2332
Ind. Eng. Chem. Res. 1997, 36, 2332-2339
Hot Gas Desulfurization with Zinc Titanate Sorbents in a Fluidized Bed. 1. Determination of Sorbent Particle Conversion Rate Model Parameters J. T. Konttinen,*,† C. A. P. Zevenhoven,‡ and M. M. Hupa‡ Carbona Corporation, P.O. Box 610, FIN-33101, Tampere, Finland, and Department of Chemical Engineering, A° bo Akademi University, Lemminka¨ isenkatu 14-18 B, FIN-20520 Turku, Finland
Regenerable mixed metal oxide sorbents are the prime candidates for the removal of hydrogen sulfide (the main pollutant) from the hot coal gas in the simplified integrated gasification combined cycle (IGCC) processes. As part of the sulfur removal process development, Carbona Corp. is developing fluidized bed reactor models for scale-up. It is essential for this work to apply a reliable and simple correlation for the conversion rate of zinc titanate or hydrogen sulfide in the sulfidation reaction. Two different models, the unreacted shrinking core (USC) model and overlapping grain (OG) model, are applied to this purpose. The parameter values obtained from ambient pressure tests are compared with those reported earlier for zinc titanates. Potential reasons for the differences are discussed. In the modeling of high-pressure sulfidation data, reaction rate constants from the literature are used, thus leaving the product layer diffusion coefficient as a fitting parameter. The values obtained indicate a linear dependence on process pressure. Introduction The simplified IGCC (integrated gasification combined cycle) process incorporates pressurized fluidized bed gasification of solid fuels and a hot gas cleanup train including a sulfur removal process with a regenerable sorbent (Salo and Hokaja¨rvi, 1994; Salo et al., 1995). The IGCC process has the advantages of improved power generation efficiency, high power-to-heat ratio for cogeneration, excellent environmental performance and simple plant configuration and modularity. The use of regenerable sorbents instead of once-through Ca-based sorbents (limestone, dolomite) for sulfur retention has recently received more attention primarily due to problems associated with disposal of large amounts of solid wastes generated with nonregenerable sorbents. With the use of regenerable sorbents, the amount of solid waste produced is minimized and the fuel-bound sulfur can be recovered as a commercial product, such as elemental sulfur (Portzer et al., 1995). Zinc titanate appears to be the leading sorbent for high-temperature high-pressure (HTHP) sulfur removal in fluidized bed reactors (Harrison, 1995; Salo et al., 1995). As part of sulfur removal process development, reactor models are needed for scale-up. It is essential for this work to apply a reliable and simple correlation for the conversion rate of a solid sorbent such as zinc titanate in the sulfur capture reaction. Several models to describe the gas-solid sulfidation reaction are available (Lew, 1990; Fenouil and Lynn, 1995; Zevenhoven et al., 1996). One of the basic models is the unreacted shrinking core model (USC), for this purpose generalized in order to account for changing effective diffusivity. A more advanced model is the overlapping grain model (OG), which was successfully applied to zinc titanate sulfidation results (Lew, 1990; Lew et al., 1992a). A reliable solid conversion model, together with fluidized bed mass and energy balances, can be used to predict the performance of a large-scale sulfidation reactor. In addition to this steady-state scale-up design, a dynamic † ‡
Carbona Corp. A° bo Akademi University. S0888-5885(96)00686-0 CCC: $14.00
Table 1. Composition of Simulated Coal Gas Used in Atmospheric TGA and High-Pressure Fluidized Bed Kinetic Tests (Mojtahedi and Abbasian, 1995a; Mojtahedi et al., 1996) compd H2 CO H2O CO2 CH4 H2S N2
in TGA, vol % 14.1 25.5 5.4 5.0 0.5, 1.2 balance
in fluidized bed, vol % 13 18 11 8 2.5 0.15, 0.02 balance
