P-k-C* Modeling of Treatment Efficiency in Vertical-Flow Constructed Wetlands with Various Substrates

Abstract

Constructed wetland beds are in widespread use for treating wastewater. Their use is well known, and current research is focused on the use of new substrates and different bed configurations, or on assisting the oxygenation process. The authors conducted an extended experiment using VF CWs with two types of filling: gravel, and a waste material called Certyd. Certyd is produced in the sintering process of coal ash, and is a type of waste from combined heat and power (CHP) plant operation. Both beds worked in parallel in order to compare their effectiveness, taking into account seasonality. The obtained database was used for statistical modeling using the P-k-C* model with correction for a trend change at a specific temperature. The obtained models were characterized by good fits to measured quantities. The study demonstrates that Certyd is a viable alternative to gravel. At all temperatures, a bed filled with Certyd has better treatment efficiency. When the temperature at which the trend changes is high, then no additional temperature dependence is recorded when this temperature is exceeded; otherwise, there is a steeper dependency below this temperature, especially in the case of the gravel-filled bed. This result suggests application of Certyd for beds located in colder climates.

1. Introduction

Constructed wetlands (CWs) have been used worldwide for the treatment of municipal sewage and some industrial sewage (mainly from the food industry). This technology has numerous advantages. These include simple construction and operation as well as high treatment efficiency with very low electric energy consumption compared to conventional systems such as activated sludge or trickling filters [1,2]. CW technology makes it possible to obtain high efficiency in removal of organic and biogenic compounds. A wide range of specific processes occur in beds, including oxidation, reduction and sorption. Numerous modifications to the technology have been made [3]. Initially, soil was used for CW bed filling [4,5]. This configuration was prone to clogging; therefore, it was replaced by sand and gravel [6,7]. However, gravel mining is related to degradation of the natural environment.

The Certyd aggregate used as filling by the authors at their research installation is a lightweight sintered ceramic aggregate made from coal or lignite combustion ashes [8]. A bed with the new filling was compared to one filled with gravel using a temperature-dependent model. The issue of modeling the functioning of constructed wetlands is one of the most important challenges in the field [9,10].

The database obtained by the authors during the research period was first used to evaluate treatment efficiency [11]. The next step presented in this paper was statistical modeling using the P-k-C* model, with correction for a trend change below the critical temperature. The research aim was to define a mathematical model to describe and compare SS-VF beds for the treatment of domestic sewage. The P-k-C* model was applied to two beds: one filled with Certyd, the other with gravel.

2. Research Installation, Sampling Methods and Modelling Methodology

2.1. Research Installation

Figure 1 presents a cross section of both beds. Figure 2 presents a view of the installation and an illustration of the scheme, with sampling points. The filtration medium was composed of three layers (gravel or Certyd) with a total depth of 0.8 m. The alternative substrate known as Certyd, which is covered by a patent [12], is a lightweight sintered ceramic aggregate made from coal or lignite combustion ashes produced during cogeneration heat and power (CHP) plant operation. Certyd as an aggregate has numerous advantages [8]. It is chemically inert; it is lightweight, porous and durable; it does not degrade; and it can be reused. The CW beds were supplied with domestic sewage from a common retention tank (Figure 2). The research installation, located in the Podlaskie Voivodeship (Poland), was operating in real conditions, and the temperature of sewage in the retention tank was dependent on meteorological conditions. The beds were operating in parallel, each with the same hydraulic load of 0.1 m³ m⁻² d⁻¹ (m d⁻¹) which is typical for domestic sewage treatment [13,14]. The beds were planted with reeds of Phragmites australis ssp. australis.

2.2. Sampling and Analytical Procedures

The research was carried out over a period of two years. In total, 45 series were collected. Each series consisted of a raw sewage sample (sampling point I after retention tank) and two samples of treated sewage (sampling points II and III). Concentrations of organic matter (BOD₅, COD), total nitrogen (TN), Kjeldakl nitrogen (TKN), ammonia nitrogen (NH₄-N), nitrate nitrogen (N-NO₃), nitrite nitrogen (N-NO₂) and total phosphorus (TP) were estimated. In addition, dissolved oxygen concentration and pH were monitored, along with sewage temperature. Measurements were conducted in a BUT laboratory in accordance with the procedures set out in the Regulation of the Minister of Maritime and Inland Waterway Economy from 12 July 2019 [15] and the guidelines of the American Public Health Association (APHA) [16]. Tests recommended by Merck for the analysis of COD, TN, TKN-N, NH₄-N, NO₃-N, N-NO₂ and TP were applied. Spectrophotometer Spectroquant Pharo 100 was used. BOD₅ was determined using OXI-TOP^®. The obtained database was used for statistical modeling with the P-k-C* model to determine the pollutant loads removed. The parameters chosen for modelling were BOD₅, COD, N-TKN and N-NH₄. Removal efficiency was calculated as a concentration reduction according to the terminology given in [13].

