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

Nilton de Freitas Souza Ramos
Alisson Carraro Borges
Eder Carlos Lopes Coimbra
Gustavo Castro Gonçalves
Ana Paula Ferreira Colares
1 and
Antonio Teixeira de Matos
Department of Agricultural Engineering, Federal University of Viçosa, Vicosa 36570-900, Brazil
Department of Sanitary and Environmental Engineering, Federal University of Minas Gerais, Belo Horizonte 31270-901, Brazil
Author to whom correspondence should be addressed.
Water 2022, 14(5), 681;
Submission received: 16 December 2021 / Revised: 31 January 2022 / Accepted: 17 February 2022 / Published: 22 February 2022
(This article belongs to the Special Issue Water Quality Engineering and Wastewater Treatment Ⅱ)


The use of constructed wetland systems (CWS) is presented as an alternative for the treatment of effluents since these have reduced implementation costs and relative ease of operation. The present research was undertaken to evaluate to study the hydrodynamic and the fitting of first-order mathematical kinetic models for the removal of pollutants in CWS. Three CWS were built, using expanded clay as filter support: one cultivated with Polygonum punctatum (CWSw), another cultivated with Chrysopogon zizanioides (CWSV), 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

The growth of the world’s population increases the demand for the extraction of natural resources, making them increasingly scarce. Water is the source most affected by this expansion, so the need for effluent treatment has become an eminent concern due to the damage caused to the environment and the population [1,2].
The main conventional effluent treatment technologies on the market are designed to treat wastewater from large areas, which makes them inaccessible and difficult to operate and maintain [3]. The lack of low-cost and simple handling technologies is evidenced in rural areas and communities of low population density, and so, research has been developed to optimize effluent treatment on small scales [4,5]. A viable alternative to wastewater treatment is nature-based treatment technologies. Among nature-based solutions, constructed wetlands systems (CWS) present the advantages of low energy requirements and easy operation and maintenance [6].
CWS are designed with materials that serve as a support for the macrophytes’ growth. In this support medium, a biofilm develops in the root’s zones to further the degradation of organic matter, nutrients, and other pollutants by physical, chemical, and biological processes [7,8]. The CW systems have been used for effluent treatment for some decades [9,10]. Currently, most studies developed in Brazil employ subsurface horizontal flow CWS as secondary treatment in the post-treatment of digesters, septic tanks, reactors, and anaerobic ponds [11,12].
There is a variability of parameters related to the sizing and operation of the CWS, highlighting the hydraulic retention time (HRT) [13], the support (filter) medium [9], the vegetation (macrophytes) [14], the applied organic loading [15], and the treatment performance evaluation period [11]. Furthermore, the performance of CWS depends upon of types or configuration of systems, i.e., the classic horizontal subsurface-flow (HSSF) constructed wetlands, the free water surface-flow (FWS) constructed wetland, duckweed ponds, the vertical-flow constructed wetlands (VF), and other variations such as French, tidal-flow, and hybrid CWS types [6].
Despite the challenges still presented in CWS such as clogging, scaling, long-term performance evaluation, and biomass harvesting and disposal [6,16,17], their uses to treat various types of wastewater are reported. Table 1 shows some of the studies that have been reported in the literature.
The proper design of CWS is one of the main factors to achieving satisfactory treatment efficiency [24]. Often, three parameters are used for the design of CWS, namely, a model derived from first-order kinetics applied to plug-flow reactors (PFR) [25]; per capita area ratio; superficial organic loading rate; and hydraulic rate [11].
The removal of pollutants in CWS depends on the time the wastewater remains in the system, and this time is influenced by the hydraulic behavior. This behavior is well understood by the use of tracers [26]. Studies with response stimulus (use of tracers) have been used to understand the hydrodynamic behavior of CWS, and these researches enable the understanding of the dispersion of pollutants in the system, aiding the fitting of first-order kinetic models [26,27].
To minimize the effects of deviations of ideality from the theoretical models PFR or continuous stirred tank reactor (CSTR), two models can be used interchangeably: the models known as dispersed-flow and the tanks-in-series (N-CSTR) [28]. Moreover, other modified first-order models were proposed to predict the performance of the CWS since the PFR and CSTR present ideal hydraulic behavior in which there is no dispersion, short circuits, or dead zones [29]. Among these modified models, the cited PFR with residual concentration, CSTR with residual concentration, Brasil et al. [30], and Shepherd et al. [31] stand out.
Thus, this study aimed to evaluate the hydrodynamic behavior of CWS treating swine wastewater by the field use of tracers and, based on the obtained data, perform the fitting of first-order kinetic models for the degradation of organic matter.

