# Swine Wastewater Treatment in Constructed Wetland Systems: Hydraulic and Kinetic Modeling

^{1}

^{2}

^{*}

## Abstract

**:**

_{V}), and a control unit (CWSc). The actual retention time was 3.12 days in the CWSc, whereas, in the CWSw and CWSv, we observed values of 4.14 and 4.11 days, respectively. The dispersion values were high in all CWS. The values of chemical oxygen demand (COD) across the length of the CWS were used to fit the kinetic models that describe the first-order decay of organic matter over the CWS. The models that showed a better fit to the experimental data were the plug-flow with residual concentration, the continuous stirred tank reactor, and Shepherd’s models.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Treatment System

^{−3}, the initial void volume of 0.870 m

^{3}m

^{−3}, and macroporosity of 0.465 m

^{3}m

^{−3}. The CWSs were filled up to the height of 30 cm, with the wet-height equivalent to 27 cm; each CWS studied had a total work volume of 0.657 m

^{3}.

^{−3}(post-treated in the HAR), and CWS received the same initial organic loading rate of 270 kg ha

^{−1}d

^{−1}as COD. To achieve this loading, a flow rate of 0.110 m

^{3}d

^{−1}was applied. The nominal hydraulic retention time (τ), for all CWS, was equal to 3.2 days. At the end of the experiment, tests were performed with tracers to assess the hydrodynamics of the CWS. Moreover, two samplings, across the CWS lengths, were carried out on different days in order to fit the kinetics of COD removal in the CWS.

#### 2.2. Experimental Design

#### 2.3. Hydrodynamic and Kinetic Studies

^{−3}).

_{V}and CWS

_{C}, while in the CWS

_{w}, five liters of saline solution were added with rhodamine WT. The injections of these pulses were performed in an interval of approximately 30s. The probes were programmed to perform readings in CWS final effluents with intervals of 20 min, and the data were stored in the internal memory of the equipment. This information was subsequently recorded on a laptop computer with the application Hidras 3 LT

^{®}. The experiment to evaluate the hydrodynamics of CWS lasted 11 days, a period equivalent to approximately 3 times the nominal retention time.

#### 2.4. Statistical Analysis

## 3. Results and Discussion

#### 3.1. Hydrodynamic Study

_{R}) found were: 3.12, 4.14, and 4.11 days for CWS

_{C}, CWSw, and CWS

_{V}, respectively. The τ

_{R}of the CWS

_{C}was lower than the τ

_{,}which suggests that in the conditions studied, the unplanted system was more conducive to clogging than vegetated ones, as the vegetated ones showed an increase in τ

_{R}. Matos et al. [34] also verified a lower τ

_{R}compared to τ

_{,}for planted and non-planted systems, and Paoli and von Sperling [35] obtained in their CWS a τ

_{R}of 1.30 (for planted CWS) and 1.43 d

^{−1}(for non-planted CWS), very close to the theoretical τ of 1.47 d

^{−1}.

_{w}and CWS

_{V}, it can be assumed that the higher τ

_{R}than τ is related to two facts, namely: (i) the evapotranspiration of plant species increases the actual retention time because the current mean flowrate in the system is lower than the influent flow rate used in the estimate of τ [37], and (ii) the presence of roots and rhizomes could be prevent clogging in these CWSs. Another factor that can also be observed is the possible tracer losses across the CWS since it is known that NaCl can be absorbed by plants, in the form of Na

^{+}and Cl

^{−}, or adsorbed in the substrate system [34]. Similarly, rhodamine WT can be adsorbed to the substrate of the systems or oxidized by photolysis [26,38].

_{C}, CWSw, and CWS

_{V}were, respectively, 1.785, 0.200, and 0.390, while the number of tanks (N) values was 1.195, 3.116, and 2.003, respectively. These values indicate a moderate to high dispersion for the CWSs studied [39]. However, all d values found refer to hydrodynamic models of large deviation of the plug-flow, being the contour condition to be applied in these cases, the one known as closed-vessels [28]. Figure 2 shows the values found in the tracer tests and the curve of the tanks-in-series models (N-CSTR). The curve of the dispersed-flow model cannot be shown, since in this condition, there is no analytical expression describing this model [28].

_{w}), suggest an internal recirculation, which may have been caused by strangulation between units [28] or indicating a dead zone within the systems [43,44].