2.3. Methodology of P-k-C* Modeling

The P-k-C* model, as expressed in (1), was investigated for describing the removal of organic matter and nitrogen compounds.

$$1-{\eta }_{app}={\left(1+{\displaystyle \frac{k\left(T\right)}{qP}}\right)}^{-P}$$

(1)

where: ${\eta }_{app}$—apparent removal efficiency [-]; k(T)—chemical reaction coefficient (temperature dependent); q—hydraulic load [m/d]; P—total apparent number of tanks in series.

Apparent removal efficiency is defined as follows:

$${\eta }_{app}=1-{\displaystyle \frac{C_{out}-C^{\ast }}{C_{in}-C^{\ast }}}$$

(2)

where: C_out—output concentration; C_in—input concentration; C*—background concentration. All concentrations are in [g/m³].

Chemical reaction coefficient $k\left(T\right)$ is modeled using first-order temperature dependency, with modification, as follows:

$$k\left(T\right)=K_{20}{\theta }^{T-20}{\theta }_m^{\min \left(T-T_k,0\right)}\equiv \exp \left(\ln K_{20}+\left[T-20\right]\ln \theta +\left[\min \left(T-T_k,0\right)\right]\ln {\theta }_m\right)$$

(3)

where: $k\left(T\right)$—direct and modified chemical reaction coefficients; $K_{20}$—direct or modified chemical reaction coefficients normalized for 20 [°C]; $\theta$—temperature coefficient; ${\theta }_m$—modifier for temperature coefficient for temperatures less than specific (critical) temperature $T_k$, where trend changes; min $\left(·,·\right)$—minimum function of 2 arguments.

Use of the additional coefficient ${\theta }_m$ allows for changes in temperature dependency below a certain temperature, $T_k$, providing greater flexibility for describing the obtained data, while preserving the first-order dependency form.

Various simplifications of the obtained equations are possible. The apparent efficiency presented in (2) models real efficiency $\eta$ in the limit $C^{*}\to 0$. If $\ln {\theta }_m=0$, Equation (3) takes the form of an ordinary first-order dependency. When $P$ is very large, i.e., $P\to \infty$, a proper limit can be obtained, as follows:

$$\underset{P\to \infty }{\lim }{\left(1+{\displaystyle \frac{k(T)}{qP}}\right)}^{-P}=\exp \left(-k(T)/q\right)$$

(4)

All presented modifications allow for 16 models, including 12 which are temperature-dependent. These are nonlinear and technically difficult to estimate, requiring a special optimization procedure [17]. As each model was equally preferred a priori, a multimodel inference was conducted [18]. Each model was weighted by the Sugiura [19] version of the Akaike information criterion [20]. The weights and parameterizations of models enable them to be grouped. The parsimony rule dictates that only the top models in each group are compared further. As a basic rule of good model fit, residuals cannot be structured based on the independent variable (temperature). The top models with such a structure were excluded. All models that pass such analysis are finally weighted. Models with sufficiently small weights have very limited influence; therefore, according to [18], these were also removed. Model fit was estimated using root mean square error (RMSE).

The R version 3.6.1 [21] statistical environment was used to perform the necessary calculations. The following functions and packages were used: the nlfb procedure from the nlsr package [22], and the AICc procedure from the AICcmodavg package [23]. An in-house implementation of the log-likelihood function was used for the resulting models.

3. Results

Applying the methodology presented in the previous chapter, multi-model analyses of 16 models were carried out separately for gravel- and Certyd-filled beds.

A total of 128 different statistical models were generated and analyzed. Clustering of the models was performed by analyzing the distribution of residuals and the values of the log-likelihood (logLik) function.

