been increasing interest in carbon dioxide sequestration in mineral form, because there are large deposits of silicate minerals in peridotite and basalt that have the potential for this option. We examined the dehydroxylation of natural serpentine ore, considered to be a candidate for mineralization of CO2. In this study, serpentine and dehydroxylated serpentine have been characterized using different techniques and the dehydroxylation kinetics of serpentine has been investigated by non-isothermal thermogravimetry. The results indicated that the thermal decomposition of magnesium serpentine [Mg3Si2O5(OH)4] proceeds via the removal of physisorbed water and, subsequently, the hydroxyl group. Kinetic modeling of the dehydroxylation shows that the reaction follows a three-dimensional diffusion-controlled mechanism in the particles. The effect of the heating rate and particle size on the dehydroxylation reaction has been investigated, and the results are found to be consistent with diffusion-controlled kinetics. The gas−solid heat-transfer resistance is shown to influence the results at a high heating rate and large particle size. fibrous.15 The carbonation of serpentine, a hydrous alteration product of olivine, is inherently slow, and to increase the rate of reaction, one way is the heat treatment of the mineral that results in the dehydroxylation of serpentine.18 Maroto-Valer et al.14 showed that heat treatment is an effective technique for reducing the inherent moisture content of the serpentine and increasing the magnesium content of the mineral. Brindley et al.19 investigated the structure of forsterite, the product of the thermal transformation of all of the known crystal structure varieties of serpentine. Zevenhoven et al.20,21 suggested multi-stage gas−solid carbonation of serpentine: first, MgO production at atmospheric pressure, followed by MgO hydration to magnesium hydroxide, and then carbonation at high pressures. O’Connor et al.22 proposed using magnesium silicate ore, serpentine or olivine, for aqueous carbonation but considered one more step for heat treatment of the serpentine to remove water from the serpentine structure. Although the dehydroxylation process is endothermic, the carbonation of minerals is exothermic, which has the potential to compensate for the energy consumed for dehydroxylation and makes the carbonation economically viable and feasible. Despite the increasing interest in using serpentine for mineral carbonation, the kinetics of the dehydroxylation is not widely known. For dehydroxylation of serpentine, the simplified reaction is as follows:
1. INTRODUCTION Increasing the atmospheric CO2 concentration as a result of burning fossil fuels is thought to be causing enhanced global warming.1−3 Reduction in CO2 emissions by fossil fuels requires the implementation of carbon capture and storage (CCS) systems.4 The reaction of magnesium-rich minerals, such as serpentine, with CO2 to stable mineral carbonates, called mineral carbonation, mimicking natural weathering, is a promising approach to carbon sequestration and was first proposed by Sefritz.5 On the basis of this method, environmentally benign and thermodynamically stable waste products are created.6 Since then, there have been numerous studies on aqueous carbonation routes using different types of alkali solids.7−9 In the dry gas−solid carbonation route, Bhatia and Perlmutter10 investigated the kinetics of the gas−solid carbonation of calcium oxide, reporting 70% calcium conversion at 500 °C. The kinetics of the simultaneous dehydroxylation and carbonation of magnesium hydroxide was studied by Butt et al.11 using helium and CO2 isothermally and non-isothermally at atmospheric pressure. In other work, Bearat et al.12 investigated gas−solid magnesium hydroxide carbonation at high CO2 pressure. They observed that increasing the CO 2 pressure above the critical pressure slows both carbonation and dehydroxylation processes. Prigiobbe et al.13 have proposed using air pollution control residues containing Mg- or Ca-bearing materials to absorb CO2 to form carbonates achieving 78.9% conversion at 450 °C in 2 h. Nevertheless, serpentine and olivine draw attention for the sequestration of CO2 as suitable raw materials because of their worldwide occurrence and high proportion of divalent cations that are required for mineral carbonation reactions.14−17 The serpentine group includes three related minerals: antigorite, lizardite, and chrysotile. They have the same crystal structure and chemical composition but differ in curvature of the lattice planes, which results in antigorite and lizardite most commonly exhibiting a platy morphology and chrysotile being © 2011 American Chemical Society
2Mg3Si2O5(OH)4 (s) ↔ 3Mg 2SiO4 (s) + SiO2 (s) + 4H2O(g) (1) Accordingly, the focus of this study is to characterize serpentine and investigate the kinetics of dehydroxylation of serpentine. The original serpentine and dehydroxylated serpentine were Received: September 9, 2011 Revised: December 19, 2011 Published: December 20, 2011 783
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characterized by several analytical techniques to determine their properties.
