Product Layer Diffusion during the Reaction of Calcium Oxide with

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Energy & Fuels 1999, 13, 999-1005

999

Product Layer Diffusion during the Reaction of Calcium Oxide with Carbon Dioxide Derek Mess,† Adel F. Sarofim,‡ and John P. Longwell* Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 Received December 10, 1998

The carbonation rate of 15-20 µm, nonporous, calcium oxide crystals has been studied over a temperature range of 550-1100 °C and a CO2 pressure range of 1-11.7 atm. At temperatures greater than 600 °C, the carbonation rate decreases more rapidly with time than would be expected from diffusion through a uniform product layer and the activation energy is initially low but increases with conversion. The product layer consists of crystalline grains, and these product layer grains grow by coalescence from less than one µm diameter to the approximate dimension of the particle. The carbonation rate can be described by a model where CO2 pressure-independent grain boundary diffusion and diffusion through the carbonate crystals act in parallel. The relative importance of bulk diffusion through the product layer crystals increases with time relative to transport through the grain boundaries and has an effective activation energy of 57 kcal/mol. Diffusion through the crystal boundaries has low activation energy and low dependence on CO2 pressure. At temperatures greater than 900 °C and times greater than 600 min, bulk diffusion through the product layer becomes dominant and the rate approaches first order in CO2 pressure.

Introduction The high-temperature reaction of calcium oxide with carbon dioxide is of importance in a number of proposed applications. Examples are (1) Advanced coal gasification processes such as The Consolidation Coal Companies CO2 Acceptor Gasification process, where the overall reaction is

2H2O + CaO + C f CaCO3 + 2H2 This reaction is exothermic and eliminates the need for oxygen to provide heat in the steam gasification step. [Since limestone (CaCO3) is the source of the calcium oxide, however, heat must be supplied in another step to form the oxide.] (2) The calcination cycle has been proposed as an energy storage and retrieval system.1,2 (3) CaO is used cyclically in the CO2 acceptor process where CO2 is removed from a mixture of hydrogen and CO2 by reaction with CaO. In all cases it is important to have reaction rates which are fast enough and of sufficient extent for practical use; however, for short cycles, the capacity of the stone has been found to decline when it is cycled between the oxide and the carbonate.3 In this work, it was noted that deactivation was accompanied by reduc* Author to whom correspondence should be addressed at MIT, Room 66-456, Cambridge, MA 02139. † Microtech, 19 Ward St., Somerville, MA 02143. ‡ University of Utah, 206 Kennicott Blvd., Salt Lake City, UT 84112. (1) Barker, R. The Reversibility of the Reaction CaCO3 S CaO + CO2. J. Appl. Chem. Biotechnol. 1973, 23, 733-742. (2) Barker, R. The Reactivity of Calcium Oxide Towards Carbon Dioxide and Its Use for Energy Storage. J. Appl. Chem. Biotechnol. 1974, 24, 221-227.

tion of pore volume and surface area. Knowledge of the rates of the several processes responsible for this deactivation is, however, quite incomplete. In particular, there is a dearth of information on the slow stage of carbonation where the pores in the original calcium carbonate have been filled or plugged by calcium carbonate and where access to the unreacted calcium oxide requires diffusion through the carbonate product layer. The onset of this slow stage limits the practical capacity of the lime. There is, however, an opportunity for regeneration of the deactivated lime by occasional complete carbonation in a separate process. This slow stage is important since it limits the conversion of lime in practical systems; however, it also offers an opportunity for regeneration of lime activity by complete recarbonation. The objective of this work is to further investigate product layer diffusion in the reaction CaO(s) + CO2(g) w CaCO3(s). Specifically, we seek to measure product layer diffusion rates as a function of CO2 pressure and temperature in a regime where gas-phase diffusional and heat transfer resistances are negligible, and the geometry of the solid phase is simple. This is done by carbonating nonporous, high purity CaO particles in a thermogravimetric analyzer which has been modified for pressurized operation. Literature Background Extensive work on the fast stage of recarbonation has been reported; however, few studies have been reported (3) Curran, G. P.; Fink, C. E.; Gorin E. CO2 Acceptor Gasification Process: Studies of Acceptor Properties. In Advances in Chemistry, Vol. 69, Fuel Gasification; Schora, F. C., Ed.; American Chemical Society: Washington, DC 1967; pp 141-165.

