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Article

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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1 Evaluation of mechanistic models for nitrate

2 removal in woodchip bioreactors

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

4 1. Re-inventing the Nation’s Urban Water Infrastructure (ReNUWIt), National Science
5 Foundation Engineering Research Center

6 2. Department of Civil & Environmental Engineering, Stanford University, Stanford, California,
7 94305-4020 USA

8 3. Department of Civil & Environmental Engineering, University of Iowa, Iowa City, Iowa,
9 52242, USA

10 ABSTRACT

11 Woodchip bioreactors (WBRs) are increasingly being applied to remove nitrate from runoff. In
12 this study, replicate columns with aged woodchips were subjected to a range of measured flow
13 rates and influent nitrate concentrations with an artificial stormwater matrix. Dissolved oxygen
14 (DO), nitrate, and dissolved organic carbon (DOC) were measured along the length of the
15 columns. A multi-species reactive transport model with Michaelis-Menten kinetics was
16 developed to explain the concentration profiles of DO, nitrate, and DOC. Four additional models
17 were developed based on simplifying assumptions, and all five models were tested for their

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18 ability to predict nitrate concentrations in the experimental columns. Global sensitivity analysis
19 and constrained optimization determined the set of parameters that minimized the root-mean-
20 squared error (RMSE) between the model and the experimental data. A k-fold validation test
21 revealed no statistical difference in RMSE for predicting nitrate concentrations between a zero-
22 order model and the other multi-species reactive transport models tested. Additionally, the multi-
23 species reactive transport models demonstrated no significant differences in predicting DO and
24 DOC concentrations. These results suggest that denitrification in an aged woodchip bioreactor at
25 constant temperature can effectively be modeled using zero-order kinetics when nitrate
26 concentrations >2 mg-N L-1. A multi-species model may be used if predicting DOC or DO
27 concentrations is desired.

28 INTRODUCTION
29 The National Academy of Engineering has identified managing the nitrogen cycle as one of the
30 14 Great Challenges for Engineering in the 21st Century,1 and woodchip bioreactors (WBRs)
31 have emerged as a promising approach to reduce nitrate exports in agricultural runoff and urban
32 stormwater.2-4 Woodchips are inexpensive and renewable, and current forest management
33 practices generate a substantial volume of low quality/low value wood.5 Additionally, woodchips
34 support high permeability, have a high C:N ratio (ranging from 30:1 to 3000:1), and robust
35 durability.6,7 Long-term field experiments indicate wood-particle media can provide consistent
36 nitrate removal for up to 15 years.8-10
37 Despite the increasing application and perceived advantages, the mechanisms governing nitrate
38 removal rates in WBRs are still poorly understood. The literature reports a wide range of
39 denitrification rates,6,11,12 ranging from 0.7-22.0 g-N m-3 media d-1. Numerous factors are
40 suggested for the large range of denitrification rates measured in the field, such as woodchip

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41 age,7,11 temperature,13,14 and carbon substrate.15 Nevertheless, there is no clear consensus on the
42 appropriate model to explain woodchip-based denitrification. The most popular model to predict
43 reactor performance is a simple zero-order model, where the denitrification rate is constant and
44 nitrate removal is linearly related to hydraulic residence time (HRT).6,13,16 However, other
45 models have been proposed. Leverenz et al.17 suggested that a first-order model provides a better
46 fit for reactors operating at low nitrate concentrations and reduced temperatures. Hoover et al.18
47 reported influent nitrate concentration influences nitrate reduction rates up to 30-50 mg-N L-1,
48 suggesting first-order or Michaelis-Menten reaction kinetics.
49 In addition to simple zero- or first-order reaction kinetic models, several one-dimensional
50 transport models have been proposed. Jaynes et al.19 proposed a dual porosity model that
51 specifies a mobile and immobile fraction of water within the woodchip reactor based on the
52 assumption that denitrification occurs primarily inside the woodchips. Results were inconclusive
53 whether zero- or first-order reaction kinetics best described the data, and the fitted parameters for
54 the mobile and immobile fraction were significantly different from experimentally measured
55 values.19 Ghane et al.20 proposed a non-Darcy transport model with Michaelis-Menten kinetics to
56 describe denitrification rates. The Forcheimer hydraulic model closely matched the tracer test
57 data for horizontal flow in woodchip reactor beds,21 but the Michaelis-Menten reaction kinetic
58 parameters were estimated without replicate measurements and thus should not be deemed fully
59 robust. In addition, the denitrification rates in the reactor were abnormally high with a maximum
60 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
61 woodchips were not fully aged.
62 A number of factors may explain the wide range of denitrification rates and models reported in
63 the literature. New woodchips have higher denitrification rates within the first year of operation

