Ind. Eng. Chem. Res. 1996, 35, 943-949
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Hydrogen Sulfide Capture by Limestone and Dolomite at Elevated Pressure. 2. Sorbent Particle Conversion Modeling Cornelis A. P. Zevenhoven,* K. Patrik Yrjas, and Mikko M. Hupa Department of Chemical Engineering, A° bo Akademi University, Lemminka¨ isenkatu 14-18B, FIN-20520 Turku/A° bo, Finland
The physical structure of a limestone or dolomite to be used in in-bed sulfur capture in fluidized bed gasifiers has a great impact on the efficiency of sulfur capture and sorbent use. In this study an unreacted shrinking core model with variable effective diffusivity is applied to sulfidation test data from a pressurized thermogravimetric apparatus (P-TGA) for a set of physically and chemically different limestone and dolomite samples. The particle size was 250300 µm for all sorbents, which were characterized by chemical composition analysis, particle density measurement, mercury porosimetry, and BET internal surface measurement. Tests were done under typical conditions for a pressurized fluidized-bed gasifier, i.e., 20% CO2, 950 °C, 20 bar. At these conditions the limestone remains uncalcined, while the dolomite is halfcalcined. Additional tests were done at low CO2 partial pressures, yielding calcined limestone and fully calcined dolomite. The generalized model allows for determination of values for the initial reaction rate and product layer diffusivity. Introduction Calcium-based sorbents such as limestone (CaCO3) and dolomite (CaCO3·MgCO3) can be used in gasifiers for in-bed removal of hydrogen sulfide. Depending on the partial pressure of carbon dioxide, the calcium carbonate calcines to calcium oxide or remains uncalcined. Thus, for calcined or uncalcined limestone, the reactions taking place are
CaCO3(s) H CaO(s) + CO2 CaO(s) + H2S H CaS(s) + H2O
(1)
CaCO3(s) + H2S H CaS(s) + CO2 + H2O
(2)
or
When dolomite is used, there are differences as compared to the use of limestone. The magnesium carbonate in the dolomite calcines to magnesium oxide both under typical atmospheric and pressurized gasifier operating conditions, giving half-calcined dolomite. The magnesium oxide formed does not react with hydrogen sulfide. Thus, depending on whether or not the calcium carbonate fraction of the dolomite calcines, the chemical reactions taking place are
CaCO3‚MgCO3(s) H CaO(s) + MgO(s) + 2CO2 CaO(s) + H2S H CaS(s) + H2O
(3)
or
CaCO3‚MgCO3(s) H CaCO3(s) + MgO(s) + CO2 CaCO3(s) + H2S H CaS(s) + CO2 + H2O
(4)
From the equilibrium of the calcium carbonate calcination reaction, it can be deduced that, for a CO2 volume fraction of 15% in the gas, the calcination will not occur * To whom correspondence should be addressed. Telephone: +358 21 2654560. Fax: +358 21 2654780. E-mail address:
[email protected].