10.1021/ef980266f CCC: $18.00 © 1999 American Chemical Society Published on Web 07/22/1999

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Mess et al.

Table 1. Literature Results for Slow Stage Recarbonation Kinetics investigators Bhatia and Perlmutter5

dependence on PCO2

temp (°C)

particles

0 order

400-725

limestone particles 74-88 µm calcined in N2/CO2 at 310 °C

Oakson and Cutler4

853-1044

rate ) KDPCO2 (1 + bPCO2)-1 Dedman and Owen6

100-600

S ) 8.55-15.6 m2/g (mercury porosimetry) sample size: 1.3 mg nonporous calcium oxide particles about 40 µm surface area is unknown and varies sample size: 240 mg “bulk” limestone calcined at 900 °C in burning town gas S ) 5 m2/g (BET) sample size: 2 or 10 mg

on the kinetics of recarbonation in the slow, product layer controlled regime. These studies are summarized in Table 1. Oakeson and Cutler4 used nonporous particles of about 40 µm, measured sample sizes of about 240 mg, and carbonated them in a TGA under CO2 pressures between 2.35 and 24.67 atm, at temperatures between 853 and 1044 °C. Their results confirmed a parabolic rate law (the square of weight change was linear with time). However, they did not present their results in a particle size-independent rate law. Their particle size, and also surface area, changed from run to run. They found that CO2 pressure had a major effect on the rate, and postulated a Langmuir-type expression relating surface coverage to CO2 pressure. An approximate activation energy of 29 ( 6 kcal/mol was reported. Bhatia and Perlmutter5 studied the recarbonation of calcined limestone particles 74-88 µm in size. They modeled this porous material with a random pore model to account for geometry changes of the CaO/CaCO3 interface. This early use of the random pore model considered the product layer to be thin compared to the radius of the pore; this is equivalent to assuming that the concentration gradients are linear across the product layer. They estimated that this was valid for conversion up to 60%. Bhatia7 found that the diffusioncontrolled stage was independent of CO2 pressure, when sufficiently above equilibrium pressure (e.g., for CO2 partial pressures greater than 0.35 atm at 725 °C, where equilibrium CO2 pressure is about 0.06 atm). From 400 to 515 °C they determined an activation energy of 21.2 ( 0.9 (95%) kcal/g mol; from 515 to 725 °C they determined an activation energy of 42.8 ( 1.7 (95%) kcal/g mol. They reported their results in the form of an effective diffusivity, since the identity and concentration gradient of the diffusing species is unknown. This effective diffusivity was defined as

Deff ) DCsMCaO/FCaO

PCO2 (atm)

(1)

where D is the “true” diffusivity, Cs is the concentration (4) Oakeson, W. G.; Cutler, I. B. Effect of CO2 Pressure on the Reaction with CaO J. Am. Ceram. Soc. 1979, 62, 556-558. (5) Bhatia, S. K.; Perlmuter, D. D. Effect of the Product Layer on the Kinetics of the CO2-Lime Reaction. AIChE J. 1983, 29, (1), 7986. (6) Dedman, A. J.; Owen, A. J. Calcium Cyanide Synthesis. Part 4 - The Reaction CaO + CO2 ) CaCO3. Trans. Faraday Soc. 1962, 58, 2027-2035.

Eact (kcal/mol)

0.2-0.42

400-515 °C: 21.2 ( 0.9 515-725 °C: 42.8 ( 1.7

2.35-24.67

16 ( 9

0.013-0.789

9.5 ( 2

driving force (equal to surface concentration at the gas interface, and assuming zero concentration at the carbonate/oxide interface), MCaO is the molar weight of calcium oxide, 56.08 g/g mol, and FCaO is the molar density of calcium oxide, 0.0596 g mol/cm3. The random pore model suggests that the expression

