# Modeling of Pollutants Removal in Subsurface Vertical Flow and Horizontal Flow Constructed Wetlands

^{1}

^{2}

^{*}

## Abstract

**:**

_{4}

^{+}-N, while SS HF bed effectiveness was at 41.4% and 62.0%, respectively. In the case of BOD

_{5}(biochemical oxygen demand), COD (chemical oxygen demand), NH

_{4}

^{+}-N, and TN (total nitrogen), the P-k-C* model was applied. Multi-model nonlinear segmented regression analysis was performed. Final mathematical models with estimates of parameters determining the treatment effectiveness were obtained. Treatment efficiency increased up to the specific temperature, then it was constant. The results obtained in this work suggest that it may be possible to describe pollutant removal behavior using simplified models. In the case of TP (total phosphorus) removal, distribution tests along with a t-test were performed. All models predict better treatment efficiency in SS VF bed, except for TP.

## 1. Introduction

_{4}

^{+}-N) and irregular flow because of periodically working devices for sewage sludge dewatering [5,6,7,8]. The problem of reject water treatment in a conventional sludge activated system is caused by low biodegrability, indicated by proportions of easily biodegradable organic matter expressed by biochemical oxygen demand (BOD

_{5}) to total organic matter expressed by chemical oxygen demand (COD).

_{4}

^{+}-N concentration [12,13,14,15]. Reject water generated during anaerobic digestion in dairy WWTPs differs from that from municipal WWTPs. There is a lack of experiments concerning constructed wetlands treatment of reject water generated during anaerobic digestion in dairy WWTPs [16].

## 2. Materials and Methods

#### 2.1. Study Sites

^{−1}.

^{2}surface area and 0.8 m height (Figure 1). The beds were used in parallel. In addition, the installation includes a sedimentation and retention tank, outflow, and sampling points (I, II, III). Figure 2 presents the cross section of SS VF and SS HF beds.

^{−2}ms

^{−1}. Both beds were planted with reeds (Phragmites australis). Reject water was taken directly from centrifuge which dewatered sludge after anaerobic digestion in a dairy WWTP.

#### 2.2. Sampling and Analytical Procedures

^{3}m

^{−2}d

^{−1}in both SS VF and SS HF beds. Hydraulic retention time (HRL) for SS HF bed was approximately 8 days. Samples were collected three times a month (influent to SS-VF and SS-HF and effluents from both beds). The air temperature during the research period varied from −11 to 26 °C, while reject water temperature varied from 4 °C to 20 °C.

_{5}, COD, total organic carbon (TOC), total suspended solids (TSS), total Kjeldahl nitrogen (TKN), ammonium nitrogen (NH

_{4}

^{+}-N), nitrate nitrogen (V) (NO

_{3}-N), nitrite nitrogen (III) (NO

_{2}-N), total phosphorus (TP), dissolved oxygen, and alkalinity. TN value was calculated as a sum of TKN, NO

_{3}–N, and NO

_{2}

^{−}-N. To evaluate biodegrability of reject water, BOD

_{5}/COD and BOD

_{5}/TN ratios were determined. Determinations were conducted in a certified laboratory in accordance with the procedures set out in the Regulation of the Environmental Protection Minister [21] from November 18, 2014, and in accordance with the American Public Health Association (2005) [22].

#### 2.3. Modeling of Pollutants Removal

_{4}

^{+}-N and TN, as well as BOD

_{5}; COD removal was performed, based on the P-k-C

^{*}model [12]:

_{out}—output concentration (g/m

^{3}), C

_{in}—input concentration (g/m

^{3}), C*—background concentration (g/m

^{3}), k(T)—chemical reaction coefficient (temperature dependent), q—hydraulic load (m/d), P—number of tanks in series.

