Kinetics of the Acid Digestion of Serpentine with Concurrent Grinding

Aug 28, 2009 - present work, a slip stream was taken off of the recirculation loop, put through a Cole Parmer Masterflex L/S peristaltic pump. (model ...
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Ind. Eng. Chem. Res. 2009, 48, 9892–9901

Kinetics of the Acid Digestion of Serpentine with Concurrent Grinding. 2. Detailed Investigation and Model Development Dirk T. Van Essendelft*,† and Harold H. Schobert The Energy Institute, The PennsylVania State UniVersity, UniVersity Park, PennsylVania 16802

The rapid extraction of magnesium from serpentine is critical to novel low-pressure mineral carbonation methodology. Though almost any acid can dissolve the magnesium, the rate plays a critical role in the industrialization of the process. It has been demonstrated that including a low-energy, attrition-type grinding with the chemical attack of the acid can more than double the extraction rate. In part 1 of this investigation, it was found that a model that accounts for surface reaction, surface speciation, the electrical double layer, particle size distribution, and ash layer diffusion can adequately describe the kinetics of the dissolution of serpentine with concurrent grinding. However, the model did not account for changes in temperature, concentration, and grinding energy input. We report here the model developments and changes as well as a detailed experimental investigation to provide validation for the model. Introduction 1

As discussed in part 1 of this investigation, it was clear that neither modeling based solely on surface limited kinetics nor diffusion limited kinetics could capture the real serpentine dissolution behavior adequately with real, physical ties to first principles. In the initial investigation, a computational model was developed that accounted for surface speciation and reaction, the electrical double layer, gel layer diffusion, and particle size distribution (PSD) via a semiempirical, bimodal distribution defined by the Rosin-Rammler distribution. It was found that the change in grinding condition could be accounted for by simply changing the effective diffusivity. Because of the initial success of the model, further experiments were carried out to validate and improve it and are the focus of the extended batch study described in this paper. Model Additions, Changes, and Theory The first change to the model was made to decrease the computation time. Once the modulus in the Rosin-Rammler distribution reached a point where the bimodal portions of the distribution were unaffected by each other, further increases in the modulus made little or no impact on the resulting modelgenerated profile. Thus, the computation was simplified by reducing the particle size distribution (PSD) to a step function, equivalent to increasing the distribution modulus to infinity. Using a step function allowed the calculation time to be greatly reduced because the number of particles that must be accounted for can drop from hundreds to just two. In this way, the small fraction accounts for that part of the system that is entirely kinetically controlled and the large fraction accounts for the part that begins in a kinetically controlled regime and experiences a transition to diffusion control. This method reduced the number of variables related to the PSD from five to three and reduced the calculation time by over 75%. The model allows one to account for the particle size distribution in three ways: measured PSD data input, Rosin-Rammler distribution, and the step function. * To whom correspondence should be addressed. E-mail: [email protected]. † Current address: National Energy Technology Laboratory, U.S. Department of Energy, 3610 Collins Ferry Rd., P. O. Box 880, Morgantown, WV 26507-0880.

The second major change was incorporation of temperature effects. The data used in the initial development of the model were all at 50 °C. However, there are four ways in which temperature can change the kinetics in the model. First, the thermal rate constant for the surface limited reaction was varied according to the Arrhenius equation,

( )

kT ) A0 exp

-Ea RT

(1)

where Ao is the frequency factor, Ea is the activation energy, R is the gas constant, T is the absolute temperature, and kT is the thermal rate constant. Second, the Einstein relation was allowed to dictate the temperature dependence of the effective diffusivity, Deff ) DeffmultT ∝ DAB ) kµAT

(2)

where k is Boltzmann’s constant, µA is the mobility of the diffusion species A in the stagnant fluid B, T is the absolute temperature, DAB is the free diffusivity of A in B, Deffmult is the diffusion temperature proportionality constant in the model, and Deff is the effective diffusivity of A in B in porous media. As outlined in part 1,1 it is assumed that the properties of the porous layer (tortuosity, porosity, and effective free area) are invariant to changes in temperature. Thus, it was assumed that the effective diffusivity was directly proportional to the absolute temperature. Third, the dielectric constant of water was allowed to change with temperature. The dielectric constant data were retrieved from a chemical handbook2 and fitted with a secondorder polynomial, as shown in εw ) 7.403050 × 10-04T2 - 0.3957267T + 87.81600 R2 ) 0.99998 (3) Here, T is temperature in celsius, and εw is the dielectric constant of water. Lastly, the temperature dependence of the acid equilibrium was allowed to vary according to standard thermodynamic models. It was assumed that the specific heat for the species involved was constant over the temperature range of interest.