There have only been a few attempts to probe the kinetics of the dehydroxylation of serpentine, and to our knowledge, it has not been studied previously in detail. Brindley et al.29 examined the dehydroxylation of serpentine isothermally under vacuum, applying the Ginstling−Brounshtein model. However, the observed kinetics differs considerably from our study, because they obtained a very high activation energy of 284 kJ/mol. This is largely because of their use of large particles, of size 180−200 μm. As we will show, the use of such large particles for the dehydroxylation leads to the intrusion of heat-transfer resistances, which affect the results. The variations are also partly attributed to the differences in experimental methods. As discussed above, non-isothermal gravimetry gives different results from the isothermal method and is a more reliable technique for measuring kinetic parameters.
2. DEHYDROXYLATION KINETICS In the field of thermal kinetics analysis, there are many kinetic models and methods for processing experimental data to identify the most likely kinetic mechanism of solid-state reactions. In analyzing the kinetics, it is common23 to use the extent of reaction (or conversion), designated as α, ranging from 0 to 1. The rate of the solid-state reaction is in general expressed as dα = k (T )f (α ) (2) dt where t is the time, f(α) represents the kinetic model and depends upon the rate-determining step in the mechanism, while k(T) is a rate constant, having an Arrhenius temperature dependence. Thus, eq 2 can be rewritten as g (α ) =
∫
dα =A f (α )
∫ e−E/(R T)dt
3. EXPERIMENTAL SECTION The serpentine [Mg3Si2O5(OH)4] used for this study was obtained from the naturally occurring form in central Queensland, Australia. The serpentine was initially ground by hand using a mortar and pestle and then in a laboratory attrition mill. To observe the effect of the particle size on kinetic parameters, ground serpentine was sieved with American Society for Testing and Materials (ASTM) standard sieves into three particle size ranges: 90 < d < 106 μm, 300 < d < 355 μm, and 425 < d < 500 μm. The prepared samples underwent dehydroxylation in a nonoxidizing environment at different heating rates. Thermal analysis using thermogravimetric techniques enables the mass loss steps, their respective temperatures, and the mechanism for the mass loss to be determined.30 Thermogravimetric analysis was performed using a Setaram Setsys 16/18 equipped with a 20 mg/200 mg balance and 1500 °C TG-DSC rod. The experiments were conducted in a nonoxidizing atmosphere of argon (Ar) at atmospheric pressure with heating from room temperature to 1173 K at different heating rates. Subsequently, the sample was held at 1173 K for 1 h before it was cooled, using a constant gas flow rate of 100 mL/min around the sample holder. The absolute or skeletal density of the sample was measured using standard helium pycnometry. The density, ρ, is equal to 2.66 g/cm3 for serpentine and 3.04 g/cm3 for the dehydroxylated serpentine. The surface area, pore volume, and average pore diameter of the samples were characterized using a Micromeritics ASAP 2010 adsorption apparatus. Adsorption isotherms were obtained under argon at a temperature of 87 K. The pore size distribution (PSD), pore volume, and specific surface area of the samples were evaluated from the isotherms using the traditional Barrett−Joyner−Halenda (BJH) method and the more advanced density function theory (DFT) technique using the oxide surface option available with the Micromeritics DFT software. The mineral phases present in the sample were determined by X-ray diffraction (XRD) analysis. A diffractometer (PANanalytical XPERT-PRO) with a Cu Kα target (λ = 0.154 06 nm) was used at room temperature, with measurements made in a step-scan mode (0.1°/step) over the 2θ range of 10−90°. The surface topography of the serpentine and the product of dehydroxylation (olivine) were examined using a Philips XL30 field emission scanning electron microscope (SEM) operating at an accelerating voltage of 5 kV and a working distance of 10−12 mm. Energy-dispersive spectrometry (EDS) spectra were collected from the samples prepared for SEM.