## 3. Results and Discussion

#### 3.1. Treatment Efficiency and Load Removal

_{5}/COD and BOD

_{5}/TN ratios give information about biodegradability [26]. Its value can be used to assess the reject water susceptibility for high efficiency of biological treatment in conventional systems (e.g., activated sludge method). An average BOD

_{5}/COD ratio was 0.59, while BOD

_{5}/TN ratio 0.43. Low BOD

_{5}/COD ratio pointed out low degradability of the organic compounds. Reject water from dairy WWTP with anaerobic sewage sludge digestion was discovered to have a higher BOD

_{5}/COD ratio than municipal WWTPs. In municipal, it ranges from 0.25 to 0.32 for reject water from the WWTP in Gdansk [27], and 0.2 for reject water from the WWTP in Minworth [8]. The WWTP in Gdansk records BOD

_{5}/TN ratios at the level of 0.37 up to 0.54. In this case, the conventional path of nitrogen removal cannot be applied as the content of easily biodegradable organics is insufficient [28,29]. A very high concentration of ammonium nitrogen should be viewed as the main reason for this.

_{5}82.12%, COD 79.79%, TOC 80.85%, TSS 85.30%, TN 51.46%, NH

_{4}

^{+}-N 74.06%, and TP 25.42%. The average calculated treatment efficiency in SS HF bed was: BOD

_{5}74.13%, COD 75.34%, TOC 66.01%, TSS 89.90%, TN 42.58%, NH

_{4}

^{+}-N 62.52%, and TP 37.20%. After the treatment, the average ratios of BOD

_{5}/COD were 0.53 for SS VF bed and 0.63 for SS HF bed, and BOD

_{5}/TN were 0.16 and 0.20, respectively.

^{−2}d

^{−1}) expressed by BOD

_{5}, COD, and TOC (Table 2), similar values to household sewage treatment with constructed wetlands were achieved [10]. In the case of TN and NH

_{4}

^{+}-N, higher efficiency was observed mainly due to high concentration of nitrogen in reject water before treatment in SS VF and SS HF beds. The TP removal effect was similar to the observed in the case of household and municipal sewage treatment.

#### 3.2. Modeling of Pollutants Removal

_{4}

^{+}-N and TN, as well as BOD

_{5}, COD removal, presented in Appendix B, revealed existence of 3 group models, each with stable core parameters, which dominate the variability of logarithmic likelihood and residuals distribution. The most-preferred parameter set was ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$—a model without temperature dependency after ${T}_{k}$, with Akaike weight greater than 0.94 in all but other cases except in one (TN removal in SS HF bed). Residual analysis suggests also ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ model selection in this case. Selected models are presented graphically in Figure 3, using efficiency scale.

_{5}, COD, TN, and NH

_{4}

^{+}-N, the treatment efficiency increased until a specific temperature ${T}_{k}$ was reached, and then it was constant. Results obtained in this work suggest that it may be possible to effectively describe pollutant removal behavior in a consistent way using simplified models. Any additional parameter, with assumption of proper overall fit, will have a large confidence interval, suggesting overall insensitivity. Simplicity of obtained models does not interfere with their statistical validity.

^{−14}). For all performed tests, significance level was set to α = 0.05.

## 4. Conclusions

_{5}82.12% and 74.13%, for TN 51.46% and 42.58%, for NH

_{4}

^{+}-N 74.06% and 62.52%, for TP 25.42% and 37.20%. A higher efficiency of main organic pollutants removal was observed in the case SS VF bed during the whole research. The efficiency of TP removal was stable and higher for the SS HF bed.

_{5}, COD, TN, and NH

_{4}

^{+}-N, the treatment efficiency increased to the specific temperature, then it was constant. Results obtained in this work suggest that it may be possible to effectively describe pollutant removal behavior using simplified models.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Statistical Modeling

- ${C}^{*}$ (allowed to vary or set to 0)
- $P$ (allowed to vary or taken limit resulting in (3) dependency)
- $\theta $ (allowed to vary or set to $1$)
- ${\theta}_{m}$ and related ${T}_{k}$ (if ${\theta}_{m}$ is present, then (5) form was used, otherwise (4)).