10.1021/ie9005832 CCC: $40.75  2009 American Chemical Society Published on Web 08/28/2009

Ind. Eng. Chem. Res., Vol. 48, No. 22, 2009 ln(Ka) ) ln(Kao) -

(

(( )

)

9893

)

∆Hro 1 To To 1 +1 + ∆Cpo ln R T To T T (4)

Here, Ka is the equilibrium constant, ∆Hr is the heat of reaction, R is the gas constant, T is the absolute temperature, and ∆Cp is the difference in specific heat between products and reagents. The subscript “o” denotes that the variable is evaluated at standard conditions. The thermodynamic parameters were retrieved from the databanks in Aspen Plus.3 The equilibrium constants were used to determine the aqueous species distribution for the protons in solution as a function of the amount of magnesium released from the serpentine. The third model change relates to correcting for unequal molar counterdiffusion. Originally, equimolar counterdiffusion was assumed, to simplify the calculations. Strictly speaking, the total flux for component A, WA, is equal to the sum of the diffusive flux, JA, and the convective flux, BA (eq 5). The convective flux of component A can be expressed in terms of the mole fraction of A, yA, and the sum of all of the component fluxes, ∑Wi (eq 6). Because any convective flux would be driven by reaction, it is only necessary to consider the total change due to generation or consumption of species involved in the reaction. For our system, the components involved are protons, magnesium ions, and water. Thus the proton flux can be expressed as in eq 7. Because the convective flux in the diffusion layer is driven by reaction, the magnesium ion and water flux can be expressed in terms of the proton (eq 9) by the law of mass action and eq 8. The total flux for the proton can now be expressed in terms of the diffusive flux and the mole fraction (eq 10). Finally, the mole fraction can be expressed in terms of concentration as in eq 11. WA ) JA + BA W A ) JA + yA

(5)

∑W

(6)

i

WH+ ) JH+ + yH+(WH+ - WMg+2 - WH2O)

(7)

+2

Mg3Si2O5(OH)4(s) + 6H+(aq) f 3Mg (aq) + 2SiO2(s) + 5H2O(l) (8) 1 5 WH+ ) JH+ + yH+ WH+ - WH+ - WH+ 2 6

(

(9)

J H+ 1 + (yH+ /3)

(10)

[H+] [H+] + [H2O] + [Mg+2]

(11)

WH+ ) yH+ )

)

The concentrations in eq 11 have to be evaluated at the site of the reaction, which is at the inner core. It was assumed that the diffusivity for the ions in solution is roughly equal. Thus the electroneutrality condition can be approximated by + + +2 2[Mg+2 B ] + [HB ] = [HD ] + 2[MgD ]

(12)

Here, brackets denote volumetric concentration, B denotes bulk concentration, and D denotes concentration just outside the double layer. Assuming that the consumption of acid to dissolve other ions is minor in comparison to that used to dissolve magnesium, the bulk magnesium concentration can be expressed in terms of the initial bulk acid concentration and the instantaneous bulk acid concentration via the law of mass

Figure 1. Fractional magnesium extraction as a function of time for repeatability Experiments, 95% confidence interval, and model fit.

action. Thus the magnesium concentration just outside the double layer can be calculated. + + 2[Mg+2 B ] + [HB ] - [HD ] ) 2 + + + + [H+ 2(([H+ Bo] - [HB ])/2) + [HB ] - [HD ] Bo] - [HD ] ) 2 2

[MgD+2] =

(13)

It was also assumed that the concentration of water remains constant at close to 55 M H2O. With these assumptions it was possible to correct for the errors in diffusivity. However, even at 5 M acid, the maximum error in diffusivity is only 2.9% and the inner core only experiences such concentration when the core radius is very close to the outer radius or close to zero. In either case, kinetics are in greater control than diffusion, and the correction makes little difference. The fourth model development relates to particle shape. Traditional particle size distribution measurement techniques (sieving and laser diffractometry) can only characterize particles by a single dimension, and the measured dimension for a particle does not reveal any quantitative information about shape. The size fractions used in this work correspond to sieve size openings, but laser diffractometry shows a significant portion of the particles are greater than the sieve opening size for each fraction (Figure 5), especially for the undersized fraction. For spherical particles, the laser measurements would agree very well with the sieve size fraction. However, for elongated particles, larger particles can pass the sieves if their two minor axes are smaller than the sieve opening, which is apparently the case as can be seen from microscopy images (Figures 6-8). We have shown previously that both spherical and cylindrical forms of the gel diffusion equation can linearly fit the data (albeit with little tie to physical principles and exhibiting consistent bias).1 Though the mathematical function is different for each, surprisingly, both seemed to produce comparable results. The only appreciable difference between the two was the slope and intercept. Thus it would seem that a single model could be used with a shape factor to adequately describe either case. To understand this, it is helpful to imagine a line of spherical particles. Viewed end-on, the length of the line-up of particles cannot be distinguished from that of a single particle. But, viewed orthogonally, it would be immediately apparent that there was a line of spheres rather than only one. In the previously developed model,1 there was no way to account for a second dimensional component. The core size of the particles

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In the current model, this second average dimensional component can be incorporated into the time integrations as eq 14 shows. This equation differs from previous theory by a single shape factor, Sf. t)

∫

R

Ro

-2FsφmSf dR r′H+ R

(14)

Here Sf is the shape factor that describes the aspect ratio of the particles as if they were a row of spheres, and the radial component, R, describes the minor diameter. Apparatus

Figure 2. Fractional magnesium extraction as a function of time for the temperature response, 95% confidence interval, and model fits.