0888-5885/96/2635-0943$12.00/0
at pressures above 3.5 bar at 850 °C or above 14 bar at 950 °C. Most work reported in the literature on limestone or dolomite sulfidation relates to conditions where calcination of the calcium carbonate occurs, viz., eqs 1 or 3 (e.g., Efthimiadis and Sotirchos, 1992; Allen and Hayhurst, 1990). Direct sulfidation of limestone was reported recently by Krishnan and Sotirchos (1994) and Fenouil et al. (1994), Fenouil and Lynn (1995a,b) using high CO2 partial pressures at atmospheric pressure, and Illerup et al. (1993) and Lin et al. (1995), who used elevated pressures up to 10 bar, respectively. An essential characteristic of noncatalytic solid-gas reactions like these, where a solid product is produced, is the changing internal structure of the particle. The molecular volumes of the calcium compounds CaCO3, CaO, and CaS are 36.9, 16.9, and 28.9 cm3/mol, respectively. 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 and heat is strongly effected by the progress of conversion. In order to get insight into reaction mechanisms and to determine parameters of reaction kinetics, mass transfer, and diffusion, the unreacted shrinking core modeling approach is widely used as a first approximation (Levenspiel, 1972). The major difficulty with this model is that process parameters, physical properties of the solid reactant, and kinetic or mass transfer parameters are lumped into one time-scale parameter. Moreover, for the case where intraparticle diffusion is considered, the concept of effective diffusivity is used to describe intraparticle diffusion, quantified by a diffusion constant, which is often applied to situations where structure changes inside the particle effect the process. In those cases the value for the effective diffusivity that is used or obtained is actually an average value for the given range of particle conversion. Therefore, the effective diffusivity is defined as a function of the overall particle conversion in the present work. Actually this gives a model which allows for a shift in the ratedetermining mechanism, according to the value of the Thiele parameter ΦT of the process. As a result of defining a conversion-dependent effective diffusivity and assuming a constant reaction rate constant, a conver© 1996 American Chemical Society
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Ind. Eng. Chem. Res., Vol. 35, No. 3, 1996
Table 1. Chemical and Physical Properties of the Uncalcined Limestones and Dolomites sorbents
CaCO3a (wt%)
MgCO3a (wt%)
Fmol,CaCO3 (mol/m3)
specific surface (m2/g)
particle porosity
particle density (kg/m3)
average pore radiusb (µm)
limestone L1 limestone L2 limestone L5 limestone L6 limestone L9 dolomite D15 dolomite D16
98.5 99.4 97.0 82.3 86.1 67.1 56.4
3.1 2.0 2.0 2.0 8.0 29.8 40.3
16 498 23 923 13 058 14 449 23 901 18 232 16 044
2.25 1.49 4.63 2.94 3.74 0.93 f 2.85c 0.060 f 0.241c
0.178 0.075 0.324 0.077 0.063 0.022 f 0.206c 0.010 f 0.162c
1681 2416 1351 1762 2786 2727 f 2213c 2855 f 2416c
0.323 0.251 0.412 0.209 0.074 0.112 f 0.342c 0.291 f 1.173c
a These values were obtained from separate calcination tests. b From mercury penetration pore size distribution. c Change due to halfcalcination, calculated assuming complete MgCO3 calcination.
sion-dependent Thiele parameter is found. For ΦT . 1 a gas-solid reaction is governed by intraparticle diffusion, while for ΦT , 1 chemical kinetics are rate determining. For the range 0.1 < ΦT < 10 both mechanisms have to be taken into account simultaneously. The objective of the work presented here is to demonstrate that unreacted shrinking core modeling can be applied to limestone or dolomite sulfidation, provided that the more general concept of variable effective diffusivity is applied. A distinction is made between pore diffusion and product layer diffusion, both contributing to the effective diffusivity. Thus, values for the reaction rate constant, pore diffusivity, and product layer diffusivity are found from time-conversion data. These are related to parameters describing the texture of the sorbent as determined in independent measurements: particle