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MASS TRANSFER IN PORE STRUCTURES OF SUPPORTED CATALYSTS

Abstract

The effects of gas-solid interaction and mass transfer in fixed-bed systems of supported catalysts were analyzed for g -Al2O3 (support) and Cu/g -Al2O3 (catalyst) systems. Evaluations of the mass transfer coefficients in the macropores and of the diffusivity in the micropores, as formed by the crystallite agglomerates of the metallic phases, were obtained. Dynamic experiments with gaseous tracers permitted the quantification of the parameters based on models for these two pore structures. With a flow in a range of 18 cm³ s-1 to 39.98 cm³ s-1 at 45ºC, 65ºC and 100ºC, mass transfer coefficients k m =4.33x10-4 m s-1 to 7.38x10-4 m s-1 for macropore structures and diffusivities Dm =1.29x10-11 m² s-1 to 5.35x10-11 m² s-1 for micropore structures were estimated

Pore structures; mass transfer; diffusivity


MASS TRANSFER IN PORE STRUCTURES OF SUPPORTED CATALYSTS

F.R.C. Silva, A. Knoechelmann, M. Benachou and C.A.M. Abreu

Laboratório de Processos Catalíticos, Departamento de Engenharia Química,

UFPE 50.740-521 Recife-PE, Brazil

(Received: March 5, 1997; Accepted: August 5, 1997)

Abstract: The effects of gas-solid interaction and mass transfer in fixed-bed systems of supported catalysts were analyzed for g -Al2O3 (support) and Cu/g -Al2O3 (catalyst) systems. Evaluations of the mass transfer coefficients in the macropores and of the diffusivity in the micropores, as formed by the crystallite agglomerates of the metallic phases, were obtained. Dynamic experiments with gaseous tracers permitted the quantification of the parameters based on models for these two pore structures. With a flow in a range of 18 cm3 s-1 to 39.98 cm3 s-1 at 45oC, 65oC and 100oC, mass transfer coefficients km =4.33x10-4 m s-1 to 7.38x10-4 m s-1 for macropore structures and diffusivities Dm =1.29x10-11 m2 s-1 to 5.35x10-11 m2 s-1 for micropore structures were estimated.

Keywords: Pore structures, mass transfer, diffusivity.

INTRODUCTION

In a catalyst pellet different pore structures may be found. In supported catalysts a two-level structure is formed, where the agglomerates of the support form the macropores and the crystallites of the supported metallic phase make up the microstructure. The process of mass transfer of a component from the bulk of the external fluid into the catalytic solid, based on the mechanism of steps in series, may be quantified as relations established between the contents of the component at each level of the pore structure. This is possible when relations at one level are applied and relations are established at an immediately lower level. The configurational diffusion identified specially in zeolithe catalysts occurs in complex porous structures where the dimensions of the pores are comparable to those of the reagent molecules. The quantification of the mass transfer effects in these structures was made possible by experimental techniques, in some cases, which could be linked to theoretical models (Dogu and Smith, 1975; Arnost and Schneider, 1994; Schneider and Valus, 1985; Ruthven and Shah, 1977; Van Deemter et al., 1956). Structured models which address the internal levels of these structures have shown themselves capable of translating the results when dynamic methods are applied (Kucera, 1965; Villermaux, 1972; Authelin et al., 1988; Rodrigues et al., 1991). In the present work the dynamic negative-step method was used with methane diluted in nitrogen as the tracer. The results for g -Al2O3 and Cu/g -Al2O3 packings were analyzed and compared with structured models for one and two porosity levels.

DYNAMIC RELATIONS OF FLUID IN SUPPORTED CATALYSTS

Relations can be established between the concentrations of a fluid component at different levels of the pore structure of a supported catalyst. Away from equilibrium, these relations modify themselves, becoming dynamic relations which can be expressed by transfer functions between the different pore sizes of the catalyst particles. Two transfer functions are identified, L(s) for the steps of mass transfer of the component from one level to another in the pore structure and H(s) for the diffusion process at each level of the structure. At the micropore structure level, the outer phase is the fluid in the macropores. The transfer functions for the fluid component between the external surface of the crystallites and their internal pores are:

(1)

where < C¢ m (s)> is the average concentration in the crystallites and C¢ m s(s) is the concentration in their internal surfaces. The expression for a mass balance applied over a small volume of the micropore struture is given by:

(2)

where C¢ m is the concentration of the fluid component in the structure and D¢ m the diffusion coefficient. The application of a mass balance for the fluid component, which diffuses from the macropores into the crystallite, yields :

