Environmental Earth Sciences

, Volume 74, Issue 6, pp 4827–4837 | Cite as

Modeling bacterial attenuation in on-site wastewater treatment systems using the active region model and column-scale data

  • Emma Engström
  • Hui-Hai Liu
Original Article


Bacterial attenuation in porous media is often higher in columns than in the field. This study investigates whether this inconsistency could be attributed to finger flow, as assessed by the active region model (ARM). It develops a numerical model of flow and transport of the fecal indicator Escherichia coli  in a wastewater infiltration basin from the literature. Modeling was based on the traditional, uniform flow approach (Richard’s equation) as well as the ARM, representing finger flow. The uniform flow model resulted in flow rates that decreased rapidly with filter depth and an underestimation of the observed average relative effluent concentration by three orders of magnitude. With the ARM, the flow rates remained high throughout the filter, more consistently with observations, and the relative effluent concentration (0.018) was relatively accurate in reproducing the field result (0.025). Considering a range of removal rates derived from laboratory studies, the ARM consistently enabled more accurate and conservative assessments of the filter efficiency; thus, results indicated that the ARM provides a more relevant approach to bacterial transport in wastewater infiltration basins with sandy, unstructured soils.


Unsaturated zone Bacterial transport Preferential flow Soil aquifer treatment Active region model 

List of symbols

Variables and coefficients

\(C_{0 }\)

Bacterial influent concentration (ML−3)


Bacterial concentration in the active region (ML−3)


Bacterial concentration in the water (ML−3)

\(C_{{{\text{effluent}} }}\)

Bacterial effluent concentration (ML−3)


Topological dimension (–)

\(d_{50 }\)

Median grain size (L)


Fractal dimension (–)


Fraction of the active region (–)


Soil water pressure head in the active region (L)


Soil water pressure head in the uniform flow model (L)


Unsaturated hydraulic conductivity in the active region (LT−1)


Unsaturated hydraulic conductivity in the whole domain (LT−1)


Saturated hydraulic conductivity (LT−1)

\(k_{{{\text{tot}} }}\)

Total bacterial attenuation rate (T−1)


Total bacterial attenuation rate, conservative approach (T−1)


Total bacterial attenuation rate, high-efficiency approach (T−1)

\(l_{\text{col }}\)

Column length (L)


van Genuchten parameter (–)


van Genuchten parameter (–)


Iteration level


Saturation in the active region (–)


Average active water saturation (\(S_{\text{e}}^{*} = fS_{{{\text{a}} }}\)) (–)


Saturation in the inactive region (–)


Time (T)


Average wastewater infiltration rate (LT−1)


Darcy flow velocity in the active region (LT−1)


Darcy flow velocity in the whole domain (LT−1)


Vertical distance (positive upward) (L)

Greek letters


van Genuchten parameter (L−1)


Empirical parameter related to the size of the active region (–)


Volumetric moisture content in the active region (–)


Volumetric total moisture content (–)


Initial volumetric water content (–)


Volumetric moisture content in the inactive region (–)


Residual volumetric moisture content (–)


Saturated volumetric moisture content (–)


Dispersivity in the active region (L)


Dispersivity in the whole domain (L)


Bacterial source–sink term in the ARM


Bacterial source–sink term in the uniform model



The manuscript benefited from constructive comments by anonymous reviewers as well as Dr. Roger Thunvik and Dr. Berit Balfors, KTH, Royal Institute of Technology, Sweden.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Lawrence Berkeley National Laboratory, Department of HydrogeologyUniversity of CaliforniaIrvineUSA
  2. 2.Department of Sustainable Development, KTH Royal Institute of TechnologyEnvironmental Science and Engineering (SEED)StockholmSweden
  3. 3.Aramco Research CenterHoustonUSA

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