Liquid Dispersion, Mass Transport, and Chemical Reaction in

19 Liquid Dispersion, Mass Transport, and

Downloaded by UNIV OF CALIFORNIA SANTA BARBARA on August 25, 2015 | http://pubs.acs.org Publication Date: June 1, 1975 | doi: 10.1021/ba-1974-0133.ch019

Chemical Reaction in Supported Liquid Phase Catalysts for SO Oxidation 2

HANS LIVBJERG, BENNY SORENSEN, and JOHN VILLADSEN Instituttet for Kemiteknik, Danmarks tekniske H0jskole, Lyngby, Denmark

A mathematical model for liquid dispersion, diffusive mass transport restnctions, and chemical reaction in supported liquid phase catalysts is presented. The liquid phase is assumed to be dispersed by capillary forces, and the length of the liquid phase diffusion path can be obtained from pore structure data for the support. Both liquid phase and gas phase pore diffusion restrictions are important in preparing supported liquid phase catalysts that exhibit the largest possible overall conversion per catalyst volume. Activity was calculated for industrial SO oxidation catalysts. A good estimate of catalyst activity can be obtained from pure liquid catalyst properties. 2

S

upported liquid phase systems (SLP systems) are gas/liquid contact systems where the liquid phase is dispersed in a porous support material. Such systems are effective contactors in mass transfer operation with high diffusion resistance in the liquid phase since the liquid must be highly dispersed to reduce the length of liquid phase diffusion paths. Rony has studied SLP catalysts (I, 2) and proposed a mathematical model to simulate the interior liquid dispersion and diffusion kinetics. He extended Thiele's original single pore model to include the liquid catalyst inside the porous support. The liquid forms a layer at the pore wall or a plug at the bottom of the long single pore. However, the liquid distribution cannot be determined independently, and thus the model cannot be used to predict a priori catalyst activity for a given liquid loading and given pore structure. Recently Abed and Rinker (3) proposed a different model for SLP systems. They consider the liquid phase to be evenly distributed throughout the pellet, and they determined diffusionfluxesthrough the pellet for different liquid loadings by steady-state counterdiffusion experiments. The diffusion mechanism was analogous to ordinary pore diffusion with an effective diffusivity which was proportional to the square of the residual porosity. The most important feature of their model is that the liquid is assumed to be so finely distributed that local diffusion resistance into the liquid phase from a pore at a given position in the pellet can be neglected. They also allow for enhancement of the effective 242

In Chemical Reaction Engineering—II; Hulburt, H.; Advances in Chemistry; American Chemical Society: Washington, DC, 1974.


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diffusivity through liquid diffusion, assumed to be proportional to the square of the liquid loading. Their model and Rony's, with a distinction between liquid in plugs and pore wall adhering liquid, predict an optimal liquid loading. This paper analyzes industrially important SLP systems where liquid phase diffusion is small enough to invalidate the assumption that local activity is proportional to liquid loading. This system requires a more detailed knowledge of liquid phase distribution to compute the local diffusion path length from the gas phase into the liquid phase. We show that liquid pore size distribution can be estimated if the catalyst pore structure is known; then the influence of liquid loading can be studied. Calculations are presented for an industrial S 0 oxidation catalyst with a severe liquid phase diffusion restriction. The catalytic oxidation of S 0 with a V 0 / K 0 catalyst is the most important industrial application of an SLP catalyst. This homogeneous reaction occurs in a melt containing the active catalyst species. The melt is distributed in the pore structure of an inactive support which is usually S i 0 based (4, 2

2

2

5

2

2

5,6).

