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Drying of Supported Catalysts: A Comparison of Model Predictions and Experimental Measurements of Metal Profiles Xue Liu,† Johannes G. Khinast,‡ and Benjamin J. Glasser*,† Department of Chemical and Biochemical Engineering, Rutgers UniVersity, 98 Brett Road, Piscataway, New Jersey 08854, and Institute for Process Engineering, Graz UniVersity of Technology, Inffeldg. 21A, A-8010 Graz, Austria
Supported metal catalysts are used in many industrial applications. Experiments have shown that drying may significantly impact the metal distribution within the support. Therefore we need to have a fundamental understanding of drying. In this work, a theoretical model is established to predict the drying process, and the model predictions are compared with experimental measurements of a nickel/alumina system. It is found that egg-shell profiles can be enhanced by increasing the drying temperature or the initial metal concentration if the metal loading is low. For high metal loadings, nearly uniform profiles are observed after drying. We have also investigated how breakage of the liquid film inside the pores of the support can affect the metal distribution during drying. It was found that film-breakage has a significant impact on the metal distribution, and it is important to correctly capture film-breakage in the model in order to get good experimental agreement. 1. Introduction Supported catalysts are used in a variety of industrial processes, ranging from catalytic converters and the production of petroleum to the production of new drugs. These catalysts consist of a porous support, one or more active catalytic materials deposited on the support, and in some cases a modifier.1 With respect to the distribution of the active component in the support, four main categories of metal profiles can be distinguished, that is, uniform, egg-yolk, egg-shell, and egg-white profiles.2,3 The choice of the desired metal profile is determined by the required activity and selectivity, and can be tailored for specific reactions and/or processes. Although the development and preparation of supported catalysts have been investigated for many years, many aspects of the various catalyst manufacturing steps are still not fully understood, and in industry the design of catalysts is predominated by trial and error experiments, which are expensive and time-consuming, and do not always offer assurances on the final manufacturing results. The preparation of supported catalysts usually involves three steps: impregnation, drying, and reduction and calcination. Experimental work has shown that the metal distribution within the support is mainly determined by the impregnation and drying steps.4-9 Therefore, to achieve an optimum metal profile a fundamental understanding of both impregnation and drying is crucial. However, most studies on controlling the metal profiles in catalysts have focused on the impact of the impregnation step. There are still many questions regarding the impact of drying that remain unanswered. The effect of drying on the metal distribution and catalyst properties has been studied experimentally by Wu et al.10,11 who investigated the impact of various preparation procedures on the mechanical strength of solid catalysts and showed that drying has a significant effect on the catalyst’s mechanical properties. Santhanam et al.12 examined the nature of the Pd precursors and the adsorption of Pd complexes during and after drying with different adsorption strengths. They showed that for strong * To whom correspondence should be addressed. Tel.: 732- 4454243. Fax: 732-445-2581. E-mail: bglasser@ rutgers.edu. † Rutgers University. ‡ Graz University of Technology.
adsorption there is no migration of the metal through the pellets during drying, while for weak adsorption migration does occur, leading to a modified final profile. Li et al.9 studied the Ni distribution during the preparation of Ni/alumina catalyst pellets and compared the experiments with simulations. They showed that the simulation fitted the experimental data well, if the metal redistribution during drying was considered. Other work has focused on the characterizations of the physicochemical processes that occur during the preparation of supported catalysts using nuclear magnetic resonance,13-17 and spatially resolved Raman and UV-visible-NIR spectroscopy.18-20 Computer simulations have also been used to predict the impregnation and drying of supported catalysts. Theoretical models describing the impregnation step have been reported in a number of papers.6,7,21-23 Because of the complexity of the drying step, only a few theoretical models have been reported for drying. However, experiments and simulations have shown that the drying procedure can significantly affect the metal profile established during impregnation, if adsorption of the metal component on the support surface is weak or moderate.12,24-27 Neimark et al.5,28 were among the first to theoretically study the metal redistribution during drying. They used a dimensionless number to characterize slow drying and fast drying regimes, and their theory is in agreement with the experiments of Komiyama et al.,8 who showed that a very high drying rate can result in a uniform profile, while a relatively low drying rate favors an egg-shell profile. More detailed drying models were formulated by Uemura et al.,29 Lee and Aris,6 and Lekhal et al.24-26 They considered the effects of the capillary flow and metal diffusion and simulated the metal migration during drying. Recently, the sensitivity of the metal distribution during impregnation and drying with respect to the physical and processing parameters was examined by Liu et al.27 They also considered the effect of crystallization in their model, and showed that metal crystallization has a significant effect on the generation of egg-shell profiles for relatively high metal concentrations. It is of particular interest to compare simulation results and experimental measurements to validate the theory and determine the key parameters used to predict the metal distribution during the preparation of supported catalysts. Most previous studies