#### 3.2. Fitting N-CSTR and Dispersed-Flow Models

_{0}, N, or d).

_{0}) and the numbers d and N obtained by the field hydrodynamics study.

^{2}, a fact observed in other studies in the literature. However, the values of the coefficients of determination (R²) were calculated for demonstration purposes only, since the R² is not adequate to measure non-linear regressions models as discussed by [45]. Hence, the root means squared error (RMSE) and the Akaike Information Criterion (AIC) were used to compare fits in order to evaluate the best models. Figure 3 shows the curves of the fitted models.

_{V}, the dispersion number d was of the order of 10

^{10}, suggesting that this system would tend to a complete mixing reactor. In their research, von Sperling et al. [25] evaluated three first-order kinetic models: plug-flow, dispersed-flow, and tanks-in-series. The authors obtained the following values of the dispersion d number, 0.084 and 0.079, for the planted and non-planted units, respectively, indicating a low to moderate dispersion. For the N-CSTR model, the results were N = 6.50 (planted unit) and N = 6.87 (non-planted unit) in the same research [25], contrasting results to the behavior observed in the present study.

_{0}, d, N) for the N-CSTR and dispersed-flow models.

_{w}). The AIC test, applied between the dispersed-flow and the adjusted tanks-in-series, for each CWS, indicated that the dispersed-flow model adjusted better than the N-CSTR model in two scenarios used. It is noted that AIC does not say whether the model had a good or bad fit: It only evaluates which of the two models best fits the data.

#### 3.3. Fitting Modified First-Order Models

^{−1}, without residual C* and k values of 1.15 and 1.12 d

^{−1}, with residual C*, for planted and non-planted CWS, respectively. The results indicated that models with residual COD always gave a better fit than those without residual COD.

^{2}) greater than 0.98.

^{−1}(summer) and 0.78 to 1.07 d

^{−1}(autumn/winter) in its four planted units. These results are similar to those obtained in this study for the cultivated systems, where the k values were 0.87 d

^{−1}(CWS

_{w}) and 1.26 d

^{−1}(CWS

_{V}).

^{−1}and C* ranged from 31 to 429 d

^{−1}, while for the second model b it ranged from 0.73 to 4.82 d

^{−1}and k ranged from 2.86 to 12.8 d

^{−1}. In this study, the adjusted values of k and C* (residual model) of CWS

_{V}were among the values found by these authors, while the values of b and k (Shepherd model) of CWS

_{w}presented adjustments close to those obtained by these authors.

#### 3.4. Fitting of Classic Models and Analysis of CW Systems Modeling

^{−1}[49] and 0.49 and 0.58 d

^{−1}[50]. However, when the AIC test was applied, it was observed that the CSTR model had better performance compared to the PFR model (for this particular study).

^{−1}in the CSTR model, 1.43 d

^{−1}in the residual model (k-C*), and 1.53 d

^{−1}for the Shepherd model. These data may be useful in predicting the efficiency of systems operating in conditions similar to those present studied.

## 4. Conclusions

^{10}d

^{−1}). Moreover, the possible strangulation between the CWS, in which they worked with a sequence of three units in the “closed-closed” vessel condition, might explain the high dispersion numbers.

^{−1}), CSTR (k equal to 1.35 d

^{−1}), and Shepherd (k equals 1.53 d

^{−1}). The importance of hydraulic behavior as a useful tool for choosing the best kinetic models to predict better performance in CWs was demonstrated.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Experimental dispersion data in CWS

_{C}(

**a**), CWS

_{w}(

**b**), and CWS

_{V}(

**c**) and N-CSTR model curves. The normalized curves were plotted for NaCl tracer (CWSc and CWSv) and rhodamine WT (CWSw).

**Figure 3.**Experimental and curves of the tanks-in-series (N-CSTR) or dispersed-flow models for each COD concentration decay across CWS. (

**a**) All the coefficients being estimated. (

**b**) Only the k coefficient is estimated (fixed C

_{0}, N, or d).