## Appendix B. Result of Statistical Modeling

Horizontal Flow Bed SS-HF | Vertical Flow Bed SS-VF | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Model | Variables | k | logLik | AICc | ${\mathbf{\Delta}}_{\mathit{i}}$ | ${\mathit{w}}_{\mathit{i}}$ | Model | Variables | k | logLik | AICc | ${\mathbf{\Delta}}_{\mathit{i}}$ | ${\mathit{w}}_{\mathit{i}}$ |

1 | ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 4 | 2.272 | 4.668 | 0.000 | >0.999 | 1 | ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 4 | −0.855 | 10.923 | 0.000 | >0.996 |

2 | $P$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 5 | 2.485 | 6.905 | 2.237 | 2 | $\theta $, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 5 | −0.260 | 12.394 | 1.471 | ||

3 | $\theta $, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 5 | 2.280 | 7.315 | 2.648 | 3 | $P$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 5 | −0.606 | 13.088 | 2.164 | ||

4 | ${C}^{*}$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 5 | 2.272 | 7.330 | 2.663 | 4 | ${C}^{*}$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 5 | −0.855 | 13.586 | 2.663 | ||

5 | $\theta $, $P$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 6 | 2.485 | 9.739 | 5.072 | 5 | $\theta $, $P$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 6 | −0.031 | 14.772 | 3.849 | ||

6 | ${C}^{*}$, $P$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 6 | 2.485 | 9.740 | 5.072 | 6 | ${C}^{*}$, $\theta $, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 6 | −0.260 | 15.229 | 4.306 | ||

7 | ${C}^{*}$, $\theta $, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 6 | 2.280 | 10.150 | 5.483 | 7 | ${C}^{*}$, $P$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 6 | −0.606 | 15.922 | 4.999 | ||

8 | ${C}^{*}$, $\theta $, $P$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 7 | 2.485 | 12.763 | 8.096 | 8 | ${C}^{*}$, $\theta $, $P$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 7 | −0.031 | 17.796 | 6.873 | ||

9 | $\theta $, ${K}_{20}$ | 3 | −8.793 | 24.293 | 19.625 | 5.476 × 10^{−5} | 9 | $\theta $, ${K}_{20}$ | 3 | −7.783 | 11.349 | 11.349 | 3.421 × 10^{−3} |

10 | $\theta $, $P$, ${K}_{20}$ | 4 | −7.897 | 25.007 | 20.339 | 10 | $\theta $, $P$, ${K}_{20}$ | 4 | −6.763 | 22.738 | 11.815 | ||

11 | ${C}^{*}$, $\theta $, ${K}_{20}$ | 4 | −8.793 | 26.799 | 22.131 | 11 | ${C}^{*}$, $\theta $, ${K}_{20}$ | 4 | −7.783 | 24.778 | 13.855 | ||

12 | ${C}^{*}$, $\theta $, $P$, ${K}_{20}$ | 5 | −7.897 | 27.670 | 23.002 | 12 | ${C}^{*}$, $\theta $, $P$, ${K}_{20}$ | 5 | −6.763 | 25.401 | 14.478 | ||

13 | ${K}_{20}$ | 2 | −31.510 | 67.364 | 62.696 | 5.430 × 10^{−14} | 13 | ${K}_{20}$ | 2 | −32.052 | 68.446 | 57.523 | 3.218 × 10^{−13} |

14 | ${C}^{*}$, ${K}_{20}$ | 3 | −31.510 | 69.727 | 65.059 | 14 | ${C}^{*}$, ${K}_{20}$ | 3 | −32.052 | 59.886 | 70.809 | ||

