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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 maysignificantly impact the metal distribution within the support. Therefore we need to have a fundamentalunderstanding of drying. In this work, a theoretical model is established to predict the drying process, and themodel predictions are compared with experimental measurements of a nickel/alumina system. It is found thategg-shell profiles can be enhanced by increasing the drying temperature or the initial metal concentration ifthe metal loading is low. For high metal loadings, nearly uniform profiles are observed after drying. We havealso investigated how breakage of the liquid film inside the pores of the support can affect the metal distributionduring drying. It was found that film-breakage has a significant impact on the metal distribution, and it isimportant 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 industrythe 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 catalysts 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

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 pro-

cesses 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 thedrying 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 mode-

rate.12,24-27 Neimark et al.5,28 were among the first to theoreti-

cally 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 capillaryflow 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

* To whom correspondence should be addressed. Tel.: 732- 445-4243. Fax: 732-445-2581. E-mail: bglasser@ rutgers.edu.

Rutgers University. Graz University of Technology.

Ind. Eng. Chem. Res. 2010, 49,26492657 2649

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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 (film-breakage). 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 constantduring 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:

Equations 1 and 2 represent the mass balances of the drying

medium (air) and the solvent (water). Equations 3 and 4represent the mass balances of the metal dissolved in the liquid

and deposited on the support. Equation 5 is the energy balance.

gand lare the volume fractions of the gas and liquid phases,Cg,a (mol/m

3) 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/(m

2 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 rateof metal adsorption, which is described using a Langmuir

model.32-34

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 assumeit to be a constant.hg,i(J/mol) represents the enthalpy of the air

or solvent vapor.hl(J/mol) andhs(J/kg) denote the enthalpy of

the liquid and solid. (J/(m s K)) is the effective thermalconductivity.

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.

where R1 represents the water volume fraction when film-

breakage 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,aand Ng,vare assumed to follow the

dusty gas model (DGM),35 which considers the effect of

molecular diffusion, Knudsen diffusion, and viscous flow.

In eq 8Pg(Pa) is the total gas pressure, R (8.314 J/(mol K))is the gas constant, T(K) is the temperature, xg,irepresents the

t(gCg,a) ) -

1

r

r(rNg,a) (1)

t(lCl,s) ) -

1

r

r(RrNl,s + rNg,v) (2)

t(lCl,i) ) -

1

r

r(RrNl,i) - FsRi (3)

t(Cs,i) ) Ri, i ) metal component (4)

t(

i)1

2

gCg,ihg,i + lCl,shl + Fshs) )

- 1

r

r(i)1

2

rNg,ihg,i + RrNl,shl - rT

r) (5)

Ri ) kadsCl,i(Csat - Cs,i) - kdesCs,i, i ) metal component

(6)

R ) 1 when fg R1

R )(R1 - f)

(R1 - R2) when R1 > f> R2

R ) 0 when fe R2

(7)

-Pg

RTxg,i -

xg,i

RT(1 -KKg,effPg

gDKnud)Pg )

j)1j*i

2 xg,jNg,i - xg,iNg,j

Dg,ij+

Ng,i

DKnud(8)

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vapor or air mole fraction in the gas phase, Dg,ij(m2/s) and DKnud

(m2/s) are the effective binary and Knudsen diffusion coefficients

estimated from the kinetic gas theory,36 andKg,effis the intrinsic

permeability of the gas phase, which has the form

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 Darcys law,41

where Kl,eff is the relative permeability of the liquid phase, l(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 pressurePc(Pa).41 In the present workPcis described

using the form proposed by Perre et al.,42

where (N/m) represents the surface tension, and Ml,s is themolecular 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

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 (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 no-

current equation:44

wheren 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.

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 differential-algebraic equations.46

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-alumina pellets provided by Saint-Gobain wereused 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 impregna-tion. 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 impregna-

tion, 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 500C 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)2concentration 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:

This equation can be used to calculate the nickel concentrationin 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 (micro-

XRF).

