Optimizing the Mechanical Strength of Fe-Based Commercial High

Li, Y.; Chang, L.; Zhang, J.; Li, Y.; Wang, R. Tianranqi Huagong 1990, 15 (4), 14. .... Yongdan Li, Dongfang Wu, Jianpo Zhang, Liu Chang, Dihua Wu, Zh...
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Ind. Eng. Chem. Res. 1996, 35, 4050-4057

Optimizing the Mechanical Strength of Fe-Based Commercial High-Temperature Water-Gas Shift Catalyst in a Reduction Process Yongdan Li* and Liu Chang Department of Chemical Engineering, Tianjin University, Tianjin 300072, China

It has been elaborated that reduction is one of the key processes for the mechanical reliability of an iron-based high-temperature water-gas shift catalyst. The process factors such as the heating rate, the reduction temperature, and the steam to gas ratio all have strong effects on the mechanical strength of the catalyst. For the catalyst pelletized in a laboratory, it has been observed that the mean value and the reliability of the mechanical strength can be increased much at suitable conditions, while under some conditions still often employed industrially these can be decreased much compared to the oxidized state. In the experiments, the best sample gains 37.3% and the worst loses 24.7% of the mean strength. In the same set of experiments with a narrow range of variation of the factors, the probability of strength failure of the best sample at 10 kg/pellet is 8 orders of magnitude lower than that of the worst. The analysis shows that the factors mentioned and the mean strength can be regressed by a second-order relationship. The temperature-programmed reduction and magnetic susceptibility measurements reveal that the ferromagnetic property of the reduced samples contributes a lot to the increase of the mean strength. The experiments with a commercial catalyst at several conditions also show a decisive effect of the factors on its mechanical reliability. It is plausible that the catalyst has different mechanical reliability in different positions in the industrial converters after reduction. Introduction An iron-based high-temperature water-gas shift (HTWGS) catalyst plays an important role in the hydrogen-based industry. The mechanical strength of catalyst is one of the key parameters for its reliable industrial performance and has been an important research field. The early literature consists of mainly one-parameter experimental reports for the purpose of increasing the mechanical strength, with major attention on the preparation process (Gupta et al., 1981; Hogue et al., 1982; PuttaChaudhuri et al., 1981). There were some publications discussing the stress state in the pellets leading to strength failure and the general aspects and the modeling of mechanical strength (Furen et al., 1975; Brasoveanu et al., 1980; Hutchings, 1986; van den Born, 1989). The statistical properties of the strength data in general and the factors influencing the strength of catalysts in several handling steps have been the topics of a series publications from this group (Li et al., 1989, 1990, 1991, 1993, 1995, 1996). The measurement and the statistical method of the mechanical strength of cylindrical catalyst pellets have been discussed based on the brittleness of the catalyst materials, the elastic mechanics, and the Weibull statistics (Li et al., 1989). It has been proposed that the Weibull parameters of the horizontal crushing strength (HCS) and the probability of failure calculated by Weibull distribution can be used as criteria for the comparison of the catalyst mechanical strength (Li et al., 1989). A statistical relationship between the density and the strength of the HTWGS catalyst has been given in another publication (Li et al., 1993). Based on the theory of brittle fracture and statistical method, the effect of the process factors in the processes of pelletization (Li et al., 1991) and calcination (Li et al., 1996) on the mechanical strength has been discussed * Corresponding author.

S0888-5885(96)00032-2 CCC: $12.00

in detail. It has been found that the abnormal treatments for this catalyst in the production and reduction reduce the mechanical reliability for several orders of magnitude (Li et al., 1995), while optimization of the process conditions increases the reliability very much (Li et al., 1991, 1996). An optimized sample in the oxidized state has been reported (Li et al., 1996), which has a Weibull modulus as high as 17.9 and a probability of failure at 10 kg/pellet as low as 6.56 × 10-13. The previous results of statistics and optimization suggest that it is worth finding the optimum conditions in every process of catalyst handling. The basis for Weibull statistics has been discussed in some detail in previous publications (Li et al., 1989, 1995). Here again the method and the parameters are used in the comparison of the strength data. Most of the sizes of the Fe-based HTWGS catalysts fall into a small range, and the shapes of these catalysts are cylindrical or cylindrical with a spherical cap. F5 and F10, the probability of strength failure at 5 and 10 kg/ pellet in HCS measurement, respectively, have been used in the discussion of the reliability of the catalyst. The relationship between the tensile fracture strength of brittle materials and its physical properties has been described by the Griffith equation (Griffith, 1920)