15 | $P$, ${K}_{20}$ | 3 | −31.510 | 69.727 | 65.059 | 15 | $P$, ${K}_{20}$ | 3 | −32.052 | 59.886 | 70.809 | ||

16 | ${C}^{*}$, $P$, ${K}_{20}$ | 4 | −31.510 | 72.233 | 67.565 | 16 | ${C}^{*}$, $P$, ${K}_{20}$ | 4 | −32.052 | 62.392 | 73.316 |

Horizontal Flow Bed SS-HF | Vertical Flow Bed SS-VF | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Model | Variables | k | logLik | AICc | ${\mathbf{\Delta}}_{\mathit{i}}$ | ${\mathit{w}}_{\mathit{i}}$ | Model | Variables | k | logLik | AICc | ${\mathbf{\Delta}}_{\mathit{i}}$ | ${\mathit{w}}_{\mathit{i}}$ |

1 | ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 4 | 18.702 | −28.193 | 0.000 | >0.965 | 1 | ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 4 | 17.528 | −25.844 | 0.000 | >0.970 |

2 | $P$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 5 | 18.823 | −25.772 | 2.421 | 2 | $\theta $, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 5 | 18.001 | −24.127 | 1.716 | ||

3 | $\theta $, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 5 | 18.711 | −25.547 | 2.645 | 3 | $P$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 5 | 17.591 | −23.307 | 2.537 | ||

4 | ${C}^{*}$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 5 | 18.702 | −25.530 | 2.663 | 4 | ${C}^{*}$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 5 | 17.528 | −23.181 | 2.663 | ||

5 | $\theta $, $P$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 6 | 18.832 | −22.955 | 5.238 | 5 | $\theta $, $P$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 6 | 18.002 | −21.295 | 4.549 | ||

6 | ${C}^{*}$, $P$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 6 | 18.823 | −22.937 | 5.256 | 6 | ${C}^{*}$, $\theta $, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 6 | 18.001 | −21.293 | 4.551 | ||

7 | ${C}^{*}$, $\theta $, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 6 | 18.711 | −22.713 | 5.480 | 7 | ${C}^{*}$, $P$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 6 | 17.591 | −20.472 | 5.372 | ||

8 | ${C}^{*}$, $\theta $, $P$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 7 | 18.832 | −19.931 | 8.261 | 8 | ${C}^{*}$, $\theta $, $P$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 7 | 18.002 | −18.271 | 7.573 | ||

9 | $\theta $, ${K}_{20}$ | 3 | 14.117 | −21.528 | 6.664 | 3.449 × 10^{−2} | 9 | $\theta $, ${K}_{20}$ | 3 | 12.794 | −18.883 | 6.961 | 2.986 × 10^{−2} |

10 | $\theta $, $P$, ${K}_{20}$ | 4 | 14.821 | −20.430 | 7.762 | 10 | $\theta $, $P$, ${K}_{20}$ | 4 | 13.497 | −17.782 | 8.062 | ||

11 | ${C}^{*}$, $\theta $, ${K}_{20}$ | 4 | 14.117 | −19.022 | 9.170 | 11 | ${C}^{*}$, $\theta $, ${K}_{20}$ | 4 | 12.794 | −16.376 | 9.468 | ||

12 | ${C}^{*}$, $\theta $, $P$, ${K}_{20}$ | 5 | 14.821 | −17.768 | 10.425 | 12 | ${C}^{*}$, $\theta $, $P$, ${K}_{20}$ | 5 | 13.497 | −15.119 | 10.725 | ||

13 | ${K}_{20}$ | 2 | −18.244 | 40.831 | 69.023 | 9.922 × 10^{−16} | 13 | ${K}_{20}$ | 2 | −20.165 | 44.672 | 70.516 | 4.726 × 10^{−16} |

14 | ${C}^{*}$, ${K}_{20}$ | 3 | −18.244 | 43.194 | 71.386 | 14 | ${C}^{*}$, ${K}_{20}$ | 3 | −20.165 | 47.035 | 72.879 | ||