The representative model of the group with the largest logLik value after clustering in most cases had a weight slightly higher than 95%. These models were characterized by a very large P parameter (Equation (4)), an insignificant background concentration (apparent and real efficiencies were equal) and a trend change around some critical temperature (Equation (3)). Such representative models of treatment efficiencies are shown graphically in Figure 3, Figure 4, Figure 5 and Figure 6, in which plots against measurement results are presented.

The models demonstrate good agreement, with minimal scatter around the measurement results.

The final models were characterized by the following parameters:

$$\begin{array}{cc}{\eta }_{BO{D}_5,Certyd}=1-\left\{\begin{array}{cc}\exp \left(-{\displaystyle \raisebox{1ex}{$0.7128\times {1.0883}^{T-20}$}\!\left/ \!\raisebox{-1ex}{$q$}\right.}\right)& T<{5.0 }^{\circ }\mathrm{C}\\ \exp \left(-{\displaystyle \raisebox{1ex}{$0.2887\times {1.0247}^{T-20}$}\!\left/ \!\raisebox{-1ex}{$q$}\right.}\right)& T\ge {5.0 }^{\circ }\mathrm{C}\end{array}\right.& RMSE=0.0144\hfill \\ {\eta }_{BO{D}_5,Gravel}=1-\left\{\begin{array}{cc}\exp \left(-{\displaystyle \raisebox{1ex}{$0.3031\times {1.0426}^{T-20}$}\!\left/ \!\raisebox{-1ex}{$q$}\right.}\right)& T<{14.4 }^{\circ }\mathrm{C}\\ \exp \left(-{\displaystyle \raisebox{1ex}{$0.2396$}\!\left/ \!\raisebox{-1ex}{$q$}\right.}\right)& T\ge {14.4 }^{\circ }\mathrm{C}\end{array}\right.& RMSE=0.0144\hfill \end{array}$$

$$\begin{array}{cc}{\eta }_{COD,Certyd}=1-\left\{\begin{array}{cc}\exp \left(-{\displaystyle \raisebox{1ex}{$0.2199\times {1.0285}^{T-20}$}\!\left/ \!\raisebox{-1ex}{$q$}\right.}\right)& T<{16.7 }^{\circ }\mathrm{C}\\ \exp \left(-{\displaystyle \raisebox{1ex}{$0.2002$}\!\left/ \!\raisebox{-1ex}{$q$}\right.}\right)& T\ge {16.7 }^{\circ }\mathrm{C}\end{array}\right.& RMSE=0.0128\hfill \\ {\eta }_{COD,Gravel}=1-\left\{\begin{array}{cc}\exp \left(-{\displaystyle \raisebox{1ex}{$0.2090\times {1.0317}^{T-20}$}\!\left/ \!\raisebox{-1ex}{$q$}\right.}\right)& T<{15.0 }^{\circ }\mathrm{C}\\ \exp \left(-{\displaystyle \raisebox{1ex}{$0.1788$}\!\left/ \!\raisebox{-1ex}{$q$}\right.}\right)& T\ge {15.0 }^{\circ }\mathrm{C}\end{array}\right.& RMSE=0.0137\hfill \end{array}$$

$$\begin{array}{cc}{\eta }_{N-N{H}_4,Certyd}=1-\left\{\begin{array}{cc}\exp \left(-{\displaystyle \raisebox{1ex}{$1.1238\times {1.1330}^{T-20}$}\!\left/ \!\raisebox{-1ex}{$q$}\right.}\right)& T<{4.0 }^{\circ }\mathrm{C}\\ \exp \left(-{\displaystyle \raisebox{1ex}{$0.2041\times {1.0181}^{T-20}$}\!\left/ \!\raisebox{-1ex}{$q$}\right.}\right)& T\ge {4.0 }^{\circ }\mathrm{C}\end{array}\right.& RMSE=0.0203\hfill \\ {\eta }_{N-N{H}_4,Gravel}=1-\left\{\begin{array}{cc}\exp \left(-{\displaystyle \raisebox{1ex}{$1.5799\times {1.1739}^{T-20}$}\!\left/ \!\raisebox{-1ex}{$q$}\right.}\right)& T<{3.8 }^{\circ }\mathrm{C}\\ \exp \left(-{\displaystyle \raisebox{1ex}{$0.1995\times {1.0333}^{T-20}$}\!\left/ \!\raisebox{-1ex}{$q$}\right.}\right)& T\ge {3.8 }^{\circ }\mathrm{C}\end{array}\right.& RMSE=0.0276\hfill \end{array}$$

