Article pubs.acs.org/IECR
Constant Thickness Porous Layer Model for Reaction between Gas and Dense Carbonaceous Materials Eric A. Morris, Rex Choi, Ti Ouyang, and Charles Q. Jia* Department of Chemical Engineering & Applied Chemistry, University of Toronto, 200 College St., Toronto, Ontario, Canada, M5S 3E5 S Supporting Information *
ABSTRACT: Using oil-sands petroleum coke as the raw material and sulfur dioxide as the activating agent at 700 °C, the process of pore development in dense carbonaceous materials was studied. The time dependence of porosity was established from measured values of specific surface area (SSA), which could not be explained using conventional porous layer theories. Incorporating the Random Pore Model with measurements of particle size and porous layer thickness, a model was developed based on the existence of a porous layer of constant thickness. The model was found to accurately reproduce experimental time dependence of SSA. The results confirm a constant thickness of the porous layer for the activation conditions studied, which results from competing effects of carbon gasification reaction and penetration of the activating agent into the carbon particle interior. The model predicts a higher achievable SSA for a greater constant porous layer thickness, smaller initial particle size, and lower inorganic ash content. This model was found to be useful in predicting the maximum porous layer thickness of a dense material undergoing activation or gasification using only measured values of SSA, pore size distribution, and particle size as inputs.
1. INTRODUCTION In the modeling of gas−solid reactions, there are two general approaches that are used: homogeneous and heterogeneous models. Homogeneous models assume that a reacting spherical particle is initially porous, and thus there is no concentration gradient of reactant gas molecules, with respect to particle radius, and the reaction proceeds uniformly throughout. The most commonly cited of these is the Random Pore Model of Bhatia and Perlmutter,1 based on a randomized network of cylindrical pores situated in parallel while taking into account a distribution in pore size and effects of overlapping pores. Despite the development of more-advanced homogeneous models,2,3 the Random Pore Model continues to be widely used, because of the simplicity of its application and the fact that it uses parameters that can easily be obtained from measured physical properties of the raw material. Using the Random Pore Model, accurate simulations of reaction rate and specific surface area (SSA) development have been achieved in the gasification of agricultural wastes4 and coal chars.5−10 Heterogeneous gas−solid reaction models generally assume an initially nonporous solid, resulting in a strictly defined reaction front which propagates from the outside of the reactant particle toward its center. Perhaps the most widely known heterogeneous model is the shrinking-core model developed by Yagi and Kunii,11 in which the reaction produces an inert solid product through which gaseous reactant and product molecules diffuse. More refined approaches have incorporated limited diffusion into the solid core to produce a three-dimensional (3D) reaction zone12,13 and secondary reactions occurring within the porous intermediate layer,14,15 as well as modeling the particle as a cluster of densely packed grains, to each of which the Shrinking Core Model is applied as the reactant gas diffuses between them.16,17 © 2012 American Chemical Society
Relatively few studies have been conducted on the properties of the porous intermediate layer and how they may change over time. This is important in the activation of dense materials because the porous layer is expected to comprise the majority of an activated particle’s surface area. Braun et al.18 modeled the growth of a product layer during oxidation of a flat sample of glassy carbon by assuming that an intermediate product layer is formed through a diffusion controlled reaction at the carbon surface, while the product layer itself is consumed through a different chemical reaction. The model was found to agree with experimental data, in that the product layer thickness tended to plateau over time. Furthermore, the magnitude of the maximum thickness and the time needed to achieve it decreased with increased temperature. In a later study, Braun et al.19 fit a time-dependent equation for surface area to experimentally determined values of the Brunauer−Emmett− Teller (BET) SSA for glassy carbon particles activated in air at 450 °C. An accurate fit was obtained, despite the fact that a constant SSA and density were assumed for the porous product layer. However, activated carbon is typically produced from less-ideal materials such as coal, coke, and agricultural wastes, which contain significant fractions of inorganic ash. It is desirable to know what effect, if any, this ash will play in the development of the SSA. This study aims to elucidate the mechanisms behind SSA development during the activation of oil-sands fluid coke. This material is produced by multiple cycles through a fluidized bed coking unit during the upgrading of bitumen. This results in Received: Revised: Accepted: Published: 14376