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only focused on a comparison of theory and experiments for the impregnation step. A systematic comparison for the drying step has not been reported as of yet. Thus, the objective of this paper is to predict the metal distribution during drying and to compare the simulation results with experimental measurements. Furthermore, it is of interest to investigate the fundamental mechanisms occurring during drying, and to study the impact of the processing parameters and material properties on the final metal distribution. 2. Model and Experiment Setup 2.1. Model Equations. In the present work, we studied the drying of a Ni/alumina system, which is widely used in processes like hydrogenation, hydrodesulfurization, and steam reforming of hydrocarbons.30,31 During the drying process, several phenomena are taking place simultaneously: heat transfer from the hot gas to the wet support, solvent evaporation near the external surface, solvent convective flow toward the external surface, and metal diffusion and adsorption inside the support. An accurate drying model must include all these phenomena. In this work, we extend the model proposed by Lekhal et al.24 by considering a cylindrical geometry and the impact of breakage of the liquid film inside the pores of the support (filmbreakage). In our model the following parameters have an impact on the drying process: the metal diffusion coefficient, the equilibrium constant of adsorption and desorption, the intrinsic permeability, the initial metal concentration in the solvent, the drying temperature, the humidity of the drying air, and the film-breakage parameters. It is important to note that although the results presented are chosen for a Ni/alumina system, the methodology is entirely general. It is not limited to specific active components and supports. There are two main assumptions in our model: (1) During drying the metal concentration in the solution is below its solubility; therefore, crystallization is not considered. (2) The equilibrium adsorption constant can be assumed to be a constant during the drying process. These assumptions have been made in order to arrive at a model that can simply yet accurately describe the important physical processes taking place during drying. Our model can capture convective flow in the gas and liquid phases, metal convection, diffusion, and adsorption on the porous support as well as heat transport. The following equations describe the drying process: ∂ 1∂ (rN ) (ε C ) ) ∂t g g,a r ∂r g,a
(1)
∂ 1∂ (RrNl,s + rNg,v) (ε C ) ) ∂t l l,s r ∂r
(2)
∂ 1∂ (RrNl,i) - FsRi (ε C ) ) ∂t l l,i r ∂r
(3)
∂ (C ) ) Ri, i ) metal component ∂t s,i
(4)
and deposited on the support. Equation 5 is the energy balance. εg and εl are the volume fractions of the gas and liquid phases, Cg,a (mol/m3) and Cl,s (mol/m3) are the concentrations of the drying air and the liquid solvent, respectively. Cl,i (mol/m3) and Cs,i (mol/kg) are the concentrations of the metal dissolved in the solvent and adsorbed on the support. Ng,a (mol/(m2 · s)) and Ng,v (mol/(m2 · s)) are the fluxes of the air and solvent vapor. Nl,s (mol/(m2 · s)) and Nl,i (mol/(m2 · s)) are the fluxes of the solvent and the dissolved metal. Fs (kg/m3) is the apparent density of the porous support. Ri (mol/kg/s) represents the rate of metal adsorption, which is described using a Langmuir model.32-34 Ri ) kadsCl,i(Csat - Cs,i) - kdesCs,i, i ) metal component (6) where kads (m3/mol/s) and kdes (s-1) are the adsorption and desorption constants of the metal component. Csat (mol/kg) denotes the metal saturation concentration. In this model we assume adsorption is not the limiting step. Consequently, the adsorbed metal is in equilibrium with its dissolved precursor, and the equilibrium adsorption constant can be calculated as Keq ) kads/kdes. Although the value of the equilibrium adsorption constant may change during drying,26 in this work we assume it to be a constant. hg,i (J/mol) represents the enthalpy of the air or solvent vapor. hl (J/mol) and hs (J/kg) denote the enthalpy of the liquid and solid. λ (J/(m · s · K)) is the effective thermal conductivity. Film-breakage is an important phenomenon during drying. At the beginning of drying, the water phase is continuously distributed in the support. As evaporation proceeds, isolated domains are gradually formed in the liquid phase. Finally, the liquid is only found in the isolated domains. To consider the effect of film-breakage in our model, a factor R is added to the flux terms in eqs 2, 3, and 5. Neimark et al.5 showed that film-breakage is related to the support pore structure and the water content in the support. Therefore, for a given solid carrier, we assume that the film-breakage factor, R, is a function of the water volume fraction. R ) 1 when εf g R1 (R1 - εf) when R1 > εf > R2 R) (R1 - R2) R ) 0 when εf e R2
where R1 represents the water volume fraction when filmbreakage starts, and R2 represents the water volume fraction when the solvent only exists in the isolated domains and the water flux completely stops. We assume that when the value of the water volume fraction is between R1 and R2, R linearly decreases with a decrease in the water volume fraction indicating that the flux in the liquid phase linearly decreases with a decrease in the water content. The gas-phase fluxes Ng,a and Ng,v are assumed to follow the dusty gas model (DGM),35 which considers the effect of molecular diffusion, Knudsen diffusion, and viscous flow.