This system was investigated by Kenney and co-workers (5, 6) who studied non-steady-state absorption kinetics of reactants into non-supported catalyst melts of large volume. Boreskov et al. {7,8) measured S 0 oxidation rates for catalyst melts on porous and non-porous supports. Using catalyst films of different thickness they extended the measurements from the purely kinetic region into the region with severe liquid phase diffusion restriction. They showed that the reaction zone in the pure liquid phase is thin; liquid phase diffusion becomes important in liquid layers > 2000 A at 4 8 5 ° C . Thus, a gradientless liquid phase reaction cannot be obtained by macrostirring in a large catalyst volume. The pure kinetics of the homogeneous reaction can only be obtained with experiments on thin liquid films. Gas phase pore diffusion restrictions at industrial reaction conditions are important (9, 10, 11, 12). Kadlec et al. (9, 10) calculated optimum catalyst loadings, assuming negligible liquid phase diffusion resistance. Thus the activity of a S 0 oxidation catalyst is a result of a complicated interaction between homogeneous liquid phase kinetics, liquid phase diffusion, and gas phase pore diffusion that is characteristic for an SLP catalyst. 2

2

Distribution of the Liquid Phase in the Pores Because the pore system used for liquid support in SLP systems (e.g., the SLP catalyst for S 0 oxidation) is finely dispersed, the forces governing the liquid distribution in the pore system will be surface forces acting at the solidliquid and gas-liquid interfaces—i.e., capillary, surface tension, and adsorption forces. The influence of gravity on the geometry of the liquid surfaces is negligible. Under the influence of the surface forces the liquid will be distributed so that the thermodynamic free energy of the system attains a minimum. For liquids with contact angle < 90° (i.e., with positive affinity to the solid surface), this implies a tendency to minimize the area of the high energy gas/liquid surface and at the same time maximize the area of the low energy liquid/solid surface. Thus, the liquid is drawn into the smaller pores, and if the liquid loading in the SLP system is increased, larger and larger pores will be filled with liquid. This phenomenon is extensively used to analyze pore structures by measuring capillary condensation of vapors (13). The mobility of the nonvolatile liquid phase in an SLP catalyst, which is necessary for redistributing 2



244

CHEMICAL

Figure 1.

REACTION

ENGINEERING

II

Liquid contained in smaller pores of support pore system

the liquid in the pores, has been proved by Tops0e and Nielsen (4). They showed that a catalyst melt initially non-uniformly distributed in a support pellet would be uniformly distributed after some time at reaction conditions. The resulting liquid distribution is shown schematically in Figure 1. The SLP system is divided into two regions. One is the pore system of larger gasfilled pores which will be called the residual pore system. The other is a twophase area consisting of a solid phase permeated by a pore system of liquidfilled smaller pores—i.e., liquid-filled region ( L F R ) . The geometry of the residual pore system—i.e., pore size distribution and porosity—is important for the rate at which reaction components diffuse through it. The geometry of the liquid-filled region is important in determining the lengths of the liquid phase diffusion paths from the residual pores and into the liquid-filled pores. These geometrical characteristics can be derived from the pore volume distribution of the support. The pore radius of the largest pores completely filled with liquid is r . Thus the total liquid volume equals the pore volume with radii < r or f

f

(1) where W L / P L * the volume of liquid per unit weight support, and v(r) is the density function of the pore volume distribution. For a given liquid loading L/PL Equation 1 can be solved iteratively for the corresponding value of r . The residual pore system is formed by all pores > r . Therefore the residual pore volume distribution is defined by: s

W

f

f

0;

r < rt v(r); r > ri

(2)

Figure 2 shows a support pore distribution curve (A) and a corresponding residual pore distribution curve (B) for a given liquid loading. For Equations 1 and 2 the liquid phase is assumed to be uniformly distributed in the LFR—i.e., jthe probability for a point in L F R at a given distance I from a residual pore to be in the liquid phase is independent of I. Under certain circumstances, much of the liquid may be concentrated in areas in immediate contact with the residual pores. This is true in general for very low liquid loadings when the liquid presumably is kept in short micropores along


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the surface of the residual pore system and for liquid molecules kept in an adsorbed state at the solid surface. Such distribution variations can be ac counted for by assuming the existence of a liquid layer of thickness t at the pore walls of all residual pores as a model perturbation to Equations 1 and 2.