g
(3)
where A is the pre-exponential factor, E is the activation energy, Rg is the universal gas constant (8.314 J K−1 mol−1), and g(α) denotes the integral form of the kinetic model. Equation 3 is readily applied for isothermal kinetic analysis. The various expressions used for f(α) and g(α) that have been developed are listed in Table 1.24 Table 1. Kinetic Function of the Most Common Mechanism Operating in Solid-State Reactions f(α)
mechanism one-dimensional diffusion two-dimensional diffusion three-dimensional diffusion Ginstling− Brounshtein contracting area contracting volume Avrami−Erofeev Avrami−Erofeev Avrami−Erofeev
g(α)
1/2α
α2
(−ln(1 − α))−1
(1 − α)ln(1 − α) + α
3/2(1 − α)2/3(1 − (1 − α)1/3)−1 3/2((1 − α)1/3 − 1)−1
(1 − (1 − α)1/3)2
2(1 3(1 2(1 3(1 4(1
− − − − −
α)1/2 α)1/3 α)(−ln(1 − α))1/2 α)(−ln(1 − α))2/3 α)(−ln(1 − α))3/4
(1 − 2α/3) − (1 − α)2/3 1 − (1 − α)1/2 1 − (1 − α)1/3 (−ln(1 − α))1/2 (−ln(1 − α))1/3 (−ln(1 − α))1/4
From the experimental perspective, non-isothermal runs are more convenient to carry out and have resolved a major problem with isothermal experiments, by overcoming the need to perform a rapid initial temperature jump of the sample. During the initial non-isothermal period, in which the temperature is rapidly increased, the sample undergoes transformations that are likely to affect the results of the subsequent kinetic analysis. This problem especially restricts the use of high temperatures in isothermal experiments.23 Thus, several recent studies have been performed under nonisothermal conditions25−28 using a constant heating rate, so that
T (t ) = T0 + ht
4. MATHEMATICAL MODEL The thermogravimetric analysis (TGA) results have first been analyzed for comparison of different models using the equations presented in Table 1. The observed data agree well with the Ginstling−Brounshtein model and are consistent with the reaction being controlled by three-dimensional diffusion in spherical particles, which was supported by results from gas
(4)
and eq 3 is then rewritten as
g (α ) =
A h
∫ e−E/(R T)dT g
(5) 784
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⎛1 1 ⎞ C H2O = −C1⎜ − ⎟ R0 ⎠ ⎝r
adsorption showing that the dense original serpentine forms a porous product as a result of dehydroxylation, illustrated in Figure 1. In the present study, an unreacted shrinking core
(9)
At the high temperature of the reaction, the diffusion in the mesopores of the product layer is characterized by the Knudsen diffusivity.
DKB(r ) = 97rp T /MB
(10)
The reaction rate for a gas−solid reaction is known to be proportional to the surface area of the gas−solid interface.30 Consequently, for the reversible dehydroxylation of serpentine, the rate of motion of the surface of the shrinking core is expressed as Figure 1. Schematic diagram of the serpentine particle, illustrating the product layer and unreacted core.
−
R c = R 0(1 − α)1/3
3k1(1 − α)2/3 dα = dt R 0[1 + β((1 − α)1/3 − (1 − α)2/3 )]
β=
aρk 2R 0 De
De
dC H2O dr
= aρ
eq PH P e−ΔG°/R gT k1 eq 2O KC = = C H2O = = o k2 R gT R gT
(15)
where K C is the equilibrium constant based on the concentration, Po is the pressure at the standard state (1.013 × 105 Pa), Rg is the universal gas constant, and ΔG° is Gibbs free energy. The Gibbs free energy change may be written in terms of the enthalpy and entropy change as follows:
ΔG °= ΔH °− T ΔS°
(16)
and under diffusion control, integration of eq 13 leads to
1 − (1 − α)2/3 − T
=A
(7)
dR c dt
(14)
Equation 13 represents the reaction rate at any position in the grain for an isothermal reaction. For non-isothermal conditions, reaction constants k1 and k2 are related to the equilibrium constant, following
∫T
0
r=R
(13)
where
(6)
C H2O = 0
(12)
Upon using the boundary condition in eq 8, eqs 9, 11, and 12 provide
where CH2O is the concentration of H2O as a function of the radius and De is the diffusion coefficient for H2O in the product layer. The boundary conditions are as follows:
r = R0
(11)
in which k1 and k2 are reaction constants for the forward and reverse reactions, respectively. The local conversion is related to the radius, R, of the shrinking core by
