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.