July 24, 2012 September 27, 2012 October 17, 2012 October 18, 2012 dx.doi.org/10.1021/ie3019643 | Ind. Eng. Chem. Res. 2012, 51, 14376−14383
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pressures might have yielded more-accurate results; thus, BET SSA is reported as “apparent” BET SSA. Sample N2 adsorption isotherms and a QSDFT pore size distribution can be found in the Supporting Information (SI). Particle size measurements were obtained with a Malvern Instruments Mastersizer S, which utilizes laser ensemble light scattering to characterize aqueous slurries of particles. This technique measured the volume-weighted mean radius using the Fraunhofer scattering model, which was subsequently transformed using the Mastersizer software to determine the arithmetic mean particle radii. This was then fit to a linear equation, with respect to time:
roughly spherical particles consisting of concentric layers of dense, highly graphitized material that is composed of ∼82% carbon, ∼7% sulfur, and ∼6% inorganic ash.20 In this study, coke particles are modeled as a series of concentric, overlapping shells of uniform thickness, each of which is assumed to react homogeneously with SO2, according to the Random Pore Model. The shells react progressively toward the center of the particle to produce a heterogeneous porous layer. The rates of unreacted core and particle shrinkage are determined experimentally and used to predict SSA evolution, which is then compared to experimentally obtained values of the BET SSA. The activating agent used in this study was sulfur dioxide (SO2), which is of interest, since its reaction with fluid coke at high temperature has been shown to add sulfur functional groups to the carbon surface.21,22 Furthermore, there is recent evidence to suggest that these SO2-added sulfur groups are beneficial, with regard to adsorption of elemental mercury in both liquid and gaseous environments.23−25 This work is not intended to replace the relatively simple model of Braun et al.19 per se, but rather to provide a more-detailed picture of the porous layer during physical activation.
R = R 0 + αt
(1)
where R is the outer particle radius (μm), R0 the initial particle radius (μm), α the rate of decrease of particle radius (μm h−1), and t the time (h). Cross-sectional samples were obtained by embedding coke particles in 1-in.-diameter epoxy casts, polishing the surface, and carbon coating the sample. Images of these casts were obtained using a Hitachi field-emission scanning electron microscopy (SEM) Model S-4500 system. The rate of decrease of core radius was determined by examining the SEM cross sections at 500× magnification. Four different particles were selected for each activation time with the criteria that they be both relatively round and large. Larger, round particles were deemed more suitable, since they were more likely sectioned near the “equator,” and thus more accurately represent the true porous layer thickness. This thickness was measured using a fine ruler at eight equally spaced points around the particle circumference. The porous layer thicknesses were then averaged and subtracted from the particle size data to determine the core radius. OriginPro regression analysis software was then utilized to fit the data to an exponential decay function of the form
2. EXPERIMENTAL SECTION 2.1. Sample Preparation. Fluid coke was obtained directly from an upgrading facility in Alberta, Canada and screened to particle diameter ranges of 53−106 μm and 212−300 μm. Prior to activation, the coke was preoxidized by spreading ∼20 g on a watch glass and placing it in a Barnant muffle furnace at 250 °C for 18 h. Air preoxidation under similar conditions has been used previously to enhance pore development during activation of carbon materials.26−32 SO2 (99.95%) and N2 (99.997%) were supplied by cylinders and each set to flow at 100 cm3 min−1 by Aalborg mass flow controllers. The reactor was a 68 cm × 2 cm quartz tube suspended within a Carbolite vertical tube furnace. Approximately 10 g of coke to be activated was placed on a porous quartz disk located at the midpoint of the reactor. Gas samples were taken from the inlet and analyzed with gas chromatography to ensure the inlet SO2 concentration was stable at 50 vol %. The furnace temperature