model for the gas−solid reaction is used to describe the dehydroxylation reaction.31,32 The shrinking core model considers the formation of the product layer [Mg2SiO4] around serpentine particles, with the thickness of the product layer increasing with the reaction time. The dehydroxylation reaction effectively takes place only at the interface between the outer product and the unreacted shrinking core of the solid. The assumptions of this model are as follows: (i) the reaction is reversible, and equilibrium is attained at the core surface; (ii) the pseudo-steady-state is considered; (iii) the particles are spherical; (iv) the influence of external mass transfer is neglected; and (v) the porosity of the parent serpentine particle is sufficiently low that a sharp interface between the serpentine and its dehydroxylated product is established. Here, we modify the traditional unreacted shrinking core model for dehydroxylation, by considering the reversibility of the reaction. The assumption of equilibrium at the core surface automatically implies that any water vapor in the interior of the core is also at equilibrium, because the partial pressure of the water cannot exceed the equilibrium value. In such a case, the reaction rate is governed by the motion of the shrinking core surface. The schematic diagram of a serpentine particle is shown in Figure 1, illustrating the spherical isoconcentration surface of radius r in the product layer through which the gaseous product diffuses. The concentration profile of the H2O in the product layer of the particle at radial position r is described by
De d ⎛ 2 dC H2O ⎞ ⎟=0 ⎜r dr ⎠ r 2 dr ⎝
dR c = k1 − k 2C H2O(R c) dt
2 α 3
T −1/2e−ΔH °/(R gT )dT
(17)
where A = (194rpεPoeΔS°/Rg)/(aRgργR02τ(MB1/2)). Here, we have used eq 16 for ΔG°, and it is assumed that the entropy and heat of reaction are temperature-independent. Further, we have assumed that De = εDKB/τ, where ε is the porosity of the product layer, τ is a tortuosity factor, and DKB is the Knudsen diffusion coefficient given in eq 10.
(8)
where ρ is the molar density of the solid reactant, a is a stoichiometric coefficient, R0 is the particle radius, and Rc is the radius of the shrinking core. Equation 6 integrates to 785
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5. RESULTS AND DISCUSSION 5.1. Characterization of Serpentine. The crystal structure of the serpentine was investigated by XRD. The XRD pattern of serpentine and dehydroxylated serpentine is shown in Figure 2. As indicated by the XRD pattern, antigorite
Figure 2. XRD pattern of serpentine and dehydroxylated serpentine.
is the primary phase present in original serpentine and no excess phase was detected. The XRD pattern obtained from the serpentine after it was dehydroxylated illustrates that serpentine was mostly transformed into a form of olivine known as forsterite. However, some MgO may also be present, indicated by the presence of weak peaks at 43° and 63°. Figure 3 shows the SEM micrographs of serpentine and dehydroxylated serpentine. As can be seen in Figure 3a, serpentine sample particles are irregular in shape with a smooth surface resulting from fracture during attrition. They appear to have a compact impervious structure with very little visible porosity (at the scale of observation) for gas (H2O) diffusion through the outer surface. Figure 3b illustrates dehydroxylated serpentine, where the surface has been clearly modified with fractures on the surface, which can be attributed to the reduction of the inherent moisture content through outward diffusion of H2O. Figure 4a shows the collected adsorption isotherms for serpentine and dehydroxylated serpentine. The shape of the isotherms is of type II based on the Brunauer−Deming−Teller (BDT) classification. The specific surface areas were evaluated from the isotherms using the traditional BJH method and the more advanced DFT technique. These methods was also used to compute the pore volumes and PSD of the serpentine, with
Figure 4. (a) Argon adsorption isotherms for serpentine and dehydroxylated serpentine and (b) PSDs of serpentine and dehydroxylated serpentine.
the pore volume of serpentine and dehydroxylated serpentine found to be 0.014 and 0.05 cm3/g, respectively. Figure 4b illustrates the PSDs of serpentine and dehydroxylated serpentine, with surface areas of 25.8 and 20.8 m2/g, respectively. In the case of serpentine, which is microporous, the PSD reported is that obtained using the DFT method, while in the case of the dehydroxylated product, which predominantly comprises meso- and macropores, the PSDs based on the DFT and BJH methods were in very good agreement and only the latter is reported. The increase in pore volume and decrease in surface area are attributed to cracks and large pores created during dehydroxylation, with the loss of the narrow micropores in the parent serpentine. Dehydroxylated serpentine exhibits a larger capacity for nitrogen adsorption than the original serpentine. The value obtained for the pore volume of the dehydroxylated product is very low, and hence,
Figure 3. (a) Original serpentine sample and (b) dehydroxylated serpentine, revealed by SEM. 786
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Figure 5. EDS spectrum of the serpentine.