density, porosity, and internal surface. Experimental Section The experimental data to which the numerical procedure has been applied were obtained from pressurized thermogravimetric tests. Limestone and dolomite particles in the size range 250-300 µm were mixed with quartz particles (one third sorbent, two thirds quartz) in a cylindrical sample holder made of platinum (inner diameter 8 mm, outer diameter 10 mm, length 2 cm). After heating and pressurizing in an inert atmosphere, the sulfidation tests were carried out in an inlet gas mixture composed of 0.2% H2S, 10% H2 (to prevent H2S decomposition), 20% CO2, and 69.8% N2 (uncalcined limestone/half-calcined dolomite) or in an inlet gas mixture composed of 0.2% H2S, 2% H2, 3.5% CO2, and 94.3% N2 (calcined limestone/fully-calcined dolomite). The results described here were obtained at 950 °C, 20 bar total pressure. See part 1 of this paper (Yrjas et al., 1995b) for more detail. Some physical and chemical properties of the sorbents described here are listed in Table 1, where L1 through L9 represent limestones and D15 and D16 are dolomites. The material codes correspond to those used in part 1 of this paper. The particle density was measured using helium-pycnometry (instrument: Micromeritics 1302), the internal surface was measured using a BET-nitrogen adsorption method (instrument: Milestone 2000), and particle porosity and pore size distribution were measured using mercury penetration porosimetry (instrument: Quantachrome Autoscan 33, covering the pore size range 6.5 nm-8.5 µm). Numerical Procedure Conventional Unreacted Shrinking Core Modeling. It is assumed that the sulfidation of the sorbents can be described with an unreacted shrinking core model for a constant size particle. Thus, four separate
processes can be distinguished, one of which might be rate determining: (1) mass transfer from the gas phase to the sample holder; (2) gas-phase diffusion inside the sample holder; (3) diffusion of the gaseous reactant inside the particle (pores and solid product layer); (4) chemical reaction. All four are quantified by a time scale, τ, which gives the time necessary for complete conversion according to that mechanism. The ratedetermining mechanism can be discriminated from a set of time-conversion (t, X) data by plotting a function f(X) vs t/τ, which gives a straight line for the rate-determining step. The time scale τ directly follows from the slope of that line. It was found and reported elsewhere (Yrjas et al., 1994a) that the external mass transfer to the sample holder does not have any effect on the conversion in our tests. Therefore, only the other three mechanisms are taken into account here. The unreacted shrinking core time-conversion equations for these mechanisms are the following (Levenspiel, 1972): (1) Diffusion of the gaseous reactant inside the sorbent particle:
t ) τdif fdif(X) ) τdif(1 - 3(1 - X)2/3 + 2(1 - X)) τdif ) Rp2Fmol,CaCO3/6Deffcgas
(5)
with Rp ) particle radius ) 1.4 × 10-4 (m), Fmol, CaCO3 ) molar density of CaCO3 in unreacted solid (mol/m3), Deff ) effective diffusivity inside the particle (m2/s), cgas ) concentration of H2S in bulk gas (mol/m3). At 20 bar, 950 °C, and 0.2 vol % H2S the value for cgas equals 0.393 mol/m3. (2) Chemical reaction, assumed to be first order in H2S, see, e.g., Lin et al. (1995):
t ) τkin fkin(X) ) τkin(1 - (1 - X)1/3) τkin ) RpFmol,CaCO3/kscgas
(6)
with ks ) reaction rate constant (m/s). (3) Diffusion inside the cylindrical sample holder (Iisa et al., 1991):
t ) τsbd(X) ) τsbd(ΩX + (1 - ΩX) ln(1 - ΩX)) τsbd )
Fmol,CaCO3Rout2 4Deff,sbdcgas
Ω)1-
Rin2 Rout2
) 0.36 (7)
with Deff,sbd ) effective diffusivity in the sample bed (m2/s), Rin ) inner radius of sample holder ) 0.004 (m), Rout ) outer radius of sample holder ) 0.005 (m), and Ω ) sample holder filling factor. For the case with more than one mechanism controlling the rate, it was shown by Sohn (1978) that the overall equation is found by
Ind. Eng. Chem. Res., Vol. 35, No. 3, 1996 945
adding the separate mechanisms using the concept of “Additive Reaction Times”:
