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Kinetics of the Acid Digestion of Serpentine with Concurrent Grinding. 3. Model Validation and Prediction 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. Although almost any acid can dissolve the magnesium, the rate plays a critical role in the industrialization of the process. As detailed in parts 1 and 2 of this study [Van Essendelft and Schobert Ind. Eng. Chem. Res. 2009, 48 (5), 2556-2565; 2009, 48 (22), 9892-9901], a computational model has been developed that explains the kinetics of the extraction of magnesium from serpentine with concurrent grinding. The model has direct ties to first principles and accounts for surface speciation and reaction, the electrical double layer, ash-layer diffusion, particle size distribution, temperature effects, and solution thermodynamics. It is desirable to demonstrate the robustness of the model and to use the model to predict useful scenarios. Presented here are experimental data obtained under various conditions not tested before and the predictions of the model under those circumstances, as well as the predictions of the model in an industrial application. Introduction Prior to the work reported here, the beneficial effect of combining attrition-type grinding with chemical digestion on the rate of magnesium extraction from serpentine had been demonstrated.1–3 However, prior to our efforts in this investigation, a detailed model that could describe the kinetics based on first principles had not been developed. This article comprises the third part of our investigation. The initial data taken to survey the kinetics and the initial developments of the computational model that describes that data were reported in part 1 of this investigation.2 The data from a detailed parametric study and further development of the model were reported in part 2.3 Because the model2–4 was able to capture the behavior of serpentine in strong sulfuric acid with grinding, it was desirable to see how the model would predict various situations. Four circumstances were tested, and the model was used to predict the results: (1) the size of the grinding medium was changed, (2) the particle size and grinding intensity were covaried, (3) two particle sizes were mixed together, and (4) a different acid system was tried at varying temperatures. Materials Approximately 550 kg of serpentine rock dust was collected from the Cedar Hill quarry in Lancaster County, PA, and was ground and wet-sieved as described in part 2.3 The 38-73- and 73-140-µm fractions prepared in part 2 were used again in this study. All acids used in the experiments were ACS reagent grade or better. For experiments using 1 M sulfuric acid, 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 using nitric acid, the concentrations were prepared via standard volumetric dilution. Experimental Procedure The same experimental procedure was used here as was documented in part 2.3 * 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 samples were analyzed by inductively coupled plasma (ICP) analysis as in part 2.3 For samples generated with experiments using sulfuric acid, the sulfur concentration used in the experiment allowed for the calculation of all other species of interest without knowledge of the dilution factor based on molar ratios calculated from the mass concentrations determined by ICP spectrometry. Samples were diluted roughly 1000-fold by volume without careful mass dilutions. However, because ICP spectrometry cannot determine nitrogen concentrations, careful mass dilutions were performed for the nitric acid samples. Results and Discussion First, the parametric study3 used 3-mm glass beads, and it was desirable to know how the model would handle differentsized grinding media. Thus, the grinding medium was switched to 2-mm glass beads, and all else was held the same as the base case in part 2 (temperature ) 50 °C, agitator speed ) 200 rpm, acid concentration ) 1.012 M, acid volume ) 700 mL, grinding-medium mass ) 800 g, grinding-medium size ) 3 mm, particle size ) 38-83 µm, serpentine mass ) 70 g, and pump rate ) 4 L/min).3 The model was able to capture the behavior through the measured change in power density. Figure 1 shows the data collected, the 95% confidence interval, and the model predictions for the 2-mm grinding medium. The measured power density was 568 W/m3. This power density correlates to a temperature-proportional diffusion multiplier of 1.06 × 10-15 m2 s-1 K-1. At 50 °C, this results in an effective diffusivity of 3.43 × 10-13 m2/s, which is consistent with previous findings,3 as seen in Figure 2. Because the fit was good for this test, it was also desirable to investigate the system response to a change in size fraction and grinding intensity. Thus, the large-sieved serpentine fraction, 73-140 µm, was used, and the agitation speed was changed to 400 rpm. The measured power density was 2.49 kW/m3, which correlates to an effective diffusivity of 2.03 × 10-12 m2/s through Figure 2. This also produced a satisfactory fit, as seen in Figure 3, although the model underpredicts this case by about 2%. Even though 2% error is quite good, the predictions could likely be improved by a more detailed investigation of the relationship between power density and effective diffusivity.