The apparatus used in part 1 was modified slightly.1 The agitator was transformed into a dynamometer that can measure the reaction torque and rotational speed of the shaft and thus calculate the direct mechanical power put into the reaction system. Second, the sampling method was also modified. In the present work, a slip stream was taken off of the recirculation loop, put through a Cole Parmer Masterflex L/S peristaltic pump (model 7532-60), which was connected to a five valve polycarbonate manifold, and finally back to the recirculation loop. The manifold outlets were connected to syringe filters and were suspended above sample tubes. These modifications are documented in detail elsewhere.4 Materials

Figure 3. Fractional magnesium extraction as a function of time for the concentration response, 95% confidence interval, and model fits. Table 1. ICP Solids Report for Sieved Serpentine Samples size fraction (%) for given sieve size

Al2O3 BaO CaO Fe2O3 MgO MnO SiO2

-38 µm

38-73 µm

73-140 µm

0.48 0.07 0.9 6.85 34.8 0.12 36.7

0.58 0.03 0.87 9.92 33.0 0.12 35.1

0.54 0.02 0.76 8.20 34.7 0.1 37.5

(assumed to be spheres) was used to calculate the amount of magnesium that should be in solution. However, knowing that spherical gel layer diffusion describes real behavior just as well as cylindrical gel layer diffusion allows an apt description of the dissolution of a cylindrical object as one made up of a line of spheres. If the hypothetical spherical particles were soluble, then the same concentration in solution resulting from the complete dissolution of one sphere would be the same as if the row of, e.g., 10 spheres had each dissolved one-tenth of their volume. Thus each of the spheres would retain a significant portion of its original size. Conversely, it would appear that the dissolution rate for the single sphere was 10 times as high as that for the hypothetical 10-sphere cylindrical particle.

Approximately 550 kg of serpentine rock dust was collected from the Cedar Hill quarry in Lancaster County, PA. The serpentine was then milled in a Hosokawa Micron Powder Systems Mikro-ACM-Pulverizer air swept mill (model 10 ACM) in conjunction with a Dust-Hog bag filter (model FJL4-5-H55) and wet-sieved into four size fractions with a Derrick inclined vibrating sieve (model k18-60A-1DDTE). The size fractionation points were set at 38, 73, and 140 µm. Approximately 5 kg were recovered in the -38 µm fraction, 60 kg in the 38-73 µm fraction, and 38 kg in the 73-140 µm fraction. The oversized fraction (+140 µm) was dried and saved for future use. Each fraction was homogenized in a clean, small, rotary cement mixer and stored in five gallon buckets for later use. A Perkin-Elmer Optima 5300 inductively coupled plasma (ICP) instrument was used to measure the elemental composition of the serpentine via the lithium meta-borate fusion technique.5-7 Table 1 shows the results for each size fraction used in the extended batch study. The balance was determined to be water. The physical composition is consistent with previously reported results for the same material type.1,8,9 The molar ratio of magnesium to silicon was 1.40 on average. This is very close to the idealized serpentine formula (Mg3Si2O5(OH)4), in which the magnesiumto-silicon ratio is 1.5. X-ray diffraction on a Scintag X2 θ-θ powder diffractometer with Cu KR1 and -2 radiation confirmed that the major form of the mineral is serpentine (antigorite and lizardite, two polymorphs of planar serpentine structure) with minor phases of magnetite, magnesite, dolomite, and vermiculite. All acids used in the experiments were ACS reagent grade or better. For experiments at 1 M concentration, 18 L of acid was prepared by mass and then titrated to confirm the molarity. This procedure allowed for consistency in experiments and time savings. For experiments at different concentrations, the acid was prepared by standard volumetric dilution techniques. Experimental Procedure The reactor system has been described in detail elsewhere.1,4 Borosilicate glass beads of known diameter and amount as well

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Table 2. Summary of Experimental Conditions run no.

temp (°C)

agitator speed (RPM)

acid concn (M)

acid vol. (mL)

media size (mm)

media mass (g)

particle size (µm)

serpentine mass (g)

pump rate (L/min)

80522 80527 80701 80703 80707 80714 80715 80716 80717 80718 80721 80722 80723 80728 80729 80730

50 50 50 30 40 75 50 50 50 50 50 50 50 50 50 50

200 200 200 200 200 200 200 200 200 200 200 200 100 50 400 800

1.012 1.012 1.012 1.012 1.012 1.012 0.100 4.893 2.500 1.012 1.012 1.012 1.012 1.012 1.012 1.012