if τkin ) constant, τdif ) constant, τsbd ) constant f t ) τsbd fsbd(X) + τkin fkin(X) + τdif fdif(X) (8) From this model fitted to the X,t data the following parameters can be found from the time scales of the relevant processes: the effective diffusivity inside the particles Deff from τdif and the reaction rate constant ks from τkin. However, in general, these “mixed mechanism” equations lead to results with one of the parameters τ being negative when a least-squares method is applied (Gullett et al., 1992), especially when the rate switches from one mechanism to another. This is the case also for the test data used here when a constant effective diffusivity Deff is assumed. Sample Bed Diffusion. It is noted that a good estimation for the time scale τsbd can be calculated beforehand. If a closest packing of identical spheres is assumed, the value for the effective diffusivity in the sample bed (with porosity and tortuosity γ) is approximately given by
0.4 Deff,sbd ) Dmol ≈ D γ 3 mol
(9)
where Dmol is the molecular diffusivity of H2S in N2 and equals 8.3 × 10-6 m2/s at 950 °C, 20 bar. In this work the value γ ) 3 is used. Thus, the contribution of the effect of sample bed diffusion to the total conversion process can be evaluated. If this indicates that this is actually the rate-determining mechanism, further analysis of the data can be omitted. Unreacted Shrinking Core Model with Variable Effective Diffusivity. An essential characteristic of most porous solid-gas reactions where a solid product is produced is the changing internal structure of the particle. As a result of that, the assumption of a constant effective diffusivity Deff in modeling often leads to physically unrealistic values for the derived parameters. Therefore, we have introduced a more general definition for effective diffusivity, where this parameter is a function of the overall particle conversion. An unreacted shrinking core model with variable effective diffusivity was originally applied to pressurized limestone and dolomite sulfation data (see Zevenhoven et al., 1995), but it appears to give even better results when applied to sulfidation data as discussed here. This procedure agrees with recent work by Krishnan and Sortirchos (1993), who describe a variable diffusivity shrinking core model where the effective diffusivity is given as a function of position inside the solid product layer. Recently, the concept of combining pore diffusion and solid-state diffusion into a single parameter was reported in this journal by Fenouil and Lynn (1995a) for a CaS product layer in limestone sulfidation at atmospheric pressure. As a consequence of using a variable effective diffusivity, a conversion-dependent Thiele parameter is found. Thus, our approach allows for modeling a shift in the rate-determining mechanism which is expressed by a change in the value of the Thiele parameter ΦT. The nomenclature used in the literature to distinguish between effective diffusivity, pore diffusivity, and product layer diffusivity is ambiguous. We define the effective diffusivity in such a way that it accounts for
Figure 1. Diffusion inside a partly converted particle composed of pores, solid product, and unreacted solid.
all diffusion effects of the gaseous species inside the solid reactant. This implies that here two mechanisms should be included in this parameter: (1) diffusion in the pores of the particle (gas phase diffusion and Knudsen diffusion); (2) diffusion through a solid product layer (assumed here to be nonporous). These two mechanisms actually occur in series: the gaseous reactant first diffuses through the pores in the particle, and in addition, has to diffuse through a product layer before it can react with the solid reactant. Here, the product layer and the porous structure are combined in an overall effective diffusivity Deff by their relative volume fractions which all change during the conversion. This does not conflict with the conventional definition of effective diffusivity because in the end still all intraparticle diffusion processes are lumped into this single parameter. This concept is illustrated in Figure 1. This gives
Vpore + Vpl Vpl Vpore ) + Deff Dpl Dpore