15 | $P$, ${K}_{20}$ | 3 | −18.244 | 43.194 | 71.386 | 15 | $P$, ${K}_{20}$ | 3 | −20.165 | 47.035 | 72.879 | ||

16 | ${C}^{*}$, $P$, ${K}_{20}$ | 4 | −18.244 | 45.700 | 73.892 | 16 | ${C}^{*}$, $P$, ${K}_{20}$ | 4 | −20.165 | 49.542 | 75.385 |

Horizontal Flow Bed SS-HF | Vertical Flow Bed SS-VF | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Model | Variables | k | logLik | AICc | ${\mathbf{\Delta}}_{\mathit{i}}$ | ${\mathit{w}}_{\mathit{i}}$ | Model | Variables | k | logLik | AICc | ${\mathsf{\Delta}}_{\mathit{i}}$ | ${\mathit{w}}_{\mathit{i}}$ |

1 | ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 4 | −4.371 | 17.954 | 0.000 | >0.980 | 1 | ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 4 | 4.583 | 0.046 | 0.000 | >0.940 |

2 | $\theta $, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 5 | −4.342 | 20.559 | 2.605 | 2 | $\theta $, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 5 | 5.060 | 1.754 | 1.708 | ||

3 | $P$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 5 | −4.370 | 20.615 | 2.662 | 3 | $P$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 5 | 4.883 | 2.109 | 2.063 | ||

4 | ${C}^{*}$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 5 | −4.371 | 20.617 | 2.663 | 4 | ${C}^{*}$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 5 | 4.583 | 2.709 | 2.663 | ||

5 | ${C}^{*}$, $\theta $, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 6 | −4.342 | 23.394 | 5.440 | 5 | $\theta $, $P$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 6 | 5.117 | 4.476 | 4.429 | ||

6 | ${C}^{*}$, $P$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 6 | −4.370 | 23.450 | 5.497 | 6 | ${C}^{*}$, $\theta $, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 6 | 5.060 | 4.589 | 4.542 | ||

7 | $\theta $, $P$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 6 | −4.638 | 23.986 | 6.032 | 7 | ${C}^{*}$, $P$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 6 | 4.883 | 4.944 | 4.897 | ||

8 | ${C}^{*}$, $\theta $, $P$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 7 | −4.638 | 27.010 | 9.056 | 8 | ${C}^{*}$, $\theta $, $P$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 7 | 5.117 | 7.499 | 7.453 | ||

9 | $\theta $, ${K}_{20}$ | 3 | −9.506 | 25.719 | 7.765 | 2.018 × 10^{−2} | 9 | $\theta $, | 3 | 0.566 | 5.574 | 5.527 | 5.932 × 10^{−2} |

10 | $\theta $, $P$, ${K}_{20}$ | 4 | −8.692 | 26.597 | 8.643 | 10 | $\theta $, $P$, ${K}_{20}$ | 4 | 1.709 | 5.793 | 5.747 | ||

11 | ${C}^{*}$, $\theta $, ${K}_{20}$ | 4 | −9.506 | 28.225 | 10.271 | 11 | ${C}^{*}$, $\theta $, ${K}_{20}$ | 4 | 0.566 | 8.080 | 8.034 | ||

12 | ${C}^{*}$, $\theta $, $P$, ${K}_{20}$ | 5 | −8.692 | 29.260 | 11.306 | 12 | ${C}^{*}$, $\theta $, $P$, ${K}_{20}$ | 5 | 1.709 | 8.456 | 8.410 | ||

13 | ${K}_{20}$ | 2 | −37.860 | 80.062 | 62.108 | 3.195 × 10^{−14} | 13 | ${K}_{20}$ | 2 | −33.102 | 70.547 | 70.500 | 4.618 × 10^{−16} |

14 | ${C}^{*}$, ${K}_{20}$ | 3 | −37.860 | 82.425 | 64.471 | 14 | ${C}^{*}$, ${K}_{20}$ | 3 | −33.102 | 72.910 | 72.863 | ||