$$\begin{array}{cc}{\eta }_{N-TKN,Certyd}=1-\left\{\begin{array}{cc}\exp \left(-{\displaystyle \raisebox{1ex}{$0.2347\times {1.0487}^{T-20}$}\!\left/ \!\raisebox{-1ex}{$q$}\right.}\right)& T<{16.3 }^{\circ }\mathrm{C}\\ \exp \left(-{\displaystyle \raisebox{1ex}{$0.1967$}\!\left/ \!\raisebox{-1ex}{$q$}\right.}\right)& T\ge {16.3 }^{\circ }\mathrm{C}\end{array}\right.& RMSE=0.0307\hfill \\ {\eta }_{N-TKN,Gravel}=1-\left\{\begin{array}{cc}\exp \left(-{\displaystyle \raisebox{1ex}{$0.2813\times {1.0704}^{T-20}$}\!\left/ \!\raisebox{-1ex}{$q$}\right.}\right)& T<{7.2 }^{\circ }\mathrm{C}\\ \exp \left(-{\displaystyle \raisebox{1ex}{$0.1671\times {1.0276}^{T-20}$}\!\left/ \!\raisebox{-1ex}{$q$}\right.}\right)& T\ge {7.2 }^{\circ }\mathrm{C}\end{array}\right.& RMSE=0.0288\hfill \end{array}$$

For the amount of organic matter defined as BOD₅, the gravel-filled bed changed its behavior at $T_k$ = 14.4 °C. Above this temperature, efficiency depended only on the load ($\theta$ = 1.0000). Below this temperature, it increased quite rapidly ($\theta$ = 1.0426). At very low temperatures ($T_k$ < 5.0 °C), the Certyd-filled bed exhibited a rapid increase in purification efficiency. Above 5 °C, this increase slowed considerably.

For the two beds, the models are numerically very similar with regard to removal of the amount of organic matter defined as COD. The beds were characterized by an increase in purification efficiency ($\theta$ = 1.0285 and $\theta$ = 1.0317 for Certyd and mineral fill, respectively) up to a temperature of about 15–17 °C, Above this temperature there was a halt in further temperature dependence ($\theta$ = 1.0000).

For both beds, the ammonium nitrogen removal model had higher temperature sensitivity below the critical temperature of about 4 °C. This sensitivity was higher for the gravel-filled bed, with $\theta$ = 1.1739 vs. $\theta$ = 1.1330 for the Certyd bed. At higher temperatures, sensitivity was lower in both beds, with the gravel-filled bed exhibiting stronger temperature dependence ($\theta$ = 1.0333 vs. $\theta$ = 1.0181). Above 4 °C, the efficiency of the gravel-filled bed approached that of the Certyd bed.

The curves of the Kjeldahl nitrogen removal model were characterized by different critical temperature values (16.3 °C—Certyd bed; 7.2 °C—gravel bed). The Certyd bed did not remain sensitive to temperature changes after exceeding the critical temperature, while the gravel bed further increased its efficiency ($\theta$ = 1.0276 for TKN). At temperatures lower than the critical temperature, the gravel bed remained more sensitive to temperature changes ($\theta$ = 1.0704 for TKN) than the bed with Certyd filling ($\theta =1.0487$ for TKN).

4. Discussion

The P-k-C* model is a black-box model which describes the behavior of a CW bed by means of a specified set of parameters that ignore the complex interdependence of the many unit processes that make up the work of such a bed. Its closed mathematical form contrasts with that of a mechanistic model expressed in a system of mutually coupled partial differential equations, the solution of which is available only through simulation methods [24,25]. Due to increasing computational capabilities and general advances in computer-aided simulation methods, mechanistic models are expected to supplant black-box models [26]. Given its rich literature base and its widespread use over many decades [13], the P-k-C* model was chosen for the analysis. The inclusion of simulation models, such as the very popular CW2D or CWM1, in the descriptions of the beds with the investigated fills is a natural extension of the conducted research. The adopted methodology for developing the bed models presents a very general approach to the final functional form within different variants of a single P-k-C* model. The final form of the models results from their averaging based on Akaike weights. The exclusion of the remaining models is justified solely by their negligible influence on this final form.