(3)

where is the concentration of the fluid component in the macropore, km is the mass transfer coefficient in the fluid present in the pores of the crystallites, and Am and Vm are their respective average surface and volume. The evaluation of the characteristic mass transfer time of the component in the bulk of the crystallites (tm =a m lm /km ) allows us to the combine equations (1), (2) and (3), and the result is Lm (s):

(4)

where a m is the partition coefficient in the micropores. The transfer functions from the bulk fluid of a fixed bed to the macropores inside the catalyst, are given by the following expressions:

(5)

where < C¢ M(s)> is the average concentration of the fluid component in the structure of the macropores and C(s) and are the concentrations of the fluid component on the external surface of the particle and on the internal surface of the pores near the crystallites of the supported metallic phase, respectively. The diffusion of the fluid component in the macropores can be represented by:

(6)

where is the diffusivity in the macropores.

The application of a mass balance between the interstitial fluid and that in the macropores yields:

(7)

where kM, AM and VM are the mass transfer coefficient in the macropores and the external area and the volume of the particle, respectively. By defining a characteristic external mass transfer time (tM) at the macro level (tM=a M lM/kM), it is possible to write the transfer function LM(s), which is given by:

(8)

where a M is the partition coefficient, BMm=((1-b m )Lm (s) + b M)/a M and s’ is a variable function which depends on the Laplace variable.

The mass transfer functions between the levels in equations (1), (4), (5) and (8) may be approximated by first-order functions. At the level of crystallites (m ) and at the macropore level (M), these relations become:

(9)

(10)

where tm and tm are the global mass transfer times and tMd and tm d the characteristic diffusion times. The effects of mass transfer and interactions in the catalytic bed may be obtained as the intraparticle steps are associated with the interstitial flow. The fixed-bed fluid-solid system is represented by the tanks-in-series with the fluid-solid interaction model. For the tracer at the outlet of the J-th tank, the transfer function G(s) is given by:

(11)

A model which takes into account the effects of the mass transfer occurring in the macro and micropore structures allows the evaluation of the contribution of each level separately. The transfer function of the model for the two levels was obtained by rewriting equation (11) so that LM (s) may be identified in (8), and by introducing the function Lm (s), in which is given equation (10) that was defined for the macro and the micropore structure interactions, as follows:

(12)


Figure 1: Distribution of crystallite diameters in the Cu/g -Al2O3 catalyst obtained by scanning electron microscopy.

For the crystallites with different forms and sizes (lm ), a direct relation of their sizes and the fluid component mass transfer times. The repartition of the set in classes identified by their global mass transfer times at the microporous level is adopted. The partition coefficient of each class i of the crystallite is given by a m i= a m Wi , where a m is the partition coefficient of the bulk of all the classes and Wi is the fraction of the fluid component adsorbed at equilibrium at site i. It is proposed that the mass transfer process occurs by a parallel mechanism with the crystallite classes interacting with the fluid in the macropores, each one with its own characteristics. Lm (s) may be expressed as a function of the distribution of the crystallite class g(lm ):

(13)

where lm 0 and tm 0 are characteristic size and transfer time for the crystallites.

The distribution function of the crystallite size g(lm ) is directly related to the transfer time distribution f(tm ) and, therefore, dW=g(lm )dlm =f(tm ) dtm ; thus, it is possible to calculate the average diffusion time in the micropores:

(14)

EXPERIMENTAL METHODS AND PARAMETER ESTIMATION

In the mass transfer processes and gas-solid contact, porous g -alumina (Rhône Poulenc, GCO-70) and Cu (18.7% in weight) supported catalyst were used. The supported catalyst was prepared from Cu(NO3)2.3H2O, using the dry impregnation method followed by calcination and programmed reduction in a temperature range from 30oC to 400oC. A scanning electron microscope (JEOL-JSM/T2000) was used to determine the distribution of the copper crystallite size in the Cu/g -Al2O3 pores and on the outer surface. The results obtained are shown in Figure 1.

Continuous samplings of the mobile phase (N2) in contact with 34.5g of the solid bed were made through a thermal conductivity detector with an AD/DA detector/microcomputer interface. The methodologies applied to estimate the flow, the mass transfer and the gas-solid interaction parameters for both CH4-N2/g -Al2O3 and the CH4-N2/Cu/g -Al2O3 systems were:

- the treatment of the negative-step curves at the entrance and outlet of the bed; the identification of the base lines and the adjustment of the lower curve by an exponential;

- the residence time distribution (RTD) determination and method of the moments applied to the normalized curves; the comparison of the experimental methods with the expressions obtained from the transfer functions G(s) (11 and 12), developed for g -Al2O3 and Cu/g -Al2O3, respectively;

- the evaluation of the model parameters considered as initialization values when obtained by linearization; the optimization of the concentration values calculated by the models in the real domain and then compared with the experimental data;

- the employment of the transfer time distribution function equivalent to the crystallite size distribution function for the two-level model for the Cu/g -Al2O3 system.