2
∑
∂ ( ε C h + εlCl,shl + Fshs) ) ∂t i)1 g g,i g,i 1∂ r ∂r
(∑ 2
i)1
rNg,ihg,i
∂T + RrNl,shl - rλ ∂r
)
-
(5)
Equations 1 and 2 represent the mass balances of the drying medium (air) and the solvent (water). Equations 3 and 4 represent the mass balances of the metal dissolved in the liquid
(7)
(
)
Pg xg,i KKg,effPg ∇x 1∇Pg ) RT g,i RT ηgDKnud 2 xg,jNg,i - xg,iNg,j Ng,i + Dg,ij DKnud
∑
(8)
j)1 j*i
In eq 8 Pg (Pa) is the total gas pressure, R (8.314 J/(mol · K)) is the gas constant, T (K) is the temperature, xg,i represents the
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vapor or air mole fraction in the gas phase, Dg,ij (m /s) and DKnud (m2/s) are the effective binary and Knudsen diffusion coefficients estimated from the kinetic gas theory,36 and Kg,eff is the intrinsic permeability of the gas phase, which has the form Kg,eff ) 1 - 1.11
() εl ε
(9)
Jones37 has shown that eq 9 can describe experimental data very well. In this work, the water vapor pressure is calculated using the Antoine equation38 and the Hailwood-Horrobin equation39 with parameters fitted by Simpson.40 We assume that the convective flow in the liquid phase follows Darcy’s law,41 Nl,s ) -Cl,s
KKl,eff ∇Pl ηl
(10)
where Kl,eff is the relative permeability of the liquid phase, ηl (Pa · s) is the viscosity of the liquid phase, K (m2) represents the intrinsic permeability, and Pl (Pa) is the liquid phase pressure, which is equal to the local gas pressure less the capillary pressure Pc (Pa).41 In the present work Pc is described using the form proposed by Perre et al.,42
(
Pc ) 1.364 × 105γ
εlcl,sMl,s Fs
)
-0.63
(11)
where γ (N/m) represents the surface tension, and Ml,s is the molecular weight of the liquid solvent. The flux of the dissolved metal is described by the Nernst-Planck equation,43 which takes into account the effect of convective flow of the solvent (capillary flow), diffusion due to the metal concentration gradient, and migration caused by electrical charges. It takes the form Nl,i ) -Cl,i
KKl,eff F ∇P - εlDl,i∇cl,i - εlCl,iZiDl,i ∇φl, ηl RT i ) metal component (12)
where Dl,i (m2/s) is the effective diffusion coefficient of the dissolved metal, Zi is the charge of the metal component, F (96500 C/mol) is the Faraday constant, and φ (V) represents the electrostatic potential. In this work we assume there is no external current and the electroneutrality condition is satisfied in the support. The gradient of the electrostatic potential, which is a function of the number of charges and the concentration gradient of the charged components, is determined by the nocurrent equation:44
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2.2. Experiment Setup and Parameter Measurement. The system studied in this work is a nickel/alumina system. Nickel nitrate powders (Sigma-Aldrich) were used as metal precursors and cylindrical γ-alumina pellets provided by Saint-Gobain were used as solid carriers. The pellets are 3 mm in diameter and around 10 mm in length with a void volume fraction of 0.3 cm3/g and a surface area of 200.7 m2/g. The basic experimental protocol includes the following steps: (1) The solid support is preheated in an oven at 120 °C for 12 h. (2) The dry alumina supports are immersed in nickel nitrate solutions for impregnation. The pH of the solutions is adjusted by adding nitric acid or NH4OH. To investigate the effect of the metal concentration, we changed the concentration of the nickel nitrate solutions from 0.01 to 4 M. Usually we hold the impregnation time sufficiently long such that a uniform profile can be obtained after impregnation, representing an equilibrium state. (3) The catalyst samples are dried in an oven at a constant temperature. The drying temperature is varied between 22 and 180 °C. (4) Calcination is carried out at 500 °C for 2 h. During impregnation and drying, nickel nitrate gives the catalyst a green color. During calcination, nickel nitrate becomes nickel oxide, and thus, the catalyst color changes. The gray or black color of the samples after calcination is most likely due to some deviation from ideal 1:1 stoichiometry of the NiO.47 The nickel concentration in the solution is measured using a UV-visible spectrophotometer at a wavelength of 190 nm. To obtain the standard curve, seven samples were prepared with the Ni(NO3)2 concentration equaling 0.001, 0.005, 0.01, 0.025, 0.05, 0.075, and 0.1 M. Then the absorbance value of each sample was measured by the UV-visible apparatus. From experiments we found that there is a linear relation between the nickel concentration, CNi and the absorbance value, Auv. Using a linear regression, we can obtain the equation: CNi ) 0.0878Auv
(15)