700 700 700 700 700 700 700 700 700 700 700 700 700 700 700 700

3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

800 800 800 800 800 800 800 800 800 800 800 800 800 800 800 800

38-73 38-73 38-73 38-73 38-73 38-73 38-73 38-73 38-73 73-140 -38 38-73 38-73 38-73 38-73 38-73

70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70

4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4

as the acid were charged to the reactor. The agitation system was set to a known speed and activated. The circulation pump and thermal control system were activated and set to known values. The reactor was allowed to reach a stable temperature. A known mass of serpentine was loaded into a drop tube used to charge the reactor for rapid injection. At a known time (demarcating t ) 0), the serpentine was released from the drop tube into the reactor through the charging port. At known time intervals, samples were taken with the side stream sampling system. For the first 21/2 min, samples were taken every 30 s (a total of five). From 5 to 15 min, five samples were taken every 21/2 min. From 20 to 110 min, 10 samples were taken every 10 min. The samples were analyzed by ICP analysis. Knowing the sulfur concentration from the sulfuric acid concentration used in the experiment allowed for the calculation of all other species of interest without having to know the dilution factor based on molar ratios calculated from the mass concentrations as reported by the ICP. Samples were diluted roughly 1000-fold by volume without careful mass dilutions. Results and Discussion A summary of the experiments is given in Table 2. These experiments were run to assess repeatability and evaluate experimental and read error (80522, 80527, 80701, and 80722); to evaluate temperature response (80703, 80707, and 80714); to assess response to changing acid concentration (80715, 80716, and 80717); to evaluate effects of changing particle size (80718 and 80721); and to evaluate the effect of changing power input (80723, 80728, 80729, and 80730).

calculated. The limit for use in experimental error was set at 0.1 min. This cutoff left 12 of the original 20 sampling times and allowed for the error evaluation from 48 data points. For each of the 12 qualifying sampling times, the standard deviation of the conversion was taken and the 95% confidence interval calculated. The calculated confidence intervals were then averaged to obtain the combined error. This error was taken to be absolute and independent of concentration or time and was evaluated to be (0.0087 fractional magnesium extraction units. The majority of data points fall within this confidence interval. Temperature Response Four temperatures were evaluated: 30, 40, 50, and 75 °C. The profiles were used to evaluate the frequency factor and the activation energy for the surface reaction. With the correct thermal rate constants, the model can be predictive in temperature response (Figure 2). The model fit the data within the 95% confidence interval for nearly every point in the four data sets. The four modes of temperature variation in the model (eqs 1-4) are adequate to describe the temperature response of the system. The activation energy for the surface reaction is 60.0 kJ mol-1, and the frequency factor is 1.49 × 1016 m4 mol-1 s-1 by fitting the model to the data. The activation energy and frequency factor reported by Teir et al. are 68.1 ( 7.3 kJ mol-1 and 8.6 × 106 s-1,

Repeatability and Error Analysis Figure 1 shows results of the experiments carried out to assess the experimental repeatability and determine the combined error, as well as the model fit to the data. The data are repeatable and the model fit is quite good. However, some of the evaluation times were not the same, due to filter failures or other experimental problems. The time error for sampling was under 30 s (less than the width of the marker, usually 6-20 s, depending on filtration speed). The plotted position represents the median time between the start and end of the sample period and the calculated chemical conversion. Because the sample time affects the conversion, it was necessary to determine the combined error for those points that were evaluated at almost identical times. The standard deviation of median sample time for each programmed sample point was

Figure 4. Fractional magnesium extraction as a function of time as a response to particle size variation, 95% confidence interval, and model fits.

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Figure 5. PSD for fractions used in this investigation.

respectively.10 However, the values in Teir’s study are relative to an empirical model that linearized the data. Further, the large difference in frequency factor is due to differences in units and reaction type. Teir assumed a first-order volumetric reaction, while our model uses a second-order surface-area-specific reaction. Two other studies on the dissolution of serpentine in strong sulfuric acid reported the activation energy to be 35.6 and 52.3 kJ mol-1.11,12 On the other hand, chemically similar materials such as olivine have had higher activation energies ranging from 66.5 to 126 kJ mol-1 (extrapolated to pH of zero).13,14 The activation energy found here falls within the bounds of what is reported within the available body of literature. Concentration Effects Figure 3 shows the magnesium extraction data at 0.100, 1.012, 2.500, and 4.893 M sulfuric acid. The model did no worse than 3% conversion difference in a 2 h profile. The model fits the data for the 1.012 M case well and for the 2.500 and 4.893 M cases falls just outside the 95% confidence interval. The comparatively poorer fit for the 0.100M Model Std case is believed to be due to the point of zero charge (PZC) of the depleted silica shell that forms around the reacted or partially reacted serpentine and the resulting interparticle interactions (a complex phenomenon not taken into account by the model). It is known that the leach layer on top of the particles is composed largely of silica.8,10,13,15 Silica materials have a point of zero charge of between 2.4 and 3.16,17 The charge on oxide surfaces is known to be pH-dependent if protons can bond to oxygen at the solid/aqueous interface.18-23 The initial pH of the solution in the 0.100 M experiment was pH 1, and according to the model the final pH was near 2.5. This is not far from the expected point of zero charge of the silica overlayer. It was likely that there was particle agglomeration during the reaction and that the smallest particles would adhere most strongly to the large particles or to each other because the adhesion force relative to any fluid shear would be the highest. This behavior would create an apparent particle size distribution with less undersize amount and larger oversize diameter relative to the original distribution. Rapid agglomeration was noted when the slurry was removed from the reactor for this run. When the particle size distribution in the model was adjusted to reflect the agglomeration, a tidy fit was once again obtained (0.100 M Model Ag). It is also likely that the opposite effect occurs in