(10)
with the volume fractions, V, of pores (porosity), solid product layer, and unreacted solid given by
product layer volume fraction ) (1 - 0)X ) Vpl porosity ) 0 ) Vpore unreacted solid volume fraction ) (1 - 0)(1 - X) ) 1 - Vpore - Vpl (11) Diffusion of a gas with molecular diffusion coefficient Dmol inside a porous structure with porosity and tortuosity γ (taken constant ) 3) is given by
0 Dpore ) Dmol+Kn γ
DKn ) 97rav(T/MH2S)1/2
1 1 1 ) + Dmol+Kn Dmol Dkn
(12)
where DKn gives the Knudsen diffusivity (see, e.g., Satterfield, 1980) for an average pore radius rav, which was found from the mercury penetration porosity measurement (Table 1). Dmol+Kn gives the combined molecular and Knudsen diffusivity in the gaseous phase inside the porous solid. Since no pore blocking should occur in calcium carbonate sulfidation, the particle porosity 0, Knudsen diffusivity DKn and hence Dmol+Kn are assumed constant. Values for the Knudsen diffusivity found here are on the order of 10-4 m2/s. Combining eqs 10-12 leads to a conversion-dependent effective diffusivity:
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Deff(X) )
A)
((
1 + AX ) Deff,0 1 + BX (1 - 0)X γ + Dmol+Kn Dpl
1 - 0 0 B)
Deff,0 ) Dpore )
0 D 3 mol+Kn
(1 - 0)Dmol+Kn ADpore ) 3Dpl Dpl
(13)
It is readily seen that Deff(X) is a constant only when the product layer diffusivity Dpl becomes of the same order of magnitude as the pore diffusivity Dpore. From eq 13 an average value for the effective diffusivity, D*eff, can be calculated, which can be related to an average value for the time scale τdif, i.e., τ*dif:
D*eff )
∫
((
Deff,0
)
)
using B . 1 and B . A, since A ) O(1...10) and B ) O(103...104). When D*eff, Deff,0, and A are known, the value for B is found within a few iterations. Dpl then follows from B. Rate-Determining Mechanism and Thiele Parameter. The rate-determining mechanism during the conversion may be quantified by a Thiele parameter, ΦT, here defined as follows:
ΦT2(X) )
Rpks 1 + BX τdif(X) Rpks ) ) τkin 6Deff(X) 6Deff,0 1 + AX
(
)
(15)
This reduces to a constant when A and B are of the same order. The kinetically controlled regime is quantified by ΦT , 0.1, while diffusion inside the particle controls for ΦT . 10. Knowing the values for the initial effective diffusivity Deff,0 and the product layer diffusivity Dpl, the value for the conversion X at which the diffusion inside the particle becomes rate-determining can be calculated. This can be used as a sorbent utilization factor, which is, for example, the value for the conversion X when ΦT becomes larger than, say, 10. A straightforward least-squares procedure applied to eq 8 does not give a physically realistic result, which indicates a Thiele parameter on the order of 0.1-10 (Szekely et al., 1976). But since at the initial stages of the reaction no significant product layer is present, eq 8 can be simplified using a Taylor series expansion around X ) 0, giving
fkin(X) ≈
t - τkin fkin(X) ) τ* dif fdif(X)
X X2 + O(X3) 3 9
and fdif( X) ≈
X2 + O(X3) (16) 3
This allows for rewriting eq 8 to yield, for small values of X and negligible sample bed diffusion:
(
)
t - τsbd fsbd(X) τdif τkin τkin t ≈ ) + X + O(X2) X X 3 3 9 (17a) which approximately equals
(18)
A conversion-dependent expression for τdif is derived from eq 8 analogously:
t - τkin fkin(X) fdif(X)
A A 1 A + ln B (14) ln(1 + B) + ≈ Deff,0 B B2 B B
(17b)
The value for τkin is found from the points of the X,t data set where X < 0.1 by plotting ln(t/X) vs X and fitting a straight line with intercept 1/3τkin. An estimation for the Thiele parameter ΦT (for 0 < X < 0.1) is found from the slope of this line. The exponential form in eq 17 improves the quality of the fit. With this value for τkin the average value τ*dif is found using the whole data set, using a linear fit
1
Deff(X) dX ) 0
))
τdif 1 τkin t ) exp - X X 3 τkin 3
0 + (1 - 0)X
) τdif(X)
(19)
Finally, a conversion-dependent Thiele parameter is defined from eq 8 by:
ΦT(X) )
x
τdif(X) ) τkin
x
t - τkin fkin(X) fdif(X) τkin
(20)
Referring to eq 8, it is noted that expressions (18) and (19) implicitly assume that
τdif(X) fdif(X) .
