# (25f) Modeling of Diffusion and Catalytic Reactions of Gases in Highly Porous Nanolayers with Dsmc and Openfoam

- Conference: AIChE Annual Meeting
- Year: 2015
- Proceeding: 2015 AIChE Annual Meeting
- Group: Catalysis and Reaction Engineering Division
- Session:
- Time:
Sunday, November 8, 2015 - 5:10pm-5:30pm

**Modeling of Diffusion and Catalytic Reactions of Gases
in Highly Porous Nanolayers with DSMC and OpenFOAM**

*G. R. Pesch*^{†,‡}*, N. Riefler ^{†}, U.
Fritsching^{†}, L. Colombi
Ciacchi^{§,‡}, L. Mädler^{†}*

*† -- Foundation Institute of Materials Science (IWT), Department of Production
Engineering, University of Bremen, Germany*

*‡ -- Chemical Engineering -- Recovery and Recycling (VdW),
Department of Production Engineering and Center for Environmental Research and
Sustainable Technology (UFT), University of Bremen, Germany*

*§ -- Hybrid Materials Interfaces Group (HMI), Department of Production
Engineering and Bremen Center for Computational Materials Science (BCCMS),
University of Bremen, Germany*

Gas diffusion in at Knudsen numbers (Kn) above 0.1 requires a mathematical treatment based on

the Boltzmann equation. Accepted solutions for the description of diffusion in

highly porous geometries are for instance the extended Fickian

Model or the Dusty-Gas-Model (DGM). Here collisions between molecules are, due

to their vast appearance, only statistically considered. Both models require

mean geometry values, such as porosity and tortuosity, to describe the porous

structure. This results in a simplification of the exact layer geometry, which

hinders an effective and accurate description of diffusion processes inside

real inhomogeneous 3 dimensional porous layers, such as gas sensors films or

catalysts.

In gas sensors for example, a probe gas diffuses into

the porous layer. Due to chemical reactions at the surface (rate of reaction is

proportional to probe gas concentration) the porous layer resistance changes,

which can be measured by two electrodes and back calculated to the probe gas

composition. Fundamental for design and response optimization of sensors of

this kind is precise knowledge about the amount and exact position of the

reaction fronts within the layer.

The Direct Simulation Monte Carlo (DSMC) method is

suitable for the simulation of gas diffusion in such sensors as it uses the

exact porous geometry to describe diffusion processes by modeling the tracks

and collisions of every single gas molecule inside the layer. Molecular

collisions are calculated by employing collision parameters acquired from

simplified solutions of the Boltzmann equation. If a model of the porous

geometry to investigate is available, the DSMC method is therefore able to

accurately describe gas diffusion processes in inhomogeneous layers, without

the knowledge of pore diameter, tortuosity, or porosity information. The OpenFOAM implementation of the DSMC code has been extended

by the Variable Soft Sphere (VSS) model for binary molecular collisions [1],

which results in a more accurate diffusion rate, compared the Variable Hard

Sphere (VHS) model. Further, diffusion of CO into a N_{2} filled layer

has been simulated by the DGM and the DSMC-VSS code. Whereas DSMC and DGM show

a good agreement for the diffusion inside isotropic layers, DSMC shows higher

accuracy for diffusion inside real gas sensor layers as obtained by an aerosol

synthesis method.

To obtain information about the chemical reaction

fronts inside the layer, the DSMC method has been extended to describe basic

heterogeneous reaction mechanisms, i.e., adsorption, co-adsorption, desorption

and reaction of gas species on the surface of the solid [2]. The adsorption is

based on the well-known sticking coefficient and implemented by the Kisluik model for precursor mediated adsorption, which

describes the chance of a molecule to stick on the surface after hitting the

solid as a function of temperature and coverage of the surface. Desorption and

surface reaction are modeled through a mean-field rate approximation, i.e., the

Polanyi-Wigner equation for desorption and a second-order Arrhenius equation

for reaction. With this model we study the catalytic oxidation of carbon

monoxide (CO) inside gas sensor layers of 1000 nm thickness in the transition

regime (*Kn* ~ 1) using kinetic parameters taken

from the literature for single-crystal Pd(111) surfaces at UHV conditions (Fig 1a).

Investigation of the reaction at different temperatures reveals a clear

transition from a kinetic limit at low temperatures (*T* < 673 K) to a

diffusion limit at high temperatures (*T* > 673 K). In the kinetic

limit, the diffusion occurs at much faster rate than the reaction; the latter

is therefore the rate-determining step of the overall process. At the diffusion

limit, the reaction consumes educts at a much higher rate than their

replenishment due to diffusion from the inlet. At this limit, diffusion of

educts is thus the rate-determining step and the process is mass-transport

limited.

At high temperatures and at steady state (Fig 1b), the

layer is separated into three distinct regions. The surface

of the layer is poisoned by CO, which is a result of the underlying co-adsorption

mechanism. Here, the surface is covered with CO, which is hindering oxygen

adsorption (competitive adsorption mechanism). Hence, the reaction rate is low,

as only one out of two species (CO) required for the reaction is adsorbed on

the surface.

With increasing depth into the layer the CO coverage

is decreasing and the oxygen coverage is increasing, which results in an

effective reaction area of the layer. The peak reaction rate is reached as both

coverages intersect. Going even deeper into the

layer, the CO coverage reaches zero, as the effective reaction area consumes

all CO. This reflects the mass-transport limitation of

the overall reaction. Hence, the reaction rate is again low as only one out of

two species needed for the reaction (oxygen) is adsorbed on the surface.

The employed parameters together with the presented

reaction system serve to demonstrate the capabilities of the newly developed

simulation algorithm. We expect that similar investigations will not only help

gaining deeper understanding of the reaction processes inside porous structures

but also for the structure optimization of gas sensors and catalysts.

[1] J.A.H. Dreyer, N. Riefler, G.R. Pesch, M.

Karamehmedovic, U. Fritsching, W.Y. Teoh, L. Mädler: Simulation of Gas

Diffusion in Highly Porous Nanostructures by Direct Simulation Monte Carlo.

Chem. Eng. Sci. (2014), 69-76

[2] G.R. Pesch, N. Riefler,

U. Fritsching, L. Colombi Ciacchi, L. Mädler: Gas-Solid Catalytic Reactions

with an Extended DSMC Model. AIChE J. (2015), in press, DOI: 10.1002/aic.14856