2. Materials and Methods

2.1. Treatment System

Three CWSs were used to carry out this experiment, developed in the rural area of the city of Viçosa, Minas Gerais, Brazil (20°49′1″ S and 42°52′06″ W), in pilot-scale. Each CWS was assembled in a serial arrangement of three containers made of high-density polyethylene (HDPE) with the following dimensions: 35 cm height, 49 cm width, and 195 cm length. The support medium used was light expanded clay aggregate (LECA), with particle size 22–32 mm, bulk density of 450 ± 10 kg m−3, the initial void volume of 0.870 m3 m−3, and macroporosity of 0.465 m3 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 m3.
The CWS were operated employing horizontal subsurface flow (HSSF) and were supplied with swine wastewater (SW), pre-treated in a hybrid anaerobic reactor (HAR). The systems were operated within one year to monitor the performance of the CWS regarding the removal of nutrients and organic matter, as shown previously by Ramos et al. [32].
The COD influent to CWS was 704 ± 362 g m−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 m3 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

The experimental design consisted of three systems, two CWSs grown with plant species and the other, unplanted, was used as control (Table 2).
The cultivated plant species were chosen according to the treatment potential, the resistance to the flooding condition, and the possible use of the plant biomass. The water pepper seedlings were collected in a natural swamp and transplanted to the CWS at a density of 10 seedlings per m², totaling 10 seedlings per container. For the vetiver grass, the density of 8 tufts of ridges per m² was used. Figure 1 shows the basic schematic of experimental units.

2.3. Hydrodynamic and Kinetic Studies

To perform the hydrodynamic study in the systems, the multiparametric probes, with sensors for reading electrical conductivity, were installed. In one of the probes, there was a coupled fluorimeter. The tracers used were: saline solution (made with NaCl at 15% m/v) and rhodamine WT (solution at 20 g m−3).
Five liters of saline solution were added in the CWSV and CWSC, while in the CWSw, 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.
The hydrodynamic evaluation of the CWS was carried out through the application of tracers in order to understand the dispersion of pollutants in each of the systems. The obtained hydrodynamic parameters as dispersion numbers and numbers of tanks-in-series were useful in dispersed-flow and N-CSTR models, respectively.
Regarding the data of COD decay profiles, for kinetic studies, two sampling campaigns were conducted on different days, one sample each day, across the CWSs (10 points with 2 COD values in each CWS profile—Figure 1) in order to observe the chemical oxygen demand (COD) behavior throughout the treatment systems by fitting first-order kinetic to N-CSTR; dispersed-flow; CSTR; CSTR with residual C*; plug-flow reactor; plug-flow with residual C*; Brasil et al. [30]; and Shepherd et al. [31] models (Table 3). The analyses for the COD were performed according to the Standard Methods for the Examination Water and Wastewater [33].

2.4. Statistical Analysis

The regression models adapted from the first-order kinetic equation were fitted to the data obtained. The results were discussed based on descriptive statistics and statistical inference. For this purpose, Microsoft Excel, SAEG, and Origin software were used.

3. Results and Discussion

3.1. Hydrodynamic Study

The nominal retention time (τ) of this study was 3.21 days for all CWSs. However, the values of the experimental (actual) retention time (τR) found were: 3.12, 4.14, and 4.11 days for CWSC, CWSw, and CWSV, respectively. The τR of the CWSC 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 τR. Matos et al. [34] also verified a lower τR compared to τ, for planted and non-planted systems, and Paoli and von Sperling [35] obtained in their CWS a τR 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.
This fact contrasts with that observed by [36], which verified a longer experimental time in the non-planted CWS. As for CWSw and CWSV, it can be assumed that the higher τR 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].
The dimensionless dispersion numbers (d) found for CWSC, CWSw, and CWSV 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].
The tail phenomenon can be observed in Figure 2 due to the diffusion of the tracer in the internal pores of the medium support; this event is common in tests with tracers, being seen in numerous studies [13,40,41,42]. The multiple peaks, observed mainly in the rhodamine WT assay (CWSw), 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