This equation can be used to calculate the nickel concentration in the solution during impregnation. To investigate the metal profiles after drying or calcination, we cut the catalyst samples in half in the radial direction and measured the radial nickel profile using micro-X-ray fluorescence spectroscopy (microXRF). To solve our drying model, we need to measure several parameters.9,32 In our work, a Langmuir equation is used to describe the adsorption and desorption processes (see eq 6). Under equilibrium conditions, the rate of the metal adsorption is equal to the rate of the metal desorption (RM ) 0). Therefore, eq 6 can be rewritten as
n
∑zN
i l,i
)0
(13)
i)1
where n is the total number of ionic species in the liquid phase. The constitutive relations proposed by Jones37 are adopted for the relative permeability Kl,eff. Kl,eff )
() εl ε
3
(14)
The boundary conditions are the zero-flux conditions at the support center and the Neumann conditions at the support surface.24,25 The resulting system of nonlinear partial differential equations is spatially discretized by a finite volume method.45 Then the resulting set of ordinary differential equations is solved by LIMEX, which is efficient for solving highly stiff differentialalgebraic equations.46
1 1 1 1 ) × + Ceq CsatKeq Cs Csat
(16)
From eq 16 it can be seen that a straight line is obtained when plotting 1/Ceq versus 1/Cs. Then the values of Csat and Keq can be calculated from the line intercept and the slope. Six samples with Ni(NO3)2 concentration equal to 0.01 M, 0.02 M, 0.04 M, 0.06 M, 0.08 M, and 0.1 M were prepared. Each sample contained 100 mL of Ni(NO3)2 solution and 1 g of alumina support with the pH equal to 6.5. The value of Cs can be calculated based on the Ni mass balance in the system, since the amount of the metal in the solution before impregnation minus the amount of the metal in the solution after impregnation equals the amount of the metal adsorbed on the support. From Figure 1, it can be seen that the amount of metal deposited on the supports increases rapidly at the beginning of impregnation.
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Figure 1. The variation of the concentration of the metal deposited on the support with the impregnation time.
Then, the adsorption rate decreases due to the increase in the surface coverage of the active sites. After approximately 3 days a plateau is reached indicating an equilibrium state, from which we can obtain the equilibrium metal concentration in the solution Ceq and the corresponding metal load on the support Cs. Using eq 16, we obtained Csat ) 0.3 mol/kg and Keq ) 0.2 m3/mol when plotting 1/Ceq versus 1/Cs. At the beginning of impregnation, the effect of desorption can be neglected. Thus, the decrease in the metal concentration in the solution is mainly due to the accumulation of the metal adsorbed on the support. Therefore, dC0 ) -kadsFCsatC0 dt
(17)
where C0 represents the initial metal concentration in the solution.9,32 When plotting dC0/dt versus C0, a straight line can be obtained and the value of the kinetic adsorption constant kads can be calculated from the slope. To obtain kads, we prepared five samples with Ni(NO3)2 concentrations equal to 0.01, 0.02, 0.03, 0.04 and 0.05 M, at a pH equal to 6.5. To reduce diffusion effects during impregnation we ground the pellet supports into powders. The particle size was between 150 and 250 µm. We used a sieve to remove large particles, and then used water to wash out fine particles. The powder supports were dried in the oven at 120 °C for 12 h before being used. For each sample, the value of the Ni concentration was measured at 10 min intervals after impregnation started. Then the value of dC0/dt was calculated. By plotting dC0/dt versus C0, we obtained kads ) 6.5 × 10-5 m3/(mol/s). The diffusion coefficient of nickel nitrate in water was taken from the work of Takahashi et al.48 as D ) 6 × 10-10 m2/s. The permeability is based on the support pore size distribution. The pore size distribution was measured by Saint-Gobain using a mercury volume test. The porosity of the support is around 0.67 with 80% small pores (average 7 nm) and 20% large pores (average 500 nm). Then the permeability of the support can be calculated using the modified Ergun equation.49 K)
∑ i
3εidci2 200
Figure 2. Variation of (a) the water volume fraction and (b) drying rate with the drying time at Tbulk ) 60 °C and C0 ) 100 mol/m3.
(18)
Using eq 18, we obtained a permeability of K ) 5 × 10-16 m2. In general, the base case conditions used in our simulations are pH ) 6.5, Csat ) 0.3 mol/kg, Keq ) 0.2 m3/mol, kads ) 6.5 × 10-5 m3/(mol/s), D ) 6 × 10-10 m2/s, K ) 5 × 10-16 m2, and 30% relative humidity. The initial metal concentration in the solution C0 was varied from 0.04 to 4 M, and the drying temperature Tbulk was varied from 22 to 180 °C. A uniform initial metal distribution was utilized indicating that impregnation reached an equilibrium state.