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64 due to the leaching of excess organic material, and after approximately one year of operation the
65 rate stabilizes.22-24 Many studies use insufficiently aged woodchips, and as a result the reported
66 rates do not reflect long-term performance. In addition, many studies have poor spatial resolution
67 along the length of the reactor or do not take replicate measurements, making the assertion of
68 trends tenuous. Temperature variation and packing density of carbon source also can
69 substantially alter denitrification rates,14,23 but wood type and grain size do not.12,15
70 The critical parameters needed to model nitrate removal in woodchip reactors are still poorly
71 understood.2 Under conditions where heterotrophic denitrification is controlled by dissolved
72 oxygen (DO), nitrate, and dissolved organic carbon (DOC) concentrations,25 a complete
73 mechanistic model of denitrification in woodchip reactors would include all three of these
74 parameters. Although a complete mechanistic model may improve understanding of the
75 processes involved in denitrification in woodchip bioreactors (WBRs), the optimal model to use
76 in practice is the most parsimonious and several simplifying assumptions may be made.
77 The objective of this work was to quantitatively evaluate mechanistic reactive transport models
78 describing denitrification in laboratory WBR columns using aged woodchips. Five models were
79 evaluated in this study. The models were calibrated using experimental data collected from
80 laboratory woodchip columns that were aged for over a year, then evaluated using sensitivity
81 analysis and a k-fold validation test. The results of this study will increase understanding of the
82 underlying mechanisms of denitrification in WBRs, while providing justification for the use of
83 the simplest model to describe WBR performance.
84 METHODS
85 Column Design

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86 Woodchips were obtained from an arborist woodchip waste pile in Portola Valley, CA. The
87 woodchips were composed of a mix of species, including California redwood (Sequoia
88 sempervirens), oak (Quercus sp.), and Douglas fir (Pseudotsuga menziesii). The woodchips were
89 dried at 50 °C for 48 hours in a drying oven then sieved to a diameter between 2-10 mm.
90 Woodchip type and particle size have been reported to have no significant effect on nitrate
91 removal rates,12,15 thus additional woodchip composition analysis was not performed.
92 Three PCV column reactor columns (10 cm ID x 50 cm) were constructed with sample ports
93 installed every 5 cm (Figure S1). For sample ports, 3.81 cm long luer-lock needles (gauge #16)
94 with ball valves were wrapped with PTFE tape and press-fit into holes drilled in the side of the
95 columns (Figure S2), allowing sampling from the center of the column. A total of 11 sample
96 ports were installed on each column. A stainless steel screen (mesh #10) was placed at the
97 bottom of each column to support the woodchips. 700 g of the dried and sieved woodchips were
98 added to each column and lightly compacted every 5 cm such that woodchips filled the column
99 to the top, corresponding to a packing density of 0.18 g cm-3. Upon completion of the
100 experiments, drainable porosity (specific yield) of the columns was determined by draining the
101 columns from the bottom over a 1-hour period, measuring the weight of the drained water, and
102 subtracting the volume of the bottom cap from the total volume drained. The woodchips were
103 then removed from the column and specific retention was determined by measuring the
104 difference between the wet and dry media after 48 hours in a drying oven at 50 °C. Total
105 porosity was determined by summing drainable porosity and specific retention.
106 Tracer Tests
107 Prior to running the experiments, linear pore-water velocity and dispersion coefficients were
108 estimated for each column with an interval-pulse bromide tracer test at a flow rate of 26 mL min-