reactor model (based on the same elements) can be used for process control system design and operator training. This paper concentrates on the experimental results of some laboratory-scale tests in order to determine kinetic parameters for the zinc titanate sulfidation rate models. The modeling work will continue in a separate paper (Konttinen et al., 1997), where the application of the USC and OG model parameters into HTHP bench-scale fluidized bed sulfidation test data (gas conversion versus solid conversion) will be reported. Experimental Methods The kinetics of sulfidation with a zinc titanate sorbent, designated here as “A” (UCI-3 or L-3758) was evaluated in a thermogravimetric analyzer (TGA). The simulated sulfidation gas used in the TGA experiments consisted of all the relevant components typical for a U-gas (air-blown) gasifier gas, including H2S in contents of 0.15-1.2 vol %. The detailed gas composition is shown in Table 1. The experiments were conducted using a DuPont 951 TGA (Gupta and Gangwal, 1992; Mojtahedi et al., 1996) designed to handle corrosive gases. Approximately 50 mg of the sorbent in the 100300 µm size range was used in each experiment. All experiments were conducted at 1.013 bar and sulfidation temperatures in the 400-600 °C range were investigated (Mojtahedi et al., 1996). Each run consisted of first heating the sample to the reaction temperature in helium followed by 15-min exposure to H2S-free U-gas to equilibrate conditions in a reducing © 1997 American Chemical Society
Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997 2333
environment. Sulfidation was then conducted for 90100 min using the simulated U-gas containing H2S at the desired concentration. Kinetics of the reaction were evaluated using the weight change (which is directly related to reaction stoichiometry) versus time curve during sulfidation. A very small weight change was observed during the initial 15-min exposure to H2S-free U-gas. A unique HTHP reactor system has been used to evaluate candidate sorbents in cyclic sulfidation/regeneration tests (Abbasian et al., 1994; Mojtahedi and Abbasian, 1995a,b). The test unit includes simulated hot coal-gas-derived gas feed systems, a 7.5 cm diameter fluidized bed reactor with associated process instrumentation and control devices. The cyclic sulfidation/ regeneration tests conducted with 500 g batches of zinc titanate will be analyzed in part 2 (Konttinen et al., 1997). In conjunction with the cyclic tests, the rate of sulfidation of the zinc titanate sorbents was experimentally determined in kinetic tests, where 15 g of zinc titanate “B” (UCI-2) and “C” (UCI-4) was fluidized at typical process conditions (550-650 °C and 20 atm) in gasifier gas (Table 1) (Mojtahedi and Abbasian, 1995b). The mixing of the small sample by fluidization will eliminate any possible sample bed diffusion effects, which can be a problem in TGA experiments. The data obtained with the test arrangements presented above will be presented in the modeling section of this text. Gas-Solid Reaction Models as Part of a Fluidized Bed Reactor Model The sulfidation reaction of zinc titanate was represented by Lew (1990) and Lew et al. (1992a) with the following:
1/xZnxTiyOx+2y(s) + H2S(g) F ZnS(s) + y/xTiO2(s) + H2O(g) (1) In sulfidation with zinc titanates at gasification conditions, the reactive gas is hydrogen sulfide (H2S), although a small fraction of carbonyl sulfide (COS) is present (Mojtahedi et al., 1994). The reactive solid can be assumed to be Zn, ZnO, or some crystal form of zinc titanate, as used by Lew et al. (1992a) in eq 1, taken into account by the stoichiometry constant 1/x. During the cyclic sulfidation/regeneration tests, Mojtahedi and Abbasian (1995a,b) reported the possible formation of different crystalline structures of the zinc titanate, in which case Zn or ZnO can be assumed as the solid reactant. The gaseous compounds H2 and CO present in experimental gas mixtures (see Table 1) can reduce the amount of reactive zinc oxide during sulfidation. However, Lew et al. (1992b) observed no effects of H2 on sulfidation kinetics when using zinc titanates. On the basis of this and the findings by Gupta and Gangwal (1992) with gases containing CO and H2, it is assumed here that the relative contribution of sorbent reduction to the rate of sulfidation is insignificant. An essential characteristic of noncatalytic gas-solid reactions like sulfidation, where a solid product is produced, is the changing internal structure of the particle (Zevenhoven et al., 1995, 1996). Another aspect that cannot be neglected is that during conversion, a product layer gradually builds up, separating the solid reactant from the gas phase. Due to this, intraparticle transport of mass is strongly affected by the progress
