Figure 2. Schematic illustration of the computational domain of the
microchannel methanol steam reformer reactor that comprises a plurality
of process microchannels transferring heat from the process
microchannels to a heat exchanger.
The present study performs research on a highly precise simulation of
diffusion of a gas in a porous material which is performed in a short
time. In pores of a porous material, while gas particles collide with
pore walls and collide with particles of at least one different type of
gas, the gas diffuses. In the gas diffusion, the collision with the pore
walls and the collision between the gas particles are combined with each
other, and a gas diffusion simulation is performed by Boltzmann
equation. Hence, the gas diffusion simulation takes a long time. In the
calculation of the Knudsen diffusion coefficient by collision between
gas particles and the pore walls, the pores of the porous material are
each assumed to have a uniform cylindrical linear shape. However, this
assumption is different from actual pores, and therefore, the precision
of the gas diffusion simulation using this Knudsen diffusion coefficient
is inferior. When a diffusion equation represented by the sum of an
interdiffusion term and a Knudsen diffusion term based on the mean
square displacement of first gas particles in spaces surrounded by wall
surfaces is used, a gas diffusion simulation can be highly precisely
performed in a short time. A gas diffusion simulation method is used to
simulate diffusion of a gas in a porous material having many pores. The
method includes: calculating, in the pores, a Knudsen diffusion
coefficient based on the mean square displacement of first gas particles
in spaces surrounded by wall surfaces and a Knudsen diffusion term using
the Knudsen diffusion coefficient, calculating an interdiffusion term
using an interdiffusion coefficient between the first and second gas
particles different therefrom, and performing simulation of the gas
diffusion of the first gas particles by using a diffusion equation of
the first gas particles represented by the sum of the Knudsen diffusion
term and the interdiffusion term.
Since the Knudsen diffusion coefficient based on the mean square
displacement of the first gas particles in the spaces surrounded by the
wall surfaces is obtained, a highly precise gas diffusion simulation
based on an actual porous material can be performed. In addition, since
the diffusion equation of the first gas particles represented by the sum
of the Knudsen diffusion term and the interdiffusion term is used, the
gas diffusion simulation can be performed in a short time. The spaces
surrounded by the wall surfaces may be defined by positional information
of the wall surfaces of the pores. Accordingly, the diffusion of the gas
in the spaces surround by actual wall surfaces can be highly precisely
simulated. The positional information of the wall surfaces of the pores
may be identified by shape information of the wall portions of the
porous material surrounding the peripheries of the pores. Accordingly,
the gas diffusion simulation based on the shapes of the wall portions to
be simulated can be highly precisely simulated. The wall surfaces of the
pores may be formed at least from surfaces of liquid water in the pores.
Accordingly, a highly precise gas diffusion simulation in consideration
of the liquid water in the pores can be simulated. The positional
information of the wall surfaces of the pores may be identified by the
shape information of the wall portions of the porous material
surrounding the peripheries of the pores and a saturation degree of the
liquid water occupied in the pores. Accordingly, since the positional
information of the wall surfaces can be obtained without performing
experiments or the like, the gas diffusion simulation can be performed
in a short time.
In the porous material, wall portions and many pores are provided. The
wall portions are formed, for example, from an organic material, such as
a resin and carbon, an inorganic material, such as glass, and a mixture
thereof. The pores are spaces, the peripheries of which are surrounded
by the wall portions, and are defined by all surfaces of the wall
portions surrounding the peripheries of the pores. In the pores, spaces
in which gas particles are movable are provided. For example, in the
case of a fuel cell, as the gas particles, hydrogen, oxygen, nitrogen,
and the like may be mentioned by way of example. According to
Stefan-Maxwell law, by expanding Fick’s first law which indicates that
diffusion of a certain component gas is influenced only by the
concentration gradient of the component, the diffusion of the gas is not
only influenced by the concentration gradient of the component but also
by the physical quantity of another component [57, 58]. In addition,
the interdiffusion coefficient of a two-component bulk can be obtained
by the Chapman-Enskog equation [59, 60]. In this simulation, the
diffusion spaces are defined by the positional information of the
defining wall surfaces of the pores of an actual porous material.
Accordingly, a highly precise gas diffusion simulation in accordance
with actual pores can be performed. The Knudsen diffusion coefficient in
the diffusion spaces defined by this positional information is
determined. Hence, the parameter of the Knudsen diffusion coefficient in
accordance with the shape of the porous material is not necessarily
obtained by experiments, and hence, the time required for the gas
diffusion simulation can be significantly reduced.