((1 - ψ ln(1 - X))1/2 - 1)/ψ

(2)

is proportional to the square root of time in the case of product layer diffusion control. (X is conversion, and ψ is a pore structure parameter with a value of about 2.) When this function was plotted, there was a linear portion, the slope of which was used for determination of diffusion rate. This was generally for times ranging from between 1 and 480 min at a temperature of 400 °C, to between 15 and 100 s at a temperature of 725 °C, corresponding to conversions of 0.1 to 0.5 and product layer thickness of up to about 0.1 µm. After the linear portion, a gradual falloff in carbonation rate occurred; this was assumed to result from filling of the smallest pores. At temperatures below 788 K (515 °C), Bhatia and Perlmutter5 suggested the counter-diffusion of CO3) and O) ions in the solid state as a possible rate-controlling mechanism. At higher temperatures, above 788 K, they postulated a sequential dissociation of the CO3) ion within the CaCO3 lattice as a possible rate-controlling mechanism. Bhatia and Perlmutter5 viewed the structure of the carbonate product layer within the framework of the random pore model; that is, they assumed that it formed concentric shells parallel to the initial gas-solid interface. The product layer was assumed to be homogeneous. Diffusivity within the layer was assumed to be described by a single diffusion coefficient at a given temperature. However, they noted that the method of preparing the calcine affects its crystallinity and its subsequent recarbonation during the slow second stage. Dedman and Owen6 focused on lower temperature carbonation of a “ball” limestone. There is, however, a remaining need for studies of the “slow stage” which occurs subsequent to pore filling. Experimental Section Single crystal lumps of calcium oxide were obtained from Goodfellow Metals, Cambridge, England. Each crystal was (7) Bhatia, S. K. The Effect of Pore Structure on the Kinetics of Fluid-Solid Reactions. Ph.D. Thesis, University of Pennsylvania, 1981.

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Product Layer Diffusion during Reaction of CaO with CO2 Table 2. Summary of TGA Runs T (°C)

run #

PCO2 (atm)

550 600 600 650 650 650 676 677 700 700 700 750 750 750 750 750 800 800 850 850 850 900 900 900 925 925 950 950 1000 1000 1000 1000 1050 1050 1050

456 464 466 455 480 482 468 467 449 450 451 469 472 473 479 510 476 478 488 489 497 483 501 500 486 490 499 484 485 487 491 498 492 493 508

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 11.74 1 1 1 6.44 11.74 6.44 6.44 11.74 6.44 6.44 11.74 6.44 6.44 6.44 6.44 11.74 11.74 11.74 11.74

Table 3. Measured Grain Boundary Lengths

X1 min

Xf

tf (min)

0.02 0.03 0.03 0.04 0.02 0.03 0.10 0.09 0.08 0.11 0.11 0.14 0.11 0.12 0.05 0.13 0.07 0.07 0.02 0.03 0.01 0.08 0.09 0.08 0.13 0.07 0.08 0.06 0.06 0.09 0.08 0.04 0.08 0.09 0.23

0.12 0.09 0.11 0.21 0.07 0.12 0.21 0.22 0.31 0.29 0.42 0.27 0.28 0.36 0.18 0.46 0.29 0.20 0.20 0.41 0.57 0.42 0.48 0.70 0.58 0.48 0.73 0.44 0.30 0.64 0.48 0.73 0.69 0.82 0.72

2412 880 2100 1573 940 1500a 1200 1420 3822 2530 5876 1060 780 2460 1140 175 1876 680 350 700 1960 780 520 2380 780 2322 2060 1520 520 1920 1500 2060 540 1920 440b

a After 1500 min at 650 °C, the temperature was raised to 850 °C for 270 min. b After 440 min at 1050 °C, the temperature was raised to 1080 °C for 940 min.