σ ) (2Eγ/πC)1/2

(1)

in which E is Young’s modulus of the material, γ the surface energy, and C a factor having a lot of statistical meanings and characterizing the size and state of the defects existing in the material. The typical defect size in fracture mechanics is in the range of nanometers to microns, which falls into the range of pore size in catalyst pellets. According to eq1, it can be deduced that, after the pellets are made and the reactor is loaded, the most decisive process for the mechanical reliability of the pellets will be the heating and reduction, in which the catalyst pellets are transformed from an oxidized state © 1996 American Chemical Society

Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996 4051

into a reduced state. During the transformation, Young’s modulus and the surface energy will change much and the existing state of the defects in the pellets will also change, and both the size and the relative directions of the defects (or the flaws) will change much in the process. The change of these physical properties and the state of defects will lead to a reforming of the mechanical strength. Furthermore, the reduced state of this catalyst is Cr3+-substituted Fe3O4, which is a ferromagnetic material. The formation and the direction of the magnetic domains would contribute to the combination energy and in consequence to the mechanical strength. After reduction, the reactor reaches a steady state and the pellets also come to a stage of steady-state working, in which the physical properties and the state of the defects will also change with time, however in a very slow rate in the sense of aging. The strong effect of the processing parameters of heating and reduction has been reflected in the data (Li et al., 1995) for the reduction process at abnormal conditions with steam and thermal shocks. As the importance of the mechanical strength of the catalyst has been recognized both in industry and in academic research, this paper gives the details of a set of optimum experiments and discusses the possibility of increasing the mechanical strength and the relationship between the strength and other physical properties in heating and reduction. Experimental Section 1. Materials. Two materials were used in the experiment. One (cat1) is originally a powder taken directly from an industrial production by coprecipitation technology, calcined at around 350 °C. The material contains around 10 wt % of Cr2O3 and 90 wt % of Fe2O3 and a major phase of γ-Fe2O3 with a trace amount of R-Fe2O3 and γ-FeOOH. The powder was used directly for pelletizing with addition and uniform mixing with 1 wt % of graphite and crushing and sieving to pass a sieve of 20 mesh. It was pelletized at a pressure of 3 kbar/cm2 in laboratory with pelletizing equipment described elsewhere (Li et al., 1991) into pellets with a size of L 9 × 6 mm. The mean HCS of the pellets formed is 45.8 kg/pellet, with m ) 10.1 and β ) 1.22 × 10-17. The others (cat2) were the pellets of a commercial catalyst, in a cylindrical shape with a cap. Its typical dimensions were as follows: the diameter is 9.6 mm, the height of the cylindrical part is around 6.2 mm, and the total height is around 8.1 mm. There is no information on the preparation process conditions of this catalyst, due to the fact that it is an imported sample. However, its X-ray diffraction (XRD) profile shows a considerable proportion of R-Fe2O3, though the major phase is γ-Fe2O3. 2. Physical and Chemical Properties Measurement. The texture data were measured by an Autopore 9220II porosimeter. The XRD patterns of the sample were obtained by a Rigaku 2038 diffractometer with Fe KR. The temperature-programmed reduction (TPR) curve was obtained with a tubular reactor with an internal diameter of 5 mm and with loading of 0.2 g of the catalyst particles between 40 and 60 mesh. The feed composition in TPR was 10 vol % H2 and 90 vol % N2, and the feed rate was 20 mL/min. The compositions of the product and feed gases during reaction were measured with an on-line gas chromatograph (GC) with thermal conductivity detector (TCD). The magnetic susceptibilities (MS) of the reduced samples were mea-

Table 1. Factors and Range of These Factors in the Experiment upper limit lower limit