of conversion. Several models to describe the combined effect of chemical kinetics and formation of solid product layer on the rate of gas-solid reaction have been developed (Zevenhoven et al., 1995, 1996; Lew, 1990; Fenouil and Lynn, 1995). However, as with all models which try to approximate the real behavior, the computational complexity is high, which can become a problem when these models are implemented into a reactor model. For (fluidized bed) sulfidation reactor modeling purposes, it is desirable to have a gas-solid reaction model with the following properties: (1) the model should be able to describe the rate of gas-solid reaction with a minimum of numerical iteration and still take the sorbent’s physical properties into account; (2) it has to have a minimum number of adjustable parameters; (3) the adjustable parameters should have a logical dependence on process variables like temperature and pressure. Conventional Unreacted Shrinking Core Model: External Mass Transfer In order to get insight into reaction mechanisms and to determine parameters on reaction kinetics, mass transfer, and diffusion, the unreacted shrinking core (USC) modeling approach can be used as a first approximation (Levenspiel, 1972, 1989; Zevenhoven et al., 1995, 1996). A rate-determining mechanism can be distinguished from a set of time-conversion data by plotting a function f(X) vs t/τ, which gives a straight line for the rate-determining step. For more than one ratedetermining mechanism the principle of “additive reaction times” applies (Sohn, 1978). In order to evaluate the effect of sample bed diffusion with the USC model, the geometrical shape of the solid sample in the TGA should be known. The shape of the solid sample in the TGA can be approximated by a hemisphere. The distance for the reactant gas to diffuse to the center of the sample bed equals the radius of the hemisphere which can be obtained from 3
Rb )
x
3Ws 2πFbulk
(2)
where Ws is the weight of the sample (50 mg), Fbulk is the bulk density of the sorbent (1.24 g/cm3 for A), and Rb is the radius of the hemisphere (cm). For the case with more than one mechanism controlling the rate, the relative importance of the sample bed diffusion can be found by the ratio tsbd/ttot, where
tsbd ) τsbd(1 - 3(1 - X)2/3 + 2(1 - X)) τsbd )
and Rb2Fmol,s (3) 6Deff,sbdCAb
where ttot is the time for reaching a certain sorbent conversion (s), Deff,sbd is the effective sample bed diffusion coefficient (m2/s), and tsbd is the time scale for sample bed diffusion (s). The determination of the effective diffusivity in the sample was recently reported by Zevenhoven et al. (1995). If the time taken for sample bed diffusion has some significance to the total time to reach a certain sorbent conversion level, further analysis of the TGA data can be omitted. Sample bed diffusion is not a problem in the tests in the pressurized fluidized bed reactor. The importance
2334 Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997
of diffusion in the solid particles and chemical reaction will be studied in detail in the following section. Models Selected To Fit the Experimental Results With respect to the selection criteria presented earlier, the unreacted shrinking core model (USC) and overlapping grain (OG) will be fitted to the experimental data. The USC model assumes the unreacted shrinking core of the particle as the reaction surface, for which the initial value equals the particle external surface area of the solid particles. In the OG model, the sulfidation rate is proportional to the reactive internal surface area of the porous particles, for which the initial value is obtained by mercury porosimetry. Thus, the latter follows the real physical behavior of the sorbent in sulfidation more closely than the former. The USC model is included because of the possibility of obtaining analytical results without numerical integration, which reduces the computational complexity, as shown by Kunii and Levenspiel (1991) for fluidized bed applications. The different approaches, however, lead to different orders of magnitude in the values of the rate parameters, as will be seen later in this text. Unreacted Shrinking Core Model with Changing Effective Diffusivity