Figure 3. Effect of the initial metal concentration on the drying rate at Tbulk ) 60 °C for (a) catalyst samples and (b) solution samples. The lines here are included as a guide for the eye.
3. Results and Discussion 3.1. Experimental Results. Typical experimental drying results are shown in Figure 2 for Tbulk ) 60 °C. In Figure 2a the water volume fraction can be seen to decrease with time until a plateau is reached. In Figure 2b the drying rate is equal to the weight of the water evaporated from the support per kilogram dry support per minute. At the beginning of the process the drying rate is constant. After about 40 min the drying rate decreases and finally the water content in the support is reduced to 1% after 75 min (see Figure 2a) indicating the end point of drying. Similar results have been reported in previous studies.25 During drying the metal concentration in the liquid phase increases due to evaporation of water. This may greatly affect the solution properties, the drying rate, and the metal distribution. Figure 3 shows experimental measurements of the evolution of the drying rate for different initial metal concentrations at a drying temperature of 60 °C. The lines here are included as a guide for the eye. By comparing the curves for C0 ) 0 M (water only) and C0 ) 0.1 M, we find that for a low initial
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Figure 4. Effect of the metal concentration on the metal profiles after drying at Tbulk ) 60 °C: (a) low metal concentrations; (b) moderate metal concentrations; (c) high metal concentrations. Effect of the metal concentration on the metal profiles after calcination: (d) low metal concentrations; (e) moderate metal concentrations; (f) high metal concentrations.
metal concentration (C0 < 0.1 M), the effect of the metal concentration on the drying rate is not significant (see Figure 3a). For C0 > 2 M, however, the drying rate is significantly reduced. In Figure 3a, the drying time for C0 ) 0.1 M is around 50 min. In contrast, the drying time required for C0 ) 4 M is more than 75 min. We believe that this is due to the decrease in the vapor pressure and the increase in the solvent viscosity with an increase in the metal concentration.50 Therefore, drying is much slower for high metal concentrations, and the drying time required for high metal concentrations is much longer than for low metal concentrations. To eliminate the effect of the support pore size distribution and pore network on the drying rate and only focus on the contribution of the initial metal concentration, 1 mL of solution (no support) with a certain amount of Ni(NO3)2 was dried in the oven at 60 °C. In Figure 3b, we show results for five samples with Ni(NO3)2 concentration equal to 0 M (only water), 0.1, 0.5, 2, and 4 M. It is clear that for a low initial metal concentration (C0 < 0.1 M), after an initial increase the drying rate reaches a plateau and then reduces rapidly at the end of drying. For a high initial metal concentration (C0 > 2 M), however, the drying rate is much lower and the drying rate evolution becomes quite different. The plateau region observed in the low initial metal concentration conditions disappears and the drying rate gradually reduces with time. This is because for high metal concentration conditions, the amount of the metal precursor is comparable to the amount of water so the increase in the molar ratio of the metal precursor in the liquid phase during drying becomes significant leading to a gradual decrease in the water vapor pressure.50 In contrast, for low metal concentration conditions the amount of water is much higher than the amount of the metal precursor. Therefore, although the molar ratio of the metal precursor keeps increasing during drying its effect on the change of the water vapor pressure is negligible. If we compare the drying rate evolution curves shown in Figure 3 panels a and b, we find that the curve shapes and the extent of the decrease in the drying rate with the initial metal concentration look quite similar for the two cases. This indicates that the effect of the initial metal concentration on the drying procedure during preparation of supported catalysts
is important. For moderate or high metal loading, an accurate drying model must be capable of capturing the change of the solvent properties due to the increase in the metal precursor concentration during drying. After impregnation, the metal inside the support has two forms: metal dissolved in the solvent or metal adsorbed on the support. From past studies we know that drying can change the distribution of the metal dissolved in the solvent, while its effect on the metal already adsorbed on the support is much smaller.12 After impregnation, the ratio of the amount of the metal dissolved in the solvent to that adsorbed on the support is determined by the adsorption strength and the initial metal concentration in the solvent. The effect of adsorption strength on the metal profiles during drying has been reported in previous work.25,27 It was found that drying can modify the metal profiles only for weak adsorption, while its effect is not significant for strong adsorption. The impact of the initial metal concentration on the final metal distribution after drying is shown in Figure 4a-c. Clearly, the total metal left in the support after drying increases with an increase in the initial metal concentration. From Figure 4a,b, we can see that for a uniform initial condition, an egg-shell profile is obtained if the metal load in the system is low or moderate. This is due to the effect of convection which drives the metal to move toward the support surface. If the initial metal concentration is sufficiently high (C0 > 3 M), nearly uniform profiles can be observed after drying (see Figure 4c). This may be related to three mechanisms. (1) For C0 > 3 M, the drying rate is greatly reduced (see Figure 3a), which favors a final uniform distribution. (2) If the metal concentration is sufficiently high, during drying the support pores can be blocked by the accumulation of metal crystals due to adsorption and crystallization. This pore-blockage mechanism can greatly reduce the water transport and the metal redistribution during drying. Similar results have been observed in previous work. Sietsma et al.47 investigated the preparation of Ni/SiO2 catalysts via the impregnation and drying method. They found that with 4.2 M initial metal concentration, the average crystal size after drying was 9 nm which was around the same size as the mesopore
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Figure 5. Effect of the drying temperature on the water volume fraction for C0 ) 100 mol/m3, R1 ) 0.53, and R2 ) 0.013.