stronger acid concentrations. That is, the smallest particles are well-solvated and are less likely to agglomerate with each other or with larger particles as the interparticle adhesion force is reduced. This may be the reason for the noticeably higher deviation from the model in the 4.893 M profile. Accounting for the physical forces in particle-particle and particle-fluid interactions is complex, requiring detailed knowledge of fluid shear, particle morphology, and pH-dependent electrostatics as well as complex finite element analysis in computational dynamics. While it is possible that this could be done, it is well beyond the scope of this investigation. In any case, the parameters related to the surface speciation have the greatest effect on the model profiles at different concentrations. Increasing the PZC for the active sites at the core interior in the dual site 2pK model has the effect of decreasing the overall conversion at all concentrations. Decreasing the spread between the dissociation constants has the effect of decreasing the spread in the conversion between profiles at different concentrations. It might be difficult, if not impossible, to measure these parameters in a mixed oxide, especially when it is complicated by an oxide overlayer. However, they can be determined by fitting to concentration curves. The dissociation constants for the 2pK model were determined to be 1.995 × 10-9 and 5.012 × 10-10 mol m-2, respectively (pK1 ) 8.7; pK2 ) 9.3), giving a PZC for the active sites of 9. The PZC of magnesium oxide has been reported to be around 10.16 The PZC for the unreacted serpentine in this investigation was measured to be 8.47 by the potentiometric mass titration technique of Bourikas et al.16 The PZC for the active sites involved in the dissolution is likely higher than serpentine and likely lower than pure magnesium oxide. Particle Size Effects Figure 4 shows the data from three experiments with three different particle size ranges (-38, 38-73, and 73-140 µm) and the model fits. The results may appear counterintuitive, in that one might expect that the smallest particle size would produce the largest conversion in the smallest amount of time, which is not the case. In fact, the medium fraction (38-73 µm) produced the greatest conversion. The large size fraction (73-140 µm) produced less conversion than the medium fraction. The particle size distributions are shown in Figure 5. The -38 µm profile in Figure 4 might be ascribed at first sight to a fraction with a greater amount of undersized and slightly larger top size because the “hump” (boundary between kinetic and diffusion dominated behavior) appears a bit higher in conversion and the outbound slope appears to be less. However, the inbound slope in the low-conversion region is telling. Typically, a greater fraction of undersized material results in a steeper inbound slope. Thus a profile with a higher hump should also have a steeper initial slope, all other factors being the same. The data do not show this. In fact, the initial points for the undersized fraction are almost outside the 95% confidence interval of the next closest fraction (38-73 µm) on the low side. This point, as well as the expectation that the undersized fraction would produce a much greater conversion relative to the mid-sized fraction, indicates that another phenomenon is at work. Understanding the data for the -38 µm fraction requires a bit more detective work. Particle shape can account for this change. Scanning electron microscopy (SEM) images show that smaller particles tend to have higher aspect ratios than larger particles. Both of the other two fractions had the same shape factor, 1. A nearly perfect fit

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Figure 6. BSE ESEM image of cross-sectioned and epoxy mounted serpentine.

Figure 7. High-magnification BSE ESEM image of cross-sectioned and epoxy mounted serpentine.

of the data was obtained with a shape factor of 5 along with an undersized fraction of 6% and a large fraction size of 52 µm. Figure 6 shows a cross-sectional view of serpentine particles of various sizes. The image was taken in a Philips FEI Quanta 200 environmental scanning electron microscope (ESEM) in backscatter (BSE) mode. The near-black regions in the image are the epoxy matrix; the gray regions are serpentine particles. The light regions are iron oxides. It appears that the aspect ratio increases as particle size decreases. Figure 7 shows a higher magnification image surrounding the fish-like-shaped particles near the center of Figure 6. The smaller particles tend not to be as spherical as the large particles. Though three-dimensional shape cannot be determined from a single set of crosssectional images, it can be inferred that there is a shape

change with size. The centrifuging process used in sample preparation will not produce a random distribution of particles in space. The shortest axis of the particle will have a tendency to align with the direction of force. This can be seen in Figures 6 and 7, where very few particles have aligned the long axis in the upward direction (the direction of the centripetal force). Since there is no apparent driving force to align the longest axis in any particular radial direction, a random orientation in the radial direction would be expected. Thus it is impossible to separate platelike shapes from fiberlike shapes in these images. Nonetheless, very few spherelike shapes exist in the small fractions, while the larger fractions do not have particles with aspect ratios exceeding ∼3:1.