**Figure 5.**CSTR, PRF with residual C*, and Shepherd et al. (2001) adjusted to mean experimental data.

Wastewater | CWS | Plant | ^{1} L/W | HRT (d) | Flow Rate (L d ^{−1}) | ^{2} OP | ^{3} Co(mg L ^{−1}) | Ref |
---|---|---|---|---|---|---|---|---|

Domestic | ^{4} Hybrid | Scirpus grossus | 2 | 3 | 120 d | 72.42 | [18] | |

Landfill leachate | HSSF | Chrysopogonzizanioides | 3 | 5 | 24 | 140 d | 16,366 | [19] |

Textile | VF | Brachiaria mutica | 0.8 | Batch | 1 yr | 493 | [20] | |

Petroleum | FWS | Phragmites australis | 10 | 7–15 | 3 yr | 390 | [21] | |

Dairy | HSSF | Typha domingensis | 2.63 | 7 | 60 | 6 m | 269.1 | [22] |

Swine | VF | Iris pseudacorus | 3 | Batch | 6 m | Stage 1:170 Stage 2:230 Stage 2:270 | [23] |

^{1}L/W: Length/width.

^{2}Operation time. d: day, m: month; yr: year.

^{3}Initial COD concentration

^{4}FWS + VSSF + HSSF. All initial (C

_{0}) concentrations refer to COD, pre-treat, or diluted before used in CWS, except for textile, which was collected after equalization tank.

Treatment | Plant Species |
---|---|

CWS_{V} | Chrysopogon zizanioides (“vetiver grass”) |

CWS_{w} | Polygonum punctatum (“water pepper” or “dotted smartweed”) |

CWS_{C} | Control unit (unplanted) |

Model | Equation |
---|---|

Dispersed-model | ${\mathrm{C}=\mathrm{C}}_{0}\frac{{4\mathrm{a}e}^{1/2d}}{{\left(1+\mathrm{a}\right)}^{2}{e}^{\mathrm{a}/2d}{\left(1-\mathrm{a}\right)}^{2}{e}^{-\mathrm{a}/2d}}$ |

N-CSTR (tanks-in-series) | $\mathrm{C}=\frac{{\mathrm{C}}_{0}}{{\left(1+\frac{k\mathsf{\tau}}{N}\right)}^{N}}$ |

Plug flow reactor (PFR) | ${\mathrm{C}=\mathrm{C}}_{0}{e}^{\left(-k\mathsf{\tau}\right)}$ |

PFR with residual C* | $\mathrm{C}-{\mathrm{C}}^{*}{=(\mathrm{C}}_{0}-{\mathrm{C}}^{*}){e}^{\left(-k\mathsf{\tau}\right)}$ |

Continuous stirred tank reactor (CSTR) | $\mathrm{C}=\frac{{\mathrm{C}}_{0}}{(1+k.\mathsf{\tau})}$ |

CSTR with residual C* | $\mathrm{C}=\frac{{\mathrm{C}}_{0}{-\mathrm{C}}^{*}}{{(1+k\mathsf{\tau})+\mathrm{C}}^{*}}$ |

Brasil et al. [30] | ${\mathrm{C}=\mathrm{C}}_{0}{e}^{(-k{.\mathsf{\tau}}^{\mathrm{n}})}$ |

Shepherd et al. [31] | ${\mathrm{C}=\mathrm{C}}_{0}{e}^{\left[(-\frac{k}{b})\mathrm{ln}\left(b\mathsf{\tau}+1\right)\right]}$ |

^{−3}); C

_{0}: influent concentration (g m

^{−3}); C*: Residual effluent concentration (g m

^{−3}); k: reaction coefficient (d

^{−1}); τ: Hydraulic retention time (d); N: Number of complete-mix tanks-in-series, dimensionless; d: Dispersion number, dimensionless; n: Equation coefficient constant, dimensionless; b: time-based retardation coefficient (d

^{−1}); a = $\sqrt{1+4k\mathsf{\tau}d}$

**Table 4.**Values of the parameters found to fit the tanks-in-series (N-CSTR) and dispersed-flow models for each CWS.

Model | Parameter | CWS_{C} | CWSw | CWS_{V} |
---|---|---|---|---|

N-CSTR | k (d^{−1}) | 1.11 | 1.7 | 2.05 |

N | 1 | 1.61 | 1.71 | |

R^{2} | 0.72 | 0.83 | 0.65 | |

RMSE | 122.17 | 92.53 | 116.91 | |

Dispersed-flow | k (d^{−1}) | 0.67 | 1.31 | 2.51 |

d | 0.63 | 1.64 | 1.18 × 10^{10} | |

R^{2} | 0.73 | 0.86 | 0.84 | |

RMSE | 120.21 | 84.67 | 79.54 |

**Table 5.**Values of the parameters found to adjust the tanks-in-series and dispersed-flow models for fixed parameters (C

_{0}, d, N) in CWS.