S

T

R

4 0.5

500 350

2 0.5

sured at ambient temperature by a thermomagnetic balance system constructed by our laboratory (Wang et al., 1989). The HCS of the pellets were measured by a MQ-200 pellet strength tester made in Dalian, China. The number of pellets measured for one experiment depends on the scattering behavior of the strength data. For the original samples in oxidized state, more than 60 pellets were measured for cat2 and 20 pellets were measured for cat1, while each reduction experiment uses 20 pellets of cat1 and 40 pellets of cat2. The density of the pellets of cat1 was calculated from the size and weight of the pellet. Due to the complex shape of cat2, its density was not measured. 3. Pellet Reduction. A gradientless reactor with internal cycling has been used in the experiment of reduction and performance testing. The setup has been described elsewhere (Li et al., 1990). The experiments were carried out at atmospheric pressure. The feed composition for reduction and reaction was 25.6 vol % of N2, 8.2 vol % CO2, 31.7 vol % CO, and 34.5 vol % H2, with different steam to gas ratios. A total flow of 200 mL/min of dry gas was employed. After loading the pellets and with the total flow of dry gas unchanged, the reactor was heated at a constant rate until the temperature reached 250 °C, and then the steam was added at a definite steam to gas ratio. The reactor was heated at the same rate up to the temperature expected, and afterward the reduction and reaction were continued. Each experiment takes around or more than 15 h including the heating, reduction, and reaction. If the composition of the products of the HTWGS reaction reaches stability in a sense with a variation of the GC peaks of the major components of less than 3% during 1 h, it was supposed that the sample had reached a stable reducing state and the experiment was stopped. After the experiment the reactor was cooled naturally to room temperature, the catalyst was unloaded carefully and was put into a hermetic bottle before the other measurements. The experimental design for cat1 is described in detail as follows. The experiments for cat2 were done in the same procedure in selected conditions given in a table together with the results. 3.1. Selected Factors for cat1. The factors investigated and the value range of these factors are given in Table 1. The range of the reduction temperature was selected according to the TPR curve of this material, in which there is a hydrogen-consuming peak in the range of 350-430 °C and another peak starting at 430 °C and ending at around 600 °C. The first peak was recognized as the reduction of Fe2O3 to Fe3O4, and the second is attributed to the process of further reduction to FeO and Fe. In the selected range of 350-500 °C the catalyst can be reduced to the active state. The ranges of heating rate and steam to gas ratio were selected according to the conditions often used by industry and the possibility with a laboratory reactor. 3.2. Experimental Design for cat1. After the linear transformation

{

x1 ) 18(S - 0.5)/15.75 - 2 x2 ) (T - 350)/37.5 - 2 x3 ) (R - 0.5)/0.375 - 2

(2)

4052 Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996 Table 2. Experimental Condition Matrix

Table 3. Mechanical Properties and Density of the Samples of cat1

real experimental conditions

design matrix number

x1

x2

x3

S

T

R

1 2 3 4 5 6 7 8 9 10 11

0 0 -1.414 1.414 -1.414 1.414 2 -2 0 0 0

0 0 -1.414 -1.414 1.414 1.414 0 0 2 -2 0

2 -2 1 1 1 1 -1 -1 -1 -1 0

2.25 2.25 1.01 3.49 1.01 3.49 4.00 0.50 2.25 2.25 2.25

430 430 377 387 480 480 440 430 502 360 420

1.99 0.497 1.62 1.62 1.62 1.62 0.87 0.87 0.87 0.87 1.24

the three factors were transformed into normalized variables taking values between -2 and 2. The experimental matrix is shown in Table 2. The 11 points design matrix was taken from literature (Zhu, 1981). The real experimental conditions given in the table do not correspond exactly to the value of the design matrix due to the fact that the heat capacity of the gradientless reactor is rather large and the control of the temperature is uncertain, the feed of water was achieved by a pump with which the setting of the flow has only two decimals anyway, the values of the heating rate, temperature, and steam to gas ratio were measured precisely, and the data in the table listed as “real experimental condition” are the real values measured. The calculations in the following part of this paper were based on the real measurement. 4. Data Treating. 4.1. Weibull Statistics. Combine the Weibull distribution equation (Weibull, 1951) m