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109 1 (described in the SI). Theoretical HRT (τ) was calculated as ߬ = V୰nୣ⁄60Q where Vr is volume
110 of the reactor (mL), ne is effective porosity (-), and Q is flow rate (mL min-1). Effective porosity
111 is the fraction of the total volume that contributes to fluid flow, and drainable porosity was used
112 as an estimate of effective porosity for the calculation of τ. Actual mean HRT (‫ ̅)ݐ‬was calculated
113 as ‫ܮ = ̅ݐ‬/߭ where L is reactor length (cm) and ν is porewater velocity (cm h-1). Hydraulic
114 efficiency, eV, of the reactor was calculated26 as ݁௩ = ‫ݐ‬⁄̅ ߬. The ideal reactor would have an eV
115 value of 1, indicating plug flow conditions. An eV value of less than 1 indicates short-circuiting,
116 while an eV value greater than 1 may indicate drainable porosity is less than effective porosity or
117 that physical retardation is occurring such as fluid entering micropores (specific retention) within
118 the woodchips.27
119 Column Experiments
120 The columns were operated at room temperature (21 °C) in up-flow mode using variable speed
121 digital peristaltic pumps (Masterflex) to maintain saturated hydraulic conditions. Each column
122 was fed artificial stormwater at a different measured flow rate (1.5 mL min-1, 3.8 mL min-1, and
123 8.4 mL min-1). The artificial stormwater matrix was composed of 0.75 mM CaCl2, 0.075 mM
124 MgCl2, 0.33 mM Na2SO4, 1 mM NaHCO3, 0.0715 mM NH4Cl, and 0.016 mM Na2HPO4,
125 representing the average concentration of major ions in urban stormwater.28 NaNO3 was added to
126 the stormwater matrix to achieve an initial nitrate concentration of 10 mg-N L-1. Columns were
127 aged for 13 months with the flowing stormwater matrix prior to conducting tracer tests and
128 column experiments. For the column experiments, all columns were exposed to three influent
129 nitrate concentrations of 11 mg-N L-1, 5 mg-N L-1, and 2 mg-N L-1. Preliminary measurements
130 showed that concentration profiles of all the columns reached steady-steady within 2-3 days

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131 following a change of influent nitrate concentration. For each concentration, the columns were
132 allowed to run for one week at the new nitrate concentration before sampling began.
133
134 Sampling and Analysis
135 The columns were sampled along the entire length for DO, nitrate, and DOC. Sampling was
136 repeated four times during a period of one week to obtain replicate measurements. Thus four
137 replicates were collected from the reactors at three different flow rates and three different
138 influent nitrate concentrations for a total of nine different conditions tested. For each sampling
139 event, samples were collected from all sample ports as well as the artificial stormwater matrix
140 tank to verify the stability of the solution. DOC and nitrate samples were collected starting at the
141 top-most sample port (at outlet) and moving downward (toward inlet) such that each sample was
142 representative of the porewater at or just above the sample port. Fifteen milliliters of sample was
143 collected in a 25 mL plastic syringe and filtered using a sterile 0.45 μm PVDF filter into a 24 mL
144 glass vial baked at 450 °C for four hours in a muffle furnace. All samples were analyzed within
145 four hours of sample collection and in random order using a random number generator. Nitrate
146 was measured using a WestCo SmartChem 200 Discrete Analyzer (detection limit: 0.05 mg-N L-
147 1). DOC was measured using a Shimadzu TOC-L Autoanalyzer. DO was measured in situ using
148 a Unisense dissolved oxygen needle probe (model DO-NP) and the Unisense SensorTrace
149 Software.
150 Model Development
151 Five models were quantitatively evaluated to describe denitrification in the experimental
152 woodchip columns. The first model evaluated was a system of one-dimensional advection
153 dispersion equations with coupled Michaelis-Menten reaction kinetics to describe the transport

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

155 chosen because similar reactive transport models have been used with success to describe
156 microbial substrate, oxygen, and nitrate uptake in porous media,29,30 contaminant degradation in
157 porous media,31,32 and denitrification in hyporheic zone sediments.33,34 The generalized model

158 for each constituent takes the form

߲‫ܥ‬௜ = ‫ܦ‬ ߲ଶ‫ܥ‬௜ − ߥ ߲‫ܥ‬௜ − ܴ௜ (1)
߲‫ݐ‬ ߲‫ݔ‬ଶ ߲‫ݔ‬

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

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

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

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

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

164 overall reaction rate. Without knowing the limiting substrate a priori, coupled Michaelis-Menten
165 kinetics is an effective method to model the overall microbial kinetics.35 The aerobic reaction

