Each Plexiglas column was designed in order to provide a physical model. The first Plexiglas column as Marriott column in 100 (cm) height and 25 (cm) diameter to supply and retain water flux and the second Plexiglas column as soil column with 50 (cm) and 10 (cm) in order to height and diameter were selected but only the 40 (cm) of soil column were used as bed and simulated. A shut-off valve was installed on the column inlet and outlet (Fig. 1).
In order to fill the soil column, topside of the soil column was first blocked with a Plexiglas cap and a hole was created to set the inlet flow pipe. The 5 (cm) of soil column height at the top and end of column was filled with gravel and sand as filter layers to unify the entrance flow and also, to prevent from rinsing its inside contents. The prepared column was put on metal stand. The two columns were accomplished until the saturation soil condition and the inflow into the soil column was considered to be upward (Healy et al. 2012).
The input flow simulation into the soil column was done as follow: By First, the flow from the using 49-liter Marriott column that contains nitrate solution was transported to the bottom of the soil bed. Besides, continuous sampling was done from the entering and exiting flow. Considering that the water velocity in the groundwater flow is between 0.1 and 0.5 (m day−1) (Al- Tabbaa et al. 2000), the flow rate was constant about 0.34 (m day−1) to create a uniform flow in the column. The exiting volumetric flow rate (ml h−1) from the soil column was also measured by determining the amount of time needed to collect a specific pore volume (PV) of the output flow until 10 PVs. Each pore volume (PV) was estimated roughly 1523 (mL).
The steps of experiment
Experiments were carried out in 6 steps. From the first to third step, water contained 24, 50 and 100 (mg l−1) of nitrate concentrations in the sterilized soil column (by sterilization we mean the complete destruction of the entire soil microbial content, this aim was done by using autoclave) until it reached to its saturation threshold. From step 4 to 6, water source with 24, 50 and 100 (mg l−1) nitrate concentrations from 0.35, 0.5 and 0.7 (g) of potassium nitrate salt was applied and the Heterotrophic bacteria fed by ethanol + methanol + acetate + glucose as carbon resource.
The nitrate removal efficiency was calculated by using the following equation (Zhou et al. 2015):
$$R \%= \frac{{C}_{i}- {C}_{ef}}{{C}_{i}} \times 100$$
1
Where Ci and Cef are inlet and outlet nitrate concentrations (mg l−1), respectively.
The nitrate removal rate (mg l−1h−1) was calculated by using the following equation (Ghane et al. 2015):
$${R}_{{NO}_{3}}= \frac{-\varDelta C}{HRT}$$
2
Where\({R}_{{NO}_{3}} and -\varDelta C\) are the drop rate and the difference of nitrate concentration (mg l−1) and HRT is actual hydraulic retention time calculated by the flowing relationship (Ghane et al. 2015):
$$HRT= \frac{L-{n}_{e}}{q}$$
3
Where L, ne and q are the column length (m), the effective porosity (dimensionless), and the hydraulic loading rate (m h−1), respectively. The hydraulic loading rate (m h−1) was calculated using the relationship proposed by Lin et al. (2008):
Where Q and A are the output flow rate (m³ h−1) and the flow cross-section (m 2), respectively.
The most widely used adsorption isotherms are Langmuir and Freundlich; the last isotherm was outperformed for the former similar researches.
$${C}^{*}= \frac{x}{m}= {K}_{F} {C}_{E}^{\beta }$$
5
Where CE: Equilibrium concentration of the substance in solution (mg cm−3), x: the amount of absorbed solution (mg l−1), β: exponential coefficient of Freundlich isotherm, and m: absorbent mass (g).
Model Theory and Simulation
Generally, the displacement and distribution of solute in soil matrix are flowed through three mechanisms, mass flow, diffusion and hydrodynamic dispersion. To Consider the effects of these mechanisms on movement of ions and solutes in the soil, the convection-diffusion equation (CDE) used in a one-dimensional homogeneous porous medium under constant flow condition (Abbasi 2015):
$$\frac{\partial C}{\partial t}= -v \frac{\partial C}{\partial Z}+D \frac{{\partial }^{2}C}{\partial {Z}^{2}}- {\mu }_{w}^{\text{'}}\theta C$$
6
Where D: diffusion coefficient (mg2 m−1), C: concentration of solute or intended ion (mg l−3), V: true average water velocity (m h−1), Z: distance (m), and t: time (h), µ´w: first-order rate constant s, Ɵ water content (l3 l−3).
In this model, the modified Richards equation is solved numerically to study the movement of water in the soil, which is expressed as the following equation (Mualem 1976):
$$\frac{\partial \theta }{\partial t}= \frac{\partial }{\partial Z} \left[ {K}_{\theta } \left(\frac{\partial h}{\partial z}+\text{cos}\beta \right)\right]-S$$
7
Where : volumetric moisture content (l3 l−3), t: time (h), K(): unsaturated hydraulic conductivity (m h−1), h: Matric suction (m),: the angle between the flow path and the vertical axis (for vertical movement of water in the soil, β = 0 for horizontal motion, β = 90 and for other routes 0 < β < 90), S: water absorbed by the root (m3 m−3h−1) and z is the distance (m). In the Richards equation, various equations have been defined to describe the hydraulic properties of the soil such as water retention curve and soil’s water conductivity. The most common equation is the van Genuchten– Mualem relationship:
$$\theta \left(h\right)= \left\{\begin{array}{c}{\theta }_{r}+ \frac{{\theta }_{s}-{ \theta }_{r}}{{\left[1+ \alpha {h}^{n}\right]}^{m}}\\ m=1- \frac{1}{n}\end{array}\right\} n>1$$
8
$$K\left({S}_{e}\right)={K}_{s} {S}_{e}^{1} {\left[1- {\left(1-{S}_{e}^{\left(\frac{1}{m}\right)} \right)}^{m}\right]}^{2}$$
9
Where θs: saturation moisture content, θr: residual moisture content, n: water retention curve shape parameter; this parameter is larger in coarse-textured soils in which soil moisture retention curve has a steep gradient compared to fine textured soils (Singh and Data 2004), Ks: Saturated hydraulic conductivity (m h−1), α: inverse of air entrance point (m−1) (which is highly dependent on the texture and structure of the soil, and has the least amount in soils with fine pores), Se: relative or effective degree of saturation, and l: the parameter of pore connectivity, which is considered to be 0.5 for most soils.
Model parameters such as soil hydraulic properties including soil moisture curve, soil saturated hydraulic (Ks), residual moisture content (θr) and residual saturated moisture content (θs) in the Van Genuchten-Moeller model by using soil mechanical analysis data and bulk density measurements were predicted by the RETC model. In this study, volumetric moisture content and porosity were measured as baseline data while simultaneously measuring moisture content and bromide (as a tracer) content in soil and groundwater used as a water source, and modeled. Due to the fact that the water flow was saturated and steady, only the boundary conditions were defined at the beginning and end of the soil column. The upper and lower boundary conditions were constant water flux and free drainage, respectively. The initial soil condition was the nitrate concentration of soil bed. The parameters of Freundlich’s isotherms and dispersivity of nitrate ions in MIM model were estimated by HYDRUS model in inverse solution.
Sensitivity Analysis
The main parameters were identified by changing their value and the results of the model underwent significant changes, all statistical analyzes were performed by SPSS 22 software using paired test at 95 (%) probability level