# Numerical Study of Sulfonamide Occurrence and Transport at the Near-Shore Area of Laizhou Bay

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## Abstract

**:**

## 1. Introduction

## 2. Governing Equations

#### 2.1. Shallow Water Equations

#### 2.2. Depth-Averaged Advection–Diffusion Equation

## 3. Lattice Boltzmann Model

#### 3.1. LBM for Shallow Water Equations

#### 3.2. LBM for Depth-Averaged Advection–Diffusion Equation

## 4. Numerical Study

#### 4.1. Research Area

#### 4.2. Acquisition of the Data

#### 4.3. Boundary Conditions

#### 4.4. Parameter Setting and Sensitivity Analysis

_{b}is in the range of 0.61–22.7, which depends on the different hydrodynamic conditions. The half-life of SA is ${t}_{\frac{1}{2}}=18.48\text{}h$ [21], and the degradation process can be expressed as:

^{2}/s. Therefore, it was necessary to perform the sensitivity test on Kij in consideration of model stability and fitting of experimental data (Figure 3). Isotropic diffusion is applied in this study, i.e., Kxx = Kyy and Kxx = Kyy = 0. When Kxx = Kyy = 10 m

^{2}/s, the simulation results were basically consistent with the experimental data [8]. When Kxx, Kyy were reduced by 10% and 20%, the simulation results decreased evenly 9.97% and 20%, respectively. Likewise, when Kxx, Kyy were raised by 10% and 20%, it also leads to an average increase of 10.03% and 20% in the simulation, respectively.

## 5. Results and Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**The occurrence of SA on the 30th day in Laizhou Bay: (

**a**) the occurrence of SMX; (

**b**) the occurrence of SMZ.

**Table 1.**SA concentrations (ng/L) in the rivers discharging into Laizhou Bay [8].

Estuary | Location | SMX | SMZ |
---|---|---|---|

Xiaoqing river | 119°00.157’ E, 37°17.210’ N | 92.9 | 23.4 |

Guangli river | 118°56.841’ E, 37°21.437’ N | 83.5 | 15.2 |

Bailang river | 119°12.557’ E, 37°11.154’ N | 194 | 15.7 |

Dihe river | 119°19.205’ E, 37°07.753’ N | 31.3 | 108 |

Yuhe river | 119°17.180’ E, 37°07.787’ N | 10.4 | 3.5 |

Zhimai river | 118°56.841’ E, 37°21.437’ N | 9.9 | 5.8 |

Jiaolai river | 119°35.177’ E, 37°06.866’ N | 3.5 | 2.8 |

Weihe river | 119°29.528’ E, 37°07.219’ N | 0.68 | 0.29 |

Dajiawa river | 119°03.886’ E, 37°14.964’ N | 527 | 0.9 |

**Table 2.**Comparison of SA concentrations (ng/L) between simulation results and experimental data [8].

Location | SA | Simulation Results | Experimental Data | Fractional Errors |
---|---|---|---|---|

P1 | SMX | 45.127 | 49.4 | 9.47% |

SMZ | 0.489 | 0.56 | 14.48% | |

P2 | SMX | 79.693 | 82.0 | 2.89% |

SMZ | 0.309 | 0.34 | 10.13% | |

P3 | SMX | 23.671 | 20.4 | −13.82% |

SMZ | 0.087 | Undetected | - |

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**MDPI and ACS Style**

Xing, L.; Liu, H.; Guo, W.; Ding, Y.; Ru, Z.; Tu, G.; Wu, X.
Numerical Study of Sulfonamide Occurrence and Transport at the Near-Shore Area of Laizhou Bay. *Water* **2019**, *11*, 2065.
https://doi.org/10.3390/w11102065

**AMA Style**

Xing L, Liu H, Guo W, Ding Y, Ru Z, Tu G, Wu X.
Numerical Study of Sulfonamide Occurrence and Transport at the Near-Shore Area of Laizhou Bay. *Water*. 2019; 11(10):2065.
https://doi.org/10.3390/w11102065

**Chicago/Turabian Style**

Xing, Liming, Haifei Liu, Wenxian Guo, Yu Ding, Zhiming Ru, Gangqin Tu, and Xuerong Wu.
2019. "Numerical Study of Sulfonamide Occurrence and Transport at the Near-Shore Area of Laizhou Bay" *Water* 11, no. 10: 2065.
https://doi.org/10.3390/w11102065