diameter of the SBA-15 support they used. (3) Since the melting point of Ni(NO3)2 is ∼56 °C, part of the nickel nitrate could be melted when the samples were dried at 60 °C. For high metal loading conditions (C0 > 3 M), the liquid Ni(NO3)2 may lead to the liquid phase remaining continuous during drying, and thus film-breakage would not occur. This will favor a final uniform distribution. The effect of film-breakage on the metal distribution during drying will be further discussed in the following section. For practical use of the catalyst it is of interest to study the effect of calcination on the distribution of the metal in the support. Figure 4 panels d-f show the metal distribution after calcination with the variation of the metal concentration from 0.05 to 4 M. It is clear that for all cases studied in this work the metal distribution after drying and after calcination is similar, indicating that the effect of calcination on the metal redistribution is not significant. Therefore, it is reasonable to assume that for our specific systems the metal profile obtained after drying can be used to predict the final metal distribution of the catalysts. 3.2. Comparison of Experiments and Simulations. In this section we focus on low metal loads where the initial metal concentration is less than or equal to 0.1 M. For these cases, the effect of the metal ions on the solvent properties during drying is small, and pore-blockage and crystallization are negligible. Therefore, the final metal distribution is determined by the initial metal concentration (C0), adsorption strength (Keq, kads, Csat), drying conditions (Tbulk), transport properties (Dl,i, K) and film-breakage conditions (R1, R2). Given a specific metal-support system, the parameters for adsorption, transport, and film-breakage are fixed and cannot be adjusted in a straightforward manner. Thus, the final metal profile can be controlled mainly by changing the initial metal concentration and the drying temperature. The variation of the water volume fraction in the support during drying for different drying temperatures is shown in Figure 5, where the symbols represent the experimental data and the lines represent the simulation results. To investigate the effect of film-breakage, two sets of simulation results are presentedsone including and one excluding the effects of film breakage. In the simulations with film-breakage, we assume R1 ) 0.53 representing the situation where film-breakage starts as the water evaporation transits from the large pores to the small pores (R1 ) voidage volume fraction x percentage of small pores in the void ) 0.67 × 0.8), and R2 ) 0.013 below which the liquid phase is completely discontinuous (solvent flux ) 0). The value of R2 was chosen on the basis of the regression of experimental data for C0 ) 0.04 M, and thereafter we held this value a constant for other cases. R2 ) 0.013 corresponds to the mass ratio of water in the support equal to 2%. In general the value of R2 is related to the hydrophilic or hydrophobic properties of the solvent on the support, the size of the small pores, and the pore network in the support.51 The structure of
Figure 6. Effect of the drying temperature on the drying rate for C0 ) 100 mol/m3, R1 ) 0.53 and R2 ) 0.013: (a) Tbulk ) 22 °C; (b) Tbulk ) 60 °C; (c) Tbulk ) 115 °C.
the pore network has a significant effect on the transport of the solvent during drying. Neimark et al. proposed that the point where the liquid phase becomes completely discontinuous (i.e., R2) can be calculated on the basis of a coordination number for the support if the porous space can be represented as a system of intersecting channels and the coordination number is the average number of channels meeting at a lattice site.28 In Figure 5, it is clear that drying is much faster at higher drying temperatures. When drying is carried out at room temperature (Tbulk ) 22 °C), drying is very slow and an unacceptable amount of water remains in the support at the end. When the drying temperature is above 60 °C, the mass fraction of the water in the support can be reduced to 1% within a reasonable amount of time. From Figure 5 it can be seen that for low to moderate drying rates (Tbulk < 60 °C), the effect of film-breakage on the change in the water content inside the support during drying is small. When the drying temperature is high, the drying rate decreases slightly when film-breakage is taken into account. This effect is observed since for fast drying rates film-breakage occurs at the support surface fairly early in the drying process. For all three cases shown in Figure 5, the comparison between the experiments and simulations is generally good, and the effect of film-breakage is rather small. Corresponding to the data in Figure 5, Figure 6 shows experimental data and simulation results for the drying rate. The simulation results in the figure include the effect of filmbreakage. Simulations without film-breakage have also been carried out (not shown) and they are very similar to the simulation results in Figure 6. As before, the drying temperature is 22, 60, and 115 °C, respectively. The variation of the
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Figure 8. Experimental measurement of the final metal distribution for C0 ) 100 mol/m3. The lines here are drawn to guide the eye.