F(σ) ) 1 - exp(-β0σ )

(3)

with the approximate relationship (Xu, 1980) in elastic mechanics for the maximum tensile stress leading to fracture during the measurement of HCS

σ ≈ 2P/πdl

(4)

thus m

F(P) ) 1 - exp(-βP )

(5)

In these formuls σ is the maximum tensile stress in kg/ cm2 leading to fracture in the measurement of HCS, P is the maximum loading in kg, F(σ) and F(P) are the probabilities of failure at stress σ and loading P, m is the Weibull modulus which characterizes the scattering behavior of the strength data, β and β0 are factors related to the size of the sample and the normalizing factor of stress, d is the diameter of the pellet in cm, and l is the length of the catalyst pellet in cm. In this case all the pellets of cat1 are the same size. The pellets of cat2 have a slightly different size and shape; however, its lateral cross-sectional area is larger than that of cat1. In eq 4 the term πdl is the term of the cross-sectional area in which the maximum stress exists. In order to be consistent with other publications, the maximum loading P and its mean value P h in kg/pellet are used in the discussion and the statistics. In the case with cat2 the stress σ is lower than that with cat1 in the same loading; nevertheless, the data of cat2 are given for comparison and illustration of the effectiveness of the factors so that we do not correct them to the same stress standard. The Weibull parameters m and β were

sample

mean HCS

1 2 3 4 5 6 7 8 9 10 11 original optimum

49.9 49.0 53.4 42.4 48.4 53.9 54.0 56.1 51.3 34.5 60.1 45.8 62.9

D h

m

2.208 5.01 2.201 3.88 2.310 4.98 2.225 3.02 2.196 5.00 2.190 11.2 2.206 7.85 2.204 4.80 2.195 5.90 2.231 5.76 2.193 7.78 2.387 10.1 2.201 12.8

β

F5

F10

2.03 × 10-9 1.92 × 10-7 1.68 × 10-9 8.33 × 10-6 2.48 × 10-9 2.20 × 10-20 1.61 × 10-14 2.82 × 10-9 5.30 × 10-11 9.01 × 10-10 9.30 × 10-15 1.22 × 10-17 6.60 × 10-24

6.45 × 10-6 9.89 × 10-5 5.08 × 10-6 1.07 × 10-3 7.75 × 10-6 1.48 × 10-12 4.94 × 10-9 6.39 × 10-6 7.05 × 10-7 9.57 × 10-6 2.55 × 10-9 1.40 × 10-10 5.84 × 10-15

2.08 × 10-4 1.46 × 10-3 1.60 × 10-4 8.68 × 10-3 2.48 × 10-4 3.49 × 10-9 1.14 × 10-6 1.78 × 10-4 4.21 × 10-5 5.18 × 10-4 5.60 × 10-7 1.54 × 10-7 4.16 × 10-11

obtained by the regression between P and F(P). F5 and F10 were calculated by Weibull distribution. 4.2. Analysis of the Mean HCS and MS. For the convenience of the analysis the mean values of the HCS data of cat1 and its MS were regressed by a secondorder equation N

Y h ) b0x0 +

∑ i)1

N

bixi +

bijxixj ∑ iej

(6)

Here Y h represents the value of mean HCS or MS, xi are the normalized factors, b0, bi, and bij are the coefficients obtained by regression, and N ) 3 is the number of factors. Results 1. cat1. 1.1. Mechanical Strength. The experimental results of the design for cat1 are given in Table 3. The coefficients in eq 6 for mean HCS have been estimated as follows

b0x0 ) 60.8,

[ ] [

-1.73 bi ) 4.26 , 0.372 -1.03 bij ) 0 0

2.68 -4.24 0

-0.256 -1.51 -2.98

]

(7)

After substituting these values into eq 6, the relationship between the factors and the mean value of HCS of the samples can be obtained. When ∂P h /∂x1 ) ∂P h /∂x2 ) ∂P h /∂x3 ) 0, eq 6 takes the maximum in the variable space. Here:

{

x1 ) -0.304 x2 ) 0.411 x3 ) -0.029

To see the correctness of the correlation, an experiment was arranged at this point, the real experimental condition measured is

{

S ) 2.10 T ) 439 R ) 1.24

The results of this experiment are given in Table 3 as the optimum sample. The calculated value of mean HCS according to eq 6 at this point is 61.9, and the experimental result is 62.9. The difference between the experimental and calculated results is small.

Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996 4053 Table 4. Activity and Weight Loss during the Reduction and the Other Physical Properties of Reduced Samples sample

Xco (%)

W (%)

η (m2/g)

θ (mL/g)

φ (nm)

MS (erg/aust2‚g)

1 2 3 4 5 6 7 8 9 10 11 optimum

63.7 62.1 43.9 43.1 77.2 77.4 69.1 66.6 74.3 42.1 70.6 51.2

11.3 12.7 11.3 11.4 13.0 13.2 12.3 11.9 12.8 10.3 12.3

68.4 69.2 70.8 75.0 64.5 55.4 69.1 68.5 57.2 80.4 73.3 65.0

0.242 0.228 0.216 0.223 0.224 0.225 0.229 0.234 0.235 0.229 0.246 0.234

14.1 13.2 12.2 11.9 14.5 16.3 13.2 13.7 16.4 11.4 13.4 14.4

286.5 298.0 076.6 243.8 105.2 224.0 230.3 157.9 183.4 103.7 335.0

1.2. Physical Properties and Activity of the Reduced Samples. Table 4 tabulates the measured CO conversion at the stable stage of the reaction and other physical properties of the reduced samples. 1.3. Regression of Magnetic Susceptibility. The coefficients in eq 6 for MS have been estimated as:

b0mx0m ) 339.6,

[ ]

31.14 bim ) 28.03 , -3.629

[

-35.13 bijm ) 0 0

-1.483 -53.21 0

13.12 -9.920 -13.44

]

(8)

the point the MS takes maximum

[ ]

0.434 xi ) 0.259 -0.019

2. cat2. The reduction condition and the mechanical properties of cat2 before and after reduction are given in Table 5. The last column of the table gives the number of pellets damaged during the reduction. For samples 1 and 2 there are several pellets after reduction of which the measured HCS value is 0, and for sample 3 there are several pellets already fractured to pieces after the reduction. In the correlation with Weibull distribution of the data of these samples, the data 0 and the fractured pieces were not used and the Weibull parameters were obtained by the regression of the other data. Discussion 1. Results with cat1. 1.1. Statistics of the Mechanical Strength Data. The data in Table 3 and in the mechanical strength measurement have several indications. First, the strength data for all the samples follow well the Weibull distribution as is shown in Figure 1, in which the points are the results of the measurement and the curves are the calculated values by Weibull distribution. Second, the density of the reduced samples does not show a clear relationship with the mean value of the HCS of the sample; however, the value of the density shows a rather large variation from 2.190 to 2.310 and shows some positive relation with the reduction temperature. Third, the Weibull modulus of the strength data depends strongly on the reduction conditions; nevertheless, the relationship between the value of the Weibull modulus and the reduction conditions cannot be described by simple models such as the second-order relationship. The probability of strength

failure at specific loading conditions such as 5 and 10 kg/pellet depends mainly on the value of the Weibull modulus. The mean HCS shows less effect on the probability of failure than the Weibull modulus. The statistics of the strength of the proven commercial HTWGS catalysts now working in most of the HTWGS converters elucidate that most of them have a large probability of strength failure at 10 kg/pellet and a comparatively small one at 5 kg/pellet (Li et al., 1996). It can be proposed that the loading force of 10 kg/pellet in HCS measurement is rather critical for the safe performance of this catalyst. The values of F5 and F10 in Table 3 show remarkable differences between the different samples reduced at different conditions. The probability of strength failure at 10 kg/pellet of the optimum sample is 4 orders of magnitude lower than the original sample before reduction and is 8 orders of magnitude lower than the sample with the lowest Weibull modulus or the worst sample. As the probability of failure in the low loading range is much more important than that in the high loading range, Figure 2 shows the decisive effect of the Weibull modulus of the strength data on the probability of strength failure in the low loading range, and it shows that sample 10 has a mean HCS of 7.9 kg/pellet lower than sample 4 and a higher Weibull modulus than sample 4. The probability of strength failure of sample 10 is lower than that of sample 4 in this loading range. These results show that the heating and reduction process is one of the most decisive processes for the mechanical reliability of this catalyst. 1.2. Effect of the Factors on the Mean Value of HCS and the Effect of MS. The effectiveness of the factors in the factors space can be expressed by the gradient of eq 6 after substituting the values in eq 7.

