# Simulation of the Nitrogen and Phosphorus Leaching Characteristics under Different Filter Materials of an Improved Subsurface Drainage

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{−}

_{3}-N), and ammonia nitrogen (NH

_{4}

^{+}-N) were effectively removed from outflow. Bruun, et al. [6] constructed subsurface flowconstructed wetlands consisting of woodchip as filter matrixes and showed that the higher NO

^{−}

_{3}-N removal rates were attributed to a longer solute residence time. Humphrey, et al. [7] studied the total dissolved nitrogen (TDN) treatment efficiency of four onsite wastewater systems (OWS) of two conventional style and two single-pass sand filters to determine OWS in clayey soils of the North Carolina Piedmont, found that the sand filter OWS reduced TDN concentrations by an average of 80% and mass loading by 50% prior to discharge to surface waters. Cui, et al. [8] analyzed nutrient removal efficiencies and mechanisms in six constructed wetlands, including combinations between evergreen submerged vegetation planting and rice straw adding under low temperature and the results show that both unvegetated and vegetated constructed wetlands achieved the highest removal rates of TN (85.1–86.6%) and NO

^{−}

_{3}-N (98.2–98.7%) with increases of approximately 56% and 68% by adding rice straw in water, respectively. Chen, et al. [9] used water hyacinth straw as an adsorbent for phosphorus removal from swine wastewater and the laboratory results show that the straw displayed a rapid TP reduction and the adsorption efficiency was about 36% upon saturation. At the same time, the water hyacinth straw enhanced NH

_{4}

^{+}-N removal efficiency as well. Paul and Hall [10] fabricated triplicates of laboratory-scale bioreactors to compare the denitrification efficiencies of biochar and zeolite to that of plastic and showed that zeolite exhibited the highest values of surface roughness in terms of arithmetic mean height, and under pseudo-steady-state conditions, zeolite displayed the highest nitrate removal efficiency.

_{4}

^{+}-N, sawdust had the top nitrogen removal efficiency of 55.1% under an envelope thickness of 10 cm, and the zeolite had the top removal rate of 76.2% under the thickness of 30 cm.

## 2. Materials and Methods

#### 2.1. Laboratory Test

#### 2.2. Simulation Theory

_{4}

^{+}-N and TP, and the nitrification of NH

_{4}

^{+}-N to NO

^{−}

_{3}-N. Mekala and Nambi [19] evaluated the reactive transport of ammonium nitrogen under the continuous and alternate wetting and drying mode of irrigation in soil columns using HYDRUS-2D. Salehi, et al. [20] assessed the ability of the HYDRUS-2D model on simulating the effect of subsurface controlled drainage on nitrate loss of paddy fields and showed that HYDRUS-2D could simulate nitrate concentration with coefficients of determination of 0.95 and 0.89 in calibration and validation periods, respectively. Hou, et al. [21] stated that Hydrus-1D was best to simulate NH

_{4}

^{+}-N transport through the soil column. Elasbah, et al. [22] pointed out that as nitrate uptake rate and leaching are affected by soil’s adsorption, it is important to determine the adsorption coefficient for nitrate.

_{4}

^{+}-N to NO

^{−}

_{3}-N, adsorption of NH

_{4}

^{+}-N, mineralization, and bio-fixation (or straw decomposition) to NH

_{4}

^{+}-N. The partial differential equations governing nitrogen transport and transformation in variable-saturated are taken as:

^{3}L

^{−3}], c

_{NH}

_{4}, and c

_{P}are the NH

_{4}

^{+}-N and TP concentration in the liquid phase [ML

^{−3}], s

_{NH}

_{4}and s

_{P}are the NH

_{4}

^{+}-N and TP concentration in the soil phase [MM

^{−1}], q

_{i}is the volumetric water flux of i [LT

^{−1}], D

_{ij}

^{WNH}

^{4}and D

_{ij}

^{WP}are the N and P dispersion coefficient [L

^{2}T

^{−1}], ${\mu}_{w}^{N{H}_{4}}$ and ${\mu}_{\mathrm{s}}^{N{H}_{4}}$ are the first-order N transformation rate constants in liquid and solid phase [T

^{−1}] and are set as ammonia volatilization decay coefficient in this study, ${\mu}^{\prime}{}_{w}^{N{H}_{4}}$ and ${\mu}^{\prime}{}_{s}^{N{H}_{4}}$ are the similar first-order N transformation rate constants in liquid and solid phase [T

^{−1}] and are set as rate constants of nitrification, ρ is the soil bulk density [ML

^{−3}], ${r}_{w}^{N{H}_{4}}$/${r}_{w}^{P}$ and ${r}_{s}^{N{H}_{4}}$/${r}_{s}^{P}$ are the zero-order N/P transformation rate constants in liquid and solid phase [ML

^{−3}T

^{−1}] and are set as rate constants of mineralization and bio-fixation, S is a sink term [T

^{−1}], and c

_{r}is the concentration of the sink term [ML

^{−3}].