∫0Xfdif(x)
dτdif(x) dx dx
(21)
This can be verified by a numerical integration assuming, for example, A ) 10 and B ) 5000. Only at X ) 0 is the left-hand term of the same order as the righthand integral. Molar Density of Calcium Carbonate in Various Sorbents. In most limestone and dolomite sulfidation studies the molar density of the calcium carbonate in the unreacted sorbent (in mol/m3 of solid) is calculated by dividing the particle density by the molar mass of calcium carbonate or simply by taking the reciprocal of the molar volume. However, the molar density Fmol,CaCO3 of the CaCO3 in the unreacted solid can be determined using a few physical characteristics of the particle (which should be measured separately):
FparticlexCaCO3 Fmol,CaCO3 )
MCaCO3
(22)
with Fparticle ) particle density (kg/m3), xCaCO3 ) mass fraction of CaCO3 (kg/kg), and MCaCO3 ) molar mass of CaCO3 (kg/kmol). The molar volume for chemically pure CaCO3 equals 36.92 cm3/mol, which gives Fmol,CaCO3 equal to 27 085 mol/m3. As shown in Table 1, the solid reactant concentration is in most cases much less than this value due to contaminations and empty pores. It is noted that after calcination of CaCO3 to CaO the molar density Fmol,CaO is equal to Fmol,CaCO3. Results and Discussion The modeling procedure described above was applied to sulfidation data for five limestones (L1, L2, L5, L6, and L9) and two dolomites (D15 and D16), obtained from tests at 950 °C, 20 bar with 0.2% H2S with the CaCO3 both uncalcined and calcined. Time-conversion
Ind. Eng. Chem. Res., Vol. 35, No. 3, 1996 947
Figure 2. Conversion vs time for uncalcined limestones at 950 °C, 20 bar.
Figure 3. Conversion vs time for calcined limestones at 950 °C, 20 bar.
Figure 4. Conversion vs time for half-calcined (HC) and fully calcined (FC) dolomites at 950 °C, 20 bar.
data are given in Figure 2 for uncalcined limestone and Figure 3 for calcined limestone, while Figure 4 gives the results for half-calcined and fully calcined dolomite. It was found that the measurements on calcined limestone, half-calcined dolomite, and fully-calcined dolomite were determined by sample bed diffusion: the values for t and τsbdfsbd(X) were almost identical. This is illustrated by Figure 5a,b, which give the relative importance mechanism during sulfidation of uncalcined and calcined limestone L1. In Figure 5b it is clearly seen that sample bed diffusion determines the conversion process. The results of the modeling on uncalcined limestone sulfidation data are given in Table 2. Limestones L2 and L5 show a much higher reaction rate than the other three limestones. For limestone L5 this can be related to its high porosity and high internal surface, making the sorbent more sensitive to rapid structure changes during the first stages of the reaction. Lin et al. (1995) recently reported a reaction rate of 2.13 × 10-2 kg of CaCO3/(kg of H2S‚s‚bar of H2S) for uncalcined limestone sulfidation (850 °C, up to 10 bar, 0.84-1 mm particles). This gives 8.52 × 10-4 kg of CaCO3/(kg of H2S‚s) for 0.2% H2S at 850 °C, 20 bar, and for sorbents with an internal surfaces between 3 × 106 and 107 m2/m3 (the limestones used here), this equates
Figure 5. Relative effects of reaction kinetics, intraparticle diffusion, and sample bed diffusion on sulfidation of (a) uncalcined limestone L1 and (b) calcined limestone L1.
Figure 6. Experimental data and model results for uncalcined limestone sulfidation.
to reaction rates between 0.001 and 0.005 cm/s. Due to our temperature level (950 °C) we find a reaction rate which is 1 order of magnitude higher. This difference is explainable when the activation energy for the reaction between CaCO3 and H2S is on the order of 260 kJ/mol, which is supported by some data from Fenouil and Lynn (1995a), who suggest values of 267-339 kJ/ mol for 820-870 °C, at atmospheric pressure. The product layer diffusivities are almost the same except for the value found for limestone L5. A comparison of experimental results and modeling is given in Figure 6 for uncalcined limestone. In order to illustrate the variable effective diffusivity issue, this parameter is plotted as a function of conversion in Figure 7a-e for uncalcined limestone sulfidation. These figures show that the value for the effective diffusivity drops a few orders of magnitude from pore diffusion to product layer diffusion at conversion levels of about 0.02 and then continues to decrease slightly due to pore closure. The conversion-dependent Thiele parameter for these measurements is given in Figure 8. Conclusions A generalized unreacted shrinking core model is described that accounts for a variable effective (intra-
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Table 2. Results of Uncalcined Limestone Sulfidation Data Modeling
limestone L1 limestone L2 limestone L5 limestone L6 limestone L9
τkin (s)
ks (cm/s)
τ*dif (s)
Dpore (×10-6 m2/s)
D*eff (×10-10 m2/s)
Dpl (×10-10 m2/s)
15 306 3 341 1 036 15 491 17 699
0.038 0.175 0.449 0.033 0.051
318 263 631 418 87 657 548 386 445 170
0.472 0.197 0.867 0.200 0.147
4.31 3.15 12.38 2.19 4.46
1.74 2.22 2.92 1.49 3.47
Figure 8. Thiele parameter vs conversion for uncalcined limestone sulfidation.