grad )

(

)

h ∂P h ∂P h ∂P , , ∂x1 ∂x2 ∂x3

In the three factors examined x2 is the most effective one, the next is x3, and the least is x1. Figures 3a, 4a, and 5a illustrate the effectiveness of the factors on the mean HCS in the selected planes in the factors space. As a comparison, the contour drawings of the magnetic susceptibility of the reduced samples in the same plane are given as Figures 3b, 4b, and 5b. It can be seen that the gradient of mean HCS in the plane x1 ) 0 is rather large, and in the plane x2 ) 0 the gradient is smaller comparatively. In the plane of x3 ) 0 it shows that there is much difference between the gradient in different directions for HCS. Anyway, these figures and the gradient analysis show that the three factors examined all have a profound effect on the mean HCS of the reduced samples. The effective correlation of the mean HCS of the reduced samples and the experimental conditions with eq 6 means that the mean HCS is a factor which can be optimized by the second-order optimum experiments, and the relationship between the mean HCS and the process factors in heating and reduction of the catalyst can be described by the secondorder equation. In Figures 3b, 4b, and 5b, the contour drawings of the MS of the reduced samples with the normalized factors, it can be seen that the MS values of the samples depend also strongly on the factors. It shows that the heating rate and the reduction temperature have a stronger effect on the MS than the steam to gas ratio. The range of MS taking higher values falls nearly the same range as that of the mean HCS. The point

4054 Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996 Table 5. Reduction Condition and the Mechanical Properties of the Samples of cat2 reduction condition sample original 1 2 3

S 2.00 2.25 2.00

T 439 360 439

experimental results R 1.24 0.87 0.00

mean HCS 24.9 25.3 33.2 32.5

m

β

5.24 3.57 3.60 4.87

3.09 × 6.47 × 10-6 2.21 × 10-6 2.82 × 10-8

Figure 1. Distribution curves of HCS data of selected samples in Table 3: 9, sample 10; b, sample original; 2, sample optimum; 1, sample 4.

Figure 2. Strength distribution curves of the typical samples in the low loading range: a, sample 4; b, sample 10; c, sample original; d, sample optimum.

calculated by eq 6 for MS taking maximum is

][ ]

S 2.86 T ) 435 R 1.24

while the point for mean HCS taking maximum is

][ ]

S 2.14 T ) 440 R 1.23

The optimum values of temperature and steam to gas ratio are nearly the same for mean HCS and for MS. There is a comparatively large difference between the two heating rates. We have observed with TPR that this catalyst reduces to Fe3O4 at around 430 °C. These results tell that the ferromagnetic property of Fe3O4 contributes a lot to the mean value of HCS of the reduced sample. The high values of the magnetic susceptibility nearly exactly account for the high values of the mean HCS of some reduced samples. The difference between the optimum heating rates for mean HCS and MS may be explained by the different statistical properties of the defects and the magnetic domains; for both of them the direction is very important for the

