Over the last 10 years the design of catalyst particles and porous
structures has made
considerable progress. Due to the complicated interaction of
diffusion and reaction in catalysts,
more detailed models of porous structures are needed. We have
based our model on a three-dimensional network of interconnected cylindrical pores as pore model,
although the treatment
is applicable to alternative pore geometries, e.g., slit pores.
The network assumed has predefined
distributions of pore radii, connectivity, and porosity. Mass
transport in the individual pores of
the network is described by the dusty-gas model. In contrast to
previous publications, the present
network model can be applied to any common reaction kinetics. This
becomes quite inevitable
in order to make three-dimensional network models applicable to
practical problems in industry.
To solve the mass balances within the entire network, the mass
balances for individual pores
have to be solved simultaneously, since these mass balances are coupled
by the boundary
conditions at the nodes of the network. The system of differential
equations has been solved by
the finite-difference method. To solve the resulting large
nonlinear system, a Schur complement
method was employed. Due to a decoupling technique, the Schur
complement method has
relatively small computer storage requirements. The use of the
algorithm is demonstrated for
a complex reaction network.
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