Yoshihiko Hibi

Estimation of mechanical dispersion and dispersivity in a soil-gas system by column experiments and the dusty gas model.

In a previous study, column experiments were carried out with Toyoura sand (permeability 2.05×10(-11)m(2)) and Toyoura sand mixed with bentonite (permeability 9.96×10(-13)m(2)) to obtain the molecular diffusion coefficient, the Knudsen diffusion coefficient, the tortuosity for the molecular diffusion coefficient, and the mechanical dispersion coefficient of soil-gas systems. In this study, we conducted column experiments with field soil (permeability 2.0×10(-13)m(2)) and showed that the above parameters can be obtained for both less-permeable and more-permeable soils by using the proposed method for obtaining the parameters and performing column experiments. We then estimated dispersivity from the mechanical dispersion coefficients obtained by the column experiments. We found that the dispersivity depended on the mole fraction of the tracer gas and could be represented by a quadratic equation.

Evaluation of a numerical simulation model for a system coupling atmospheric gas, surface water and unsaturated or saturated porous medium

Numerical simulations that couple flow in a surface fluid with that in a porous medium are useful for examining problems of pollution that involve interactions among the atmosphere, surface water and groundwater, including, for example, saltwater intrusion along coasts. We previously developed a numerical simulation method for simulating a coupled atmospheric gas, surface water, and groundwater system (called the ASG method) that employs a saturation equation for flow in a porous medium; this equation allows both the void fraction of water in the surface system and water saturation in the porous medium to be solved simultaneously. It remained necessary, however, to evaluate how global pressure, including gas pressure, water pressure, and capillary pressure, should be specified at the boundary between the surface and the porous medium. Therefore, in this study, we derived a new equation for global pressure and integrated it into the ASG method. We then simulated water saturation in a porous medium and the void fraction of water in a surface system by the ASG method and reproduced fairly well the results of two column experiments. Next, we simulated water saturation in a porous medium (sand) with a bank, by using both the ASG method and a modified Picard (MP) method. We found only a slight difference in water saturation between the ASG and MP simulations. This result confirmed that the derived equation for global pressure was valid for a porous medium, and that the global pressure value could thus be used with the saturation equation for porous media. Finally, we used the ASG method to simulate a system coupling atmosphere, surface water, and a porous medium (110m wide and 50m high) with a trapezoidal bank. The ASG method was able to simulate the complex flow of fluids in this system and the interaction between the porous medium and the surface water or the atmosphere.

Estimation of Knudsen diffusion coefficients from tracer experiments conducted with a binary gas system and a porous medium

A previous study has reported that Knudsen diffusion coefficients obtained by tracer experiments conducted with a binary gas system and a porous medium are consistently smaller than those obtained by permeability experiments conducted with a single-gas system and a porous medium. To date, however, that study is the only one in which tracer experiments have been conducted with a binary gas system. Therefore, to confirm this difference in Knudsen diffusion coefficients, we used a method we had developed previously to conduct tracer experiments with a binary carbon dioxide-nitrogen gas system and five porous media with permeability coefficients ranging from 10-13 to 10-11 m2. The results showed that the Knudsen diffusion coefficient of N2 (DN2) (cm2/s) was related to the effective permeability coefficient ke (m2) as DN2 = 7.39 × 107ke0.767. Thus, the Knudsen diffusion coefficients of N2 obtained by our tracer experiments were consistently 1/27 of those obtained by permeability experiments conducted with many porous media and air by other researchers. By using an inversion simulation to fit the advection-diffusion equation to the distribution of concentrations at observation points calculated by mathematically solving the equation, we confirmed that the method used to obtain the Knudsen diffusion coefficient in this study yielded accurate values. Moreover, because the Knudsen diffusion coefficient did not differ when columns with two different lengths, 900 and 1500 mm, were used, this column property did not influence the flow of gas in the column. The equation of the dusty gas model already includes obstruction factors for Knudsen diffusion and molecular diffusion, which relate to medium heterogeneity and tortuosity and depend only on the structure of the porous medium. Furthermore, there is no need to take account of any additional correction factor for molecular diffusion except the obstruction factor because molecular diffusion is only treated in a multicomponent gas system. Thus, molecular diffusion considers only the obstruction factor related to tortuosity. Therefore, we introduced a correction factor for a multicomponent gas system into the DGM equation, multiplying the Knudsen diffusion coefficient, which includes the obstruction factor related to tortuosity, by this correction factor. From the present experimental results, the value of this correction factor was 1/27, and it depended only on the structure of the gas system in the porous medium.

Evaluation of a coupled model for numerical simulation of a multiphase flow system in a porous medium and a surface fluid.

Numerical simulations that couple flow in a surface fluid with that in a porous medium are useful for examining problems of pollution that involve interactions among atmosphere, water, and groundwater, including saltwater intrusion along coasts. Coupled numerical simulations of such problems must consider both vertical flow between the surface fluid and the porous medium and complicated boundary conditions at their interface. In this study, a numerical simulation method coupling Navier-Stokes equations for surface fluid flow and Darcy equations for flow in a porous medium was developed. Then, the basic ability of the coupled model to reproduce (1) the drawdown of a surface fluid observed in square-pillar experiments, using pillars filled with only fluid or with fluid and a porous medium and (2) the migration of saltwater (salt concentration 0.5%) in the porous medium using the pillar filled with fluid and a porous medium was evaluated. Simulations that assumed slippery walls reproduced well the results with drawdowns of 10-30 cm when the pillars were filled with packed sand, gas, and water. Moreover, in the simulation of saltwater infiltration by the method developed in this study, velocity was precisely reproduced because the experimental salt concentration in the porous medium after saltwater infiltration was similar to that obtained in the simulation. Furthermore, conditions across the boundary between the porous medium and the surface fluid were satisfied in these numerical simulations of square-pillar experiments in which vertical flow predominated. Similarly, the velocity obtained by the simulation for a system coupling flow in surface fluid with that in a porous medium when horizontal flow predominated satisfied the conditions across the boundary. Finally, it was confirmed that the present simulation method was able to simulate a practical-scale surface fluid and porous medium system. All of these numerical simulations, however, required a great deal of computational effort, because time was incremented in 0.05- to 0.10-s steps. Hereafter, the present simulation method needs to be improved so that the simulations can be conducted with less computational effort.

Method for obtaining the Knudsen diffusion coefficient

Graphical abstract