1 + BX t ) τkin fkin(X) + τdif,0 f (X) 1 + AX dif
(4)
where 1/3
fkin(X) ) 1 - (1 - X)
(
A)
(1 - 0) 0
Z - (1 + ZX - X)2/3 - (1 - X)2/3 Z-1 B)
(5)
)
(6)
Rp2Fmol,s τdif,0 ) 6Deff,0CAb
Vmol,solid product (7) Vmol,solid product
τkin )
RpFmol,s kUSCCAb
Lew (1990) presented a model to describe the sulfidation reaction with zinc titanates and oxides, where the porous solid is simulated as an assemblage of grains randomly distributed in space with overlapping of the grains permitted. In the case where the solid product occupies more volume than the stoichiometrically equal volume of reactant (as in sulfidation with zinc titanates), i.e. Z > 1, pore closure is possible. The grain size distribution n(r) of the solid zinc titanate reactant was determined with the help of SEM micrographs. The internal surface per unit volume (Sv,0) and porosity (0) of the particle (corrected for overlapping of grains) is determined with the following equations (Lew, 1990; Lew et al., 1992a):
-ln(0) ) 0,x )
∫rr
4π 3
r3 n(r) dr
(9)
r2 n(r) dr
(10)
max
min
∫rr
max
min
where 0 and Sv,0 are the initial internal porosity and surface area (m2/g) of the solid from standard laboratory analysis, 0,x and S0,x are the corresponding porosity and surface area (m2/m3) without correction of overlapping, and rmin and rmax are the minimum and maximum size of grains (m) with grain size distribution n(r). When a uniform grain size distribution is assumed (n0 grains with diameter r0), the above equations can be combined to give the initial grain radius (r0) based on randomly overlapping spherical grains:
4 -ln(0) ) πr03n0 3 f r0 )
Sv,0 ) 4π0r02n0 -30 ln 0 Sv,0
(8)
In eqs 4-8 Vmol is molar volume (m3/mol), τkin is the time-scale parameter for chemical reaction control (s), and τdif,0 is the initial time-scale parameter for diffusion
(11) (12)
The basic equations of the model are the following:
-bkOGCAb drr Fmol,s ) dt kOG Fg-1 1r I Dpl r r
where
(
I)
drp drr rrrFg-1 )(Z - 1) dt dt r Fg-1
ADeff,0Z Dpl Z)
Overlapping Grain Model
Sv,0 ) 0S0,x ) 04π
In order to account for the changing internal structure of the particle, a more general version of the USC model is used, where the effective diffusivity is defined as function of overall particle conversion. In the model pore diffusion and product layer diffusion are separated. The model has been successfully used for the modeling of sulfidation and sulfation with limestone and dolomite particles (Zevenhoven et al., 1995, 1996). As will be shown here, the USC model with changing effective diffusivity complies with the requirements presented above for the gas-solid reaction model as part of reactor modeling. The USC time-conversion equations for the combination of reaction kinetics and intraparticle diffusion (under neglible external mass transfer limitations) give the following relation between time and overall sorbent conversion:
fdif(X) ) 3
control (s), 0 is porosity, Deff,0 is the initial effective diffusivity (m2/s), Dpl is the product layer diffusivity (m2/s), and kUSC is the reaction rate constant (m/s). More details of this model are given in Zevenhoven et al. (1996a,b).
p p
)
∫rr (t′)rdrF -1 r
p
g
(13) (14)
where rp is the radius of a grain at the surface of the product layer (m), rr is the radius at the surface where the chemical reaction takes place (these are found with integration over time t) (m), b is the stoichiometry constant, p is the porosity of the grain outer surface (reactant + product), r is the porosity at the reaction surface, Fg is the grain shape factor (1 for plates, 2 for cylinders, and 3 for spheres), and Z is the stoichiometric molar volume ratio of solid product to solid reactant. Thus the solid product layer thickness equals rp - rr.
Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997 2335
Figure 1. Fit of unreacted shrinking core (USC) and overlapping grain (OG) models into TGA data with sorbent A; 12 000 ppmv H2S at 400, 500, and 600 °C.
Figure 2. Fit of USC and OG models into TGA data with sorbent A; 5000 ppmv H2S at 400, 500, and 600 °C.