The final forms of all analyzed models did not include background concentration (C* = 0) but did include very large numbers of apparent reservoirs (P → ∞). Most of the studies compiled by [13] report both of these parameters as important in describing installation performance, along with their values. All final models have the $T_k$ parameter, which is not a standard component of the P-k-C* model.

Ref. [27] states explicitly that the assumption of C* = 0 is inappropriate. The background concentrations reported in the literature are generally low, not exceeding 10 g/m³. They should be compared with the concentrations at the inflow and outflow of the two beds during baseline studies. In order to establish the background concentration, some researchers have used prepared wastewater to determine this parameter [28]. Small values of the C* parameter bring a small efficiency correction which is very difficult to detect and generates minor changes in the structure of the residuals while introducing an additional parameter to the model. In some works, such as [29,30], the value of this parameter has been taken directly from the literature. Our own results presented here show a statistically insignificant effect of this parameter in the studied ranges of concentrations and hydraulic loads.

P is generally within the range of 2–10 [13]. Study [29] is particularly relevant in the context of the obtained results due to its sensitivity analysis of developed P-k-C* models with respect to parameter P (as well as other components of the full P-k-C* model). The developed models exhibit low sensitivity to the value of this parameter. Study [31] adopts the value of P based on a literature review. Parameter P affects the entire curve of the P-k-C* model, not only in the low concentration range. The results obtained in this study confirm low sensitivity to the number of apparent tanks in series. A larger number of samples may ultimately outweigh the statistical cost of adding this parameter. This also represents a natural direction for the future development of the research presented in this work.

Reports in the literature show that the $K_{20}$ and $\theta$ parameters depend on the hydraulic load and input concentration. There is nothing to indicate that an increased load could leave the $T_k$ parameter unchanged. However, an increased load could mean relatively less evapotranspiration (it depends mainly on bed surface area) and lower output concentration. At the beginning of the century, Kadlec [27] presented evidence for the limited validity of the P-k-C* model for bed work. The P-k-C* models presented here were used as a tool to compare two beds by incorporating some form of temperature dependency, and to enrich the results presented in [11], where only seasonality was included. It is suspected that this tool is deficient, and a more modern approach could give better results.

5. Conclusions

The conducted research confirmed the possibility of using Certyd aggregate, formed in the process of sintering furnace waste, for effective treatment of domestic sewage in a constructed wetland bed with vertical flow.

The long study time, covering both vegetation and non-vegetation periods, made it possible to obtain a database necessary to carry out modelling of CW operation based on the P-k-C* model with respect to BOD₅, COD, ammonium nitrogen, total nitrogen and Kjeldahl nitrogen.

The applicability of the P-k-C* model was confirmed by appropriate statistical diagnostics. It can be used to estimate the efficiency of wastewater treatment in beds with either gravel or Certyd filling. The obtained models of pollutant removal in the CW bed include changes with regard the temperatures at which trends change. When the temperature at which the trend changes is high, then no further temperature dependence is recorded when this temperature is exceeded; otherwise there is a steeper dependency below the temperature at which the trend changes. In almost all models (except for BOD₅), the gravel-filled bed had a steeper temperature dependency than the Certyd-filled one. Due to the specificity of the installation (the bed was located in a field), sewage temperature served as an indicator of air temperature. By connecting these facts, one can conclude that a Certyd-filled bed should behave even better in a colder climate.

Overall, a higher effectiveness in removal of organic matter and nitrogen compounds was obtained in the CW bed filled with Certyd. In beds with both types of filling, a clear relation was observed between wastewater temperature and removal efficiency. For BOD₅, the gravel-filled bed changed its behavior at T = 14.4 °C; in the case of the Certyd-filled bed, the trend change occurred at 5 °C. For COD, both temperatures were similar (In the range 15–17 °C). The ammonia nitrogen removal trend changed at about 4 °C. With regard to efficiency of TKN removal, the trend changed at 14.6 °C in the case of the Certyd-filled bed and at 7.2 °C in the case of the gravel bed.

In the bed filled with Certyd, a better nitrification effect was obtained, which was confirmed by tests on ammonium and nitrate nitrogen concentrations before and after the treatment process.