was then increased to 700 °C for the duration of the experiment (1−14 h). At the end of the experiment, SO2 was immediately shut off and the reactor allowed to cool under flowing N2. The activated coke sample was then weighed to determine sample burnoff. The apparatus and technique used for activation of coke samples has been described in greater detail elsewhere.22 2.2. Analysis of Samples. SSA, pore volume, and pore size distribution were measured by N2 adsorption at 77 K using a Quantachrome Autosorb-1-C. Forty (40) adsorption points between relative pressures of 0.025 and 0.995 were obtained and analyzed using the quenched solid density functional theory (QSDFT), available as an analysis kernel within the Quantachrome ASiQwin software. QSDFT is the preferred technique for characterizing pore size distribution of amorphous carbons, since it takes into account physical and chemical heterogeneity.33 The specific analysis kernel used assumed slit-shaped micropores (50 μm. A shell was considered “activated” when it is overlapped by the reaction front as it moves inward toward the particle center. The activated portion of that shell expands with the movement of the reaction front until it reaches its designated maximum thickness. This activated shell remains at constant thickness and volume until the outer edge of the porous layer (the slow reaction front) coincides with the outer edge of the shell. The activated portion of the shell then shrinks until it is completely consumed. Figure 1 illustrates how these spherical shells change with time to form the three regions of a coke particle undergoing activation: the unreacted core, the porous layer, and the wholly consumed outer layers. Although this method was developed independently, a similar approach was used by Mitchell et al.9 for the combustion of coal char in 6% oxygen. In that work, changes in particle dimensions were calculated analytically based on an oxygen mass balance, while particle dimensions were measured directly in the current study. The surface area for each active section is calculated using the Random Pore Model developed by Bhatia and Perlmutter:1 Si = S0(1 − Xi) 1 − ψ ln(1 − Xi)
Figure 1. A coke particle consisting of 11 spherical shells undergoing activation. Shells 1−3 were once activated, but are now entirely consumed; shell 4 is partly activated, with the activated portion shrinking; shells 5−7 are within the porous layer, and thus are currently activated; shell 8 is partly activated, with the activated portion growing; shells 9−11 are within the unreacted core, and are yet to be activated.
(3)
4πL0(1 − ε0) S0 2
(4)
V0(rP) rP 2
drP
(6)
4 π (R i 3 − ri 3) 3
(7)
Mi = Vi ρC (1 − Xi)
(8)
Vi =
ε0 is the void fraction of the unreacted coke, determined using the following relationship: VP0 ε0 = VP0 + (1/ρC )
0
∫∞
where rP is the pore radius (nm). More information regarding V0(rP) and how it is used to calculate L0 can be found in the SI. The fractional conversion of carbon within each shell i (Xi in eq 3) is assumed to increase linearly with time, starting from the point at which the shell is first breached by the porous layer and ending when it is fully consumed. It should be noted that increasing Xi represents carbon conversion in the form of increasing porosity, and it does not indicate a change in shell volume. A linear decrease in particle density, which is inversely proportional to an increase in porosity, was observed with increasing burnoff by Hashimoto et al., using coal and coconut shell char.35 Nevertheless, the small shell thickness used served to mitigate errors resulting from this assumption, even if it is not entirely accurate. The volume and mass for every porous layer section are calculated according to eqs 7 and 8:
where Si is the surface area per unit volume for spherical shell i (cm2 cm−3), S0 the initial surface area per unit volume of the unreacted solid (cm2 cm−3), Xi the fractional conversion of shell i, and ψ the Random Pore Model parameter: ψ=
1 πVP0
L0 =
where Ri and ri are, respectively, the outer and inner radii of the activated portion of spherical shell i (cm); Vi is the volume of this activated portion (cm3); and Mi is its mass (g). The single-particle mass is estimated using eq 3:
(5)
where ρC is the unreacted core density (estimated to be 1.5 g cm−3),34 and VP0 is the initial total pore volume (cm3 g−1). In eq 4, L0 is the length of pores per unit volume in the unreacted coke (cm cm−3), estimated via the QSDFT pore volume distribution function, V0(rP):
n
MP =
∑ Mi + ρC VC + 0.06ρC VPL i=1
14378
(9)
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Figure 2. Apparent BET SSA versus activation time (left), and coke burnoff (right) for particle diameter ranges of (◇) 53−106 μm and (●) 212− 300 μm.