Model | Parameter | CWS_{C} | CWSw | CWS_{V} |
---|---|---|---|---|

N-CSTR | k (d^{−1}) | 0.97 | 1.22 | 3.45 |

R^{2} | 0.72 | 0.83 | 0.6 | |

RMSE | 115.56 | 88.75 | 119.33 | |

Dispersed-flow | k (d^{−1}) | 0.7 | 0.95 | 1.59 |

R^{2} | 0.72 | 0.85 | 0.72 | |

RMSE | 114.76 | 82.99 | 98.68 |

**Table 6.**Fitting coefficients of the first-order COD removal models to the data obtained for each CWS.

Model | Coefficient | CWS_{C} | CWSw | CWS_{V} |
---|---|---|---|---|

1 | k (d^{−1}) | 0.85 | 1.56 | 2.4 |

C* (g m^{−3}) | 0 | 6.28 × 10^{−8} | 1.07 × 10^{−16} | |

R^{2} | 0.72 | 0.86 | 0.84 | |

RMSE | 121.37 | 85.71 | 74.03 | |

2 | k (d^{−1}) | 0.78 | 1.25 | 3.5 |

C* (g m^{−3}) | 148.6 | 115.57 | 160.09 | |

R^{2} | 0.73 | 0.86 | 0.90 | |

RMSE | 119.48 | 83.6 | 62.58 | |

3 | k (d^{−1}) | 0.54 | 0.87 | 1.26 |

n | 0.86 | 0.73 | 0.28 | |

R^{2} | 0.72 | 0.86 | 0.90 | |

RMSE | 121.2 | 86.22 | 62.21 | |

4 | k (d^{−1}) | 0.66 | 0.87 | 10.91 |

b (d^{−1}) | 0.35 | 0.73 | 29.13 | |

R^{2} | 0.73 | 0.86 | 0.90 | |

RMSE | 120.09 | 86.22 | 62.45 |

**Table 7.**Adjusted parameters for models that do not predict deviations of ideality for the experimental data of all the studied CWS.

Model | Parameter | CWS |
---|---|---|

CSTR | k (d^{−1}) | 1.35 |

R^{2} | 0.71 | |

RMSE | 115.72 | |

PFR | k (d^{−1}) | 0.62 |

R^{2} | 0.66 | |

RMSE | 125.47 |

**Table 8.**RMSE values were obtained in the adjustment of the studied models to the mean data of the COD profiles performed in the studied CWS.

Model | RMSE |
---|---|

Dispersed-flow | 16.58 |

Tanks-in-series (N-CSTR) | 59.37 |

PRF with residual C* | 11.74 |

CSTR with residual C* | 16.58 |

Brasil | 23.25 |

Shepherd | 14.62 |

PFR | 55.54 |

CSTR | 15.51 |

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## Share and Cite

**MDPI and ACS Style**

Ramos, N.d.F.S.; Borges, A.C.; Coimbra, E.C.L.; Gonçalves, G.C.; Colares, A.P.F.; de Matos, A.T.
Swine Wastewater Treatment in Constructed Wetland Systems: Hydraulic and Kinetic Modeling. *Water* **2022**, *14*, 681.
https://doi.org/10.3390/w14050681

**AMA Style**

Ramos NdFS, Borges AC, Coimbra ECL, Gonçalves GC, Colares APF, de Matos AT.
Swine Wastewater Treatment in Constructed Wetland Systems: Hydraulic and Kinetic Modeling. *Water*. 2022; 14(5):681.
https://doi.org/10.3390/w14050681

**Chicago/Turabian Style**

Ramos, Nilton de Freitas Souza, Alisson Carraro Borges, Eder Carlos Lopes Coimbra, Gustavo Castro Gonçalves, Ana Paula Ferreira Colares, and Antonio Teixeira de Matos.
2022. "Swine Wastewater Treatment in Constructed Wetland Systems: Hydraulic and Kinetic Modeling" *Water* 14, no. 5: 681.
https://doi.org/10.3390/w14050681