Modelling of supported porous catalysts using 3D digital

Modelling of supported porous catalysts using 3D digital reconstruction
Petr Kočí a,*, Vladimír Novák a, František Štěpánek b, Milan Kubíček c, Miloš Marek a
a
Department of Chemical Engineering, b Chemical Robotics Laboratory, c Department of
Mathematics, a,b,c Institute of Chemical Technology, Prague, Technická 5, CZ 166 28 Praha,
Czech Republic
*
Corresponding author, [email protected], http://www.vscht.cz/monolith
Keywords: Porous catalyst, Microstructure, Multi-scale modelling
Abstract
Electron microscopy (SEM, TEM) and other high-resolution imaging techniques (e.g., X-ray
microtomography) together with the increasing computation power of commonly available
computers enabled development of detailed modelling of porous materials [1]. The approach
is based on a digital 3D reconstruction of porous medium that can provide realistic description
of its morphology, and consequent simulation of reaction, transport and transformation
processes inside the 3D reconstructed system [2]. In this contribution the methods for detailed
modelling of supported metal catalysts are presented (i)–(xi).
First the models of the catalyst preparation steps are discussed: (i) aggregation of primary
nano-particles of the catalyst support material, (ii) packing of the formed micro-particles of
the supporting material, and (iii) evaluation of the resulting pore size distribution [2,3].
The porous support is then impregnation with a solution of the active metal precursor,
followed by drying and calcination whereby metal crystallites are deposited in the pores of the
support. Simulations of the impregnation and drying steps utilise (iv) the generalised volumeof-fluid method with local mass balances including diffusion of the dissolved species,
(v) nucleation and crystal growth in the pore space (including size-dependent effects such as
Ostwald ripening), and (vi) evaporation of the solvent coupled with (vii) propagation of liquid
menisci in the pore space (governed by the Kelvin equation).
Reaction-transport processes during the catalyst operation are then simulated within the
reconstructed medium, accounting for (viii) local effective diffusion (determined by local
pore sizes [3]) and (ix) local reaction activity (affected by distribution, size and surface area
of the metal crystallites [2]). Finally, a multi-scale approach is demonstrated that is based on
(x) calculation of volume-averaged reaction rates and effectiveness factors in dependence on
boundary concentrations and temperature. These pre-calculated characteristics are then
employed for direct evaluation of local reaction rates in (xi) a macroscopic model of entire
reactor, so that integral conversions over the reactor can be obtained [2].
References
[1] Kosek J., Štěpánek F., Marek M. Modelling of transport and transformation processes in
porous and multiphase bodies. Advances in Chemical Engineering 30 (2005), 137.
[2] Kočí P., Novák V., Štěpánek F., Marek M., Kubíček M. Multi-scale modelling of reaction
and transport in porous catalysts. Chemical Engineering Science 65 (2010), 412-419.
[3] Novák V., Štěpánek F., Kočí P., Marek M. Evaluation of local pore sizes and transport
properties in porous catalysts. Chemical Engineering Science (2010), in press,
http://dx.doi.org/10.1016/j.ces.2009.09.009