Evaluation of Mechanistic Models for Nitrate Removal in Woodchip

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Evaluation of mechanistic models for nitrate removal in woodchip bioreactors Brian James Halaburka, Gregory H. LeFevre, and Richard G Luthy Environ. Sci. Technol., Just Accepted Manuscript • DOI: 10.1021/acs.est.7b01025 • Publication Date (Web): 10 Apr 2017 Downloaded from http://pubs.acs.org on April 10, 2017

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Environmental Science & Technology

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Evaluation of mechanistic models for nitrate

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removal in woodchip bioreactors

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Brian J. Halaburka1,2, Gregory H. LeFevre1,3, Richard G. Luthy1,2,*

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1. Re-inventing the Nation’s Urban Water Infrastructure (ReNUWIt), National Science

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Foundation Engineering Research Center

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2. Department of Civil & Environmental Engineering, Stanford University, Stanford, California,

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94305-4020 USA

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3. Department of Civil & Environmental Engineering, University of Iowa, Iowa City, Iowa,

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52242, USA

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ABSTRACT

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Woodchip bioreactors (WBRs) are increasingly being applied to remove nitrate from runoff. In

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this study, replicate columns with aged woodchips were subjected to a range of measured flow

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rates and influent nitrate concentrations with an artificial stormwater matrix. Dissolved oxygen

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(DO), nitrate, and dissolved organic carbon (DOC) were measured along the length of the

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columns. A multi-species reactive transport model with Michaelis-Menten kinetics was

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developed to explain the concentration profiles of DO, nitrate, and DOC. Four additional models

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were developed based on simplifying assumptions, and all five models were tested for their

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ability to predict nitrate concentrations in the experimental columns. Global sensitivity analysis

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and constrained optimization determined the set of parameters that minimized the root-mean-

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squared error (RMSE) between the model and the experimental data. A k-fold validation test

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revealed no statistical difference in RMSE for predicting nitrate concentrations between a zero-

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order model and the other multi-species reactive transport models tested. Additionally, the multi-

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species reactive transport models demonstrated no significant differences in predicting DO and

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DOC concentrations. These results suggest that denitrification in an aged woodchip bioreactor at

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constant temperature can effectively be modeled using zero-order kinetics when nitrate

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concentrations >2 mg-N L-1. A multi-species model may be used if predicting DOC or DO

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concentrations is desired.

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INTRODUCTION

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The National Academy of Engineering has identified managing the nitrogen cycle as one of the

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14 Great Challenges for Engineering in the 21st Century,1 and woodchip bioreactors (WBRs)

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have emerged as a promising approach to reduce nitrate exports in agricultural runoff and urban

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stormwater.2-4 Woodchips are inexpensive and renewable, and current forest management

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practices generate a substantial volume of low quality/low value wood.5 Additionally, woodchips

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support high permeability, have a high C:N ratio (ranging from 30:1 to 3000:1), and robust

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durability.6,7 Long-term field experiments indicate wood-particle media can provide consistent

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nitrate removal for up to 15 years.8-10

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Despite the increasing application and perceived advantages, the mechanisms governing nitrate

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removal rates in WBRs are still poorly understood. The literature reports a wide range of

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denitrification rates,6,11,12 ranging from 0.7-22.0 g-N m-3 media d-1. Numerous factors are

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suggested for the large range of denitrification rates measured in the field, such as woodchip


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age,7,11 temperature,13,14 and carbon substrate.15 Nevertheless, there is no clear consensus on the

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appropriate model to explain woodchip-based denitrification. The most popular model to predict

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reactor performance is a simple zero-order model, where the denitrification rate is constant and

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nitrate removal is linearly related to hydraulic residence time (HRT).6,13,16 However, other

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models have been proposed. Leverenz et al.17 suggested that a first-order model provides a better

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fit for reactors operating at low nitrate concentrations and reduced temperatures. Hoover et al.18

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reported influent nitrate concentration influences nitrate reduction rates up to 30-50 mg-N L-1,

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suggesting first-order or Michaelis-Menten reaction kinetics.

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In addition to simple zero- or first-order reaction kinetic models, several one-dimensional

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transport models have been proposed. Jaynes et al.19 proposed a dual porosity model that

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specifies a mobile and immobile fraction of water within the woodchip reactor based on the

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assumption that denitrification occurs primarily inside the woodchips. Results were inconclusive

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whether zero- or first-order reaction kinetics best described the data, and the fitted parameters for

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the mobile and immobile fraction were significantly different from experimentally measured

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values.19 Ghane et al.20 proposed a non-Darcy transport model with Michaelis-Menten kinetics to

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describe denitrification rates. The Forcheimer hydraulic model closely matched the tracer test

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data for horizontal flow in woodchip reactor beds,21 but the Michaelis-Menten reaction kinetic

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parameters were estimated without replicate measurements and thus should not be deemed fully

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robust. In addition, the denitrification rates in the reactor were abnormally high with a maximum

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nitrate removal rate of 7.1 mg-N L-1 hr-1 at 23.5 °C, or 144.8 g-N m-3 media d-1, indicating the

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woodchips were not fully aged.