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Figure 8. High-resolution ESEM image of small serpentine particles.

Figure 8 shows an ESEM image of -38 µm serpentine particles. This image supports the idea that the smaller particles tend to have either a platelike or fiberlike morphology with a high aspect ratio. Given the sheetlike structure of serpentine and the relatively weak bonding between the sheets, it is not difficult to imagine the formation of platelike particles during grinding. However, the development of high aspect ratio particles is consistent with the understanding of the “planar” structure of antigorite and lizardite. The difference in lattice parameters between the brucite-like layer and the silica-like layer results in longer range, periodically inflected curvature, much like a wave in the ocean.15,24 The wavelike structure results in anisotropic mechanical properties, making the particles stronger in the direction of the axis of the wave than transverse to the wave. The period of the wave has been reported to be about 10 nm.24 Further, it is expected that the wavelike structure is only directionally consistent within single grains. The propensity of having multigrain particles grows with particle size, thus further reducing the anisotropic properties. This reasonably explains why smaller serpentine particles have higher aspect ratios than larger particles. Presently, understanding particle morphology and its effects on reaction progress remain a challenge. It is clear from Figure 4 that both size and morphology play critical roles in the kinetics. The model at its current stage of development is able to capture the behavior of both, but not predictively. Characterizing both aspect ratio and size may be enough for the model to be predictive. Clearly, treating all particles as though they were spheres in a size analysis is not sufficient. Effect of Changing Mechanical Power Density As shown previously, changes in grinding conditions can be captured by changing the effective diffusivity in the model.1 The relationship between applied mechanical power and effective diffusivity was further explored in the present investigation. Figure 9 shows dissolution profiles for several experiments in

Figure 9. Fractional magnesium extraction as a function of time as a response to agitation speed, 95% confidence interval, and model fits.

which only the RPM (grinding energy) was varied. The figure also shows the model fits to the data, with the only variation being Deffmult in eq 2. In these tests, the reaction torque on the agitator shaft was measured by the load cell in the mixing head assembly (see previous work for detailed description4). Because a stepper motor was used, a known and constant rotational velocity could be maintained. This allowed for the calculation of mechanical power input to the system. The power density, i.e., the ratio of mechanical energy into the system to the reaction volume (excluding grinding media), was used to correlate to effective diffusivity. The power density was used because it should be a more consistent indicator across different reactor (grinding apparatus) types. The best relationship between measured mechanical power and agitation speed was a power law relationship (Figure 10).

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experienced low-energy attrition grinding before being spit out into the general solution again. The cavity that secures the magnetic stirrer showed signs of a high amount of wear relative to the rest of the cell. It is unlikely that the action of a Teflon stirring bar could account for the wear through the hard-anodized coating and into the underlying aluminum. It is likely that particles got between the aluminum housing and the magnetic stirrer and caused the wear. In doing so, the particles experienced mechanical grinding.

Figure 10. Mechanical power input vs agitator shaft RPM.

Figure 11. Relationship between effective diffusivity and mechanical power density at 50 °C.

The correlation is quite strong. However, this relationship is specific to this kind of vessel and should not be applied to other geometries as changes in geometry will affect the power-RPM relationship. A second-order polynomial can adequately describe the relationship between power density and effective diffusivity. For each experimental profile in Figure 9, Deffmult was varied until the squared error between the model and the data was minimized. The fitted values were then plotted against the calculated power density and curve fit. Figure 11 shows the correlation of effective diffusivity vs mechanical power density. Initially it was not immediately obvious how or why the phenomenon of diffusion should be correlated with changes in mechanical grinding intensity. However, a serendipitous discovery shed light on this issue. In an attempt to measure PSDs of small quantities of serpentine in the small stir cell of the laser diffractometer (Malvern 2600c), the action of the rotating stir bar had an unexpected effect on measured PSD. The PSD shifted with time. The weighted center of the large fraction shifted to the small side, and the fraction of fine undersized material grew. It was also observed that the large particles settled to the bottom of the sample cell in the particle sizing apparatus and fell into the cavity that held the stirrer in place. There, they