by limestone (calcined and uncalcined) and dolomite (fully-calcined and half-calcined) particles at 950 °C, 20 bar. Pore diffusivities, product layer diffusivities, and reaction rate constants are given for the sulfidation of uncalcined limestone. It was found that for the calcined limestone samples and the dolomite samples the conversion rate of the sorbents was determined by the diffusion inside the sample bed of sorbent particles. It is concluded that the initial reaction rate is determined by both porosity and internal surface. In all cases a product layer diffusivity was found that was 3 orders of magnitudes smaller than the pore diffusion. The spread that was found in the reaction rate constant cannot be explained easily when catalytic effects from others elements are excluded. Implications of these findings are that using a more porous limestone does not automatically result in a quicker sulfur takeup, since neither the initial reaction rate nor the product layer diffusivity can be ranked according to porosity. At given process conditions a sorbent can have a relatively high initial reaction rate and a low product layer diffusivity, while this can be vice versa for another. Acknowledgment This work is part of the Finnish National Combustion and Gasification program, LIEKKI 2. TEKES Technical Development Centre of Finland, Enviropower Inc., and A. Ahlstrom Corp. are acknowledged for financial support. C.A.P.Z. currently resides at A° bo Akademi University on a Human Capital and Mobility postdoc fellowship granted by the Commission of the European Communities. Nomenclature Figure 7. Effective diffusivity vs conversion for uncalcined limestone sulfidation: (a) L1, (b) L2, (c) L5, (d) L6, (e) L9.
particle) diffusivity which results from structure changes inside the reacting solid particle. Basically, the effective diffusivity is separated into a diffusion coefficient for pore diffusion and a diffusion coefficient for diffusion through the solid product layer. This model has been applied to conversion data from the absorption of H2S
A, B ) constants defined by eq 13 cgas ) bulk gas concentration of H2S, mol/m3 of gas D ) diffusion coefficient, diffusivity, m2/s ks ) reaction rate constant, m/s MCaCO3 ) molar mass of CaCO3 ) 100.36, kg/kmol MH2S ) molar mass of H2S ) 32.04, kg/kmol Rp ) sorbent particle radius, m rav ) average pore radius, m
Ind. Eng. Chem. Res., Vol. 35, No. 3, 1996 949 T ) temperature, K t ) time, s X ) overall particle conversion xCaCO3 ) mass fraction CaCO3 in solid, kg of reactant/kg of solid V ) volume fraction, m3/m3 γ ) tortuosity ) 3 ) porosity, m3 of pores/m3 of particle 0 ) initial particle porosity, m3 of pores/m3 of particle Fmol,CaCO3 ) molar density of solid reactant in unreacted solid, mol/m3 of solid phase Fparticle ) initial sorbent particle density, kg/m3 of particle τ ) time scale, s ΦT ) Thiele parameter Ω ) sample-holder filling factor Subscripts eff ) effective kin ) kinetics Kn ) Knudsen mol ) molecular pore ) pore pl ) product layer Superscript * ) average value (average over X)
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Received for review August 28, 1995 Accepted December 1, 1995X IE950539J X Abstract published in Advance ACS Abstracts, February 1, 1996.