The porosity of the solid (product + reactant) is found by
p ) 0 - (Z - 1)(r - 0)
(15)
and the fractional conversion of the solid reactant to product is
X)
0 - p (Z - 1)(1 - 0)
(16)
Lew (1990) and Lew et al. (1992a) modeled the test data of sulfidation with zinc oxide with the model by assuming the solid particles to consist of spherical overlapping grains. For different zinc titanates (mixtures of zinc oxide and titanium dioxide) a discrete bimodal grain size distrubution was used, in which 50% of the grains in the solid particle were assumed as spherical and 50% as platelike grains. In addition two different porosities had to be included, which were evaluated from SEM analysis. Fit of the Models Presented into Time Versus Solid Conversion Data. Results and Discussion During the years of the development of the fluidized bed sulfur removal process with regenerable sorbents, the laboratory-scale data were produced for the needs of selecting the optimum sorbent for the process, rather than for producing input data for fundamental modeling purposes. Therefore the data used for model parameter fitting include two different laboratory reactor types and pressure levels (atmospheric TGA and a pressurized fluidized bed) and three different sorbents (A, B, and C). The sulfur removal reactor will operate at high pressure, but the data from the ambient pressure TGA with sorbent A are included because they give information on the temperature dependence of the model parameters. The preliminary analysis of the ambientpressure TGA test data was recently published by Mojtahedi et al. (1996), and the analysis of highpressure data, by Mojtahedi and Abbasian (1995a,b). In this paper, in addition to model parameter determination for USC and OG models, the values obtained will be compared with those reported in the literature. In Figures 1 and 2, the experimental sets of data points obtained with sorbent A in TGA tests are shown. The figures indicate that gas film mass transfer cannot be rate-determining, since the data points do not
Figure 3. Fractional effect of the time reguired by sample bed diffusion on the overall reaction time as function of solid conversion.
produce straight lines. The concentration of the reactant H2S at the surface of the solid sample bed as a result of possible gas film diffusion resistance can also be estimated by determining film mass transfer rate constants (Levenspiel, 1972; Kunii and Levenspiel, 1991) and assuming a hemispherical surface for the sample bed. With film mass transfer rate constant values of 0.03-0.05 m/s, the relative effect of gas film mass transfer on the initial sulfidation rate is not significant at temperatures below 500 °C. Figure 3 shows the relative importance of sample bed diffusion using eqs 2 and 3. In Figure 3, the TGA results with lower H2S concentration are used, because then the effect of diffusion is stronger, based on eq 3. It can be seen that the effect of sample bed diffusion increases to a maximum of 30% of the overall rate of solid conversion at higher temperatures. It should be noted, however, that the effect of sample bed diffusion can actually be 10-30% lower, because the shape of the sample bed is not an ideal hemisphere. The conclusion of the results in Figure 3 is that the data and parameters obtained at 550 and 600 °C should be used with caution, which is in agreement with the preliminary analysis of these data by Mojtahedi et al. (1996). Due to the moderate gas flow rate (200 cm3 (stp)/min) used in TGA experiments in Figures 1 and 2 and relatively high sulfur capture rate by the sample, the concentration of the reactive sulfur gas was slightly reduced at the TGA exit. However, at temperatures of
2336 Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997 Table 2. Chemical and Physical Properties of the Fresh and Used Sorbents (Mojtahedi and Abbasian, 1995a; Mojtahedi et al., 1996) property
A
B
C
B (after 30 cycles)
C (after 50 cycles)
Zn/Ti (molar ratio) zinc, w % bulk density, g/cm3 particle density, g/cm3 mercury pore volume, cm3/g porosity surface area, m2/g median pore diameter, Å average particle size, µm initial reactive surface area, SUSC (USC model), m2/m3 initial reactive surface area, SOG (OG model), m2/m3 ×106
NAa 47.3 1.24 1.97 0.28 0.55 2.5 4000 200 30 000 4.93
1.46 46.6 1.32 1.51 0.273 0.412 3.3 4500 308 19 480 4.98
1.5 45.3 1.37 2.21 0.240 0.53 1.9 5000 267 22 472 4.2
1.47 NA 1.69 1.96 0.14 0.274 2.7 2600 300 20 000 5.29
1.44 NA 1.625 2.51 0.153 0.384 1.3 4500 250 24 000 3.26
a
NA ) not available.