the internal diffusion model for the kinetics of the dehydroxylated reaction could be excluded. The EDS profile is given in Figure 5, with the key elements of serpentine identified as magnesium (Mg), silicon (Si), oxygen (O), and iron (Fe), and the amount of calcium (Ca) was found to be insignificant. The peak at 8 keV on the spectrum is from the Ag coating and can be neglected. Non-isothermal TGA mass loss experiments have been performed to obtain the kinetics for dehydroxylation of serpentine and to compare the validity of existing models. Figure 6 shows the TGA profile of the dehydroxylation of
than the theoretical water content derived from magnesium serpentine [Mg3Si2O5(OH)4], namely, 12.99%; the difference is mostly attributable to adsorbed moisture loss. The actual fraction of weight loss was calculated for different particle size ranges and different heating rates, plotted versus the temperature as shown in panels a and b of Figure 7. The dehydroxylation reactions were considered to be complete for each experiment, and in calculating α, the final weight losses were considered to correspond to α = 1. Different particle sizes were used to probe the effect of the particle size on the kinetic parameters. Most of the dehydroxylation kinetics reported in Figure 7 showed a similar shape, and the curves are in close agreement with each other, except for the smallest particle size range (90−106 μm), in which the reaction is to some extent faster and starts earlier than the larger particle sizes (Figure 7a). A similar trend can be seen in Figure 7b, with the slowest kinetics belonging to the highest heating rate of 50 K/min. This implies that particle size and heating rate chosen for TGA experiments have a considerable effect on the observed kinetics of dehydroxylation. 5.2. Determination of Kinetics. As discussed in section 3, to find ΔH° from eq 17, the TGA results were fitted with good accuracy to calculate the enthalpy change of the reaction (ΔH°) and the constant A. Nonlinear regression was used to estimate these quantities, fitting the left-hand side to its value obtained from the measured conversion at temperature T used in the upper limit of the integral on the right-hand side of eq 17. Figure 8 illustrates the results of the curve fitting for the proposed equation by plotting the left side of eq 17 versus the temperature. The fitted curve of the model is consistent and in good agreement with the experimental data; however, it did not completely match the actual data for the temperature range from 900 to 1100 K, in which the model prediction yields a slightly faster rate than the experimental data. There are two possible explanations: First, it can be attributed to the presence
Figure 6. TGA profile for the particle size range of 90−106 μm and heating rate of 100 K/min.
serpentine for 100 K/min and size of 90−106 μm. The weight loss of serpentine occurred in two stages, where the first initial small mass loss (less than 1%) is ascribed to dehydration, occurring between 298 and 423 K, and the second principle weight loss called dehydroxylation falls in the range of 873− 1173 K, corresponding to the evolution of the hydroxyl group. The total weight loss was 13.53%, which is only slightly more 787
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of impurities in the sample because the serpentine used was naturally occurring, as shown in Figure 5. Second, there may be an additional resistance step related to olivine nucleation, which affects the observed kinetics at small time, i.e., low temperatures. This would suggest that the dehydroxylation of serpentine most likely follows the two-step reaction, where the first step occurs from 400 to 873 K, which is not accompanied by weight loss because the considered reaction, nucleation, takes place within the crystal structure of the sample. The second step, which is the release of water, occurs from 873 to 1123 K. The mechanisms can be explained by the nucleation of the olivine and then the three-dimensional diffusion of water molecules. The next phase of this research involves investigating the multiple steps of the dehydroxylation reaction mechanism. The enthalpy change of the reaction with the single-step model was investigated to analyze the effect of the particle size and the heating rate on the kinetic parameters. The change of enthalpy obtained from the curve fitting for different particle sizes and heating rates is tabulated in Tables 2 and 3, Table 2. Fitted Model Parameters for Different Particle Sizes, at a Heating Rate of 100 K/min Figure 7. TGA results for (a) three different particle size ranges, for a heating rate of 100 K/min, and (b) heating rate of 10, 20, and 50 K/ min, for a particle size of 300−355 μm.