15 | $P$, ${K}_{20}$ | 3 | −37.860 | 82.425 | 64.471 | 15 | $P$, ${K}_{20}$ | 3 | −33.102 | 72.910 | 72.863 | ||

16 | ${C}^{*}$, $P$, | 4 | −37.860 | 84.931 | 66.978 | 16 | ${C}^{*}$, $P$, ${K}_{20}$ | 4 | −33.102 | 75.416 | 75.370 |

Horizontal Flow Bed SS-HF | Vertical Flow Bed SS-VF | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Model | Variables | k | logLik | AICc | ${\mathit{\Delta}}_{\mathit{i}}$ | ${\mathit{w}}_{\mathit{i}}$ | Model | Variables | k | logLik | AICc | ${\mathsf{\Delta}}_{\mathit{i}}$ | ${\mathit{w}}_{\mathit{i}}$ |

1 | ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 4 | 14.709 | −20.206 | 0.000 | >0.838 | 1 | ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 4 | 5.926 | −2.640 | 0.000 | >0.992 |

2 | $\theta $, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 5 | 14.744 | −17.613 | 2.593 | 2 | $\theta $, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 5 | 6.384 | −0.893 | 1.747 | ||

3 | ${C}^{*}$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 5 | 14.709 | −17.543 | 2.663 | 3 | ${C}^{*}$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 5 | 5.926 | 0.023 | 2.663 | ||

4 | $P$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 5 | 14.709 | −17.543 | 2.663 | 4 | $P$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 5 | 5.926 | 0.023 | 2.663 | ||

5 | ${C}^{*}$, $\theta $, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 6 | 14.744 | −14.779 | 5.428 | 5 | ${C}^{*}$, $\theta $, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 6 | 6.384 | 1.942 | 4.582 | ||

6 | $\theta $, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 6 | 14.732 | −14.755 | 5.451 | 6 | $\theta $, $P$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 6 | 6.384 | 1.942 | 4.582 | ||

7 | ${C}^{*}$, $P$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 6 | 14.709 | −14.709 | 5.498 | 7 | ${C}^{*}$, $P$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 6 | 5.926 | 2.858 | 5.498 | ||

8 | ${C}^{*}$, $\theta $, $P$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 7 | 14.732 | −11.731 | 8.475 | 8 | ${C}^{*}$, $\theta $, $P$, ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$ | 7 | 6.384 | 4.966 | 7.605 | ||

9 | $\theta $, ${K}_{20}$ | 3 | 11.810 | −16.915 | 3.291 | >0.161 | 9 | $\theta $, ${K}_{20}$ | 3 | −0.182 | 7.071 | 9.710 | 7.729 × 10^{−3} |

10 | $\theta $, $P$, ${K}_{20}$ | 4 | 11.887 | −14.562 | 5.644 | 10 | $\theta $, $P$, ${K}_{20}$ | 4 | −0.084 | 9.381 | 12.020 | ||

11 | ${C}^{*}$, $\theta $, ${K}_{20}$ | 4 | 11.810 | −14.409 | 5.798 | 11 | ${C}^{*}$, $\theta $, ${K}_{20}$ | 4 | −0.182 | 9.577 | 12.216 | ||

12 | ${C}^{*}$, $\theta $, $P$, ${K}_{20}$ | 5 | 11.887 | −11.899 | 8.307 | 12 | ${C}^{*}$, $\theta $, $P$, ${K}_{20}$ | 5 | −0.084 | 12.044 | 14.683 | ||

13 | ${K}_{20}$ | 2 | −2.405 | 9.154 | 29.360 | 3.532 × 10^{−7} | 13 | ${K}_{20}$ | 2 | −9.124 | 22.590 | 25.229 | 3.297 × 10^{−6} |