The performance of COD conversion kinetics was adjusted considering the dispersed-flow and tanks-in-series (N-CSTR) models. To determine the kinetic coefficients for the N-CSTR and dispersed-flow models, the Origin statistical software was used, and the analyses were carried out in two scenarios: (i) with all the coefficients being estimated and (ii) only the k coefficient being estimated (fixed the field-obtained data of C0, N, or d).
In the adjustment made by the first scenario, no variables of the equations of the models were fixed, allowing the software to fit them in the best way to the experimental data. In the second scenario, the variables found in this study were fixed, such as the mean concentration of the influent (C0) and the numbers d and N obtained by the field hydrodynamics study.
To perform the fitting of all models in this study, the mean experimental data (average of the two campaigns) were not used, but all the data from the two samples referred to the decay studies. If the means were used, there would be an increase in the value of R2, 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.
The values of k and N for the tanks-in-series model and the values of k and d for the dispersed-flow model, with all parameters varying, are presented in Table 4. It is observed that in the CWSV, the dispersion number d was of the order of 1010, 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.
Matos et al. [34] found that the dispersion d number values were 0.32 and 0.14 and the N number of tanks-in-series were 2 and 4 for planted and non-planted units, respectively. These authors found that planted CWS have a more turbulent flow regime than the non-planted ones, results that corroborate with those obtained in the present study.
The high dispersion numbers can be explained by the way the CWSs were assembled using interconnected units and not a single unit (Figure 1). The liquid suffered strangulation when it passed through the connections between the units of the same CWS (Figure 1) This way, each CWS worked with a sequence of three units in the closed–closed vessel condition.
This disturbance in the flow may have caused increased dispersion in the CWS, with possible recirculation of part of the tracer, this fact being one of the possible explanations for the high d values. High N values mean small deviations in flow, whereas the opposite means large deviations [28]. The results found in this study corroborate this statement, since high values for the dispersion number d and low values for N were obtained.
Table 5 shows the second scenario, in which only the k coefficient is estimated (fixed obtained field parameters (C0, d, N) for the N-CSTR and dispersed-flow models.
Observing the RMSE values obtained, the best fittings were observed in the CWS cultivated with the P. punctatum (CWw). 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

Other first-order kinetic models were adjusted to the data obtained in this work; these fittings were obtained using the Origin software. The coefficients found for each model are presented in Table 6.
It noted that, for the adjustment of all models tested, similar performances were obtained. However, when analyzing the RMSE values, it can be noticed that with the plug-flow reactor with residual C*, the lowest values of RMSE were obtained.
von Sperling et al. [25], performed adjustments with the PFR model with and without residual C*, in planted and non-planted systems. These authors obtained k values of 0.81 and 0.84 d−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.
Matos et al. [46] adjusted four kinetic models for the estimation of organic matter decay in CWS of different configurations. These authors obtained decay coefficients (k), ranging from 0.52 to 0.74 for the model of Brasil et al. [30] and 0.62 to 2.3 for the model of Shepherd et al. [31]. These models presented the best adjustments among the four studied models, having a coefficient of determination (R2) greater than 0.98.
Matos et al. [47] used the model of Brasil et al. [30] to adjust its data and obtained k values ranging from 0.94 to 1.52 d−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 (CWSw) and 1.26 d−1 (CWSV).
Figure 4 shows the experimental data and curves of the models that were proposed adapting to the first-order kinetics: CSTR with residual C*, the plug-flow model with residual C*, Brasil et al. [30], and Shepherd et al. [31].
Shepherd et al. [31], studying vinasse treatment in CWSs, found adjustments for the modified models of residual first-order and those modified by them. For the first model, the k value ranged from 2.40 to 11.10 d−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 CWSV were among the values found by these authors, while the values of b and k (Shepherd model) of CWSw presented adjustments close to those obtained by these authors.