particle size (μm)
ΔH (kJ/mol of H2O)
A (K−1/2)
90−106 300−355 425−500
108 128 169
6.42 × 107 3.05 × 108 9.38 × 107
Figure 8. Data fitting of the unreacted shrinking core model for different particle sizes: (a) 90−106 μm, (b) 300−355 μm, and (c) 455−500 μm, at 100 K/min. 788
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steady-state temperature rise for the largest and smallest particle sizes. The temperature difference between the particle and the hot medium may be obtained from the energy balance
Table 3. Fitted Model Parameters at Different Heating Rates, for a Particle Size Range of 300−355 μm heating rate (K/min)
ΔH (kJ/mol of H2O)
A (K−1/2)
10 20 50
102 118 121
8.84 × 109 1.71 × 109 2.32 × 108
h(T0 − T )4πR 02 4 dα 4 dT = πR 03aΔH ρ + M ρ πR 03C p 3 dt 3 dt
respectively. For the dehydroxylation reaction, eq 1, the enthalpy of reaction is calculated theoretically as 98 kJ/mol at 700 K for pure serpentine based on the ΔH of formation.33 The values obtained for the smallest particle size (90−106 μm) of 108 kJ/mol and slowest heating rate (10 K/min) of 102 kJ/mol are consistent with the enthalpy of reaction calculated from thermodynamic data at 700 K.33 The discrepancies are due to the impurities that the natural serpentine contains and the many different forms serpentine can take in nature.15 The good agreement of the enthalpy of reaction based on the fitting of the TGA curves, for the smallest particles and also for the lowest heating rate, with the thermodynamic value, confirms the assumption of equilibrium at the core surface and the model assumptions. Also tabulated in Tables 2 and 3 are the fitted values of the parameter A for each combination of particle size and heating rate used. Of these, the most reliable values are those corresponding to the particle size range of 90−106 μm at the heating rate of 100 K/min and the particle size range of 300− 355 μm at the heating rate of 10 K/min because of the intrusion of the gas−solid heat-transfer resistance at other conditions, as discussed below. From the definition of A (A = (194rpεPoeΔS°/Rg)/(aRgργR02τ(MB1/2))), obtained in the model derivation, it is now possible to estimate values of the entropy change of the dehydroxylation reaction. In the estimations, we used the values of rp = 37.5 Ǻ (on the basis of Figure 4b), ε = 0.115 (on the basis of a serpentine density of 2.6 g/cm3), and τ = 3 assuming randomly oriented cylindrical pores. For the case of the 90−106 μm particles and the heating rate of 100 K/min, for which A = 6.42 × 107 K−1/2, we obtain ΔSo/Rg = 18, while for the case of the 300−355 μm particles and heating rate of 10 K/min, for which A = 8.84 × 109 K−1/2, we obtain ΔSo/Rg = 23, in reasonable agreement with each other. These are very reasonable values for dehroxylation reactions, because one expects the bound water to have an entropy somewhat similar to that of ice, so that the entropy change of dehydoxylation may be expected to be of similar magnitude as that for sublimation of ice, of 146.95 J mol−1 K−1.34 The latter value is close to that obtained in this study, of about 20Rg or about 166 J mol−1 K−1. As another comparison, the entropy of dehydroxylation of the phyllosilicate mineral muscovite [KAl2(Si3A1)O10(OH)2] is 13Rg.34 5.3. Significance of the Heat-Transfer Resistance. From Table 2, it is seen that the fitted enthalpy change of reaction of the thermal decomposition of serpentine dramatically increases as the particle size increases. This behavior is explained by taking into account the heat-transfer resistance. In the estimation of the parameters A and ΔH° for the dehydroxylation of serpentine by TGA, it was postulated that serpentine particles are at the temperature of the gas measured by the thermocouple. It was also assumed that the particles are isothermal and that there are no significant temperature gradients in the particles. However, these assumptions may not hold for larger particle sizes. To provide theoretical justification for the assumption, we have calculated the pseudo-
(18)
where h is the heat-transfer coefficient, ΔH is the enthalpy change of the reaction, M is the molecular weight of the solid reactant, T0 is the surrounding gas temperature, and Cp is the specific heat capacity. It is also assumed that the time taken to reach the pseudo-steady state is negligible compared to the reaction time for the initial rapid conversion. This yields the pseudo-steady-state temperature difference as follows:
h(T0 − T )4πR 02 =
4 3 dα πR 0 aΔH ρ 3 dt
(19)