166 rate can be expressed in the form

‫ܱܥ‬
ܴை = ܺைܸை ൬‫ ܿܭ‬+ ‫ܥ‬൰ ൬‫ ݋ܭ‬+ ܱ൰ (2)
167 where RO is the rate of oxygen uptake (mg-O2 L-1 h-1), XO is the concentration of aerobic
168 heterotrophs (mg-biomass L-1), VO is the maximum uptake rate of DO (mg-O2 mg-biomass-1 h-1),
169 C is the concentration of DOC (mg-C L-1), Kc is the half-saturation constant for DOC (mg-C L-
170 1), O is the concentration of DO (mg-O2 L-1), and Ko is the half-saturation constant for DO (mg-
171 O2 L-1).

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

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

174 denitrification. This reaction rate takes the form

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ܴே = ܺே ܸே ‫ܥ‬ ‫ܥ‬൰ ܰ ܰ൰ ൬‫ܭ‬ூ‫ܭ‬+ூ ܱ൰ (3)
൬‫ ܿܭ‬+ ൬‫ܭ‬ே +

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

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

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

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

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

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

181 processes. The DOC reaction term takes the form

ܴ஼ = ߚைܺைܸை ‫ܥ‬ ‫ܥ‬൰ ܱ ܱ൰ + ߚேܺேܸே ‫ܥ‬ ‫ܥ‬൰ ܰ ܰ൰ ൬‫ܭ‬ூ‫ܭ‬+ூ ܱ൰ (4)
൬‫ ܿܭ‬+ ൬‫ ݋ܭ‬+ ൬‫ ܿܭ‬+ ൬‫ܭ‬ே +

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

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

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

185 respectively.

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

187 term for cellulose hydrolysis. Cellulose hydrolysis is the enzymatic process by which microbes
188 cleave crystalline cellulose into smaller soluble oligosaccharides.36 Cellulose in woody material

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

190 adsorption. As more cellulose is hydrolyzed, fewer binding sites are available so the DOC
191 hydrolysis rate decreases over time following a power-law function.22,37 After an initial sharp

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

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

194 reactors where reaction rates drop rapidly within the first year of operation but then stay
195 relatively constant.6,11,24 The presence of fungi in oxic zones may increase the rate of DOC

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196 release due to their ability to break down lignin, making available more cellulose to be
197 hydrolyzed.36 To account for different DOC release rates in oxic and anoxic zones, DOC release

198 kinetics are modeled using the equation

‫ܭ‬௛ = ܸ௛ଵ ܱ ܱ൰ + ܸ௛ଶ ൬‫ܭ‬ூ ‫ܭ‬ூ ܱ൰ (5)
൬‫ܭ‬ை + +

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

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

201 1 h-1). The values for KO and KI are assumed to be the same as those in the reaction rate equations

202 for DO uptake and denitrification, respectively.

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

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

205 constant within each region and fixed to surfaces so that the microbial biomass terms XO and XN
206 can be combined with VO and VN, (3) substrate and electron acceptors (O2 and NO3-) are the only

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

208 substrate is taken up by bacteria, (5) insoluble substrate mass remains relatively constant due to
209 the longevity of woodchips,16 and (6) sorption and intra-particle diffusion of DOC through