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

After the adjustments made considering (i) models that take into account the dispersion of the systems, through the use of tracers and with values of d and N being estimated, and (ii) adapted first-order kinetic models that use coefficients in order to minimize the deviation of the ideality of the systems, it was also chosen to adjust the more simplified models, which do not consider deviations of ideality in CWS.
The adjusted models were the common plug-flow (PFR) model and the common complete mixing model (CSTR). Taking into account that during the routine monitoring of the CWS, no statistical difference was observed regarding the removal of COD, it was chosen to adjust all monitored data for the three systems. Kadlec et al. [48] state that the use of such models contains some inadequacies; however, in the previous adjustments, it was verified that they could be tested when compared to models with a larger number of previously tested variables (Table 7).
For the PFR model, which is very widespread in the literature, some comparisons can be cited. The global k values obtained in this study, for this model, are within the range reported by the authors who studied swine wastewater treatment in HSSF-CW, which reports values between 0.49 and 1.39 d−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).
The models with very adjustable parameters can be adjusted to a wide variety of experimental data, and the modeling process, in these cases, is nothing more than a simple adjustment of curves [51]. In the case of models with similar performance, the option should always be for those more simplified, with a smaller number of variables. A final comparison between the models tested was performed, this time using the mean data of the two sampling campaigns performed. Table 8 shows the values of the root mean square error (RMSE) obtained for each adjustment.
It is noted that the smallest RMSE errors correspond to the PFR models with residual C*, Shepherd, and CSTR, respectively. The equations that do not predict the influence of flow ideality deviation were the ones that presented the best fit. Shepherd et al. [31] state that the change in degradability values (k) across the CWS has a higher relative influence than dispersion.
Figure 5 shows the fittings of the three models cited to the average data (obtained by the average of the two profiles) of the studied CWSs. The coefficients of determination in these adjustments exceeded the value of 0.99. Performing three cross-comparisons between the models, using the AIC test, the following order was obtained: (1) PFR with residual C*, (2) CSTR, and (3) Shepherd.
Overall, it is noted that the models presented good adjustments to the experimental data. For the specific case studied, the CSTR model presents itself as an interesting alternative, considering that it was diagnosed with high dispersion across the units and that this equation is less complex. However, any of the presented models can come to be used in the design of CWS. The global k values found were close: 1.35 d−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

In the hydrodynamic tests, the unplanted unit (CWSc) provided an actual retention time lower than nominal retention time, which made them more favorable clogging than vegetated CW systems. The large dispersion within the CWS was observed, a fact associated with the type of configuration adopted in the present study, presenting trends for complete mixing, mostly in CWv (d~1010 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.
As for the first-order mathematical kinetic models studied, all are considered viable in terms of use in CWS projects. The models that presented the best fit to the experimental data of the CWS were the plug-flow with residual C* (k equal to 1.43 d−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

Conceptualization: A.C.B. and A.T.d.M.; methodology: N.d.F.S.R. and G.C.G.; data curation: E.C.L.C. and A.P.F.C.; formal analysis: N.d.F.S.R., G.C.G., E.C.L.C., A.P.F.C. and A.C.B.; writing—original draft preparation: N.d.F.S.R., G.C.G., E.C.L.C., and A.P.F.C.; writing—review and editing: A.C.B. and A.T.d.M. All authors have read and agreed to the published version of the manuscript.


We acknowledge the Coordination for the Improvement of Higher Education Personnel (CAPES), Brasil (Finance Code 001) for funding this research.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data are available from the corresponding author upon reasonable request.

Conflicts of Interest

The authors declare no conflict of interest.