Figure 4. Arrhenius plot of the reaction rate parameter for USC and OG models from ambient-pressure TGA data.
400-500 °C, 93-95% of the initial sulfur gas flow remained at the exit. Thus, the effect of this on the assumption of constant gas concentration (used in modeling) is within the experimental error. The values of reaction rate constants were obtained by using the initial rates of sulfidation, and the product layer diffusion coefficient was used as a fitting parameter in the USC and OG models. The physical properties of sorbents in Table 2 were used as inputs. The value for parameter Z was evaluated to be 1.38 based on the literature (Lew 1990; Lew et al., 1992a). Figures 1 and 2 show the fit of the TGA data with A at ambient pressure at temperatures 400, 500, and 600 °C with two different H2S levels. Generally, the USC model seems to fit the TGA data slightly better. This must be due to the simplified assumption of the particle to consist of uniform-size spherical grains in the OG model. A better fit could most probably be obtained by using the grain type distribution and the porosity of different grain types as model input based on SEM analysis. In this study, this was not possible. The method of more than one type of grains and porosities should be used with caution, because it increases the number of adjustable parameters. As a result of the ambient-pressure TGA tests with sorbent A, the Arrhenius fits of the reaction rate constant (k) and product layer diffusion coefficient (Dpl) with both models are shown in Figures 4 and 5. Special attention was paid to the results at 400, 450, and 500 °C, due to the possible error described above. At these lower temperatures, the activation energy for the reaction rate constant is about 25 kJ/mol. For the product layer diffusion coefficient the activation energy is about 110 kJ/mol. For the zinc titanates tested by Lew (1990)
Figure 5. Arrhenius plot of the product layer diffusion coefficient of USC and OG models from ambient-pressure TGA data.
and Lew et al. (1992a) the corresponding activation energy for the reaction rate constant was about 38 kJ/ mol, and for the product layer diffusion 110-115 kJ/ mol. Yrjas et al. (1996) reported 33 kJ/mol for the initial reaction rate. These values are at the same order of magnitude as the results reported here. The initial sulfidation reaction rates are 1.6-2.5 times lower than those reported by Lew (1990) and Lew et al. (1992a). Since their reported values are measured intrinsic solid phase reactivities, there is reason to suspect that the lower values obtained here could have been caused from sample bed diffusion or pore diffusion effects in the TGA tests. The different sorbent manufacturing technique can also have an influence. The possible error caused by using lower reaction rate constant values will be studied in connection with sulfidation reactor modeling results (Konttinen et al., 1997). The values found for the reaction rate for the USC and OG model differ by more than 2 orders of magnitude due to the fact that the OG model takes into account the internal surface area for the reaction, while the USC model does not. In fact, the USC model approach implies a thick product layer deposited on little surface, while the OG model implies a much thinner product layer on a much larger surface. Therefore, it is reasonable to compare the intrinsic reaction rate constants, i.e. based on the reaction per unit surface. The relations between the intrinsic reaction rate constant, k′ (1/s), and the reaction rate constant k (m/s) are given by and related to the reaction surface (m2/m3) by
3 k′USC ) bkUSCSUSC ) kUSC Rp
(17)
k′OG ) kOGSOG
(18)
Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997 2337 Table 3. Parameter Values of the USC Model and OG Model Obtained by Fitting into High-Pressure (20 bar) Solid Conversion Rate Data (in Figures 6 and 7) sorbent B (550 °C)
Dpl, m2/s (OG) k′ (OG),a 1/s Dpl, m2/s (USC) a
sorbent C (650 °C)
cycle 1, 1500 ppmv H2S
cycle 30, 1500 ppmv H2S
cycle 1, 200 ppmv H2S
cycle 1, 1500 ppmv H2S
cycle 50, 1500 ppmv H2S
cycle 1, 200 ppmv H2S
cycle 50, 200 ppmv H2S
4 × 10-14 67.69 5 × 10-9
2 × 10-14 71.9 3 × 10-9
2.7 × 10-14 67.69 4 × 10-9
9 × 10-14 105.6 7.5 × 10-9
1 × 10-13 82.06 4 × 10-9
1 × 10-13 105.6 8 × 10-9
2 × 10-13 82.06 5 × 10-9
Based on the reaction rate constant expression by Lew (1990) and Lew et al. (1992a,b).
