Changes in the salt concentration distribution in surface water (seawater) due to seawater recirculation in a porous medium under tidal fluctuations.

Many studies have used numerical simulations and experiments to simulate saltwater intrusion in a nearshore aquifer. Thus, it is known that seawater recirculation occurs in a porous medium just below a sloping beach, and a saltwater wedge occurs in the medium below where the slope intersects the water level at low tide. This study investigated the salt distribution in the surface water when subterranean recirculation of seawater is occurring and there is a saltwater wedge in an underlying porous medium, along with the relationships between the seawater recirculation and the tidal amplitude and beach gradient. The salt distribution in a subterranean aquifer and in surface seawater where the shore sloped gently seaward with a constant slope of 1/10 or 1/5 under tidal amplitudes of 0.5, 1.0, or 2.0 m was numerically simulated by the ASGMF method, which couples water pressure and water flow in a porous medium with those in the overlying surface water and can simulate variable-density flows and the salt concentration distribution in both the porous medium and the surface water. The results showed that the recirculation of seawater depended on the tidal amplitude, being greater when the amplitude exceeded 1.0 m, but that it was unlikely to occur when the beach gradient was steep. Thus, the aspect ratio (width to depth) of the seawater recirculation decreased as the tidal amplitude increased above 1.0 m. Furthermore, the simulated surface water level was often lower than the tidal water level; thus, the surface water level was not consistent with the tidal water level imposed at the right boundary of the simulation domain but varied slightly under the influence of water flow in the surface water and gas flow in the atmosphere. The salt concentration in the surface water was not always the same as the seawater salt concentration because a thin freshwater layer and a brackish water layer of mixed freshwater and saltwater overlay the seawater.

Modeling variable density flow in subsurface and surface water in the vicinity of the boundary between a surface water-atmosphere system and the subsurface.

When seawater intrudes into a subterranean estuary, there is interaction between groundwater and surface water, and ocean tides and waves can influence the salt concentration distribution in subsurface of the estuary. However, numerical simulations of seawater intrusion into a subterranean estuary often neglect the atmosphere and surface water and simply specify hydrostatic pressure and a constant seawater salt concentration. This study examined the influence of fluid flow and pressure in a surface water-atmosphere system consisting of both atmosphere and surface water on the salt distribution in subsurface and in the surface water by a numerical simulation that couples fluid flows in the surface water-atmosphere system and groundwater. This study first confirmed the precision of the simulation method by comparing experimentally determined salt concentration distributions in silica beads unsaturated with water. This study then conducted an experiment in a two-dimensional tank filled with seawater and glass beads (mean diameter 0.2 mm) and carried out two simulations of this tank experiment: one of a limited system consisting of the porous medium and surface water only, and the other of a full system, consisting of the porous medium, surface water, and atmosphere. Darcy's law has frequently been applied in limited system simulations by assigning extremely high permeability to the surface water. This study therefore also conducted a third, simpler numerical simulation of the limited system that used only Darcy's law. The salt concentration distribution obtained by the full system simulation was closer to the experimental distribution than that obtained by the limited system simulation. This result implies that fluid flow and pressure in both the atmosphere and surface water influence water flow and water pressure in the porous medium. Furthermore, the third simulation using Darcy's law only could not precisely reproduce flow in the surface water. Therefore, when variable-density flow in surface water and a shallow subsurface are numerically simulated, the simulation system needs to include atmosphere and surface water to take account of the influence of fluid flow and fluid pressure in both the atmosphere and surface water on the fluid flow and transport of salt in a shallow subsurface.

Method for obtaining the Knudsen diffusion coefficient.

Recently, we developed a method for obtaining the Knudsen diffusion coefficient from the results of tracer experiments with a binary gas system and a porous medium in a column. The developed method employs dusty gas model (DGM) equations that consider molecular diffusion, nonequimolar fluxes, and Knudsen diffusion. The equations derived from the DGM equations for the calculation of the Knudsen diffusion coefficient can also be used to obtain the molecular diffusion coefficient and the ratio of the Knudsen diffusion coefficients of the two chemicals composing the binary gas system. We performed an inversion simulation to fit the advection-diffusion equation to the distribution of molar fractions determined by mathematically solving the advection-diffusion equation. The results confirmed that our method of obtaining the Knudsen diffusion coefficient from tracer experiment results yielded accurate values.

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.

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 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.