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

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

212 Dissolved Oxygen: (Model 1)

߲ଶܱ ߲ܱ ‫ܱܥ‬
0 = ‫ݔ߲ ܦ‬ଶ − ߥ ߲‫ ݔ‬− ܸை ൬‫ ܿܭ‬+ ‫ܥ‬൰ ൬‫ ݋ܭ‬+ ܱ൰

213 Nitrate:

0 = ‫ܦ‬ ߲ଶܰ − ߥ ߲ܰ − ܸே ‫ܥ‬ ‫ܥ‬൰ ܰ ܰ൰ ൬‫ܭ‬ூ ‫ܭ‬ூ ܱ൰
߲‫ݔ‬ଶ ߲‫ݔ‬ ൬‫ ܿܭ‬+ ൬‫ܭ‬ே + +

214 Dissolved Organic Carbon:

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0 = ‫ܦ‬ ߲ଶ‫ܥ‬ − ߥ ߲‫ܥ‬ − ߚைܸை ‫ܥ‬ ‫ܥ‬൰ ܱ ܱ൰ − ߚேܸே ‫ܥ‬ ‫ܥ‬൰ ܰ ܰ൰ ൬‫ܭ‬ூ‫ܭ‬+ூ ܱ൰
߲‫ݔ‬ଶ ߲‫ݔ‬ ൬‫ ܿܭ‬+ ൬‫ ݋ܭ‬+ ൬‫ ܿܭ‬+ ൬‫ܭ‬ே +

+ ܸ௛ଵ ൬‫ܭ‬ை ܱ ܱ൰ + ܸ௛ଶ ൬‫ܭ‬ூ‫ܭ‬+ூ ܱ൰
+

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

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

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

218 4.5 mg L-1. One explanation is that micropores within the woodchips create anaerobic

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

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

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

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

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

224 Nitrate: (Model 2)

߲ଶܰ ߲ܰ ‫ܰܥ‬
0 = ‫ݔ߲ ܦ‬ଶ − ߥ ߲‫ ݔ‬− ܸே ൬‫ ܿܭ‬+ ‫ܥ‬൰ ൬‫ܭ‬ே + ܰ൰

225 Dissolved Organic Carbon:

߲ଶ‫ܥ߲ ܥ‬ ‫ܰܥ‬
0 = ‫ݔ߲ ܦ‬ଶ − ߥ ߲‫ ݔ‬− ߚேܸே ൬‫ ܿܭ‬+ ‫ܥ‬൰ ൬‫ܭ‬ே + ܰ൰ + ܸ௛ଶ

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

227 denitrification is not dependent on DOC concentrations. DOC has been identified as the limiting
228 reactant in WBR denitrification.13,39 Nevertheless, a number of published denitrification models
229 ignore DOC concentrations, yet adequately fit experimental nitrate data.20,40 If denitrification in

230 WBRs is carbon limited, then C << Kc, and the term VN[C/(KC + C)] ≈ VN(C/KC). Furthermore,

231 under carbon-limiting conditions DOC concentrations may not vary substantially and (C/Kc)

232 may be combined with the uptake rates VO and VN. Model 3 takes the form

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233 Dissolved Oxygen: (Model 3)

߲ଶܱ ߲ܱ ܱ
0 = ‫ݔ߲ ܦ‬ଶ − ߥ ߲‫ ݔ‬− ܸை ൬‫ ݋ܭ‬+ ܱ൰

234 Nitrate:

0 = ‫ܦ‬ ߲ଶܰ − ߥ ߲ܰ − ܸே ܰ ܰ൰ ൬‫ܭ‬ூ‫ܭ‬+ூ ܱ൰
߲‫ݔ‬ଶ ߲‫ݔ‬ ൬‫ܭ‬ே +

235 The fourth model (Model 4) assumes both DO inhibition and DOC concentrations have little

236 impact on the denitrification rate, thus both the DO and the DOC equations are removed from

237 Model 1 and Model 4 takes the form

238 Nitrate: (Model 4)

߲ଶܰ ߲ܰ ܰ
0 = ‫ݔ߲ ܦ‬ଶ − ߥ ߲‫ ݔ‬− ܸே ൬‫ܭ‬ே + ܰ൰

239 The last model evaluated (Model 5) is a zero-order reaction rate equation commonly used to

240 describe nitrate reduction rates in WBRs:

241 Nitrate: (Model 5)

ܰ = ܰ଴ − ܸே(‫ݔ‬/ߥ)
242 where N is nitrate concentration, NO is influent nitrate concentration, VN is the zero-order

243 denitrification rate, ν is porewater velocity, and x is distance along the column. Model 5 was

244 constrained such that N ≥ 0 in order to provide a more accurate comparison between models.