14 | ${C}^{*}$, ${K}_{20}$ | 3 | −2.405 | 11.517 | 31.723 | 14 | ${C}^{*}$, ${K}_{20}$ | 3 | −9.124 | 24.953 | 27.592 | ||

15 | $P$, ${K}_{20}$ | 3 | −2.405 | 11.517 | 31.723 | 15 | $P$, ${K}_{20}$ | 3 | −9.124 | 24.953 | 27.592 | ||

16 | ${C}^{*}$, $P$, ${K}_{20}$ | 4 | −2.405 | 14.023 | 34.229 | 16 | ${C}^{*}$, $P$, ${K}_{20}$ | 4 | −9.124 | 27.459 | 30.099 |

**Figure A1.**Diagnostic for BOD

_{5}models. (

**A**) Horizontal bed, model ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$; (

**B**) vertical bed, model ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$; (

**C**) horizontal bed, model $\theta $, ${K}_{20}$; (

**D**) vertical bed, model $\theta $, ${K}_{20}$.

**Figure A2.**Diagnostic for COD models. (

**A**) Horizontal bed, model ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$; (

**B**) vertical bed, model ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$; (

**C**) horizontal bed, model $\theta $, ${K}_{20}$; (

**D**) vertical bed, model $\theta $, ${K}_{20}$.

**Figure A3.**Diagnostic for NH

_{4}

^{+}-N models. (

**A**) Horizontal bed, model ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$; (

**B**) vertical bed, model ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$; (

**C**) horizontal bed, model $\theta $, ${K}_{20}$; (

**D**) vertical bed, model $\theta $, ${K}_{20}$.

**Figure A4.**Diagnostic for TN models. (

**A**) Horizontal bed, model ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$; (

**B**) vertical bed, model ${T}_{k}$, ${\theta}_{m}$, ${K}_{20}$; (

**C**) horizontal bed, model $\theta $, ${K}_{20}$; (

**D**) vertical bed, model $\theta $, ${K}_{20}$.

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**Figure 2.**Cross section of SS VF (subsurface vertical flow) and HF (subsurface horizontal flow beds) beds.

**Table 1.**The characteristics of reject water before and after treatment in SS VF and SS HF beds (38 research series, 114 samples).

Before Treatment (mg L^{−1}) | After Treatment (mg L^{−1}) | ||
---|---|---|---|

Parameter | SS-VF | SS-HF | |

BOD_{5} | 120.53 ± 16.97 | 21.55 ± 8.27 | 31.18 ± 10.04 |

COD | 201.92 ± 21.48 | 40.82 ± 12.14 | 49.79 ± 12.44 |

TOC | 53.18 ± 9.91 | 10.18 ± 4.52 | 18.08 ± 5.58 |

TSS | 141.01 ± 18.12 | 20.60 ± 4.84 | 26.88 ± 4.61 |

TN | 276.66 ± 42.71 | 134.29 ± 19.44 | 158.87 ± 20.29 |

NH_{4}^{+}-N | 195.53 ± 38.32 | 50.71 ± 16.60 | 73.29 ± 20.53 |

NO_{3}^{−}-N | 0.69 ± 0.28 | 12.68 ± 4.76 | 3.31 ± 1.33 |

NO_{2}^{−}-N | 0.17 ± 0.07 | 0.13 ± 0.05 | 0.63 ± 0.20 |

TP | 22.17 ± 3.54 | 16.43 ± 2.00 | 13.95 ± 2.54 |

- | Removed Load (g m^{−2} d^{−1}) | |
---|---|---|

Parameter | SS-VF | SS-HF |

BOD_{5} | 9.90 | 8.93 |

COD | 16.11 | 15.21 |

TOC | 4.30 | 3.51 |

TSS | 12.00 | 11.41 |

TN | 14.24 | 11.78 |

NH_{4}^{+}-N | 14.48 | 12.22 |

TP | 0.57 | 0.82 |

Horizontal Flow Bed SS-HF | Vertical Flow Bed SS-VF | ||||||
---|---|---|---|---|---|---|---|