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A number of factors may explain the wide range of denitrification rates and models reported in

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the literature. New woodchips have higher denitrification rates within the first year of operation


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due to the leaching of excess organic material, and after approximately one year of operation the

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rate stabilizes.22-24 Many studies use insufficiently aged woodchips, and as a result the reported

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rates do not reflect long-term performance. In addition, many studies have poor spatial resolution

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along the length of the reactor or do not take replicate measurements, making the assertion of

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trends tenuous. Temperature variation and packing density of carbon source also can

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substantially alter denitrification rates,14,23 but wood type and grain size do not.12,15

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The critical parameters needed to model nitrate removal in woodchip reactors are still poorly

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understood.2 Under conditions where heterotrophic denitrification is controlled by dissolved

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oxygen (DO), nitrate, and dissolved organic carbon (DOC) concentrations,25 a complete

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mechanistic model of denitrification in woodchip reactors would include all three of these

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parameters. Although a complete mechanistic model may improve understanding of the

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processes involved in denitrification in woodchip bioreactors (WBRs), the optimal model to use

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in practice is the most parsimonious and several simplifying assumptions may be made.

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The objective of this work was to quantitatively evaluate mechanistic reactive transport models

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describing denitrification in laboratory WBR columns using aged woodchips. Five models were

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evaluated in this study. The models were calibrated using experimental data collected from

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laboratory woodchip columns that were aged for over a year, then evaluated using sensitivity

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analysis and a k-fold validation test. The results of this study will increase understanding of the

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underlying mechanisms of denitrification in WBRs, while providing justification for the use of

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the simplest model to describe WBR performance.

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METHODS

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Column Design


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Woodchips were obtained from an arborist woodchip waste pile in Portola Valley, CA. The

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woodchips were composed of a mix of species, including California redwood (Sequoia

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sempervirens), oak (Quercus sp.), and Douglas fir (Pseudotsuga menziesii). The woodchips were

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dried at 50 °C for 48 hours in a drying oven then sieved to a diameter between 2-10 mm.

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Woodchip type and particle size have been reported to have no significant effect on nitrate

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removal rates,12,15 thus additional woodchip composition analysis was not performed.

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Three PCV column reactor columns (10 cm ID x 50 cm) were constructed with sample ports

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installed every 5 cm (Figure S1). For sample ports, 3.81 cm long luer-lock needles (gauge #16)

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with ball valves were wrapped with PTFE tape and press-fit into holes drilled in the side of the

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columns (Figure S2), allowing sampling from the center of the column. A total of 11 sample

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ports were installed on each column. A stainless steel screen (mesh #10) was placed at the

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bottom of each column to support the woodchips. 700 g of the dried and sieved woodchips were

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added to each column and lightly compacted every 5 cm such that woodchips filled the column

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to the top, corresponding to a packing density of 0.18 g cm-3. Upon completion of the

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experiments, drainable porosity (specific yield) of the columns was determined by draining the

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columns from the bottom over a 1-hour period, measuring the weight of the drained water, and

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subtracting the volume of the bottom cap from the total volume drained. The woodchips were

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then removed from the column and specific retention was determined by measuring the

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difference between the wet and dry media after 48 hours in a drying oven at 50 °C. Total

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porosity was determined by summing drainable porosity and specific retention.

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Tracer Tests

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Prior to running the experiments, linear pore-water velocity and dispersion coefficients were

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estimated for each column with an interval-pulse bromide tracer test at a flow rate of 26 mL min-


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(described in the SI). Theoretical HRT (τ) was calculated as = V n ⁄60Q where Vr is volume

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1

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of the reactor (mL), ne is effective porosity (-), and Q is flow rate (mL min-1). Effective porosity

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is the fraction of the total volume that contributes to fluid flow, and drainable porosity was used

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as an estimate of effective porosity for the calculation of τ. Actual mean HRT (̅) was calculated

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as ̅ = / where L is reactor length (cm) and ν is porewater velocity (cm h-1). Hydraulic

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̅ . The ideal reactor would have an eV efficiency, eV, of the reactor was calculated26 as = ⁄

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value of 1, indicating plug flow conditions. An eV value of less than 1 indicates short-circuiting,

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while an eV value greater than 1 may indicate drainable porosity is less than effective porosity or

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that physical retardation is occurring such as fluid entering micropores (specific retention) within

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the woodchips.27

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Column Experiments

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The columns were operated at room temperature (21 °C) in up-flow mode using variable speed

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digital peristaltic pumps (Masterflex) to maintain saturated hydraulic conditions. Each column