where MP is the single particle mass (g), VC the volume of the unreacted core (cm3), and VPL the total volume of the porous layer (cm3). The expression 0.06ρCVPL represents the mass of ash in the porous layer, using 6 wt % as an estimate of the particle ash content.20 Equations 10 and 11 are used to calculate the amount of ash in the particle and ash that has been shed due to particle shrinkage since t = 0 (i.e., loose ash), respectively: MAP = 0.06ρC VC + 0.06ρC VPL
(10)
MAL = MAP,0 − MAP
(11)
The results of particle size analyses on activated coke from both size ranges is shown in Figure 3. Equation 1 was fitted to
where MAP is the mass of ash in the particle (g), MAP,0 the initial mass of ash in the particle (g), and MAL the mass of loose ash (g). The SSA is then found using the summed surface areas of all porous layer sections and the initial surface area: SSA =
n ∑i = 1 SiVi
Figure 3. Change in average particle size with time for particle diameter ranges of (◇) 53−106 μm and (●) 212−300 μm.
+ S0VC
MT
(12)
each data series, and the resulting parameters and correlation coefficients are shown alongside the points. In both cases, the decrease in average R with respect to time follows a linear trend. Despite the lower burnoff, the rate at which R decreases is somewhat greater for the larger particles. This can be explained as a result of the higher SO2 to external surface area ratio present with larger particles. Figure 4 shows cross-sectional SEM images taken for activated coke in the 53−106 μm size range. Upon visual inspection, it appears as though the porous layer, which appears as a pale outer band surrounding each particle, increases in thickness up to ∼4 h of activation. After this point, subsequent changes in δ are not apparent. Values of r were determined for each activation time based on measurements of R and δ. Within the range of 0−4 h, these were fit to eq 2, while those in the range of 4−7 h were fit to eq 1 (see Figure 5). It can be seen that the slope of the linear portion matches closely with that of R in Figure 4, which supports the existence of a constant δ. As previously mentioned, δ was not directly measured for the larger particles. Table 1 provides a summary of the important parameters used in this analysis, including those necessary for the Random Pore Model. 4.2. Effect of Maximum Porous Layer Thickness. Simulation of SSA development was performed for coke particles in the smaller size range (R0 = 36.6 μm) for three values of δmax: 10, 12, and 14 μm. These values were chosen based on the direct measurements of δ made using the SEM images in Figure 4: for the activation times of 4, 5, 6, and 7 h, measured values of δ were 11.4, 12.0, 12.0, and 12.3 μm, respectively. The best-fit parameters for eq 2 (y0, A, and n) as
where MT is the total mass of ash and particle, or the sum of MP and MAL (g). As a result of Assumption 1, eq 12 holds for both a single particle and for the bulk material. Lastly, burnoff is defined as the percentage weight loss of sample, including ash: burnoff (%) =
MP0 − M T × 100 MP0
(13)
where MP0 is the initial particle mass (g). Additional information that involves the setup of a spreadsheet for modeling porous layer development can be found in the SI.