BOD_{5} | |||||||

Parameter | Estimate/Value | Lower 95% CI | Upper 95% CI | Parameter | Estimate/Value | Lower 95% CI | Upper 95% CI |

${T}_{k}$ | 11.959 | 10.302 | 13.616 | ${T}_{k}$ | 12.580 | 10.836 | 14.323 |

${\theta}_{m}$ | 1.106 | 1.073 | 1.140 | ${\theta}_{m}$ | 1.087 | 1.061 | 1.113 |

${K}_{20}$ | 0.180 | 0.170 | 0.190 | ${K}_{20}$ | 0.225 | 0.213 | 0.238 |

RSS | 1.974 | - | RSS | 2.327 | - | ||

COD | |||||||

Parameter | Estimate/Value | Lower 95% CI | Upper 95% CI | Parameter | Estimate/Value | Lower 95% CI | Upper 95% CI |

${T}_{k}$ | 15.578 | 13.293 | 17.864 | ${T}_{k}$ | 17.000 | 14.656 | 19.344 |

${\theta}_{m}$ | 1.048 | 1.035 | 01.06 | ${\theta}_{m}$ | 1.043 | 1.033 | 1.052 |

${K}_{20}$ | 0.179 | 0.172 | 0.187 | ${K}_{20}$ | 0.209 | 0.200 | 0.218 |

RSS | 0.831 | - | RSS | 0.884 | - | ||

NH_{4}^{+}-N | |||||||

Parameter | Estimate/Value | Lower 95% CI | Upper 95% CI | Parameter | Estimate/Value | Lower 95% CI | Upper 95% CI |

${T}_{k}$ | 15,087 | 12,82 | 17,355 | ${T}_{k}$ | 16.007 | 14.153 | 17.862 |

${\theta}_{m}$ | 1.101 | 1.073 | 1.131 | ${\theta}_{m}$ | 1.074 | 1.058 | 1.089 |

${K}_{20}$ | 0.151 | 0.139 | 0.164 | ${K}_{20}$ | 0.195 | 0.184 | 0.207 |

RSS | 2.800 | - | RSS | 1.748 | - | ||

TN | |||||||

Parameter | Estimate/Value | Lower 95% CI | Upper 95% CI | Parameter | Estimate/Value | Lower 95% CI | Upper 95% CI |

${T}_{k}$ | 12.401 | 9.132 | 15.671 | ${T}_{k}$ | 10.312 | 7.860 | 12.763 |

${\theta}_{m}$ | 1.051 | 1.024 | 1.078 | ${\theta}_{m}$ | 1.077 | 1.033 | 1.122 |

${K}_{20}$ | 0.065 | 0.060 | 0.069 | ${K}_{20}$ | 0.083 | 0.077 | 0.089 |

RSS | 1.026 | - | RSS | 1.629 | - |

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**MDPI and ACS Style**

Dąbrowski, W.; Karolinczak, B.; Malinowski, P.; Boruszko, D.
Modeling of Pollutants Removal in Subsurface Vertical Flow and Horizontal Flow Constructed Wetlands. *Water* **2019**, *11*, 180.
https://doi.org/10.3390/w11010180

**AMA Style**

Dąbrowski W, Karolinczak B, Malinowski P, Boruszko D.
Modeling of Pollutants Removal in Subsurface Vertical Flow and Horizontal Flow Constructed Wetlands. *Water*. 2019; 11(1):180.
https://doi.org/10.3390/w11010180

**Chicago/Turabian Style**

Dąbrowski, Wojciech, Beata Karolinczak, Paweł Malinowski, and Dariusz Boruszko.
2019. "Modeling of Pollutants Removal in Subsurface Vertical Flow and Horizontal Flow Constructed Wetlands" *Water* 11, no. 1: 180.
https://doi.org/10.3390/w11010180