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Mathematical modeling of the biodegradation of residual hydrocarbon in a variably-saturated sand column

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Abstract

The biodegradation of heptadecane in five sand columns was modeled using a multiplicative Monod approach. Each column contained 1.0 kg of sand and 2 g of heptadecane, and was supplied with an artificial seawater solution containing nutrients at a flow rate that resulted in unsaturated flow through the column. All nutrients were provided in excess with the exception of nitrate whose influent concentration was 0.1, 0.5, 1.0, 2.5, or 5.0 mg N/L. The experiment was run around 912 h until no measurable oxygen consumption or CO2 production was observed. The residual mass of heptadecane was measured at the end of the experiments and the biodegradation was monitored based on oxygen consumption and CO2 production. Biodegradation kinetic parameters were estimated by fitting the model to experimental data of oxygen, CO2, and residual mass of heptadecane obtained from the two columns having influent nitrate–N concentration of 0.5 and 2.5 mg/L. Noting that the oxygen and CO2 measurements leveled off at around 450 h, we fitted the model to these data for that range. The estimated parameters fell in within the range reported in the literature. In particular, the half-saturation constant for nitrate utilization, \( K_{\text{N}} \), was estimated to be 0.45 mg N/L, and the yield coefficient was found to be 0.15 mg biomass/mg heptadecane. Using these values, the rest of experimental data from the five columns was predicted, and the model agreed with the observations. There were some consistent discrepancies at large times between the model simulation and observed data in the cases with higher nitrate concentration. One plausible explanation for these differences could be limitation of biodegradation by reduction of the heptadecane–water interfacial area in these columns while the model uses a constant interfacial area.

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Abbreviations

\( \mu \) :

Gross growth of the active biomass (day−1)

\( \mu_{\max } \) :

Maximum growth rate (day−1)

\( \rho_{\text{sand}} \) :

True density of the sand (mg/cm3)

\( \sigma^{2} \) :

Squared error of estimation

\( \varepsilon \) :

Constant fraction of the decayed biomass

\( \omega_{ij} \) :

Weights

\( \varphi \) :

Shape factor

\( A_{s} \) :

Specific surface area of sand (cm2/g)

C :

CO2 production

\( d_{\text{dvg}} \) :

Average particle size (mm)

\( F \) :

Objective function

\( H \) :

Hessian matrix

\( k_{d} \) :

Endogenous biomass decay rate (day−1)

\( K_S \) :

Half-saturation concentration (mg/cm2)

\( K_N \) :

Half-saturation concentration for nitrogen consumption (mg N/L of pore water)

n :

Number of observations

\( N \) :

Nitrate concentration (mg N/L of pore water)

\( N_{K} \) :

Number of measurements of dependent variable

O2 :

Oxygen

p :

Number of estimated parameters

\( S \) :

Substrate

\( S_{\text{area}} \) :

Surface-area normalized concentration of heptadecane (mg/cm2)

\( S_{\text{mass}} \) :

Concentration of heptadecane (mg/kg of dry sand)

\( X \) :

Active biomass concentration (mg/cm2)

\( X_i \) :

Inert biomass concentration (mg/cm2)

\( X_{0} \) :

Initial biomass concentration (mg/cm2)

\( Y_{CS} \) :

Stoichiometric coefficient for CO2 production from substrate (mg C/mg S)

\( Y_{CX} \) :

Stoichiometric coefficient for CO2 produced during complete mineralization of biomass (mg C/mg X)

\( Y_{OS} \) :

Stoichiometric coefficient for oxygen consumption based on complete mineralization of substrate (mg of O2/mg of S)

\( Y_{OX} \) :

Stoichiometric coefficient for oxygen consumption during the complete mineralization of biomass (mg of O2/mg of X)

\( Y_X \) :

Biomass yield coefficient for growth on substrate (mg X/mg S)

\( u_S \) :

Simulated result for the dependent variable

\( u_O \) :

Observed result for the dependent variable

\( V_x \) :

Covariance matrix

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Acknowledgments

This work was supported in part by funding from the Exxon Valdez Trustee Council under project no. 11100836. This article does not necessarily reflect the views of the funding agency and no official endorsement should be inferred.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, Center for Natural Resources Development and Protection, New Jersey Institute of Technology, Newark, NJ, 07102, USA

    Xiaolong Geng, Michel C. Boufadel & Brian Wrenn

  2. Department of Mathematics, Anshan Normal University, Anshan, Liaoning, 114001, China

    Xiaolong Geng

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  1. Xiaolong Geng
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  2. Michel C. Boufadel
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Correspondence to Michel C. Boufadel.

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Geng, X., Boufadel, M.C. & Wrenn, B. Mathematical modeling of the biodegradation of residual hydrocarbon in a variably-saturated sand column. Biodegradation 24, 153–163 (2013). https://doi.org/10.1007/s10532-012-9566-5

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