4. RESULTS AND DISCUSSION 4.1. Characterization of Activated Coke. Figure 2 shows the change in apparent BET SSA with activation time and burnoff for two particle diameter ranges of petroleum coke activated with SO2 at 700 °C. For both diameter ranges, the SSA initially increased rapidly, then leveled off and appeared to begin to decrease. For the smaller diameter range, SSA peaked at 447 m2 g−1 at 5 h (63% burnoff), while the larger diameter range peaked at 244 m2 g−1 at 9 h (52% burnoff). According to conventional porous layer models such as the Shrinking-Core Model, SSA should plateau once the entire particle has become porous and then remain constant. Furthermore, the maximum attainable SSA should not be dependent on particle size. These observations suggest that a different mechanism is at work in this system, which led to the development of the conceptual model described in Section 3. 14379
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Figure 4. Cross-sectional SEM images of activated coke (53−106 μm initial diameter, scale bar = 200 μm).
δmax values of 10 and 14, which coincided with the observed time to reach δmax (4 h). The results of the simulation are shown in Figure 6, alongside the measured BET SSA data. Using a value of δmax = 12 μm, Figure 6 shows that the simulated results closely follow the measured BET SSA values. This verifies that homogeneous reaction models such as the Random Pore Model can be used to simulate SSA development in a heterogeneously reacting particle, provided that it is applied successively to individual volumetric segments. Reducing the value of δmax from 12 μm to 10 μm resulted in a lower achievable SSA. This result was anticipated, as the reduced porous layer thickness resulted in a lower porous volume for a given unreacted core radius. The core comprises the majority of a particle’s mass, but contributes very little surface area. On the other hand, increasing the value of δmax to 14 μm entails a larger porous layer volume-to-mass ratio, and thus results in a higher achievable SSA. The right side of Figure 6 shows the simulated and measured results plotted versus coke burnoff. The predicted SSA rapidly drops off after its peak value at ∼75% burnoff, because of the accumulation of inorganic mineral matter that has been shed by the reacting particles. Assumption 3 used in this model states that ash does not have any inherent surface area of its own and, thus, acts as dead weight. For the same reason, the SSA drops to zero at a burnoff of 94%, corresponding to the assumed ash content of 6%. 4.3. Effect of Initial Particle Size. Figure 7 shows the results of changing the initial particle diameter on SSA development, as predicted by the current model. The results shown were found assuming all particle sizes exhibited structural parameters identical to those found for the 53−106 μm particle diameter range. Although this would not be the case in reality (as shown in Figure 3, for example), this assumption is adequate for illustrative purposes. It is readily seen that a smaller initial particle size results in a higher achievable SSA, as was observed experimentally in Figure 2. This result comes about due to the limitation in porous layer thickness, which, for larger particles, means a lower porous layer volume-to-total-mass ratio. The limited value of δ also explains the drastic change in the shape of the SSA profile as particle size increases (i.e., a less-pronounced peak and more trapezoidal). The profile initially plateaus early as δmax is reached, and then proceeds to increase gradually as the particle mass diminishes over time. The peak is reached at the point
Figure 5. Change in unreacted core radius, outer particle radius, and porous layer thickness with activation time for coke with an initial diameter of 53−106 μm. Symbol legend: (◇) measured outer particle radius, R; (◆) averaged measured core radius, r; (×) porous layer thickness, δ = R − r. Line legend: linear fit for outer particle radius R (· · ·); exponential fit for unreacted core radius, 0−4 h (); linear fit for unreacted core radius, 4−7 h (− − −); fitted R − r, 0−4 h (solid gray line); and fitted R − r, 4−7 h (dashed gray line).
