# (600e) Modelling of Diffusion-Reaction Interaction inside the Co-Based Catalyst Particles for the Fischer-Tropsch Synthesis

- Conference: AIChE Annual Meeting
- Year: 2016
- Proceeding: 2016 AIChE Annual Meeting
- Group: Catalysis and Reaction Engineering Division
- Session:
- Time: Wednesday, November 16, 2016 - 4:35pm-4:55pm

**1.
**

**Introduction**

Fischer-Tropsch synthesis (FTS) is a

heterogeneous reaction used to convert synthesis gas into a range of

hydrocarbon products. This reaction is a pivotal part of the Gas-to-Liquid

(GTL) process in which natural gas is converted into liquid fuels and

value-added chemicals. As such, FTS is often conducted inside of multi-tubular

fixed bed reactors filled with cobalt-based catalyst particles. In order to

avoid high pressure drops inside of the catalyst bed, relatively large

particles (1-3 mm) are typically applied [1,2]. This

may lead to intraparticle diffusional limitations for

highly active catalysts. This means that the particle size, shape and operating

process conditions may have a profound influence on the catalyst effectiveness

and FTS selectivity. Several literature studies modelled diffusion with

chemical reaction with Co based FTS catalysts [3,4],

but focused mainly on spherical geometry and utilized rate equations based on experiments

with a low activity catalyst [5].

In recent years Velocys [6] developed micro-channel

reactors for FTS. These reactors utilize “super-active” Co catalysts compared

to fixed-bed reactors in order to improve reactor volumetric productivity. It

is expected that transport resistances could play a significant role with these

reactors as well. Models of diffusion-reaction interaction are helpful in

determining an optimal layer thickness that maximizes catalyst effectiveness

and improves FTS product selectivity.

Here we present results from simulations utilizing one-dimensional

particle models for Co-based FTS catalysts. Several critical parameters, such

as the effects of shape (sphere, hollow cylinder and slab), diffusion length,

temperature distribution inside the particle, diffusivity coefficients (gas-

and wax-filled) and catalyst activity, and their influence on catalyst

effectiveness and selectivity have been examined.

**2.
**

**Diffusion-reaction model**

FTS reaction can

be simplified using the following stoichiometric relation:

Our

model assumes that the average hydrocarbon product is n-hexane (i.e. n = 6).

Therefore, the components considered in the model are: carbon-monoxide,

hydrogen, water and n-hexane.

The

equation describing diffusion with chemical reaction inside FTS catalyst particle

can be expressed as:

where

*x* is the dimensionless distance,

superscript *g* stands for geometry (g

= 2, 1 and 0 for sphere, cylinder and slab, respectively), *y _{i}* is dimensionless

concentration (

*i*

= CO, H

_{2}, H

_{2}O and n-hexane), stoichiometric coefficient

(α

_{i}= 1, 13/6, 1 and 1/6 for CO, H

_{2},

H

_{2}O and n-hexane, respectively),

*Ψ*

is the dimensionless CO consumption rate and

*φ*is the

_{i}dimensionless parameter (

). This parameter includes catalyst density (

*ρ*),

_{p}characteristic length (

*L*), reactant surface

concentrations (

), and effective diffusivity coefficients (D

_{e,i}). Set of second

order ordinary differential equations (Eq. 2) was solved in Matlab

using the bvp4c solver.

Reaction rate was

described using the Yates-Satterfield expression [5]:

The

parameters *k* and *a* in Eq. (3) were estimated from experimental data with

0.48%Re–25%Co/Al_{2}O_{3} catalyst [7]. Rates of H_{2}

disappearance and H_{2}O and n-hexane formation are calculated based on

Eq. (3) and stoichiometry of Eq. (1). It is worth noting that this catalyst is

approximately an order of magnitude more active under typical FTS operating

conditions compared to the original Yates-Satterfield catalyst [8], and as such

is more representative of modern Co catalysts used in industrial applications.

Two approaches to

effective diffusion calculations were used, one assuming wax-filled and the

other gas-filled catalyst pores. The former used correlations for diffusivity

in FTS wax developed by Akgerman

et al. [9], which is a representative of the porous catalyst transport

environment over a significant portion of the reactor bed. For gas-filled

particle we used multi-component diffusion approach, adjusted with Knudsen

diffusion, and this is an extreme representation of segments of the reactor bed

in which catalyst pores are not entirely filled with wax.

The key aspect of

FTS catalyst selectivity is methane selectivity. Methane formation rate was

calculated using Ma et al. [10] expression:

where numerical

values of kinetic parameters were estimated from the same set of data as those

in Eq. (3), i.e. with 0.48%Re–25%Co/Al_{2}O_{3} catalyst [7]. Solution

of Eq. (2) provides partial pressures needed to evaluate methane formation rate

and calculate methane selectivity as:

which is valid for

Co-catalysts due to their low WGS activity, i.e. low CO_{2} formation.

**3.
**

**Results and discussion**

Our simulations show that with very small spherical particles (< 150

μm) diffusional resistance is small, even with highly

active Co catalyst used in our study. This is consistent with literature

results [2-4]. However, with larger particle sizes (e.g. 2 mm) diffusion

resistances are present both with the highly active Co catalyst and low activity

catalyst used in previous studies [3,4]. Figure 1

shows model results for a 2 mm diameter spherical pellet, filled with wax, with

kinetic parameters obtained with 0.48%Re–25%Co/Al_{2}O_{3} catalyst.