_{k}and c

_{k}is described by a generalized nonlinear equation of the form

_{d,k}[for linear sorption, L

^{3}M

^{−1}, for Freundlich sorpion L

^{3β}M

^{−β}], β

_{k}[-] and η

_{k}[L

^{3}M

^{−1}] are empirical coefficients. The Freundlich, Langmuir, and linear adsorption equations are special cases of Equation (3). When β

_{k}= 1, Equation (3) becomes the Langmuir equation, when η = 0, Equation (3) becomes the Freundlich equation, and when both β

_{k}= 1 and η

_{k}= 0, Equation (3) leads to a linear adsorption isotherm.

#### 2.3. Model Calibration and Validation

_{4}

^{+}-N loss were the soil adsorption capacity, filter adsorption capacity, N dispersion coefficient of the filter, N dispersion coefficient of the soil, and nitrification coefficient of the filter. Hence, during the calibration and validation, the absorbtion was mainly considered which could also provide a reference for the filter chosen.

^{wNH4}) for nitrogen is 1.52 cm

^{2}d

^{−1}[4,25], the molecular diffusion coefficient (D

^{wP}) for phosphorus is one thousandth of D

^{wNH4}, taking the literature [26] and [27] as references. The D

_{L}of the soil is 3 cm [28] and the D

_{L}of the gravel is 30 cm [25,29], and the D

_{L}of other materials is determined by taking the partical size as reference. The D

_{T}of all materials equals one-fifth of the D

_{L}. Other calibrated parameters were shown in Table 3. The comparisons of the observed and simulated NH

_{4}

^{+}-N concentrations are shown in Figure 3.

_{4}

^{+}-N concentrations were sharply increased when the HRT was 1 d and the large concentrations lasted until 3 d. Then, the NH

_{4}

^{+}-N concentrations were sharply decreased. The mechanism of this process is not clear and it may be an error of measurement, so the influence of this period is ignored in the statistical parameters. Totally speaking, the simulation results may be accepted whose relative errors were within 25%.

#### 2.4. Simulated Scenarios

## 3. Results

#### 3.1. The Adsorption of Different Materials

_{4}

^{+}-N and TP are given in Figure 6. The adsorption capacity of NH

_{4}

^{+}-N from large to small is zeolite, soil, silica sand, sand, gravel, and straw. For TP, the order from large to small is zeolite, soil, straw, silica sand, sand, and gravel. The zeolite showed good adsorption characteristics for both NH

_{4}

^{+}-N and TP, while the straw’s adsorption characteristics were very different for NH

_{4}

^{+}-N and TP.

#### 3.2. Effect of Materials in Scenarios 1

_{4}

^{+}-N concentrations in outflow decreased with the increasing HRT. Because of the good adsorption of zeolite, NH

_{4}

^{+}-N concentrations under the filter materials of zeolite or straw+ zeolite cases were the lowest. Straw and zeolite + straw filter may lead a larger nitrogen concentration with a larger HRT. The main reason may be that straw would release NH

_{4}

^{+}-N and the amount of the NH

_{4}

^{+}-N would increase with the increasing HRT, which may lead to a larger concentration of the outflow. When HRT was 5 d, NH

_{4}

^{+}-N concentration was 46.3 mg/L for the straw case. It could be seen that filters of straw + zeolite and zeolite + straw generated a big difference in the NH

_{4}

^{+}-N loss. The materials around the outlet may be more important. For the situation of the sand filter, the effect of NH

_{4}

^{+}-N reduction may be obvious if the HRT is large enough.

#### 3.3. Effect of Soil Depth and Location in Scenario 1

_{4}

^{+}-N concentrations were affected little by filter materials, except for the sand filter case, which had a little effect until that lower soil depth was 10 cm. The NH

_{4}

^{+}-N concentrations with more than a 5 cm-lower soil depth in all cases were about 1.65 mg/L.