Figure 6. Fit of USC and OG models into solid conversion rate data produced in a fluidized bed at high pressure with sorbent B, 200 and 1500 ppmv H2S.
Figure 7. Fit of USC and OG models into solid conversion rate data produced in a fluidized bed at high pressure with sorbent C, 200 and 1500 ppmv H2S.
where kUSC and kOG can be found from Figure 4 and b is a stoichiometry coefficient (used in the OG model but not in the USC model). The values of SUSC and SOG for different sorbents are shown in Table 2. Figure 4 shows the intrinsic reaction rate constants obtained with eqs 17 and 18. The values obtained are reasonably close to each other to prove that the different approach on reactive surfaces is the reason for the difference in USC and OG model parameters. The models were also applied to the results obtained at high pressure using a 15 g batch of sorbent in a fluidized bed (Mojtahedi and Abbasian, 1995a,b). Due to the obvious differences in initial sulfidation rates in Figure 4 and by Lew et al. (1992a), the values of the latter will be used for the high-pressure data modeling in this work. By doing this, we minimize the number of adjustable parameters. Thus, the product layer diffusion coefficient in the USC and OG models is the only parameter that has to be fitted into the experimental data. The reported Arrhenius expression for reaction rate constant kOG of Lew (1990) and Lew et al. (1992a) with different zinc titanates is 0.004 exp(-38.911 kJ/mol/(RT)) (m/s). A time scale parameter of USC model (eq 8), can now be modified, based on eqs 17 and 18:
analysis of the sorbent’s internal grain types and porosities required for this were not available. The values of product layer diffusion coefficient in Table 3 can be compared with ambient pressure values reported in the literature (Lew, 1990; Lew et al., 1992a) by assuming that the effect of pressure is linear. The extrapolated value of fresh sorbent B at 550 °C at ambient pressure is 3 × 10-13 to 5 × 10-13 m2/s, and the corresponding value for sorbent C at 650 °C is 2 × 10-12 to 4 × 10-12 m2/s. These values are at the same level as reported by Lew (1990) and Lew et al. (1992a) for different zinc titanates at corresponding temperatures. Figures 6 and 7 also show the fit of the models to data obtained with sorbent samples obtained after 30-50 consecutive sulfidation/regeneration cycles. As can be seen from Table 2, the physical properties of the sorbents change in cycling. It could be assumed that the value of the product layer diffusion coefficient decreases due to decreasing sulfur capture capacity. The quality of the fit of the models produced this way is as good for fresh sorbents as for sorbents after cycling. By using the USC model the value of the product layer diffusion coefficient after cycling is 30-50% lower with both sorbents. With the OG model the decrease in sulfur capacity can be modeled while the product layer diffusion coefficient is kept at a constant level. This difference in the behavior of the two models can be explained from the fact that no correlation for sorbent internal surface area is included in the USC model.