F5 10-8

1.43 × 2.01 × 10-3 7.25 × 10-4 7.15 × 10-5 10-4

F10

pellets damaged

5.40 × 2.35 × 10-2 8.76 × 10-3 2.09 × 10-3

1 close to 0 2 close to 0 5 fractured

10-3

overall values reflected in the mean HCS and MS. The statistical analysis of trying to find a direct relationship between mean HCS and MS values of the samples has been unsuccessful due to their different statistical nature. 1.3. Effect of the Reduction Conditions on the Other Properties of the Catalyst. During the reduction process the structure and the texture of the catalyst reform, and as a consequence all the other properties of the catalyst change a lot. Table 4 gives the data of the properties of the catalyst samples. The CO conversion is given for reference, which is the value measured in the stable stage of the reduction and which is mainly related to the thermodynamic equilibrium and kinetic controlling at different temperatures due to the comparatively large amount of catalyst and the small total flow of the feed gas and use of an internal stirred gradientless reactor. The differences between the weight losses of the different samples during the reduction are related to the equilibrium state of the reduction which depends on the atmosphere and the conditions. The specific surface area, the porosity, and the mean pore diameter show also a strong dependence on the reduction conditions. XRD measurements of the reduced samples have been done; however, for all the samples only one phase Fe3O4 can be identified. Though there exist small differences in peak intensities among different samples, in this case XRD is less sensitive than MS in measuring the reduction depth. Statistical analysis was tried, and it was difficult to find a direct correlation between the mechanical strength and these physical properties. It seems that there is not a unique property which leads to the difference of the strength reliability between the samples. However, the reforming of these physical properties should contribute to the change of the mechanical strength distribution of the sample. These results indicate that there exists an optimum reduction condition for the activity of the HTWGS reaction. 2. Results with cat2. The data in Table 5 represent the effect of the reduction conditions on the mechanical strength of cat2. It shows that for this catalyst when in an oxidized state its mean value of HCS and its Weibull modulus are much smaller than cat1. After reduction, the Weibull moduli of all the samples become smaller than the original, while at some conditions the catalyst gains some mean HCS when not counting the damaged pellets in the process. Sample 1 was reduced at nearly the same conditions as that of the optimum sample of cat1; however, its mean HCS and its Weibull modulus are not the highest among the three reduced samples of this set of experiments for cat2. Sample 3 was reduced at a lower steam to gas ratio; its mean HCS grows higher than the oxidized state when not counting the fracture pellets, and its Weibull modulus is highest among these three reduced samples. Its probability of failure at the two critical stress conditions is also the lowest among the three samples. The way of the pellet damage during the reduction indicates that the brittleness of the pellets also changes. For sample 3, several

Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996 4055

Figure 3. Contour drawing of the mean HCS and MS with eq 6 for cat1 in the plane of x1 ) 0.

Figure 4. Contour drawing of the mean HCS and MS with eq 6 for cat1 in the plane of x2 ) 0.

fractured pellets were found and the damage was typical brittle fracture; the pellets became more brittle when reduced at this condition. For samples 1 and 2 several pellets were found with HCS of 0, and the pellets were less brittle after reduction. These results tell that, although the optimum condition for this sample is different from that for cat1, the effectiveness of the process factors of heating and reduction on the mechanical strength is obvious. Figure 6 gives the illustration of the distribution curves of the HCS data of these samples in Table 5. It shows that all the data after reduction have a substantial deviation from the standard Weibull distribution curves; part of the reason for this deviation is that the uncertainty in measuring of the several points used in the regression for getting the Weibull parameters or the change of the brittleness of the pellets in one experiment in reduction was not in the same direction or extent. Anyway, the data points in the middle range of the curve seem to be better fitted by the Weibull distribution; however, the value of the Weibull parameters should be different from that illustrated in the figure, which were obtained by the regression of all nonzero data. However, if this figure is not beautifully presented

concerning the fitting by the Weibull distribution, the information of the reliability of the mechanical strength as a dependent factor of the reduction condition can be derived. Figure 7 gives a comparison of sample 3 with the optimum sample in the experiment set for cat1. It shows that in the low loading range this commercial catalyst after reduction has a much higher probability of strength failure than the catalyst pelletized in a laboratory and reduced at good conditions for the mechanical strength. 3. General Proposal. The results presented here show clearly that the mechanical reliability of the ironbased HTWGS catalyst depends strongly on the reduction process parameters such as the heating rate, the reduction temperature, and the steam to gas ratio. These lead us to think about the case in the industrial converter in which there exist temperature and gas concentration profiles and a difference in heating rate between different positions during the heating and reduction process. There should be a large difference in the mechanical reliability between the catalyst pellets in different positions in the catalyst bed. Most of the heterogeneous catalysts need heating and reduction

4056 Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996

Figure 5. Contour drawing of the mean HCS and MS with eq 6 for cat1 in the plane of x3 ) 0.

