#### 2.1. Field Survey and Analysis

The Ningyo-toge mine is a closed uranium mine located in the Okayama Prefecture, Japan (35°18′47.58″ N, 133°55′52.21″ E) [

17,

18,

19]. The Yotsugi mill tailings pond, an artificial pond, was constructed to receive slag and other materials generated by the smelter during operation, and now has partially become an artificial wetland near the inlet. After the closure of the smelting facility in 1982, this tailing pond was utilized as a remediation pond [

23]. The pond has four main inlets as sources of mine drainage from the surrounding area that flow through underground pipes towards the pond—one comes from an opencast mine, two are from underground mines, and one is from the upstream part of the mill tailings pond (

Figure 1). The AMD from the four inlets flow towards a dam located at the western end of the pond. The depth of the Yotsugi mill tailings pond in summer and winter was 1.4 m and 1.2 m at point H, respectively. This decreased towards the upstream area of the Yotsugi mill tailing pond from point H to A. The depth at point A was 0.0 m.

Field surveys were conducted three times in the summer and winter of 2016, respectively. For each survey, three water samples were collected from the source of each of the four inlets (points i–iv,

Figure 1). In addition, three water and sediment samples at each point of the surface were collected along the Yotsugi mill tailings pond in the direction of water flow (

Figure 2 and

Table 1). Using a thin tube with a diameter of 20 mm, a 100 mm thick sedimentary layer was collected from the bottom of the Yotsugi tailings mill pond.

The pH, temperature, oxidation–reduction potential (ORP), electric conductivity (EC), and concentration of dissolved oxygen (DO) of the water samples were measured on-site, using a pH/DO meter (OM-70, HORIBA, Kyoto, Japan). After the measurement of pH, temperature, ORP, EC, and DO concentration, the water samples were filtered using a 0.45-μm membrane filter. We also confirmed that no colloidal particles were present in the sample water after extra filtration. The concentration of all cations in the filtrates was analyzed by an inductively coupled plasma-mass spectrometer (ICP-MS, 7700X, Agilent, Santa Clara, CA, USA), using the mode of semi-quantitative analysis. The concentration of a ferrous ion in the inlet was measured beforehand by the phenanthroline absorption spectrophotometric method, and the total iron ion was almost the same as the concentration of the ferrous ion. The concentration of the arsenite ion in the inlet was measured beforehand through separation, using high selectivity inorganic separating bulk (MetaSEP AnaLig TE-01, GL Sciences, Tokyo, Japan) [

24], and the total arsenic ion was almost the same as the concentration of the arsenite ion. Therefore, the valency of iron and arsenic ions in the inlet was treated as ferrous and arsenite ions, respectively. Each sample was measured three times, and it was confirmed that their error was within 5%. Other cation ions of iron and arsenic obtained from the ICP–MS analysis resulted in less than several mg/L of sodium, potassium, calcium, magnesium, and aluminum. Sulfate and chloride ions were also measured by ion chromatography (IC, IC850, Metrohm, Tokyo, Japan) and were below the 50 mg/L. From the chemical equilibrium calculation using PHREEQC [

4], we neglected the effect of these ions for the removal reaction of iron and arsenic ions in this study.

The sediment samples were vacuum dried and the mineral phases were ascertained using X-ray diffraction analysis (XRD, RINT Ultima III, Rigaku, Tokyo, Japan), with Cu-Kα radiation at 40 kV and 30 mA. The scan range was from 2°–80°, with a scan rate of 2°/min. The XRD specimens on the plane glass holder were prepared using a front-loading technique. The objective of the XRD analysis in this study was to detect low crystalline materials of an iron hydroxide, such as 2-line ferrihydrite. Therefore, to observe the peak of the low crystalline materials, background subtraction was not conducted on the obtained XRD patterns.

#### 2.2. Simulation Model Using GETFLOWS

The GETFLOWS simulation software was used to simulate the mass transport processes in the Yotsugi mill tailings pond. GETFLOWS is a fully distributed and integrated watershed modeling tool that treats the transport processes of water, air, various dissolved and volatilized materials, suspended sediments in water, and heat from the surface to the underground, on arbitrary temporal-spatial scales. The surface water flow and dissolved materials transport in surface water functions were applied in this study.

The governing equation of surface water was based on the mass conservation law, as described in Equation (1):

where

$\nabla $ is the differential operator,

${M}_{w}$ is the mass flux of surface water (kg/m

^{2}/s),

${\rho}_{w}$ is the density of water (kg/m

^{3}),

${q}_{w}$ is the volumetric flux of the sink and source (m

^{3}/m

^{3}/s),

${S}_{w}$ is the saturation of water calculated from the surface water depth and the grid height (m

^{3}/m

^{3}), and

$t$ is the time (s).

The simulator solved the Manning’s law for estimating the surface water flow velocity, and it also solved the depth-averaged diffusion wave approximation of open channel shallow water Saint-Venant equations in two dimensions, for modeling the flows of water on land, in streams, and on slopes. Instead of solving the momentum conservation equations following Tosaka et al. [

25], we embedded the velocity field in the flow term in Equation (1) (i.e., the first term on the left-hand side). The mass flux of surface water per unit area

${M}_{w}$ in flow terms for surface flow could be expressed by adapting Manning’s law as Equation (2):

where

${n}_{l}$ is Manning’s roughness coefficient (m

^{−1/3} s),

$R$ is the hydraulic radius (m),

$h$ is the surface water depth (m),

$l$ is the distance of surface water flow direction (m), and

$z$ is the elevation from the datum level (m). The surface water depth

$h$ was computed from the water saturation

${S}_{w}$ and the height of the grid block in the surface environment.