Figure 7. Effect of the drying temperature on the final metal profile for C0 ) 40 mol/m3, R1 ) 0.53, and R2 ) 0.013: (a) Tbulk ) 22 °C; (b) Tbulk ) 115 °C; (c) Tbulk ) 180 °C.
temperature in the support during drying was also examined in this work (not shown). For a low drying temperature, initially the temperature in the particle decreases due to evaporation, reaches a plateau, and then increases (Tbulk ) 22 °C). Corresponding to the change of the particle temperature, the drying rate shows three stages (see Figure 6a), i.e., a decrease in the rate, a plateau stage, and a second decrease in the rate. The sharp drop in the drying rate in the first stage is due to the sharp drop in the particle temperature at the beginning of drying. The third stage occurs when the drying front starts to move from the support surface to the center due to the loss of water in the support. For a moderate drying temperature (Tbulk ) 60 °C), the particle temperature only changes slightly before reaching a plateau. Thus, only two stages can be observed in Figure 6b. For a high drying temperature (Tbulk ) 115 °C), initially the temperature in the particle increases, reaches a plateau, and then increases again. Therefore, we observe a preheating period, followed by a constant-rate period, and a falling-rate period (see Figure 6c). Similar results have been reported in previous work.25 In general, the simulation results match the experimental measurements fairly well. The final metal profiles for different drying temperatures are shown in Figure 7 when the initial metal concentration is 0.04 M. Clearly, more metal is accumulated near the surface with an increase in the drying temperature. This is due to the competition between convection and diffusion. For low drying temperatures, diffusion dominates the drying procedure, which leads to a uniform profiles (see Figure 7a). For relatively high drying temperatures, convection dominates the drying process at the early stages of drying, which transports the water and metal ions toward the external surface, leading to pronounced egg-shell profiles. Although at the late stages of drying, diffusion may control the drying process, causing the metal to move toward the support center and the metal distribution to flatten,
the final metal distribution still remains egg-shell (see the experimental data in Figure 7b,c). One can see from Figure 7 that film-breakage is very crucial to capture the egg-shell profiles observed in the experiments. If the effect of film-breakage is not considered, egg-white profiles are predicted for relatively high drying temperatures (see Figure 7b,c). When the effect of film-breakage is taken into account, egg-shell profiles can be obtained for relatively high drying temperatures (see Figure 7b,c). In all the cases studied in Figure 7, the egg-shell profiles are greatly enhanced and the simulations show a good agreement with the experiments if the effect of film-breakage is considered. This is due to the effect of film-breakage on convection and diffusion. If film breakage occurs at the early stage of drying, it will reduce the liquid flux and thus reduce the effect of convection. At the late stages of drying, diffusion may dominate the drying process, and its effect is also reduced by filmbreakage. Therefore, we believe film-breakage suppresses the egg-shell distribution at the early stages of drying and favors the egg-shell distribution at the late stages of drying. In Figure 7, our simulations show that the egg-shell distribution is enhanced by film-breakage, indicating that under the drying conditions used in Figure 7 film-breakage does not start at the very early stage of drying so its main contribution is to reduce the effect of diffusion. On the other hand, if the drying rate is sufficiently high and film-breakage occurs at the surface nearly immediately, the effect of convection should be reduced and the extent of the egg-shell distribution should be reduced. To validate our hypothesis, we experimentally measured the metal profiles for different drying rates (see Figure 8). The lines in Figure 8 are only meant as a guide for the eye. For a low drying temperature (Tbulk ) 25 °C) the effect of convection and film-breakage is not significant so a nearly uniform profile is observed. For a relatively high drying temperature (Tbulk ) 120 °C) convection accumulates the metal near the surface at the early stage of drying and film-breakage reduces the effect of back-diffusion at the late stage of drying so a more pronounced egg-shell profile can be obtained. If the drying rate is sufficiently high (Tbulk ) 500 °C) isolated domains occur at the surface nearly immediately during drying and the metal has no time to migrate from the center toward the surface so the egg-shell profile is less pronounced. Similar results have been observed in previous work.8 In Figure 9, we compare the final metal profiles for experiments and simulations for a higher initial metal loading of C0 ) 0.1 M. We found that for all the cases studied, film-breakage enhances the egg-shell profiles, and simulations show good agreement with the experiments only if the effect of filmbreakage is considered. This is in agreement with our previous results at lower initial metal concentrations (see Figure 7). From Figure 7 and 9, it can be seen that for the cases we have examined, film-breakage must be considered if one is to capture the metal profiles observed in the experiments. Therefore, it is of
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4. Conclusions
Figure 9. Effect of the drying temperature on the final metal profile for C0 ) 100 mol/m3, R1 ) 0.53, and R2 ) 0.013: (a) Tbulk ) 22 °C; (b) Tbulk ) 115 °C; (c) Tbulk ) 180 °C.