_{4}

^{+}-N concentrations under sand, straw, and zeolite+ straw cases decreased obviously. The decreased percentages from large to small, in turn, were under straw, zeolite + straw, and sand with 96.3%, 96.2%, and 54.5%, respectively. While for the cases of zeolite and straw + zeolite, the lower soil layer may increase the drainage of NH

_{4}

^{+}-N concentration. When the lower soil depth was 5 cm, the NH

_{4}

^{+}-N concentrations would be five times more than that without lower soil.

_{4}

^{+}-N concentrations were 4.46 mg/L, 4.43 mg/L, 4.38 mg/L, and 4.30 mg/L, respectively, corresponding to upper soil depths of 10 cm, 15 cm, 20 cm, and 25 cm without lower soil.

_{4}

^{+}-N concentrations. TP concentrations with more than 5 cm lower in soil depth in all cases, except zeolite filters were about 0.28 mg/L. Compared with no lower soil cases, when lower soil depth was 5 cm, the TP concentrations under sand, straw, and zeolite + straw cases decreased obviously. The decreased percentages from large to small, in turn, were under filters of straw, zeolite + straw, and sand, with 96.2%, 84.1%, and 84.1%.

#### 3.4. Mixed Filter with Straw in Scenario 2

_{4}

^{+}-N concentrations from large to small, in turn, were Case 4, Case 1, Case 2, and Case 3 with 0.33 mg/L, 0.67 mg/L, 1.16 mg/L, and 4.56 mg/L, respectively, when HRT was 60 min and 0.09 mg/L, 1.72 mg/L, 4.05 mg/L, and 44.94 mg/L when HRT was 5 d. It could be seen that when the straw was set near the outlet, the NH

_{4}

^{+}-N concentrations of drainage would become large. In Case 4, the NH

_{4}

^{+}-N concentration was the same as that of the zeolite filter without the straw case; that is to say, the mixed filter would be feasible. For Case 6 and 8, the ratios of straw and zeolite were 1:2 and 2:1, and the zeolite was set near the outlet without hierarchy, and the NH

_{4}

^{+}-N concentration was still the same as the whole zeolite filter case. In the view of the cost, the Case 8 may be more suitable.

_{4}

^{+}-N concentrations of Case 3 and Case 7 were the smallest when HRT was 60 min. That was because the NH

_{4}

^{+}-N volume that came from the straw decomposition was still small. When HRT was 5 h, Case 4 showed the better effect on NH

_{4}

^{+}-N concentration reduction, with 3.55 mg/L, than Case 6, with 4.55 mg/L. The difference from Case 4 and 6 in Case 8 is that the NH

_{4}

^{+}-N concentrations with a HRT of 2 d had a slight decrease and then increased. It could be found that when straw and sand are mixed as the filter, the ratio of straw and sand was 1:1, and the sand set near the outlet may be better for NH

_{4}

^{+}-N reduction.

_{4}

^{+}-N concentrations. That the ratio of straw and zeolite was 2:1 and the zeolite was set near the outlet may be better for TP reduction.

_{4}

^{+}-N and TP concentrations of the drainage, the case that the ratio of straw and sand was 1:1 and the sand was set near the outlet could be better.

## 4. Discussion

## 5. Conclusions

_{4}

^{+}-N from large to small is zeolite, soil, silica sand, sand, gravel, and straw. While for TP, the order from large to small is zeolite, soil, straw, silica sand, sand, and gravel. Secondly, in views of NH

_{4}

^{+}-N and TP reduction, upper soil depth has little influence when the HRT was a short time, while the materials around the outlet have obvious effects on the drainage concentrations. The straw was not suggested to be set around the outlet, and if the mixed filter with straw was accepted, the straw would be put in the top layer. Thirdly, considering the mixed ratio and layout of the mixed materials, the ratio of straw and sand was 1:1, but the ratio of straw and zeolite was 2:1 may be better. Long-time running for the drainage with different materials as the filter should be measured, and particle size of the filter and the degree of straw decay should be concerned in the future.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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Location | Case 1 | Case 2 | Case 3 | Case 4 | Case 5 |
---|---|---|---|---|---|