The mass balance equation could be modified as Equation (3), when considering the behavior of the reactive substance

i dissolved in water [

26]:

where

${C}_{w,i}$ is the mass fraction of dissolved material

$i$ in water (kg/kg),

${D}_{w,i}$ is the diffusion coefficient of dissolved material

$i$ (m

^{2}/s),

${m}_{w,i1\to i2}$ is the rate of generation/decomposition of a chemical reaction from dissolved material

$i1$ to

$i2$ in water (kg/m

^{3}/s), and

${m}_{w\to s,i}$ is the adsorption rate of the dissolved material

$i$ (kg/m

^{3}/s). The first term on the left-hand side of Equation (3) is the advection term, the second term is the diffusion term, and the third term is the sink/source term for drainage and precipitation. The fourth and fifth terms are the decomposition and generation terms for chemical reactions in water, respectively. The sixth term represents a transfer from the water phase to the solid phase by adsorption.

These governing equations were discretized spatially using the integral finite difference method and temporally by the fully implicit method. Due to their nonlinearity, the governing equations were iteratively converged using the Newton–Raphson method. Matrix factorization was performed using the conjugate residual method, with preconditioning by nested factorization, which targeted the nested structure of the structured mesh. To speed up the numerous calculations, we used the successive locking process [

27] to remove the grids where sufficient convergence was achieved in the nonlinear iterative process. The governing equations, required data, and solution procedures were explained in detail in a previous paper [

26]. To ensure its accuracy and applicability, the GETFLOWS simulator was applied to many verification test problems involving theoretical and analytical solutions. In addition, GETFLOWS was applied to more than 500 sets of field and laboratory data in Japan and overseas to validate its utility [

20,

21,

22,

26,

28].

A three-dimensional topographic model of the Yotsugi mill tailings pond was developed using the Geographic Information System software MapInfo

^{®}, with field elevation data provided by the Japan Atomic Energy Agency [

23]. The three-dimensional topographic model was used to perform geosphere fluid analysis. The model domain was set as the catchment area of the pond to consider all water flowing into the pond. The ridge surrounding the pond was set as the boundary of the analysis area (

Figure 3). No flow boundary condition was applied except for a pond outlet. All water inflow from outside of the pond was considered as surface water.

Advection–diffusion analysis was performed using GETFLOWS. The topographic model, inlet flow rate, precipitation, evaporation, and water quality were utilized as input data in this simulation. Percolation and recharge in the ground did not need to be considered. The Manning’s roughness coefficient was set to 0.03 as a parameter related to the surface flow. Precipitation and evaporation data were measured and provided by the Japan Atomic Energy Agency and the inlet flow rates were provided by the Ningyo-toge Environmental Technology Center [

23].

#### 2.3. Kinetics Model

In geochemical modeling, the kinetics model of both ferrous and arsenite ions oxidation was considered in this study. For the oxidation reaction of ferrous, the kinetics model used in the quantitative model is considered in Equation (4), as proposed by Singer and Stumm [

29]:

where [Fe(II)] is the activity of ferrous ion; [OH

^{−}] is the activity of the hydroxide ion;

P_{O2} is the oxygen partial pressure; and

k_{1} and

k_{2} are rate constants with reference values of 2.91 × 10

^{−9} and 1.33 × 10

^{12}, respectively. Equation (4) has been used by many researchers, including our group, to show that the kinetics of ferrous oxidation depend on pH and DO. Although the kinetic constants of

k_{1} and

k_{2} should be affected by several chemical and biogeochemical conditions, the usefulness of these values was confirmed under the atmosphere and without any biogeochemical influence.

For the oxidation reaction of arsenite, the kinetics model used in the quantitative model is reported in Equation (5):

where [

As(III)] is the activity of arsenite;

k_{3} is a rate constant with a reference value of 3.0 × 10

^{−3} [

30].

The ORP in the Yotsugi mill tailings pond was almost stable at around 0.2 V. According to the Eh-pH diagram reported by Bednar et al. [

31], the dominant species of arsenic was HAsO

_{4}^{−} as an arsenate ion. Bednar et al. [

31] reported that arsenite was oxidized according to Equation (6) in the acidic pH area, when iron and arsenic ions co-existed.

However, it was considered that the oxidation reaction of arsenite did not proceed according to Equation (6) because our target pH area was a neutral pH area and iron ion was precipitated. Thus, we did not consider the oxidation reaction of arsenite, according to Equation (6) in this study.

Bednar et al. [

31] also reported that the ratio of arsenate/total-arsenic in the acidic pH area was larger than that in the neutral pH area. The reason for this was the arsenite/arsenate adsorption reaction for iron (hydr)oxide (e.g., ferrihydrite and magnetite) in the neutral pH area [

31,

32,

33,

34]. Since iron (hydr)oxide adsorbed more arsenate than arsenite in the neutral pH area, the ratio of arsenate was small. It was considered that this arsenite/arsenate adsorption reaction occurred in our target system.

Based on the above discussion, we introduced Equation (5) to show the kinetics of the oxidation reaction of arsenite. Since the ORP was almost stable in the Yotsugi mill tailings pond, it was treated as a constant value and unified into the kinetics constant of k_{3} in Equation (5).