interest to investigate the sensitivity of the metal distribution after drying to the film-breakage parameters, R1 and R2. Generally, the egg-shell profile is enhanced with an increase in R1 (not shown). However, when R1 is sufficiently high (R1 > 0.53) we find that the metal distribution changes only slightly when further increasing this number. This is because two mechanisms occur with the variation of R1. For a high R1 value, film-breakage occurs at the beginning of drying, which reduces the water flux toward the surface, and thus suppresses the accumulation of the metal at the surface. With continued drying, metal starts to move back to the support center due to the gradient of the metal concentration in the solvent. Film-breakage can reduce this back diffusion, and this reduction effect increases with an increase in R1. Therefore, for a high R1 value film-breakage suppresses the egg-shell profile at the earlier stages of drying and favors the egg-shell profile at the later stages of drying. Consequently, the effect of R1 on the final metal profiles is due to the compensation of these two contributions. To enhance the egg-shell profile, an optimum R1 is required. The egg-shell profile can be greatly enhanced with increasing the value of R2 (not shown). This is because the variation of the value of R2 has only a slight effect on the early stage of drying, while its effect on the final stage of drying is significant. Therefore, for a high value of R2 (R2 ) 0.13), the pronounced eggshell profile formed in the early stage of drying may be still observed at the end of drying. The sensitivity analysis was also carried out for other parameters based on our nickel/alumina system (not shown). In general, the egg-shell profiles can be enhanced by increasing the permeability and uniform profiles can be obtained by increasing the diffusion coefficient. This is in agreement with our previous work.25,27 In our specific case the adsorption process is much faster than the transport process; we found that the metal redistribution is not sensitive to the variation of the kinetic adsorption constant.
We established a theoretical model to predict the metal distribution during drying and compared the simulation results with experimental measurements for a nickel/alumina system. The adsorption and transport parameters used in the simulations are obtained from separate experiments/calculations. From the experiments, several interesting phenomena were observed. (1) We found that egg-shell profiles can be enhanced by increasing the drying temperature and the initial metal concentrations, if the metal load in the system is low or moderate. For high metal loadings, nearly uniform metal profiles are observed from the experiments. (2) We compared the metal profiles after drying and after calcination and showed that for our specific situation the effect of calcination on the metal distribution is not significant. Thus, the metal profiles obtained after drying can be used to predict the final metal distribution of the catalysts. (3) By plotting the variation of the water content and the drying rate with the drying time for different initial metal concentrations, we found that if the initial metal concentration is high the solvent properties may change dramatically during drying because of water evaporation and high metal concentration in the liquid phase. We also compared the simulations with experiments to validate our theory. Since the effect of crystallization and poreblockage is not considered in our model, our comparison only focused on low metal load conditions. To investigate the effect of film-breakage on the metal redistribution during drying, we assume that once film-breakage occurs the solvent flux linearly decreases with the decrease in the water volume faction until the water volume fraction reaches a certain point, at which the liquid flux completely stops and the metal is enclosed in isolated liquid domains. We found that film-breakage is crucial to capture the metal profiles observed in the experiments and the simulations show an excellent agreement with experiments if the effect of film-breakage is considered. In summary, the goal of this study is to better understand the fundamental mechanisms during drying, and to determine the key parameters used to generate a desired metal profile, using theoretical simulations and experiments. We have compared experiments and simulations for low metal concentration conditions (C0 < 0.1 M). For moderate and high metal concentrations, crystallization may become important and the change of the solvent properties during drying due to the increase in the metal concentration in the solvent may greatly affect the drying process. Pore-blockage may also become important at high metal concentrations. It remains to be seen what is the relative importance of these additional phenomena that occur at moderate and high metal concentrations, and future work should investigate how these phenomena interact to impact drying. Acknowledgment We wish to acknowledge partial financial support for this work from the National Science Foundation and the Rutgers Catalyst Manufacturing Science and Engineering Consortium. Literature Cited (1) Ertl, G.; Kno¨zinger, H.; Weitkamp, J. Preparation of Solid Catalysts; Wiley-VCH: Weinheim, Germany, 1999. (2) Shyr, Y. S.; Ernst, W. Preparation of nonuniformly active catalysts. J. Catal. 1980, 63, 425–432. (3) Gavrilidis, A.; Varma, A.; Morbidelli, M. Optimal distribution of catalyst in pellets. Catal. ReV.-Sci. Eng. 1993, 35, 399–456.
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ReceiVed for reView September 16, 2009 ReVised manuscript receiVed February 1, 2010 Accepted February 2, 2010 IE9014606