approximately 1 g in weight. The material was 99.9% pure (manufacturer’s specs). This was verified by a semiquantitative emission spectrographic analysis (Huffman Laboratories, Inc.) which indicated 0.02% Al and 0.07% Si impurities, and a detectable quantity of Na, which was less than 0.02%. Powders of nonporous calcium oxide were prepared by crushing, grinding, and sieving the single crystals under de-watered hexane inside a glovebox, purged with dried nitrogen. The material in the 15-20 µm size fraction was used in this study. Each batch of 15-20 µm powder was stored under dewatered hexane in a glass weighing jar. Its cap was sealed with vacuum grease in the glovebox. An eyedropper was used to “suction dredge” a slurry of the 15-20 µm powder from the bottom of the jar. Several drops of slurry were dried at a time in a platinum boat, which was suspended in the TGA, where the material was heated to about 130 °C under dry nitrogen for several minutes. A Dupont 951 TGA was used in this study as a microbalance with the pan suspended in a hot reaction chamber. This TGA was used in research by Doerr8 and Chrostowski9 and is well described in their theses. Resolution is about 5 µg, and typical sample size is 3 mg. The limiting factor in measuring fast reactions is the time required for gas changeover. At atmospheric pressure, this is several seconds; at 12 atm, absolute gas velocities within the reactor are small and it takes about a minute to effect complete gas changeover (from N2 to CO2, for instance). A flow manifold allows several gases to be (8) Doerr, W. W. The Effects of the Magnesium Constituent on the Removal of Sulfur Dioxide by Fully Calcined Dolomite. Ph.D. Thesis, Massachusetts Institute of Technology, 1979. (9) Chrostowski, J. W. Regeneration of Spent Sulfided Dolomite. Ph.D. Thesis, Massachusetts Institute of Technology, 1980.

T (°C)

run #

tt (min)

Xt

LA (90%) (cm-1)

600 650 650 650 676 700 750 750 750 750 750 800 850 850 850 850 900 900 950 950 1000 1000 1000

466 455 480 482 468 451 472 473 479 509 510 478 457 488 489 497 483 501 484 499 485 487 498

2100 1573 940 1500 1200 5876 780 2460 1140 594 175 840 3860 350 700 1960 780 520 1520 2060 520 1920 2060

0.11 0.21 0.07 0.11 0.21 0.42 0.28 0.36 0.18 0.44 0.46 0.21 0.53 0.12 0.41 0.57 0.42 0.48 0.44 0.73 0.30 0.64 0.73

7700 ( 2300 6200 ( 2100 8400 10100 5500 ( 400 6400 ( 2300 3000 ( 900 1100 ( 300 1800 ( 400 6000 ( 1000 12500 ( 2000 1180 ( 160 750 2900 ( 1100 780 5400 1400 1500 1500 ( 400 1300 ( 640 1500 180 ( 40 1200

no. of particles examined 6 4 2 1 4 6 5 4 3 6 7 4 2 4 3 1 2 2 7 2 1 7 2

metered and fed to the reactor from cylinders. In this work, N2 and CO2 were used. The high-pressure TGA was located in a blocked-off area and all controls were outside this area and were protected by walls. Used hexane was collected for disposal by the MIT safety office for subsequent transfer to an outside company for final disposal. Two methods were used in determining the length of grain boundary on a given particle. Where several contiguous grains were visible in a mosaic pattern on the surface of a particle, length of grain boundary per unit surface area, LA, of the reacted particle was measured from the SEM picture by using the line intercept method of quantitative stereology.10 By counting intersections of grain boundaries with a grid of lines, the number of intersections per unit length, PL (LA)-1 is recorded, and from this

LA ) (π/2)PL (cm-1)

(3)

is determined. For this to be strictly true, the grain boundaries must be oriented randomly with respect to the test grid and they must lie in the plane of the grid. The first condition is satisfied by overlaying the grid upon the SEM picture 6 times, each with a different orientation. The second condition is harder to satisfy, since the SEM records the three-dimensional surface of the particle, and not a plane. Grain boundaries were counted only where a face of particle lay approximately in a plane parallel to the image plane. The error associated with this is estimated by assuming that the plane of the face of the particle is, on average, about 10° misaligned with the image plane. The measurement would overpredict PL by a factor of (1/cos 10°), or 1.015. This was not corrected for since the error is so small. A line spacing of 0.5 cm was used on SEM pictures at a magnification of 4000, or 1.25 µm at the particle scale. Table 4.2 presents values of PL and LA. Where only 1 or 2 grains and/or boundaries were visible on the face of a particle, grain boundary length was measured directly from SEM pictures with a ruler. Again measurements were made only where the face of the particle lay largely in a plane parallel to that of the image. It is difficult to estimate the error inherent in this technique, but the values for LA did not generally vary by more than about 20%. (10) Underwood, E. E. Quantitative Sterology; Addison-Wesley: Reading, MA, 1970.