Upper 10 cm | soil | soil | sand | silica sand | silica sand |

Middle 20 cm | sand | straw | zeolite | straw | zeolite + straw |

Lower 10 cm | gravel | gravel | gravel | gravel | gravel |

For short | soil + sand | soil + straw | zeolite | straw | zeolite + straw |

Material | θr (cm^{3} cm^{−3}) | θs (cm^{3} cm^{−3}) | a (cm^{−1}) | n | Ks (cm min^{−1}) | l |
---|---|---|---|---|---|---|

Soil | 0.05 | 0.44 | 0.014 | 1.8 | 0.0629 | 0.5 |

Sand | 0.01 | 0.42 | 0.02 | 1.9 | 2 | 0.5 |

Gravel | 0.005 | 0.42 | 0.16 | 2.8 | 4 | 0.5 |

Straw | 0 | 0.48 | 0.018 | 1.9 | 0.69 | 0.5 |

Zeolite | 0.01 | 0.42 | 0.02 | 1.9 | 2 | 0.5 |

Silica sand | 0.01 | 0.42 | 0.02 | 1.9 | 0.8 | 0.5 |

Material | Adsorption Coefficient of N | D_{L}(cm) | Zero-Order N Transformation Rate Constants K_{dN}^{o} (min^{−1}) | Adsorption Coefficient of P | Zero-order P Transformation Rate Constants K _{dP}^{o} (min^{−1}) | ||
---|---|---|---|---|---|---|---|

K_{dN}(cm ^{3}·mg^{−1}) | β_{N} | K_{dP}(cm ^{3}·mg^{−1}) | β_{P} | ||||

Soil | 0.0032 | 1 | 3 | - | 0.002 | 0.7 | - |

Sand | 0.001 | 1 | 20 | - | 0.0006 | 1 | - |

Gravel | 0.00046 | 1 | 30 | - | 2 × 10^{−6} | 1 | - |

Straw | 0.000085 | 0.51 | 12 | 4 × 10^{−9} | 0.0016 | 0.7 | 1.8 × 10^{−9} |

Zeolite | 0.01 | 0.8 | 4 | - | 0.004 | 0.45 | - |

Silica sand | 0.0012 | 1 | 10 | - | 0.001 | 1 | - |

Case | Case 1 Soil + Sand | Case 4 Straw | Case 3 Zeolite | Case 2 Soil + Straw | Case 5 Zeolite + Straw |
---|---|---|---|---|---|

R | 0.57 | 0.90 | 0.81 | 0.60 | 0.68 |

RE (%) | 9.46 | −21.1 | −14.4 | −10.8 | −11.2 |

Case | Case 1 Soil + Sand | Case 4 Straw | Case 3 Zeolite | Case 2 Soil + Straw | Case 5 Zeolite + Straw |
---|---|---|---|---|---|

R | 0.88 | 0.60 | 0.94 | 0.60 | 0.85 |

RE (%) | −7.49 | −2.3 | 0.31 | −10.8 | 9.45 |

Impact Factor | Values of the Parameters |
---|---|

Upper soil depth | 10 cm, 15 cm, 20 cm, 25 cm |

Filter material | Straw, zeolite, sand, straw (upper) + zeolite (lower), zeolite (upper) + straw (lower) |

Filter thickness | Based on the upper and lower soil depth |

Lower soil depth | 0 cm, 5 cm, 10 cm, 15 cm |

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**MDPI and ACS Style**

Tao, Y.; Chang, X.; Wang, S.; Guan, X.; Liu, J.
Simulation of the Nitrogen and Phosphorus Leaching Characteristics under Different Filter Materials of an Improved Subsurface Drainage. *Water* **2022**, *14*, 3744.
https://doi.org/10.3390/w14223744

**AMA Style**

Tao Y, Chang X, Wang S, Guan X, Liu J.
Simulation of the Nitrogen and Phosphorus Leaching Characteristics under Different Filter Materials of an Improved Subsurface Drainage. *Water*. 2022; 14(22):3744.
https://doi.org/10.3390/w14223744

**Chicago/Turabian Style**

Tao, Yuan, Xiaomin Chang, Shaoli Wang, Xiaoyan Guan, and Jing Liu.
2022. "Simulation of the Nitrogen and Phosphorus Leaching Characteristics under Different Filter Materials of an Improved Subsurface Drainage" *Water* 14, no. 22: 3744.
https://doi.org/10.3390/w14223744