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Figure 1. Schematic representation of the pilot-scale CWS. HAR: Hybrid Anaerobic Reactor.
Figure 1. Schematic representation of the pilot-scale CWS. HAR: Hybrid Anaerobic Reactor.
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Figure 2. Experimental dispersion data in CWSC (a), CWSw (b), and CWSV (c) and N-CSTR model curves. The normalized curves were plotted for NaCl tracer (CWSc and CWSv) and rhodamine WT (CWSw).
Figure 2. Experimental dispersion data in CWSC (a), CWSw (b), and CWSV (c) and N-CSTR model curves. The normalized curves were plotted for NaCl tracer (CWSc and CWSv) and rhodamine WT (CWSw).
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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 C0, N, or d).
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 C0, N, or d).
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Figure 4. Experimental data of each CWS (CWSC (a), CWSW (b), and CWSV (c)) and the modified models’ curves of Brasil et al. [30], Shepherd et al. [31], and CSTR and plug-flow with residuals C*, fitted to data.
Figure 4. Experimental data of each CWS (CWSC (a), CWSW (b), and CWSV (c)) and the modified models’ curves of Brasil et al. [30], Shepherd et al. [31], and CSTR and plug-flow with residuals C*, fitted to data.
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Figure 5. CSTR, PRF with residual C*, and Shepherd et al. (2001) adjusted to mean experimental data.
Figure 5. CSTR, PRF with residual C*, and Shepherd et al. (2001) adjusted to mean experimental data.
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Table 1. Studies on CWS-based various types of wastewater treatment.
Table 1. Studies on CWS-based various types of wastewater treatment.
WastewaterCWSPlant1 L/WHRT
Flow Rate
(L d−1)
2 OP3 Co
(mg L−1)
Domestic4 HybridScirpus grossus23 120 d72.42[18]
Landfill leachateHSSFChrysopogonzizanioides3524140 d16,366[19]
TextileVFBrachiaria mutica 0.8Batch1 yr493[20]
PetroleumFWSPhragmites australis107–15 3 yr390[21]
DairyHSSFTypha domingensis2.637606 m269.1[22]
SwineVFIris pseudacorus 3Batch6 mStage 1:170
Stage 2:230
Stage 2:270
1 L/W: Length/width. 2 Operation time. d: day, m: month; yr: year. 3 Initial COD concentration 4 FWS + VSSF + HSSF. All initial (C0) concentrations refer to COD, pre-treat, or diluted before used in CWS, except for textile, which was collected after equalization tank.
Table 2. Description and nomenclature of CW systems used in this study.
Table 2. Description and nomenclature of CW systems used in this study.
TreatmentPlant Species
CWSVChrysopogon zizanioides
(“vetiver grass”)
CWSwPolygonum punctatum
(“water pepper” or “dotted smartweed”)
CWSCControl unit (unplanted)
Table 3. Summary of equations utilized for hydraulic and kinetic modeling studies.
Table 3. Summary of equations utilized for hydraulic and kinetic modeling studies.
Dispersed-model C = C 0   4   a e 1 / 2 d ( 1 + a ) 2 e a / 2 d     ( 1   -   a ) 2 e - a / 2 d
N-CSTR (tanks-in-series) C   = C 0 ( 1 + k   τ N ) N
Plug flow reactor (PFR) C = C 0   e ( k     τ )
PFR with residual C* C   -   C * = ( C 0   -   C * )     e ( k     τ )
Continuous stirred tank reactor (CSTR) C = C 0 ( 1 + k . τ )
CSTR with residual C* C = C 0   -   C * ( 1 + k   τ ) + C *
Brasil et al. [30] C = C 0   e ( - k . τ n )
Shepherd et al. [31] C = C 0   e [ ( -   k b )   ln ( b   τ + 1 ) ]
C: effluent concentration (g m−3); C0: 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 = 1 + 4 k τ d
Table 4. Values of the parameters found to fit the tanks-in-series (N-CSTR) and dispersed-flow models for each CWS.
Table 4. Values of the parameters found to fit the tanks-in-series (N-CSTR) and dispersed-flow models for each CWS.
N-CSTRk (d−1)
Dispersed-flowk (d−1)0.671.312.51
d0.631.641.18 × 1010
Table 5. Values of the parameters found to adjust the tanks-in-series and dispersed-flow models for fixed parameters (C0, d, N) in CWS.
Table 5. Values of the parameters found to adjust the tanks-in-series and dispersed-flow models for fixed parameters (C0, d, N) in CWS.
N-CSTRk (d−1)0.971.223.45
Dispersed-flowk (d−1)0.70.951.59
Table 6. Fitting coefficients of the first-order COD removal models to the data obtained for each CWS.
Table 6. Fitting coefficients of the first-order COD removal models to the data obtained for each CWS.
1k (d−1)0.851.562.4
C* (g m−3)06.28 × 10−81.07 × 10−16
2k (d−1)0.781.253.5
C* (g m−3)148.6115.57160.09
3k (d−1)0.540.871.26
4k (d−1)0.660.8710.91
b (d−1)0.350.7329.13
(1) CSTR with residual C*, (2) plug-flow (PFR) with residual C*, (3) Brasil et al. [30], (4) Shepherd et al. [31].
Table 7. Adjusted parameters for models that do not predict deviations of ideality for the experimental data of all the studied CWS.
Table 7. Adjusted parameters for models that do not predict deviations of ideality for the experimental data of all the studied CWS.
CSTRk (d−1)1.35
PFRk (d−1)0.62
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.
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.
Tanks-in-series (N-CSTR)59.37
PRF with residual C*11.74
CSTR with residual C*16.58
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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.

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.

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.

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