A low-energy attrition grinding mechanism can account for the observed changes in the PSD with time. There is enough energy to break off small irregularities of high surface potential energy (i.e., the sharp edges) and transform the larger irregular pieces into ones that are more rounded or spherelike. In doing so, the large particles may have shrunk very slightly, but created a great number of small, broken off pieces coming from originally irregular exterior surfaces. Attrition-type grinding fits with the type of particle size reduction found in the small cell grinding test. Further, this type of grinding action explains why increasing the effective diffusivity can capture the effect of increasing the power density. Consider two identical, spherical particles. Each has undergone the same amount of reaction and, therefore, has the same internal core diameter. The first does not experience grinding in reaction; the second does. Thus the exterior radius of the first particle is the same as the original particle, and the exterior radius of the second particle has shrunk due to the action of the attrition-type grinding but is still larger than the core diameter. The diffusivity constant relates concentration change to physical distance. The higher the diffusivity, the shallower the slope will be. The diffusivity of ions through the porous layer is very slow (steep slope), and the diffusivity of ions through open solution is fast (shallow slope). In the model, the initial, outer particle diameter was assumed to be constant. These factors combine such that a new effective diffusivity (at a slope between the solution diffusivity and the gel layer diffusivity) is reached which allows for higher concentration at the core surface and faster overall rate. The drawing in Figure 12 illustrates this discussion. It is yet unclear as to why the effective diffusivity remains constant. Whatever the cause, it is apparent that the thickness of the diffusion barrier is set both by the attrition grinding rate and the dissolution kinetics and that the relationship remains consistent throughout the entire reaction, allowing for a single parameter to describe the effect of grinding. Attrition grinding is likely not the only way to produce a fresh or partially refreshed surface during the reaction. However it is likely to be among the lowest energy solutions. The combination of attrition grinding with the chemical attack of the acid reduces the energy consumed to generate fines. The reduction of energy is likely due to the chemical attack which significantly weakens the structure24 and therefore allows for easy fracture of the silica layer that develops during digestion. In comparison, impact breakage would require more energy, because generating fines of the same size would require long crack propagation distances through a solid, strong material as compared to short propagation distances through a porous, weak structure. The energy difference is further evident in the amount of the energy needed to first reduce the particles to a fine size and then do a fast digestion25 as compared to the current study, in which attrition grinding and digestion are combined. Combining a fast impact grinding with digestion is likely to increase

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Figure 12. Visualization of diffusion both with and without attrition grinding for the same conversion. This is a simplified schematic diagram to aid conceptualization, since the profiles are not linear in spherical geometry.

the kinetics but the energy consumed is not likely to differ greatly from doing them separately. Summary and Conclusions In general, the proposed kinetic model is successfully able to capture the behavior of the dissolution of serpentine in sulfuric acid. Within the limits of this investigation, the model was able to capture the experimental extraction of magnesium from serpentine within ∼3% in every case and within 1% for most cases. The model did best at capturing temperature response, the response to increased power density and to changes in particle size. The model struggled most with capturing the response to changes in acid concentration. It is clear that some particle behaviors which are pH-dependent, while not accounted for in the model, do affect the dissolution behavior such as gel layer surface charge and agglomeration. Further, both particle size and shape play critical roles in the dissolution kinetics. However, the ability to characterize and measure particle shape before, after, and during the progress of the reaction was not available during this study. Even so, the model was still able to match the measured behavior with the addition of a shape factor and reasonable changes to the semiempirical PSD. It is felt that particle shape characterization could lead to a completely predictive model without the need to use a semiempirical PSD. That said, the model can be reasonably predictive, in its current state, if it is primed with experiments run with the PSD that will be used in the system of interest and under pH conditions far from the gel layer’s PZC. Finally, evidence was found that supports the notion that the grinding action is due to attrition, not impact, and can be accounted for by changing a single parameter, the effective diffusivity. The development and use of the model has provided invaluable insight and information into how serpentine behaves in strong acids. Acknowledgment Several people provided necessary components and skills for this research to occur. All work herein was funded by private donation to The Pennsylvania State University (PSU). Joe and

Doris Soltis provided financial support through generous giving to PSU. Henry Gong, Senior Analytical Chemist at the Materials Characterization Laboratory, PSU, gave his expertise in sample preparation and analysis for ICP. John J. Cantolina, Research Support Technician, also with the Materials Characterization Laboratory, spent many hours assisting with ESEM imaging. Nichole Wonderling, Research Assistant, at the Materials Research Institute, PSU, assisted with the XRD for this project. Jamie Clark, research assistant, helped to conduct many of the experimental runs. Dr. Lee Donohue, Richter Precision Inc., gave his expertise and experience and worked with us to develop acid and wear-resistant coatings for the agitators. The anonymous reviewers also deserve thanks as they ensure the scientific rigor of the works published herein. Sincere appreciation for all of these gifts and efforts is deserved. Literature Cited (1) Van Essendelft, D. T.; Schobert, H. H. Kinetics of the Acid Digestion of Serpentine with Concurrent Grinding. 1. Initial Investigations. Ind. Eng. Chem. Res. 2009, 48, 2556–2565. (2) Weast, R. C., Handbook of Chemistry and Physics, 52nd ed.; The Chemical Rubber Co.: Cleveland, OH, 1964. (3) Aspen Plus, 2004; Aspen Technology: Cambridge, MA, 2008. (4) Van Essendelft, D. T. Kinetics of the Acid Digestion of Serpentine with Concurrent Grinding for the Purpose of Carbon Dioxide Sequestration. Dissertation, The Pennsylvania State University, University Park, PA, 2008. (5) Suhr, N. H.; Ingamells, C. O. Solution Technique for Analysis of Silicates. Anal. Chem. 1966, 38, 730–734. (6) Medlin, J. H.; Suhr, N. H.; Bodkin, J. B. Atomic Absorption Analysis of Silicates Employing LiBO2 Fusion. At. Absorp. Newsl. 1969, 8 (2), 25– 29. (7) Ingamells, C. O. Lithium Metaborate Flux in Silicate Analysis. Anal. Chim. Acta 1970, 52, 323–334. (8) Park, A. H. A.; Fan, L. S. CO2 Mineral Sequestration: Physically Activated Dissolution of Serpentine and pH Swing Process. Chem. Eng. Sci. 2004, 59 (22-23), 5241–5247. (9) Park, A. H. A.; Jadhav, R.; Fan, L. S. CO2 Mineral Sequestration: Chemically Enhanced Aqueous Carbonation of Serpentine. Can. J. Chem. Eng. 2003, 81 (3-4), 885–890. (10) Teir, S.; Revitzer, H.; Eloneva, S.; Fogelholm, C. J.; Zevenhoven, R. Dissolution of Natural Serpentinite in Mineral and Organic Acids. Int. J. Miner. Process. 2007, 83 (1-2), 36–46.