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was fed artificial stormwater at a different measured flow rate (1.5 mL min-1, 3.8 mL min-1, and

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8.4 mL min-1). The artificial stormwater matrix was composed of 0.75 mM CaCl2, 0.075 mM

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MgCl2, 0.33 mM Na2SO4, 1 mM NaHCO3, 0.0715 mM NH4Cl, and 0.016 mM Na2HPO4,

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representing the average concentration of major ions in urban stormwater.28 NaNO3 was added to

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the stormwater matrix to achieve an initial nitrate concentration of 10 mg-N L-1. Columns were

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aged for 13 months with the flowing stormwater matrix prior to conducting tracer tests and

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column experiments. For the column experiments, all columns were exposed to three influent

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nitrate concentrations of 11 mg-N L-1, 5 mg-N L-1, and 2 mg-N L-1. Preliminary measurements

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showed that concentration profiles of all the columns reached steady-steady within 2-3 days


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following a change of influent nitrate concentration. For each concentration, the columns were

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allowed to run for one week at the new nitrate concentration before sampling began.

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Sampling and Analysis

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The columns were sampled along the entire length for DO, nitrate, and DOC. Sampling was

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repeated four times during a period of one week to obtain replicate measurements. Thus four

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replicates were collected from the reactors at three different flow rates and three different

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influent nitrate concentrations for a total of nine different conditions tested. For each sampling

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event, samples were collected from all sample ports as well as the artificial stormwater matrix

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tank to verify the stability of the solution. DOC and nitrate samples were collected starting at the

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top-most sample port (at outlet) and moving downward (toward inlet) such that each sample was

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representative of the porewater at or just above the sample port. Fifteen milliliters of sample was

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collected in a 25 mL plastic syringe and filtered using a sterile 0.45 μm PVDF filter into a 24 mL

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glass vial baked at 450 °C for four hours in a muffle furnace. All samples were analyzed within

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four hours of sample collection and in random order using a random number generator. Nitrate

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was measured using a WestCo SmartChem 200 Discrete Analyzer (detection limit: 0.05 mg-N L-

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1

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a Unisense dissolved oxygen needle probe (model DO-NP) and the Unisense SensorTrace

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Software.

). DOC was measured using a Shimadzu TOC-L Autoanalyzer. DO was measured in situ using

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Model Development

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Five models were quantitatively evaluated to describe denitrification in the experimental

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woodchip columns. The first model evaluated was a system of one-dimensional advection

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dispersion equations with coupled Michaelis-Menten reaction kinetics to describe the transport


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of DO, nitrate, and DOC (Model 1). This system of 1-D advection-dispersion equations was

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chosen because similar reactive transport models have been used with success to describe

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microbial substrate, oxygen, and nitrate uptake in porous media,29,30 contaminant degradation in

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porous media,31,32 and denitrification in hyporheic zone sediments.33,34 The generalized model

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for each constituent takes the form = − − (1)

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where Ci is the concentration of the ith species (mg L-1), t is time (h), D is the dispersion

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coefficient (cm2 h-1), ν is the effective porewater velocity (cm h-1), x is distance along the column

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(cm), and Ri is the biological reaction rate term for the ith species (mg L-1 h-1). The biological

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reactions modeled in the woodchip columns are aerobic respiration, denitrification, and cellulose

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hydrolysis. For aerobic respiration of DOC, both the availability of DO and DOC can limit the

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overall reaction rate. Without knowing the limiting substrate a priori, coupled Michaelis-Menten

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kinetics is an effective method to model the overall microbial kinetics.35 The aerobic reaction

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rate can be expressed in the form =

! "

' &" & (2) #$ + #( + '

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where RO is the rate of oxygen uptake (mg-O2 L-1 h-1), XO is the concentration of aerobic

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heterotrophs (mg-biomass L-1), VO is the maximum uptake rate of DO (mg-O2 mg-biomass-1 h-1),

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C is the concentration of DOC (mg-C L-1), Kc is the half-saturation constant for DOC (mg-C L-

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1

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O2 L-1).

), O is the concentration of DO (mg-O2 L-1), and Ko is the half-saturation constant for DO (mg-

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Denitrification can similarly be expressed as a coupled Michaelis-Menten reaction, with the

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addition of a non-competitive inhibition term representing the inhibiting effect of DO on

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denitrification. This reaction rate takes the form


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* =

+ #, &" &" & (3) #$ + #* + + #, + '

* !* "

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where RN is the rate of denitrification (mg-N L-1 h-1), XN is the concentration of heterotrophic

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denitrifiers (mg-biomass L-1), VN is the maximum rate of denitrification (mg-N mg-biomass-1 h-

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1

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N L-1), and KI is the inhibition constant of DO (mg-O2 L-1).