1002 Energy & Fuels, Vol. 13, No. 5, 1999

Figure 1. Selected carbonation conversion histories.

Results TGA Conversion Histories: General Observations. Data from the TGA were transformed into conversion vs time data. Table 2 shows the temperature, CO2 pressure, conversion at 1 min, final conversion, and final time for the experimental runs. The 15 -20 µm starting material was from the same sample for each run. Temperatures ranged from 550 to 1100 °C and CO2 pressures from 1 to 11.7 atm. Some runs were terminated after as little as 2 h, but most lasted 10 to 40 h, with several that are substantially longer. Figure 1 illustrates the conversions with time of four selected runs, chosen to demonstrate the range in behavior. At low temperature, 602 °C, and atmospheric CO2 pressure, a prompt step of several seconds duration and a 1 min conversion of 0.0349 is followed by a slow increase in weight, to a final conversion of 0.1114 after 2100 min. At 800 °C under 1 atm of CO2, run #476 illustrates that the early reaction rate, in the minutes following the prompt step, is much faster, but declines rapidly, so that reaction rate is quite low for times greater than ∼800 min. At 850 °C, under 11.74 atm of CO2, run #497, the initial “slow” stage rate is faster, but also declines to a slower rate. At 1050 °C and 11.74 atm, the initial slow stage carbonation curve is steeper, and the long-term rate is higher than at 850 °C. The reaction is 82% complete after 1920 min. Figure 2 shows results for a typical particle from run #466 (reacted at 600 °C for 2100 min under 1 atm CO2 pressure). “Prompt” conversion was X1 ) 0.035 (indicative of a starting material which was not significantly hydrated), and final conversion was X ) 0.111. The grain boundaries were easily observed, and grain sizes were less than 1 µm. Figure 3 presents a photograph of a particle processed in run #472. Intergranular cracking is a prominent feature. Scanning Electron Microscope Observations at Intermediate and High Conversions. Specimens from about 30 different carbonation runs were examined with the SEM. Reaction temperatures ranged from 550 to 1100 °C, CO2 pressures from atmospheric to 11.74 atm. Overall particle shape was more rounded than that of the parent CaO, the more so as conversions increased. Generally, an adherent product layer was observed. The observed morphologies support the concept of a product layer whose thickness is approximately uniform but made up of grains which were characteristic of a

Mess et al.

Figure 2. Conversion vs time for carbonations at 600 °C and 1 atm CO2 pressure.

recrystallized structure whose boundaries met at 120° angles. These grains were roughly polygonal, and grain size distributions were essentially normal. The length of grain boundary per unit surface area, LA, was measured. LA and average grain size, Dg, were found to be related by

LA ) 2/Dg

(4)

At very long times and low temperatures (e.g., 5876 min at 700 °C in the case of run #451) or shorter times at higher temperatures (e.g., several hundred minutes at 850 °C), other crystalline features appear. Closely spaced ledges are found on parts of the particle surface. Small regions of the surface develop facets (crystal orientations of low surface energy), indicating significant anisotropy in surface energy with crystal orientation. Grain Boundary Length Measurements Grain boundary length per unit area (LA) ranged from about 12500 cm-1 for run #510 at 750 °C, down to almost no boundaries for the highest temperatures. Grain boundary lengths are presented in Table 3 and are plotted as a function of time in Figure 4. The uncertainty for LA is large, due to the small number of particles examined at each condition. Visual evidence indicates that small grains are present at short times, and undergo grain growth in the plane of the free surface at temperatures of 600-700 °C. Over this temperature interval, grain boundary length per unit surface area reaches an asymptotic value of about 6000 cm-1. At temperatures of 750 °C and above, grains grow continuously until grain boundaries are a scarce feature. Grain growth is more rapid at higher temperatures. Discussion Rate-Controlling Mechanisms. The rate data are interpreted assuming spherical geometry. Equivalent spheres with the same surface area-to-volume ratio as the starting material used here are 10.3 µm in diameter. If chemical reaction at the CaO/CaCO3 interface were to control the rate of reaction of these non-porous particles, the rate would depend on the area of that interface, which for a sphere would be

Product Layer Diffusion during Reaction of CaO with CO2

Energy & Fuels, Vol. 13, No. 5, 1999 1003

Figure 3. Particle from run #472: the CaCO3 product layer has undergone intergranular cracking, exposing the CaO core. Bar ) 10 µ. Product layer thickness is about 1-1.5 µm, T ) 750 °C, PCO2 ) 1 atm, X1 ) 0.11, X1 ) 0.28, t1 ) 780 min. LA for this run is 3000 ( 900 cm-1.