Table 1. Parameters Used in Simulation of Porous Layer and Surface Area Formation for Both Particle Diameter Ranges Measured Parameters R0 (μm) VP0 (cm3 g−1) S0 (cm2 cm−3) Derived Parameters ε0 L0 (cm cm−3) ψ Best-Fit Parameters α (μm h−1) y0 (μm) A (μm) n (h−1) δmax (μm)
53−106 μm
212−300 μm
36.6 1.12 × 10−2 2.87 × 105
110 6.45 × 10−3 1.23 × 105
1.67 × 10−2 2.08 × 1013 3.10 × 103
9.58 × 10−3 3.22 × 1013 2.64 × 104
−1.50 15.6 21.1 0.486 12.0
−1.90 54.5 48.3 0.116 16.0
shown in Table 1 are therefore suitable for a δmax value of 12 μm. These parameters were artificially altered in order to obtain 14380
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Figure 6. Comparison between measured SSA and simulated SSA using the current model plotted versus activation time (left) and coke burnoff (right) for different values of δmax, R0 = 36.6 μm. Symbol legend: (◇) measured BET SSA. Line legend: simulated SSA for δmax = 10 μm (solid line, ), simulated SSA for δmax = 12 μm (dashed line, − − −), and simulated SSA for δmax = 14 μm (dotted line, · · ·).
Figure 7. Predicted SSA evolution with activation time (left) and coke burnoff (right) over 50 h of reaction for different initial particle diameters. Symbol legend: measured BET SSA for particle diameter ranges of (◇) 53−106 μm, R0 = 36.6 μm, and (●) 212−300 μm, R0 = 110 μm. Line legend: simulated SSA for an initial radius of 2.5 μm (solid gray line), 5 μm (dotted gray line), 12 μm (dashed gray line), 25 μm (dotted black line, · · ·), 37.5 μm (solid black line, ), 50 μm (dashed black line, − − −), and 100 μm (dash-dotted black line, − · −). Best-fit parameters for the particle diameter range of 53−106 μm were used for all model results.
Figure 8. Predicted SSA evolution with activation time (left) and coke burnoff (right) for coke with an initial diameter of 12 μm (R0 = 6 μm) with different inorganic ash contents. Line legend: simulated SSA for ash content 0% (gray dotted line), 0.1% (solid gray line), 1% (dashed gray line), 3% (dotted black line, · · ·), 6% (solid black line, ), and 12% (dashed black line, − − −). Best-fit parameters for the particle diameter range of 53−106 μm were used for all model results.
where accumulating ash begins to offset the effect of decreasing particle mass, which is evident from the fact that all particle sizes reach their respective SSA peaks at roughly the same level of burnoff. The SSA peak is more pronounced for smaller particles, because of the fact that accumulating ash takes up a significant fraction of the total mass at an earlier stage, thus precluding the SSA plateau. An important observation to be made from Figure 7 is that the improvement in SSA that is attainable through using
smaller particle sizes is limited. Decreasing initial particle size from 24 μm to 10 μm gives little benefit in terms of maximum SSA, and a further decrease to 5 μm results in no enhancement at all. Because of their low initial radii, particles in this size range will be completely porous before δmax is achieved. Although this could conceivably result in a very high SSA, the weight of the inorganic ash contained within the coke rapidly becomes a limiting factor. Since this effect is stronger for 14381
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pores. The kinetic data of Bejarano et al.36 suggests that increasing the temperature from 700 °C to 800 °C would increase the rate constant by a factor of ∼6. On the other hand, not taking into account tortuosity effects, the diffusion coefficient is expected to increase with T3/2 (where T is temperature) according to the Chapman−Enskog theory. Thus, the increase in reaction rate would be much greater than that of diffusion, resulting in a decreased δmax in this diffusion-limited system. Conversely, decreasing temperature would bring about a greater value of δmax, which was previously noted by Braun et al.18 for flat sheets of glassy carbon. Thus, for dense materials that exhibit a constant porous layer thickness during physical activation, a lower temperature is anticipated to produce higher SSA values. In a practical setting, however, the benefits of using a lower temperature would need to be evaluated against the longer time needed to achieve maximum SSA. Future work will experimentally address the question of optimal activation temperature.