Ind. Eng. Chem. Res., Vol. 48, No. 22, 2009 (11) Fouda, M. F. R.; Amin, R. E.; Mohamed, M. Extraction of Magnesia from Egyptian Serpentine Ore via Reaction with Different Acids. 1. Reaction with Sulfuric Acid. Bull. Chem. Soc. Jpn. 1996, 69 (7), 1907–1912. (12) Apostolidis, C. I.; Distin, P. A. Kinetics of Sulfuric-Acid Leaching of Nickel and Magnesium from Reduction Roasted Serpentine. Hydrometallurgy 1978, 3 (2), 181–196. (13) Jonckbloedt, R. C. L. Olivine Dissolution in Sulphuric Acid at Elevated TemperaturessImplications for the Olivine Process, an Alternative Waste Acid Neutralizing Process. J. Geochem. Explor. 1998, 62 (1-3), 337–346. (14) Chen, Y.; Brantley, S. L. Dissolution of Forsteritic Olivine at 65 Degrees C and 2 < pH < 5. Chem. Geol. 2000, 165 (3-4), 267–281. (15) White, A. F.; Brantley, S. L., Chemical Weathering Rates of Silicate Minerals; Book Crafters: Chelsea, MI, 1995; Vol. 31. (16) Bourikas, K.; Vakros, J.; Kordulis, C.; Lycourghiotis, A. Potentiometric Mass Titrations: Experimental and Theoretical Establishment of a New Technique for Determining the Point of Zero Charge (PZC) of Metal (Hydr)oxides. J. Phys. Chem. B 2003, 107, 94419451. (17) Fuerstenau, D. W.; Pradip. Zeta Potentials in the Flotation of Oxide and Silicate Minerals. AdV. Colloid Interface Sci. 2005, 114, 9– 26. (18) Stumm, W., Aquatic Surface Chemistry: Chemical Processes at the Particle-Water Interface; John Wiley & Sons: New York, 1987.

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(19) Harris, R. G.; Wells, J. D.; Johnson, B. B. Selective Adsorption of Dyes and Other Organic Molecules to Kaolinite and Oxide Surfaces. Colloids Surf., A 2001, 180 (1-2), 131–140. (20) Harris, R. G.; Johnson, B. B.; Wells, J. D. Studies on the Adsorption of Dyes to Kaolinite. Clays Clay Miner. 2006, 54 (4), 435–448. (21) Harris, R. G.; Wells, J. D.; Angove, M. J.; Johnson, B. B. Modeling the Adsorption of Organic Dye Molecules to Kaolinite. Clays Clay Miner. 2006, 54 (4), 456–465. (22) Blum, A. E.; Eberl, D. D. Measurement of Clay Surface Areas by Polyvinylpyrrolidone (PVP) Sorption and Its Use for Quantifying Illite and Smectite Abundance. Clays Clay Miner. 2004, 52 (5), 589–602. (23) Tombacz, E.; Szekeres, M. Surface Charge Heterogeneity of Kaolinite in Aqueous Suspension in Comparison with Montmorillonite. Appl. Clay Sci. 2006, 34 (1-4), 105–124. (24) Kosuge, K.; Shimada, K.; Tsunashima, A. Micropore Formation by Acid Treatment of Antigorite. Chem. Mater. 1995, 7, 2241–2246. (25) Kim, D. J.; Chung, H. S. Effect of Grinding on the Structure and Chemical Extraction of Metals from Serpentine. Part. Sci. Technol. 2002, 20 (2), 159–168.

ReceiVed for reView April 10, 2009 ReVised manuscript receiVed July 24, 2009 Accepted August 3, 2009 IE9005832