Ainterface ) 4πri2(1 - X)2/3

(5)

where X is the fractional conversion of the CaO to CaCO3. Figure 5 illustrates the shape of the conversion curves that would arise under interface (chemical) control and also for product layer diffusion control, calculated by matching the initial rate of the slow stage, and compares them to typical conversion data (run #499). In Figure 6, measured rate is plotted against product layer thickness for three different CO2 pressures at 850 °C. While reflecting a trend of increased rate with CO2 pressure, the rates are clearly not first ordersor even fixed orders in CO2 pressure.

High-Temperature, Steady-State Diffusivities. SEM micrographs show that at high temperatures (850 °C and above), after several hundred minutes, there are virtually no grain boundaries left, and partially reacted particles are very rounded. The shape of the conversion curve at long times is suggestive of a steady-state bulk diffusional process. For spherical particles, one would expect rate, R, to obey:

( )

rorc dr (1/ro - 1/rc) ) (4πDeff∆CCO2) dt ro - rc

F

(6)

Steady state rates from run #’s 484, 499, 487, and 498, shown in Figure 7, indicate an approximately first-order

1004 Energy & Fuels, Vol. 13, No. 5, 1999

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Figure 4. Length of grain boundary per unit surface area, LA, as a function of time and temperature.

Figure 7. Rate vs concentration gradient for two runs each at 950 and 1000 °C, showing order of unity.

Figure 5. Comparison of typical conversion data with the conversion curves expected for a rate controlled by a (chemical) step at the CaO/CaCO3 interface, and by diffusion through the product layer with constant diffusivity, respectively. Figure 8. Effective diffusivity is seen to be virtually constant for times greater than about 600 min.

Figure 6. Rate as a function of product layer thickness (µ) for carbonations at 850 °C at three different CO2 pressures.

dependence of reaction rate on concentration gradient at high temperatures (950 and 1000 °C) and long times (620 min). Effective diffusivities for the steady-state portion of the high-temperature runs are calculated from eq 6. Figure 8 shows that effective diffusivity is approximately constant for a typical high-temperature run (#493; 1000 °C) for times greater than about 600 min. These effective diffusivities are also plotted against reciprocal temperature in Figure 9, and effective product layer diffusion coefficients can be described by

Deff ) 0.65 (cm2/s) exp(-56.9 (kcal/g mol)/kT)

(7)

The activation energy for diffusion of 56.9 kcal/g mol, determined from the slope, is much lower than the 88

Figure 9. High-temperature, steady-state effective product layer diffusivities, based on the concentration driving force, CCO2 - CCO2eq.

kcal/mol measured for lattice diffusivities in single crystals of calcite.11,12 This suggests a difference in defect structure between these reaction-formed, calcite product layers, and large, optically clear single crystals. Kronenberg et al.12 observed an order of magnitude reduction in diffusivity of carbon in the calcite lattice (11) Anderson, T. F. Self-Diffusion of Carbon and Oxygen in Calcite by Isotope Exchange with Carbon Dioxide. J. Geophys. Res. 1969, 74, (15), 3918-3932. (12) Kronenberg, A. K.; Yund, R. A.; Giletti, B. J. Carbon and Oxygen Diffusion in Calcite: Effects of Mn Content and PH2O, Phys. Chem. Miner. 1984, 11, 102-112.