245 For Models 1 through 4, the system of partial differential equations was solved at steady state
246 using the central finite-difference method in Matlab41 with a grid spacing of 1 cm. A fixed

247 concentration (Dirichlet-type) boundary condition was used at the inlet (i.e., C(0) = C0), and an
248 advection transport (Neumann-type) boundary condition was used at the effluent (i.e., dC/dx =

249 0).

250

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251 Model Evaluation and Parameter Estimation
252 A maximum of ten unknown parameters needed to be estimated through inverse modeling (i.e.,
253 Model 1). The maximum, minimum, and median values for the microbial model parameters were
254 determined from a review of the denitrification literature for wastewater and environmental soils
255 (Table 1).
256

257 Table 1. Maximum, minimum, and median value of microbial kinetic parameters for
258 denitrification and aerobic respiration.

Parameter Range Units Reference

VO 1.0-20 (10.0) mg-O2 L-1 hr-1 33, 42-45

VN 0.05-2.0 (0.5) mg-N L-1 hr-1 9, 14, 24, 39

KO 0.05-0.2 (0.1) mg-O2 L-1 33, 35, 43, 44, 46, 47

KN 0.05-1.0 (0.2) mg-N L-1 33, 35, 46, 48, 49

KC 0.1-3.0 (1.0) mg-C L-1 33, 35, 42, 43, 47

KI 0.01-0.3 (0.1) mg-O2 L-1 33, 35, 42, 43, 47

Vh1 0.1-2.5 (1.0) mg-C L-1 hr-1 14, 22, 37

Vh2 0.05-0.5 (0.1) mg-C L-1 hr-1 14, 22

BO 0.038-0.375 (0.188) mg-C mg-O2-1 35

BN 0.107-1.07 (0.54) mg-C mg-N-1 35

259

260 A sensitivity analysis was performed on all the models using the Morris Method to reduce the

261 number of parameters to be estimated by inverse modeling (described in the SI). Parameters

262 determined to be insensitive were fixed at the most common value reported in the literature

263 (Table 3).

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264 The root-mean-squared error (RMSE) was used as the objective function to evaluate model
265 performance. RMSE was calculated as follows:

ܴ‫ܧܵܯ‬ = ඨ ∑௡௜ ∑௠௫ (‫ܥ‬መ௜,௫ − ‫ܥ‬௜,௫ )ଶ (6)
݊×݉

266 where Ĉi,x is the predicted concentration of the ith species (DO, nitrate, and DOC) at sample

267 point x, and Ci,x is the measured concentration of the ith species at sample point x, n is the

268 number of species, and m is the number of sample points per column. Parameter estimation was
269 performed using the fmincon() function in Matlab.41 Fmincon() is a constrained nonlinear
270 optimization algorithm that uses a sequential quadratic programming method.50 The algorithm

271 finds the set of parameters within a trust-region specified by the user that minimizes the

272 objective function. The upper and lower bounds of the trust region used for each model

273 parameter are listed in Table 3.
274 Model performance was evaluated using a k-fold cross validation test.51,52 Five folds were

275 chosen so that at least seven of the data sets were used to train the model, and either one or two

276 datasets were used to test the model. Each model was then parameterized using all the data sets

277 and plotted against the experimental data to validate goodness-of-fit.

278 RESULTS AND DISCUSSION

279 Tracer Tests

280 Hydraulic properties of the columns determined from the drainage and tracer tests are

281 presented in Table 2. The average column porosities were 0.54 ± 0.04 for drainable porosity,

282 0.33 ± 0.02 for specific retention, and 0.87 ± 0.03 for total porosity. Hydraulic efficiency in the

283 experimental columns ranged from 1.4 to 1.6 (Table 2). One possible cause for eV > 1 is that τ
284 was underestimated by using drainable porosity instead of true effective porosity. Tracer tests in

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285 other WBRs have revealed that drainable porosity underestimated effective porosity, with eV
286 values (1.3 – 2.1) similar to those reported in this study.11,27 Effective porosity for columns 1-3
287 using the tracer data was calculated to be 0.81, 0.85, and 0.78, respectively. These values
288 approach the measured total porosity. Cameron and Schipper27 suggested that effective porosity
289 within WBRs is composed of both the mobile (drainable porosity) and immobile (specific
290 retention) phase, with fluid moving in and out of the media particle, whereas Ghane et al.20
291 suggested that physical (reversible) retardation might be responsible for the higher than expected
292 residence times. At present, there is insufficient evidence to suggest which hypothesis is correct.
293 For the purposes of this study, we assumed that flow through the columns was adequately
294 modeled using the advection and dispersion terms as determined from the tracer tests.
295
296 Table 2. Measured hydraulic properties of the experimental woodchip bioreactor columns as
297 determined by the bromide tracer tests.

