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Application of divided convective-dispersive transport model to simulate conservative transport processes in planted horizontal sub-surface flow constructed wetlands

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Abstract

We have created a divided convective-dispersive transport (D-CDT) model that can be used to provide an accurate simulation of conservative transport processes in planted horizontal sub-surface flow constructed wetlands filled with coarse gravel (HSFCW-C). This model makes a fitted response curve from the sum of two independent CDT curves, which show the contributions of the main and side streams. The analytical solutions of both CDT curves are inverse Gaussian distribution functions. We used Fréchet distribution to provide a fast optimization mathematical procedure. As a result of our detailed analysis, we concluded that the most important role in the fast upward part of the tracer response curve is played by the main stream, with high porous velocity and dispersion. This gives the first inverse Gaussian distribution function. The side stream shows slower transport processes in the micro-porous system, and this shows the impact of back-mixing and dead zones, too. The significance of this new model is that it can simulate transport processes in this kind of systems more accurately than the conventionally used convective-dispersive transport (CDT) model. The calculated velocity and dispersion coefficients with the D-CDT model gave differences of 24–54 % (of velocity) and 22–308 % (of dispersion coeff.) from the conventional CDT model, and were closer to actual hydraulic behaviour.

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Abbreviations

CW:

Constructed wetland

FSCW:

Free-surface flow constructed wetland

SFCW:

Sub-surface flow constructed wetland

VSFCW:

Sub-surface flow constructed wetland with vertical flow direction

HFSCW-C:

Horizontal sub-surface flow constructed wetland using coarse gravel filter media

HRT:

Hydraulic retention time

D (m2/h):

Dispersion coefficient

D x (m2/h):

Longitudinal dispersion coefficient

q (1/h):

Specific loading rate

ε (−):

Porosity

ε 0 (−):

Porosity of filter media

x (m):

Longitudinal coordinate

TSS (mg/l):

Total suspended solids

CDT:

Convection-dispersion transport model

CSTR:

Completely stirred tank reactor transport model

LiCl:

Lithium-chloride

C (mg/l):

Concentration

w (m):

Width of seepage zone

m (m):

Height of seepage zone

t (h):

Time

t elm (h):

Theoretical HRT

M (g):

Mass of tracer

v x (m/h):

Longitudinal velocity in porous regime

L (m):

Length of seepage zone

R (−):

Retention rate

μ (s):

Mean of fitted C-t curve

σ (s):

Standard deviation of fitted C-t curve

a, b, c:

Parameters of inverse Gaussian distribution

S/1, S/2, S/3 and S/4:

Reference numbers of own measurements

N/1, N/2, N/3, N/4 and N/5:

The reference numbers of analysed international measurements

Pe (−):

Pelcet number

D-CDT:

Divided convective-dispersive transport model

R 2 :

Statistical coefficient of determination

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Acknowledgments

The Katholieke Hogeschool Kempen, Geel (Belgium) began scientific cooperation with the Agricultural Faculty of the University of Szeged (Hungary) in 2003. One result of this cooperation is that the analysed natural wastewater treatment plant was built with scientific objectives. The project was financed by the Co-operation Programme between Flanders and Central and Eastern Europe, Department of Foreign Policy of the Flemish Government. More detailed information about the project is available at http://www.constructedwetlands.net/.

We express our thanks to our scientific supervisor, Ferenc Szilágyi, and to the Department of Water Utilities and Env. Eng. of the Budapest University of Technology and Economics.

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Authors and Affiliations

  1. Pollack Mihály Faculty of Engineering and Informatics, Department of Environmental Engineering, University of Pécs, Boszorkány u. 2, H-7624, Pécs, Hungary

    Ernő Dittrich

  2. Pollack Mihály Faculty of Engineering and Informatics, Department of Mathematical Sciences, University of Pécs, Pécs, Hungary

    Mihály Klincsik

Authors
  1. Ernő Dittrich
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  2. Mihály Klincsik
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Correspondence to Ernő Dittrich.

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Responsible editor: Marcus Schulz

Appendix

Appendix

Table 5 Main data of own tracer measurements
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Table 6 Main data of tracer measurements of international scientists
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Dittrich, E., Klincsik, M. Application of divided convective-dispersive transport model to simulate conservative transport processes in planted horizontal sub-surface flow constructed wetlands. Environ Sci Pollut Res 22, 18148–18162 (2015). https://doi.org/10.1007/s11356-015-4950-4

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