), N is the concentration of nitrate (mg-N L-1), KN is the half-saturation constant for nitrate (mg-

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DOC is consumed through both aerobic respiration and denitrification, and the DOC reaction

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rate is modeled as a combination of the Michealis-Menten reaction equations for the two

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processes. The DOC reaction term takes the form . = /

' &" & + /* #$ + #( + '

! "

* !* "

+ #, &" &" & (4) #$ + #* + + #, + '

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where RC is the rate of DOC uptake (mg-C L-1 h-1), βO is the uptake coefficient for DO (mg-C

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mg-O2-1), βN is the uptake coefficient for nitrate (mg-C mg-N-1). The uptake coefficients for DO

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and nitrate are the ratios of the mass of DOC consumed per mass of DO or nitrate consumed,

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respectively.

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In addition to the degradation term, the DOC transport equation includes a DOC production

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term for cellulose hydrolysis. Cellulose hydrolysis is the enzymatic process by which microbes

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cleave crystalline cellulose into smaller soluble oligosaccharides.36 Cellulose in woody material

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is obstructed by lignin such that only certain surface binding sites are available for cellulase

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adsorption. As more cellulose is hydrolyzed, fewer binding sites are available so the DOC

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hydrolysis rate decreases over time following a power-law function.22,37 After an initial sharp

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decrease in DOC release, the power law function reaches a quasi-steady state wherein the DOC

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release rate remains relatively constant. This behavior is observed in field-scale woodchip

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reactors where reaction rates drop rapidly within the first year of operation but then stay

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relatively constant.6,11,24 The presence of fungi in oxic zones may increase the rate of DOC


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release due to their ability to break down lignin, making available more cellulose to be

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hydrolyzed.36 To account for different DOC release rates in oxic and anoxic zones, DOC release

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kinetics are modeled using the equation #1 = !12 "

' #, & + !1 " & (5) # + ' #, + '

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where Kh is the DOC production rate (mg-C L-1 h-1), Vh1 is the aerobic maximum DOC

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production rate (mg-C L-1 h-1), and Vh2 is the anaerobic maximum DOC production rate (mg-C L-

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1

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for DO uptake and denitrification, respectively.

h-1). The values for KO and KI are assumed to be the same as those in the reaction rate equations

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Three coupled equations (DO, nitrate, and DOC) comprise the model. The model assumes that

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(1) the system is in steady-state and the transient term is zero, (2) the microbial biomass is

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constant within each region and fixed to surfaces so that the microbial biomass terms XO and XN

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can be combined with VO and VN, (3) substrate and electron acceptors (O2 and NO3-) are the only

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limitations to sustaining growth, (4) all DOC is labile and bioavailable, and only dissolved

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substrate is taken up by bacteria, (5) insoluble substrate mass remains relatively constant due to

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the longevity of woodchips,16 and (6) sorption and intra-particle diffusion of DOC through

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woodchips is not important because the equations are solved at steady-state. Thus the three

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partial differential equations to model DO, nitrate, and DOC mass transport are

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213

Dissolved Oxygen:

Nitrate:

(Model 1) ' ' ' − ! " &" & 0 = − #$ + #( + '

0= 214

+ + + #, − − ! " & " & " & * #$ + #* + + #, + '

Dissolved Organic Carbon:


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' + #, 0 = − − / ! " &" & − /* !* " &" &" & #$ + #( + ' #$ + #* + + #, + ' ' #, + !12 " & + !1 " & # + ' #, + '

215

The second model (Model 2) simplifies Model 1 by assuming DO does not significantly

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impact the overall denitrification rate. It is well established that DO inhibits denitrification;35

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however, denitrification has been observed in WBRs13,38 with DO concentrations between 0.5-

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4.5 mg L-1. One explanation is that micropores within the woodchips create anaerobic

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environments where denitrification can occur,25 suggesting that bulk solution DO concentrations

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have little effect on the overall denitrification rate of WBRs. Alternatively, aerobic respiration

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and denitrification may occur in the bulk solution, but aerobic respiration occurs at a much faster

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rate and DO inhibition has a relatively minor effect on the over nitrate removal rate. The DO

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terms are removed from the system of equations, and the model takes the form

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Nitrate:

(Model 2) 0=

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Dissolved Organic Carbon: 0=

+ + + − − !* " &" & #$ + #* + +

+ − − / ! " & " & + !1 * * #$ + #* + +

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The third model (Model 3) is an alternate simplification of Model 1 by assuming

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denitrification is not dependent on DOC concentrations. DOC has been identified as the limiting

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reactant in WBR denitrification.13,39 Nevertheless, a number of published denitrification models

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ignore DOC concentrations, yet adequately fit experimental nitrate data.20,40 If denitrification in

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WBRs is carbon limited, then C

Evaluation of Mechanistic Models for Nitrate Removal in Woodchip

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