RESULTS AND DISCUSSION

From the operations with the CH4-N2 gas phases and g -Al2O3 and Cu/g -Al2O3 systems in a flow range of 18.00 cm3 s-1 to 39.98 cm3 s-1, at 1 atm and at temperatures of 45oC, 65oC and 100oC, changes in concentration in the gas flow at the entrance and outlet of the fixed bed were obtained. The suppression of methane in the nitrogen feed stream in the fixed bed resulted in normalized negative-step curves for the two systems. The values of the parameters tm, a M and J were obtained (equation 11) from the moments of the RTD curves for the systems and were used in the initialization of G(s) optimization in the time domain. This procedure introduces modifications in the values of the initialized parameters, reducing to a minimum the differences between the concentrations calculated in the model and those measured by the RTD experiment. The concentrations at the outlet of the bed were calculated by:

(15)

where the fast Fourier inverse TF-1 (CVTFR algorithim) was used. Defining a quadratic objective function (f0), as

(16)

where and were the concentrations calculated by equation (15) and the experimental concentrations in the gas flow at the outlet of the fixed bed, respectively. The optimized final values of the parameters were obtained by the sequential research method (Box, 1965). The initialization values of the mass transfer coefficients at 45oC, 65oC and 100oC for both the CH4-N2/g -Al2O3 and the CH4-N2/Cu/g -Al2O3 systems used to start up the optimization calculation, were obtained by following this methodology. The results obtained are given in Table 1.

TkM 104 (m s-1)(0C) CH4-N2/g -Al2O3 CH4-N2/Cu/g -Al2O3 456.847.38654.416.961004.336.46
Table 1: Gas-solid mass transfer coefficients for the CH4-N2/g -Al2O3 and CH4-N2/Cu/g -Al2O3 systems

The development of a structured method at two internal levels of the pore structure is proposed for the Cu/g -Al2O3 catalyst. Taking into account the decomposition of the global mass transfer time tm into tM and tm , the times for the respective macro and micropore levels, it is possible to establish the following relationships:

(17)

tm=tM (g -Al2O3) and a M=a M (g -Al2O3) (18)

a M (g -Al2O3)=b M + (1-b M) a m (Cu) (19)

The sequences of these levels allowed the establishment of a new transfer function G(s) (eq. (12)). The dependence of Lm (s) is given by equation (13) and the partition coefficient a m is established for the gas between the macro and micropores. The function f(tm ) was identified as the transfer time tm of CH4 at the micropore level. It was related directly to the crystallite size g(lm ) distribution (Figure 1), and it is represented by a log-normal function. It is supposed that the mass transfer of the gas in the crystallites is diffusive and the transfer time of the process (tm d) is given by:

(20)

where l m is the form factor of the crystallites and lm an average dimension of the crystallites.

With these values applied to equation (12), by following the inversion and optimization methodologies, one has access to the diffusion coefficient in the micropores of the metallic phase of the Cu/g -Al2O3 catalyst. Table 2 shows the calculated micro/macropore partition coefficients and the diffusivities in the micropores for the Cu/g -Al2O3 system.

Figure (2a) shows a typical experimental RTD curve obtained at the outlet of the bed compared with the values of the simulated structured model at two levels from concentration curves obtained at the entrance of the system. Figure (2b) amplifies the retention effects in the internal structure indicated at the lower part of the curves.


Figure 2: (a) Simulation of the RTD at 650C, Cu/g -Al2O3; (b) Lower part of figure (a) amplified

10T (0C) a m 1011 (m2 s-1)45 65 100 5.35 4.39 3.54 1.29 1.97 2.81
Table 2: Partition and diffusion coefficients for the CH4-N2/Cu/g -Al2O3 system

CONCLUSIONS

Using the partition of the transfer times at the macro and micropore levels of the Cu/g -Al2O3 system, one can observe the orders of magnitude which indentify the mass transfer of methane in the macropores as the controlling step of the process. Orders of magnitude of 10-4 s identify the controlling step in relation to the values of 10-1 s for the transfer of the crystallites in the micropores. The two-level structured model represents the mass transfer processes of gaseous components in the micropores of the crystallite agglomerates and in the macropores of the support and associates them with the methane flow in the fixed bed of the supported catalyst.