10.1021/ie901159t 2010 American Chemical Society Published on Web 01/12/2010
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Figure 1. Model predictions with a change in media size. Figure 3. Model predictions for large particles at higher grinding intensity.
Figure 2. Relationship between effective diffusivity and mechanical power density at 50 °C.3
Third, it was desirable to investigate whether the model could match the behavior if two particle sizes were mixed in a known ratio. Thus, a 50/50 mixture of the 38-73- and 73-140-µm serpentine particles was tested. Figure 4 shows the results of this experiment, as well as the results from each fraction alone. The model predicted that the fractional conversion would lie precisely in the middle of the values for the two individual fractions. This would be expected for particles of the same shape factor. However, the experimental data show a conversion about 2% lower than predicted by the model. This is not far from the 95% confidence interval, but could suggest that there is a slight shape difference between the large and small particle fractions. However, without better instrumentation, there is no way to quantify this suspected difference. Finally, it was desirable to observe the system response and the model predictions for a different acid system. Hence, 1 M
Figure 4. Test and model predictions for a 50/50 particle mixture.
nitric acid was tested at different temperatures to assess the frequency factor and activation energy. Figure 5 shows the system response to nitric acid at various temperatures, along with the model predictions. As it turns out, a reduction in the frequency factor from 1.487 × 1016 to 0.60 × 1016 m4 mol-1 s-1 in addition to changing the solution chemistry thermodynamic model to nitric acid can adequately capture the temperature response. The frequency factor was determined by fitting the model to the data at 50 °C, and that value was then used to predict the other temperature profiles. The predictions matched the data quite well. There was no need to change the activation energy, which suggests that the rate-determining surface reaction mechanism does indeed involve only the irreversible decomposition of the protonated surface sites. However, the change in frequency factor does
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predict results within 2% conversion in every case tested. The model performed best at predicting changes in grinding media size and in the acid system. The model developed in parts 1 and 2 of this investigation was able to predict the kinetics of the acid digestion of serpentine under conditions that significantly differed from the test cases that were used to develop the model. The success of the model to reasonably predict dissolution kinetics shows the validity of the model. Acknowledgment Several people provided necessary components and skills for this research to occur. Joe and Doris Soltis provided financial support through generous giving to Penn State University. Henry Gong, Senior Analytical Chemist at the Materials Characterization Laboratory, Penn State University, gave his expertise in sample preparation and analysis for ICP. 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 wearresistant coatings for the agitators. Sincere appreciation for all of these gifts and efforts is deserved. Figure 5. Data, 95% confidence interval, and model predictions for the temperature response of the 1 M nitric acid serpentine system.
suggest that the solution composition can affect either the collision frequency or the steric factor. The reasons for this are unclear. What is true is that the collision theory is based on ideal-gas reactions and that the farther the system is from the ideal reaction, the greater the observed frequency factor shifts from the calculated value. The steric factor is nothing more than an empirical factor that relates observed successful collisions to the results calculated based on ideal conditions. Surface reaction mechanisms are quite far from ideal-gas reactions, and the frequency factor cannot be predicted. That said, it is apparent that the developed digestion model is able to predict the behavior under various acid systems if the acid dissociation constants are modeled in the solution chemistry model and if the frequency factor is determined from the fit to a single measured profile. Conclusions The model did indeed prove to be robust under conditions outside the initial parametric study. The model was able to
Literature Cited (1) 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. (2) 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 (5), 2556–2565. (3) Van Essendelft, D. T.; Schobert, H. H. Kinetics of the Acid Digestion of Serpentine with Concurrent Grinding. 2. Detailed Investigation and Model Development. Ind. Eng. Chem. Res. 2009, 48 (22), 9892–9901. (4) Van Essendelft, D. T. Kinetics of the Acid Digestion of Serpentine with Concurrent Grinding for the Purpose of Carbon Dioxide Sequestration. Ph.D. Dissertation, The Pennsylvania State University, University Park, PA, 2008.
ReceiVed for reView July 24, 2009 ReVised manuscript receiVed December 3, 2009 Accepted December 29, 2009 IE901159T