Reaction rate results show that FTS follows “abnormal” kinetics (increase in

rate with conversion followed by decrease at high CO conversions). Ratio of H_{2}

to CO diffusivity is higher than the corresponding consumption ratio. This

means that the ratio of H_{2} and CO concentrations is increasing

inside the particle. Because of this, as well as the positive reaction order in

H_{2} and negative order in CO, we get that the reaction rates inside

the particle initially increase starting from the particle surface. However,

for large particles, reactants are consumed relatively fast and reaction rate

drops to zero leaving a large fraction of the particle unutilized (Figure 1). The calculated effectiveness factor for such a

particle is only 0.52. Even more interesting is the behaviour of selectivity

inside the spherical particle (Figure 1). Because methane selectivity follows

the trend of H_{2}/CO ratio, S(CH_{4})

increases rapidly inside the particle. As concentration of CO goes to zero, H_{2}/CO

ratio becomes so high that methane selectivity at a certain point inside the

particle becomes 100%. Additional insights were obtained from simulations with

a lower activity catalyst, different size particles and assumption of gas-filled

pores. Results strongly suggest that the eggshell catalyst distribution is the

only viable option for large catalyst particles utilized in multi-tubular fixed

bed reactors.

Similar simulations were performed for a slab geometry present in

wall-coated micro-channel reactors with various slab thickness and reaction

rates. Figure 2 shows results obtained with 300 μm

thickness layer. Catalyst effectiveness for this thickness is 0.65, suggesting

that lower thickness should be used in order to fully utilize the coated

catalyst. Also, methane selectivity is extremely high. This is contrary to the

goal of increasing the reactor productivity by adding more catalyst (i.e. using

thicker layers). Therefore, an optimal solution between high catalyst

effectiveness and reactor productivity has to be found. Selectivity has to be

taken into account also. Our simulation show that, similar to spherical

particles, methane selectivity rises almost exponentially inside of 300 μm catalyst slab and reaches 100% well before FTS rate

drops to zero. Thus, selectivity has to be considered in selection of the

optimal slab thickness.

**4.
**

**Conclusions**

A one-dimensional model of diffusion-reaction interaction inside the

FTS cobalt catalyst was developed. A number of simulations for sphere and slab

geometry were performed. Results show that intraparticle

diffusional limitations are severe with a highly active cobalt-based catalyst.

Results suggest that large 2 mm spherical particles should utilize eggshell

design in order to minimize the negative impact of pore diffusion on activity and

selectivity. Also, pore diffusional limitations were found to be significant

for a thin layer of catalyst (300 mm). Good understanding of diffusion-reaction

interplay inside FTS catalyst is required in order to optimize reactor

productivity, catalyst effectiveness and product selectivity.

**Figure **** SEQ Figure \* ARABIC
**

**1**

**– Distribution of**

dimensionless CO concentration (y

dimensionless CO consumption rate (Ψ) and methane selectivity (S(CH

= 2).

dimensionless CO concentration (y

_{CO}),dimensionless CO consumption rate (Ψ) and methane selectivity (S(CH

_{4})) within a spherical particle (d_{p}= 2 mm, T = 473 K, P = 25 bar, bulk H_{2}/CO= 2).

**Figure 2 – Distribution of dimensionless CO
concentration (y _{CO}), dimensionless CO
consumption rate (Ψ) and methane selectivity (S(CH_{4}))
within a slab geometry (slab thickness = 300 **

**mm,**

T = 473 K, P = 25 bar, bulk H

T = 473 K, P = 25 bar, bulk H

_{2}/CO = 2).**Acknowledgements **

This publication was made possible by NPRP grant 7-559-2-211 from

the Qatar National Research Fund (a member of Qatar Foundation). The statements

made herein are solely the responsibility of the authors.

**References**

[1] A.P. Steynberg, M.E. Dry, B.H. Davis and B.B. Breman, Stud. Surf. Sci. Catal., 152

(2004) 64.

[2] E. Rytter, N.E. Tsakoumis, A. Holmen, Catal.

Today, 261 (2016) 3.

[3] D. Vervloet, F. Kapteijn, J. Nijenhuis, J.R. van Ommen, Catal. Sci. Technol., 2 (2012) 1221.

[4] S.A. Gardezi, B. Joseph, Ind. Eng. Chem. Res., 54 (2015) 8080.

[5] I.C. Yates,

C.N. Satterfield, Energy Fuels, 5 (1991) 168.

[6] H.J. Robota, L.A. Richard, S. Deshmukh,

S. LeViness, D. Leonarduzzi,

D. Roberts, Catal. Surv.

Asia, 18 (2014) 177.

[7] B. Todic, T. Bhatelia, G.F. Froment, W. Ma, G.

Jacobs, B.H. Davis, D.B. Bukur, Ind. Eng. Chem. Res., 52 (2013) 669.

[8] C. Maretto, R. Krishna, Catal.

Today, 52 (1999) 279.

[9] Akgerman, Final Report DOE AC22-84PC70032, (1984).

[10] W. Ma, G.

Jacobs, T.K. Das, C.M. Masuku, J. Kang, V.R.R. Pendyala, B.H. Davis, J.L.S. Klettlinger,

C.H. Yen, Ind. Eng. Chem. Res., 53 (2014) 2157.