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

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

Keqcan be calculated from the line intercept and the slope. Six

samples with Ni(NO3)2concentration 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 onthe supports increases rapidly at the beginning of impregnation.

Kg,eff) 1 - 1.11(l ) (9)

Nl,s ) -Cl,sKKl,eff

lPl (10)

Pc ) 1.364 105(

lcl,sMl,s

Fs)

-0.63

(11)

Nl,i ) -Cl,iKKl,eff

l

P - lDl,icl,i - lCl,iZiDl,iF

RTl,

i ) metal component (12)

i)1

n

zi

Nl,i

) 0 (13)

Kl,eff)(l )3

(14)

CNi ) 0.0878Auv (15)

1

Ceq)

1

CsatKeq

1

Cs+

1

Csat(16)

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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 supportCs. 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,

where C0 represents the initial metal concentration in the

solution.9,32 When plotting dC0/dtversusC0, a straight line can

be obtained and the value of the kinetic adsorption constant

kadscan be calculated from the slope. To obtainkads, 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 m. We

used a sieve to remove large particles, and then used water towash 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 becalculated using the modified Ergun equation.49

Using eq 18, we obtained a permeability ofK) 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 Tbulkwas varied from 22 to 180 C. A uniform initial

metal distribution was utilized indicating that impregnationreached an equilibrium state.

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 timeuntil 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 distribu-

tion. Figure 3 shows experimental measurements of the evolu-

tion 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

Figure 1. The variation of the concentration of the metal deposited on thesupport with the impregnation time.

dC0

dt ) -kadsFCsatC0 (17)

K) i

3idci2

200 (18)

Figure 2. Variation of (a) the water volume fraction and (b) drying ratewith the drying time at Tbulk) 60 C and C0 ) 100 mol/m

3.

Figure 3. Effect of the initial metal concentration on the drying rate atTbulk) 60 C for (a) catalyst samples and (b) solution samples. The lineshere are included as a guide for the eye.

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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 thesupport 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)2concentra-

tion 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 concentra-

tion (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. Thisis 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 onthe 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 isdetermined 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 drivesthe 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 crystal-

lization. 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/SiO2catalysts via the

impregnation and drying method. They found that with 4.2 M

initial metal concentration, the average crystal size after dryingwas 9 nm which was around the same size as the mesopore

Figure 4.Effect of the metal concentration on the metal profiles after drying atTbulk ) 60C: (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 metalconcentrations; (f) high metal concentrations.

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diameter of the SBA-15 support they used. (3) Since the melting

point of Ni(NO3)2is 56C, 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)2may 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 redistribu-

tion 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 arenegligible. 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 investigatethe 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 assumeR1)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 fractionxpercentage 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 forC0) 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 smallpores, and the pore network in the support.51 The structure of

the pore network has a significant effect on the transport of the

solvent during drying. Neimark et al. proposed that the pointwhere 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 (Tbulk0.53) we find that the

metal distribution changes only slightly when further increasing

this number. This is because two mechanisms occur with the

variation ofR1. For a high R1 value, film-breakage occurs at thebeginning 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 highR1value 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 ofR1 on the

final metal profiles is due to the compensation of these two

contributions. To enhance the egg-shell profile, an optimumR1is

required. The egg-shell profile can be greatly enhanced with

increasing the value ofR2(not shown). This is because the variationof the value ofR2 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 ofR2(R2 ) 0.13), the pronounced egg-

shell 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 thekinetic adsorption constant.

4. Conclusions

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 concen-

tration 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 tovalidate our theory. Since the effect of crystallization and pore-

blockage 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 simula-

tions show an excellent agreement with experiments if the effect

of film-breakage is considered.

In summary, the goal of this study is to better understandthe 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.

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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)115C; (c) Tbulk) 180 C.

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ReceiVed for reView September 16, 2009ReVised manuscript receiVed February 1, 2010

Accepted February 2, 2010

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