Figure 2. Support pore distribution (curve A) (with mean pore radius r = 2500 A and variance β = 0.3 for In τ) and residual pore distributions for 75% liquid loading. Curve Β cor responds to Equations 1 and 2, curves C-F correspond to Equations 3 and 4. m

Γ

1000

2000

PORE RADIUS

If part of the liquid is enclosed in pores with radii < r and the rest is in a layer of thickness t at the walls of pores with radii > r , the formula corresponding to Equation 1 becomes f

f

W>L/PL =

1

v(r)dr +f

T{

£l -

(3)

~\^v(r)dr

assuming non-intersecting cylindrical pores. For a given liquid loading and liquid layer thickness t, Equation 3 can be solved iteratively for r . The corre sponding residual pore distribution is defined by: f

r < ri — t

o;

r > π

(4)

Figure 2 shows a family of residual pore distribution curves generated by Equations 3 and 4 for different values of t. Curve F corresponds to the highest t that is possible for the given liquid loading. This curve is constructed by substituting r = t in Equations 3 and 4. The corresponding liquid distribution represents an extreme type compared with that defined by Equations 1 and 2 in that as much as possible of the liquid is distributed as a homogeneous layer at the pore walls of the residual pore system. When r has been computed by Equations 1 or 3, the following geometrical properties of the L F R become available. The pore volume of the LFR—i.e., the total volume of liquid filled pores, is f

f

v(r)dr

(5)

and the total volume of the L F R per unit weight support:

yι

= -

+v

(6) 9t


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CHEMICAL REACTION ENGINEERING

II

where p is the true density of the solid phase. The porosity of the L F R is defined by: g

(7) The "external" surface area of the L F R S —i.e., the area exposed by the L F R to the residual pores (or a liquid layer, if any)—equals the surface area of support pores > r . Thus for non-intersecting cylindrical pores: £


f

2 - v(r)dr r

Γ I Jrt

00

St

(8)

where 2/r is the surface to volume ratio for infinitely long cylinders. If S and V are known, one can compute the average diffusion length 8 in the L F R which equals the volume to surface ratio: £

f

f

(9) Further geometrical characteristics for the L F R are developed below. Catalytic Reaction and Diffusion in the Liquid Phase The liquid-filled region of the catalyst is considered a homogeneous phase. Diffusion occurs in all directions, and reaction occurs at every point. The reac tion rate and diffusivity are, of course, smaller than in a pure liquid phase since part of the total volume of the region is taken up by the solid. This is our basic assumption of a uniformly distributed liquid phase in the L F R , and it agrees with generally accepted pseudo-homogeneous models for diffusion and chemical reaction in porous bodies (e.g., Ref. 14, chap. 4 for further details).

fit*- LFR

segment of volume _ Vf

Λ

and surface

_-Sf

(

Liquid filled region.

/ A?k

;/

Residual pore

/

•A ··-!.'^°°

W ) ;

t - 1,..., s

(29)

with boundary conditions: Yi = Fio at the external pellet surface. Note that v' is the liquid phase reaction rate without diffusion restriction for the gas phase concentration Y The assumption of a small liquid phase diffusivity for at least one com ponent used in deriving Equation 12 leads to a decoupling of the microscopic liquid phase diffusion and the macroscopic pore diffusion and results in the simple form of Equation 29 for the macroscopic continuity equation. The decoupling is not necessarily violated even in the unlikely situation where liquid phase diffusion for some components contributes significantly to the macroscopic diffusion rate. However, for such components the effective diffusivity cannot be estimated from ordinary pore diffusion models. To characterize the mass transport efficiency of SLP catalysts three differ ent effectiveness factors are defined besides the effectiveness factor η ( δ ) for diffusion in an L F R segment used in Equation 29. (Normal) Pore Diffusion Effectiveness Factor η . η is defined in the usual way for porous catalysts as the ratio of the observed reaction rate to the rate which would have been observed in the absence of pore diffusion resistance: 1#

&

bM

i f f ^

__ J

J

J

pellet volume

f J

œ

&

^ ( δ ) ] dV. (30)

0

where V is the support pellet volume and subscript ο refers to conditions at the external support pellet surface. Local Average Liquid Effectiveness Factor η η is the ratio of the actual local reaction rate to the rate that would have been observed with negligible liquid phase diffusion restriction. The volumetric average of η at a given s

ν

ι


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position in the pellet is obtained using Equation 25:

r°

ι m

7,δΩ

Liquid Dispersion, Mass Transport, and Chemical Reaction in

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