NOMENCLATURE

Am Average surface of crystallite, m2 AMm External area of the particle, m2 BMm Function of Lm C(s) Concentration of the bulk fluid in the fixed bed, mol m-3 CM(s) Concentration of the fluid in the macropores (s) Concentration in the structure of the macropores, mol m-3 (s) Concentration on the internal surface of the macropores, mol m-3 (s) Concentration in the macropores, mol m-3 (s) Concentration of the fluid in the crystallite micropore, mol m-3 (s) Concentration on the internal surface of the crystallite, mol m-3 CE(s) Concentrations at the inlet of the fixed bed, mol m-3 (t) Calculated concentrations at the outlet of the fixed bed, mol m-3 (t) Experimental concentrations at the outlet of the fixed bed, mol m-3 (t) Calculated concentrations, mol m-3 Cs(s) Concentration at the outlet of the fixed bed, mol m-3 Diffusivity in the macropores, m2 s-1 Diffusivity in the micropores, m2 s-1 G(s) Transfer function H(s) Transfer function HM(s) Transfer function in the macropores Hm (s) Transfer function in the micropores L(s) Transfer function from one level to another LM(s) Transfer function from bulk fluid to the macropores Lm (s) Transfer function from macropores to the micropores VM Volume of the particle, m3 Vm Volume of the crystallite, m3 W Fraction of the fluid Wi Fraction of the fluid component f0 Objective function f(tm ) Transfer time distribution g(lm ) Distribution function of crystallite sizes J Number of tanks-in-series kM Mass transfer coefficient in the macropores, m s-1 km Mass transfer coefficient in the micropores, m s-1 Lm Dimension of crystallites, m Lm 0 Characteristic dimension of crystallites, m Lmax Maximal dimension of crystallites, m s Laplace variable s’ Variable dependent on Laplace variable TF-1 Fourier inverse transform t Variable time, s tm Global time of mass transfer, s t0 Spatial time, s tM Time of mass transfer in macropores, s tm Time of mass transfer in micropores, s tm 0 Characteristic time of mass transfer in crystallites, s tMd Diffusive time in macropores, s tm d Diffusive time in micropores, s

Greek

a M Partition coefficient in macropores a m Partition coefficient in micropores b M Macropore porosity e Bed void faction l m Form factor of crystallites

Subscript

E Inlet of the bed i Component M Macropores md Diffusion in macropores m Mass transfer max Maximal O Objective s Outlet of the bed m Micropores m 0 Characteristic micropores

Superscript

‘ in the structure " in the pores

REFERENCES

Arnost, D. and Schneider, P., Effective Diffusivities from Dynamic Diffusion Cell: The General Moment Analysis, Chem. Eng. Sci., 49 (3), 393 (1994).

Authelin, J. R.; Schweich, D. and Villermaux, J., A New Appraisal of Mass Transfer Processes in Zeolithes of Transient Methods , Chem. Eng. Tec., 11, 432 (1988).

Box, P., A New Method of Constrained Optimization and a Comparison with Other Met hods, Computer Journal, 8, 42-52 (1965).

Dogu, G. and Smith, J. M., A Dynamic Method for Catalyst Diffusivities, A.I.Ch.E. Journal, 21 (1), 58 (1975).

Kucera, K., Contribution to the Theory of Chromatography: Linear non Equilibrium Elution Chromatography, Journal of Chromatography, 19, 237 (1965).

Schneider, P. and Valus, J., Transport Parameters of Porous Catalyst via Chromatography with a Single Pellet-String Column , Chem. Eng. Sci., 40 (8), 1457 (1985).

Rodrigues, A. E.; Zuping, L. and Loureiro, J. M., Residence Time Distribution of Inert and Linearly Adsorbed Species in a Fixed Bed Containing Large-Pore Supports: Application in Separation Engineering , Chem. Eng. Sci., 46 (11), 2765 (1991).

Ruthven, D. M. and Shah, D. B., Measurements of Zeolithic Diffusivities and Equilibrium Isotherms by Chromatography, A.I.Ch.E. Journal, 23, 4 (1977).

Van Deemter, J.J.; Zuiderweg, F. J. and Klinkenberg, A., A Longitudinal Diffusion and Resistance to Mass Transfer as Causes of non-Ideality in Chromatography, Chem. Eng. Sci., 5, 271 (1956).

Villermaux, J., Analyse des Processus Chromatographiques Lineaires à l’Aide des Modeles Phenomenologiques, Chem. Eng. Sci., 30, 955 (1972).

Publication Dates

  • Publication in this collection
    09 Oct 1998
  • Date of issue
    Sept 1997

History

  • Received
    05 Mar 1997
  • Accepted
    05 Aug 1997
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