In the TGA, the sample is placed in a thin layer in a holder, which has some dead volume above the solid. Consequently, we use a Nusselt number (2hR0/k) of 2, corresponding to stagnant fluid.35 Thus, by rearranging eq 19 and substituting the value of the Nusselt number, we obtain
T0 − T =
aΔHR 02ρ dα 3k dt
(20)
where k is the gas-phase thermal conductivity. The calculations, using ΔH = 108 kJ/mol and k = 0.05 W/mK36 in eq 20, show that the steady-state temperature difference for the smallest particle size range (90−106 μm) is 0.24 K, which is negligible, while for the largest particle size range, it is 9.9 K, which is quite significant. As a result, the measured conversion−time and temperature−time data and, therefore, the kinetic parameters calculated are considerably affected by the particle size. Consequently, the determination of the change of enthalpy of the reaction for the lowest heating rate, 10 K/min, and the smallest particle size, 90−106 μm, is the most reliable result, because when the heating rate is low, the temperature of the particles can adjust more rapidly to the gas temperature. Further, using smaller particles avoids temperature gradients in the particle. Briendly et al.29 used large particle sizes ranging between 180 and 200 μm for their experiments, a 110% increase in particle diameter from the smallest particle sizes used for our experiments. This, along with the use of isothermal techniques, led them to obtain an activation energy of 284 kJ/ mol (under vacuum), which is considerably higher than the endothermic reaction heat determined in our experiments.
6. CONCLUSION Serpentine has been characterized before and after dehydroxylation using XRD, SEM, and EDS, as well as the adsorptionbased pore size distribution, surface area, and pore volume, to obtain an understanding of the mechanism of the reaction. It was shown that serpentine had a very low porosity, causing the outward diffusion of H2O through the dehydroxylated layer, with equilibrium at the surface of the unreacted core, to be the rate-limiting step. This is confirmed by the agreement of the heat of reaction estimated from the experimental kinetics with the known thermodynamic value. The TGA study of serpentine indicated that the thermal decomposition of this compound proceeds via the evolution of dehydroxylated water over the range of 873−1123 K. The mechanism and kinetics of the 789
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dehydroxylation were analyzed using experimental results recorded at different heating rates and different particle sizes. Diffusion of H2O through the product layer was believed to be the rate-limiting step in the dehyroxylation reaction, and the kinetics of the dehydroxylation followed a diffusion-controlled unreacted shrinking core model, governed by the threedimensional diffusion equation. The results of the modeling suggested that the dehydroxylation of serpentine may best be interpreted as a two-step reaction, with the first step being the nucleation reaction, followed by the three-dimensional outward diffusion of the water molecule. It was found that heat-transfer resistance was significant for large particle sizes and high heating rates, leading to higher apparent values for the heat of reaction.
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AUTHOR INFORMATION
Corresponding Author
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ACKNOWLEDGMENTS We thank Dr. Jun-seok Bae for assistance with pore volume, PSD, and surface area determinations.
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NOMENCLATURE a = stoichiometric coefficient CH2O = concentration of water in the gas phase (mol/m3) Cp = specific heat capacity (J kg−1 K−1) De = diffusivity constant (m2/s) DKB = Knudson diffusivity (m2/s) h = heat-transfer coefficient (W m−2 K−1) k = thermal conductivity (W K−1 m−1) k1 = reaction constant for the forward reaction (m/s) k2 = reaction constant for the reverse reaction (m4 mol−1 s−1) KC = equilibrium constant (mol/m3) M = molecular weight of the solid reactant (kg/mol) MB = molecular weight of gas (g/mol) R = radius of the shrinking core (m) R0 = initial radius (m) Rg = gas constant (8.314 J mol−1 K−1) t = time (min) T = temperature (K) T0 = initial temperature (K) α = extent of the reaction ΔG0 = standard Gibbs free energy of the reaction (kJ/mol of H2O) ΔH0 = standard enthalpy change of the reaction (kJ/mol of H2O) ΔS0 = standard entropy change of the reaction [kJ (mol of H2O)−1 K−1] γ = heating rate (K/m) ρ = molar density of the reactant in serpentine (mol/m3)
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REFERENCES
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dx.doi.org/10.1021/ef201360b | Energy Fuels 2012, 26, 783−790
