Application of divided convective-dispersive transport model to simulate variability of conservative transport processes inside a planted horizontal subsurface flow constructed wetland

Environmental Science and Pollution Research https://doi.org/10.1007/s11356-020-10965-z RESEARCH ARTICLE Application of divided convective-dispersive transport model to simulate variability of conservative transport processes inside a planted horizontal subsurface flow constructed wetland Ernő Dittrich 1 2 1 1 1 & Mihály Klincsik & Dávid Somfai & Anita Dolgos-Kovács & Tibor Kiss & Anett Szekeres 3 Received: 3 April 2020 / Accepted: 21 September 2020 # The Author(s) 2020 Abstract This paper offers a novel application of our model worked out in Maple environment to help understand the very complex transport processes in horizontal subsurface flow constructed wetland with coarse gravel (HSFCW-C). We made tracer measurements: Inside a constructed wetland, we had 9 sample points, and samples were taken from each point at two depths. Our model is a divided convective-dispersive transport (D-CDT) model which makes a fitted response curve from the sum of two separate CDT curves showing the contributions of the main and side streams. Analytical solutions of CDT curves are inverse Gaussian distribution functions. This model was fitted onto inner points of the measurements to demonstrate that the model gives better fitting to the inner points than the commonly used convective-dispersive transport model. The importance of this new application of the model is that it can resemble transport processes in these constructed wetlands more precisely than the regularly used convective-dispersive transport (CDT) model. The model allows for calculations of velocity and dispersion coefficients. The results showed that this model gave differences of 4–99% (of velocity) and 2–474% (of dispersion coefficient) compared with the CDT model and values were closer to actual hydraulic behavior. The results also demonstrated the main flow path in the system. Keywords Divided convective-dispersive transport (D-CDT) model . Fréchet distribution . Inverse Gaussian distribution . Subsurface flow constructed wetlands . Transport processes . Tracer test . Hydraulic variability inside the constructed wetland Nomenclature CW FSCW SFCW VSFCW Constructed wetland Free-surface flow constructed wetland Subsurface flow constructed wetland Responsible editor: Marcus Schulz * Ernő Dittrich 1 Faculty of Engineering and Informatics, Department of Environmental Engineering, University of Pécs, Boszorkány u. 2, Pécs H-7624, Hungary 2 Faculty of Engineering and Informatics, Department of Mathematical Sciences, University of Pécs, Boszorkány u. 2, Pécs H-7624, Hungary 3 Hidro-consulting Ltd., Budai Nagy Antal u. 1, Pécs H-7624, Hungary HSFCW-C HRT D [m2/h] Dx [m2/h] q [1/h] x [m] CDT CSTR LiCl C [mg/l] vx [m/h] L [m] R [-] a, b, c Subsurface flow constructed wetland with vertical flow direction Horizontal subsurface flow constructed wetland using coarse gravel filter media Hydraulic retention time Dispersion coefficient Longitudinal dispersion coefficient Specific loading rate Longitudinal coordinate Convection-dispersion tank Continuous stirred-tank reactor Lithium-chloride Concentration Longitudinal velocity in porous regime Length of seepage zone Retention rate Parameters of Inverse Gaussian distribution Environ Sci Pollut Res S/1, S/2, S/3, and S/4 D-CDT R2 Reference numbers of own measurements Divided convective-dispersive tank Statistical coefficient of determination Introduction Constructed wetlands (CWs)—also known as treatment wetlands—are engineered systems for wastewater treatment. Constructed wetlands have a very low or zero energy demand; therefore, operation and maintenance costs are significantly reduced compared to conventional treatment systems (Almuktar et al. 2018). There are two main types of constructed wetland: freesurface flow systems (FSF-CW) and subsurface flow systems (SSF-CW). SSF-CWs can be further divided according to the direction of the wastewater flow. Wastewater in SSF-CWs runs either horizontally (in HSSF-CWs) or vertically (in VSSF-CWs) towards the filter media. In VSFCWs, there is an unsaturated, non-permanent flow, and in HFSFCWs there is a saturated, non-permanent flow (Wu et al. 2015; Valipour and Ahn 2016). Our experiments and calculations were performed on HFSFCWs only. We investigated HFSFCWs using coarse gravel as filter medium (HFSCW-C). Constructed wetlands can treat a wide variety of polluted water, including municipal, domestic, agricultural, or industrial wastewaters (Vymazal 2009). There are important differences between the ideal and the actual flow. One of the reasons is weather conditions, such as rainfall (Kadlec 1997, 1999; Rash and Liehr 1999), evapotranspiration (Galvão et al. 2010; Beebe et al. 2014), and snow melting that can have a huge impact on the flow within constructed wetlands. Another important factor is the construction of the CW: the differences in porosity and hydraulic conductivity of filter media in volume and over time (Dittrich and Klincsik 2015a; Licciardello et al. 2019), the active volume of the porous system (Goebes and Younger 2004), and the inlet and outlet positions (Alcocer et al. 2012; Wang et al. 2014; Okhravi et al. 2017). Finally, there are the clogging processes caused by solids accumulation (Carballeira et al. 2016, Lancheros et al. 2017,Liu et al. 2019), biofilm development (Button et al. 2015; Aiello et al. 2016; Vymazal 2018; de Matos et al. 2018), and root density and distribution (De Paoli and Sperling 2013,Tang et al. 2017) . Due to the factors mentioned above, the hydrodynamic modeling of SFCWs is a challenging task for experts. In these constructions, biofilm activity and root density can be very intense, and more importantly, biofilm development and root system growth over time may also be significantly more rapid (Samsó and Garcia 2013; Rajabzadeh et al. 2015). These processes can affect the micro-porous system, hydraulic conductivity, and clogging processes as well (Tanner and Sukias 1995). It is quite challenging and often problematic to estimate these processes or, even further, to incorporate these factors into a model. Conservative tracer tests are commonly used to analyze the hydraulic behavior of constructed wetlands (Levenspiel 1972). Scientists have frequently analyzed SFCWs with conservative tracer tests used as experimental tools to gain more detailed information about the internal hydrodynamics of constructed wetlands (Netter 1994; Suliman et al. 2006; Barbagallo et al. 2011; Wang et al. 2014). Our method was also based on tracer tests. Conservative tracer tests allow for calculations of the hydraulic retention time (HRT) and dispersion coefficient (D) of a hydraulic system. Some scientists have also conducted the same tests in HSFCWs with the same goal. Netter (1994) measured two horizontal subsurface flow constructed wetlands. Tracer tests were taken from each CW. They were filled with different, homogeneously mixed media, gravelly sand and sandy gravel, and both filter materials conta (...truncated)