Product Layer Diffusion during Reaction of CaO with CO2

by annealing the crystal at 700 °C for 24 h. This indicates that the history of a crystal influences its structure and the diffusivity. Thus, initially, rate shows a less than linear dependence on CO2 pressure, yet after long times at high temperatures, rate is first order in CO2 pressure. This suggests that there is a change in the dominant mechanism for transport. The rate decreases with increasing product layer thickness for a given ∆PCO2. Comparing the results at 5.9 and 11.2 atm driving force (Figure 6), the rate is approximately proportional to pressure drop across the layer for a layer thickness greater than 1.0 µm and is less responsive to ∆p for thinner layers. If we then consider that two independent and parallel processes are taking placesone a diffusional process that is proportional to LA and is independent of the CO2 driving force at the CO2 pressures being used, and the second is a bulk diffusional process of CO2 through the CaCO3 crystals which cover the surface but increase in thickness with timesthe major features of the above observations can be modeled by eq 6. Examination of Figures 1, 2, and 4 indicates a finite carbonation rate at low conversions indicating a finite reaction at the CaO surface. This rate at low conversion was modeled by assuming that it was proportional to access of the CO2 to CaO surface by grain boundary diffusion and that, for the conditions reported here, was independent of the CO2 pressure driving force (CCO2 - CCO2eq).

FdR/dt ) 4πLADgb+ 4π (CCO2 - CCO2eq)Deff/(1/ro -1/rc) (6) The first term describes diffusion through the grain boundaries and is proportional to the grain boundary length, LA, which decreases with time as the carbonate crystals grow by coalescence but is independent of ∆C. The second term represents diffusion through the crystals to the surface of the inner sphere of calcium oxide where it reacts to form the carbonate. For runs where the CO2 pressure is varied, the unknowns LA and Dgb, for the crystal boundary diffusion and the unknowns Cn and Deff, for diffusion through the carbonate layer, can be determined by simultaneous solution of results from runs at two different temperatures. The runs at 850 °C (Figure 6) are of particular interest, since they encompass three different pressures. The effective diffusivity, Deff, determined this way at 850 °C from runs 489 and 497 is plotted vs time in Figure 8 and is seen to decline with time. Run #489 does not extend past 700 min, and Deff is still decreasing. The Deff calculated from the slope at 1900 min, assuming no grain boundary contribution, is still slightly above the trend line of the other high-temperature steadystate diffusivities. The behavior is consistent with an annealing of the CaCO3 lattice with time, which reduces the effective diffusivity, as noted by Kronenberg et al.13 At 120 min the grain boundary component contributes

Energy & Fuels, Vol. 13, No. 5, 1999 1005

64% of the total reaction rate; this declines to about 30% at 680 min. Unfortunately, the data for the first few hundred minutes of the runs at 950 and 1000 °C embody too many experimental artifacts to accurately establish values for Deff, but the shape of the conversion curves is consistent with rapid grain growth with grain boundary diffusion giving way to a bulk diffusion controlled regime. Conclusions (1) The carbonation rate of 20 µm CaO nonporous crystals is initially rapid but decreases more rapidly with time than would be expected from diffusion through a uniform product layer. (2) At temperatures of 600 °C and above, the CaCO3 product layer on the CaO particles comprises crystalline grains, whose boundaries form approximately 120° angles. Grain size varies from less than 1 µm to as big as the whole particle (20 µm). (3) Product layer grains grow by coalescence, and the grain growth rate is dependent on temperature; as grains grow, grain boundary length per unit surface area decreases. (4) As grains grow and the length of grain boundary per unit surface area decreases, the rate can be described by a dual mechanism where an activated, CO2 pressure-independent process acts in parallel with bulk diffusion through the product layer (which is first order in CO2 pressure). (5) The importance of bulk diffusion through the product layer crystals increases with time, relative to transport through the grain boundaries. (6) At temperatures of 900 °C and above, carbonation kinetics for 15-20 µm nonporous particles at times greater than 600 min are consistent with bulk diffusion through the product layer, and rate is first order in CO2 pressure driving force. (7) Diffusion through the grains is characterized by an activation energy of 57 kcal/g mol, much less than the value of about 88 kcal/g mol reported in the literature for solid-state diffusion in single calcite crystals. This, and the faster diffusion rates, suggest that this reaction-formed CaCO3 product layer has a “less perfect” structure than large, optically clear single crystals. Nomenclature Deff D Dg MCaO X ψ Cs ∆CCL LA PL k

effective diffusivity, cm2/s diffusivity, cm2/s average grain size molar wt of CaO g/g mol conversion pore structure parameter CO2 surface concentration concentration difference across carbonate layer length of grain boundary per unit of surface area number of grain boundary intersection per unit length gas constant EF980266F