smaller particles, the achievable SSA effectively reaches a ceiling. It was initially assumed that, because of similar activation conditions, δmax would be the same, regardless of particle size. However, results indicate that this may not be the case. Figure 7 shows the experimentally determined BET SSA for fluid coke in the 212−300 μm particle diameter range (R0 = 110 μm), and it can be seen that the results predicted based on the best-fit parameters of the smaller particle size range significantly underestimate the SSA. As indicated in Table 1, a good fit for the experimental data was found using a different set of best-fit parameters: δmax was increased to 16 μm, while y0, A, and n were altered such that the time to reach δmax was increased to 10 h. The increase in both δmax and the time needed to achieve it for the larger particles is likely related to the greater rate of particle shrinkage (α) shown in Figure 3. As mentioned previously, a larger particle size results in a higher ratio of SO2 to external surface area. In other words, the SO2 supply at the particle surface was greater. The time at which δmax is reached is largely dependent on the difference between the fast and slow reaction rates at the unreacted core surface and the outer particle surface, respectively. An accelerated rate of carbon consumption at the outer edge of the porous layer would thus entail a longer time necessary to reach the point of becoming diffusion limited. Similarly, the diffusion of SO2 through the porous layer would be enhanced due to the higher concentration gradient, resulting in a greater value of δmax. 4.4. Effect of Inorganic Ash Content. Since most activated carbons are produced from inexpensive materials that contain considerable fractions of inorganic matter, the effect of ash content is an important factor in modeling SSA development during physical activation. Figure 8 shows the simulated SSA development for particles with an initial diameter of 12 μm while varying the ash content between 0 and 12%. The importance of ash content in determining the magnitude and timing of the SSA maximum is readily apparent: reducing the ash content of the raw material allows for a higher achievable SSA. The maximum SSA is effectively doubled from 600 m2 g−1 to 1200 m2 g−1 by decreasing the ash content from 6% to 0.1%. However, according to the model results, this degree of SSA enhancement is only attainable at a significantly higher activation time (∼2.5 h), at which the coke burnoff is virtually complete at 99%. For an ash content of 6%, the SSA maximum is reached at ∼1 h and 75% burnoff. At a similar burnoff level, the SSA of the 0.1% ash coke was greater by ∼150 m2 g−1. For practical adsorption situations, the potential benefits of an additional 150 m2 g−1 of surface area in the adsorbate would need to be weighed against the costs of acquiring or producing a raw material of such low ash content. For the case when the inorganic ash content is zero, the SSA is predicted by the current model to increase continually to well in excess of 2000 m2 g−1 as the activation time approaches 4 h. The reason for this exceptional result is the extremely large number of very small, highly porous particles that would be required to compose 1 g of material in the absence of ash. This finding is merely academic, however, as the extremely high burnoff that is required makes it virtually impossible to achieve in a real situation. 4.5. Effect of Temperature. Although the effect of temperature was not studied, it is interesting to surmise its impact on the porous layer. Increasing temperature would have the effect of raising both the C−SO2 reaction rate constant as well as the effective diffusion coefficient of SO2 through the
5. CONCLUSIONS A gas−solid reaction model was developed to explain observed trends in the surface area development of oil-sands petroleum coke activated with SO2 at 700 °C. This model was based upon a heterogeneous reaction system in which a porous layer of constant thickness is formed due to diffusion limitations. The Random Pore Model of Bhatia and Perlmutter1 was used to associate the specific surface area (SSA) with the porous layer dimensions. This homogeneous model was employed by dividing the particles into concentric spherical shells, to each of which the model was applied individually in sequence as specified by experimental data. For particles in the diameter range of 53−106 μm, the model accurately reproduces SSA development when a maximum porous layer thickness of 12 μm obtained after 4 h of activation is used. This finding was substantiated by direct observations of particle cross sections. For larger particles in the range of 212− 300 μm, the best fit was obtained when the maximum porous layer thickness was set to 16 μm and the time to reach this thickness was increased to 10 h. The reason for this difference is believed to be the greater ratio of SO2 to external surface area, which increases the SO2−carbon reaction rate in the outer porous layer. The model results predict that a greater SSA value is achieved with a thicker porous layer and by using particles of small initial diameter, although there appears to be a ceiling with respect to achievable SSA for particles