Figure 6. Distributions curves of the oxidized and reduced samples of cat2: 2, original; 9, sample 1; b, sample 2; 1, sample 3.

Figure 7. Distribution curves of selected samples in the low loading range: a, sample optimum of cat1; b, sample 3 of cat2.

before the steady-state running of the reaction. As most of these catalysts are typical brittle material, in the design of the catalytic converters the optimum heating and reduction conditions should be explored and the difference of the reliability in different positions in the converter should be considered. Conclusions The experimental results presented here show that the heating and reduction process is one of the most decisive processes for the mechanical reliability of the iron-based HTWGS catalyst. The process parameters in the heating and reduction such as the heating rate, the reduction temperature, and the steam to gas ratio all have strong effects on the mechanical properties of the catalyst. Among the three factors examined, the

temperature and the steam to gas ratio have a stronger effect on the strength than the heating rate. The scattering properties of the HCS data can be well described by the Weibull distribution. The statistics of the strength data show that the probability of strength failure at critical stress conditions can vary for 8-9 orders of magnitude. The catalyst reduced at suitable conditions possesses very high reliability in strength. The probability of strength failure can be made as low as 4.16 × 10-11 at a critical stress condition of 10 kg/ pellet; however, with the sample reduced at unsuitable conditions, this probability can increase very much. The catalyst can gain much strength under good conditions and lose much strength under unsuitable conditions. The optimum condition of reduction for the catalyst depends also strongly on the properties of the materials, which leads to the conclusion that different brands of catalyst would need optimization separately for finding the best reduction conditions for itself. These results tell that there is a great possibility in increasing the mechanical reliability of the HTWGS catalyst through optimization of the heating and reduction conditions. The positive effect of the magnetic susceptibility of the reduced samples on the mean value of HCS suggests that the ferromagnetic property and the direction of the magnetic domains contribute a lot to the increased mean HCS of some samples in the reduced state. The existence of different mechanical reliabilities at different positions in industrial converters due to the isocondition pathways of the pellets undergone in the process should be considered in the design and the performance prediction of the converter. Acknowledgment This work has been supported in part by NSF of China and by the Doctoral Program of Institution of High Education of the National Education Committee of China. Nomenclature b0, bi, bij ) coefficients in the second-order regression for mean HCS b0m, bim, bijm ) coefficients in the second-order regression for magnetic susceptibility C ) flaw size factor in the Griffith equation d ) diameter of the catalyst pellets, cm

Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996 4057 D h ) mean value of the density of the catalyst pellets, g/cm3 E ) Young’s modulus, kg/cm-2 F(σ), F(P) ) probability of strength failure F5 ) probability of strength failure at 5 kg/pellet F10 ) probability of strength failure at 10 kg/pellet HCS ) horizontal crushing strength, kg/pellet HTWGS ) high temperature water-gas shift l ) length of the catalyst pellets, cm m ) Weibull modulus MS ) magnetic susceptibility, erg/aust2‚g P ) maximum loading in horizontal crushing strength measurement, kg/pellet P h ) mean value of the horizontal crushing strength, kg/ pellet R ) steam to gas ratio in reduction and reaction, mol/mol S ) heating rate, °C/min t ) time, h T ) temperature, °C W ) weight loss during reduction, % x0, x1, x2, x3, xi ) normalized factors Xco ) CO conversion, % Greek Letters β ) Weibull size factor γ ) surface energy of the material, J/cm2 η ) specific surface area, m2/g φ ) mean pore diameter, nm θ ) porosity, mL/g σ ) tensile stress leading to fracture, kg/cm2

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Received for review January 17, 1996 Revised manuscript received August 5, 1996 Accepted August 7, 1996X IE960032O X Abstract published in Advance ACS Abstracts, October 15, 1996.