τkin )
3Fmol,s bk′OGCAb
(19)
The results of the modeling are shown in Figure 6 (sorbent B, 20 bar, 550 °C, 200/1500 ppmv H2S) and Figure 7 (sorbent C, 20 bar, 650 °C, 200/1500 ppmv H2S). The values of the parameters used in modeling are shown in Table 3. Sorbent C has a slightly lower surface area than A or B, the properties otherwise being the same. Figure 7 shows that the fit of the models is not as good as with ambient pressure tests. The fit with the OG model was proven to be good with high gas concentrations by using several types of grains as model inputs (Lew, 1990; Lew et al., 1992a), but the SEM
Conclusions Two different models, the unreacted shrinking core (USC) and the overlapping grain (OG) models, were applied to the modeling of zinc titanate sulfidation. All the experimental data can be fitted with two parameters, reaction rate constant and product layer diffusion coefficient. The activation energies obtained from ambient-pressure TGA tests for the reaction rate constant (26 kJ/mol) and for the product layer diffusion coefficient
2338 Ind. Eng. Chem. Res., Vol. 36, No. 6, 1997
(110 kJ/mol) agree reasonably with previously reported data, although the initial sulfidation rates seem to be significantly lower than those obtained earlier by Lew et al. (1992a). Potential reasons for this difference are discussed. The Arrhenius expression for reaction rate constant by Lew et al. (1992a) was used to fit the experimental data at high pressure, using the product layer diffusion coefficient as a fitting parameter. This way the number of adjustable parameters was minimized. By extrapolating the values of product layer diffusion coefficient to ambient pressure, they were found to be reasonably close to the values reported by Lew (1990) and Lew et al. (1992a). The solid conversion rate model and its parameters obtained here will be used further as part of the fluidized bed reactor model (Konttinen et al., 1997). In the OG model the sulfidation rate is proportional to the reactive internal surface area of the porous particles; thus it follows the real physical behavior of the sorbent in sulfidation more closely than the USC model. However, for best results with the OG model, the grain shapes and porosities of the zinc titanate sorbent samples should be determined, which practically increases the number of adjustable parameters. The USC model with changing effective diffusivity is included because of the possibility of obtaining analytical results without numerical integration, thus matching the requirements of a desirable gas-solid reaction model as part of the sulfidation reactor model better than the OG model. The OG model can be preferred in the modeling of laboratory-scale solid conversion rate data, since, as the results show, the parameter values obtained have logical dependence on both process temperature and pressure. Acknowledgment The work on the development and testing of regenerable sulfur removal sorbents and processes has been carried out as part of the “LIEKKI 2” Combustion Research Program and “SIHTI 2” Energy and Environmental Technology Program, which are partly financed by the Technology Development Centre of Finland (TEKES). The development of the sulfidation models was funded partly by the Imatran Voima Foundation. The authors greatly appreciated the comments and suggestions given by Prof. Dr. Maria Flytzani-Stephanopoulos of Tufts University, Medford, MA, during the evaluation of the modeling results. The authors acknowledge the valuable contributions of Dr. Javad Abbasian of the Institute of Gas Technology and Dr. Santosh Gangwal of the Research Triangle Institute, Research Triangle Park, NC, in producing the test data used for the model parameter fit in this article. Notation A, B ) constants defined by eq 7 b ) stoichiometric factor CAb ) bulk-gas concentration of the gaseous reactant, mol/ m3 gas D ) diffusion coefficient, m2/s Fg ) grain shape factor k ) reaction rate constant, m/s k′ ) intrinsic reaction rate constant, 1/s n0 ) number of grains (with diameter r0) Rp ) sorbent particle radius, m Rb ) sample bed radius, m r ) grain radius, m
S ) particle surface area per unit volume of solid, m2/m3 particle t ) time, s Ws ) weight of the TGA sample, g X ) overall particle fractional conversion Z ) stoichiometric volume ratio of solid product to solid reactant ) porosity, m3 pores/m3 particle Fmol,s ) molar concentration of solid reactant, mol/m3 particle Fbulk ) bulk-density of solid, kg/m3 particle τ ) time scale in USC model, s Subscripts dif ) intraparticle diffusion eff ) effective kin ) kinetics max ) maximum min ) minimum mol ) molecular OG ) overlapping grain p ) product surface pl ) product layer r ) reaction surface sbd ) sample bed diffusion tot ) total USC ) unreacted shrinking core v ) internal x ) without correcting for grain overlap 0 ) initial
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Received for review October 28, 1996 Revised manuscript received January 30, 1997 Accepted March 15, 1997X IE960686X
X Abstract published in Advance ACS Abstracts, May 1, 1997.