Column Drainable Specific Total Q τ νD ‫̅ݐ‬ eV
Por. Ret. Por. (h) (h) (-)
(mL (cm (cm2
(-) (-) (-) min-1) h-1) h-1) 1.6
1.5
1 0.50 0.34 0.84 1.5 21.8 1.4 3.4 35.7 1.4

2 0.56 0.31 0.87 3.8 9.6 3.4 11.2 14.7

3 0.57 0.33 0.90 8.4 4.4 8.2 24.1 6.1

298

299 Column Experiments
300 Nitrate removal rates in the experimental columns ranged from 0.10 to 0.16 mg-N L-1 h-1, with
301 an average removal rate (mean ± SD) of 0.13 ± 0.02 mg-N L-1 h-1 (Table S2, Figure 1). This
302 corresponds to a removal rate of 2.53 ± 0.39 g-N m-3 media d-1 using an average effective
303 porosity of 0.81, which is at the lower end of rates reported (1-20 g-N m-3 media d-1) for long-

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304 term field trials at temperatures of 2-20 °C with similar media.6 Van Driel et al.12 reported
305 reaction rates of 1.5-3.4 g-N m-3 media d-1 for coarse woodchip media at 13 °C in field reactors
306 with an effective porosity of 0.7. At temperatures of 21-23.5 °C, Robertson11 reported removal
307 rates of 6.4-8.5 g-N m-3 media d-1 in laboratory reactors using aged woodchips with an effective
308 porosity of 0.67. The larger effective porosity of the columns used in this study may explain the
309 lower nitrate removal rates. DOC concentrations in all the experimental conditions averaged 1.0
310 ± 0.5 mg-C L-1 and never exceeded 2.7 mg-C L-1 (Figure S4). Mean DOC concentrations only
311 increased above 2 mg-C L-1 where nitrate concentrations dropped below 0.5 mg-N L-1 mid-
312 column (Figures 1.a and S4.a). Robertson11 similarly found that DOC concentrations in
313 woodchip columns increased significantly only after nitrate was depleted to less than 1 mg-N L-1.
314 The slope of DOC concentrations over the column length for all conditions tested was
315 significantly different from zero (p < 0.005), but no correlation was observed between the DOC
316 production rate and nitrate removal rate for each experimental condition (p = 0.95; Table S2).
317 DO was depleted in the columns within 1-3 hours based on HRTs, or within the first 5-10 cm
318 of the columns (Figure S5). For the column with a porewater velocity of 7.1 cm hr-1, DO was
319 exhausted within the first 5-10 cm of the column (Figures S5.c, S5.f, S5.i). In the lower-flow
320 columns, DO was consumed within 5 cm or less (Figure S5). Gibert et al.53 similarly found a
321 decrease in DO from 4 to 1.2 mg L-1 within the first 10 cm of a 90 cm column. DO
322 concentrations between 1.7-3.7 mg L-1 reportedly did not inhibit denitrification in woodchip
323 columns.13,54 However, due to the rapid consumption of DO in the experimental columns, it was
324 not possible to spatially decouple denitrification within micropores from the bulk fluid. The
325 micropore hypothesis may hold true for woodchip reactors, but additional research is needed.
326

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327
328 Model Evaluation and Parameter Estimation
329 The sensitivity analysis indicated that the most sensitive parameters were not consistent across
330 the models, but the least sensitive parameters were consistently the Michaelis-Menten half
331 saturation constants KO and KN, and the oxygen inhibition constant, KI (Table 3). This suggests
332 that using Michaelis-Menten kinetics to describe oxygen and nitrate degradation has little impact
333 on model performance for the conditions tested. One explanation for this phenomenon is that the
334 range of values for these parameters applies to only a small fraction of the data collected. For
335 example, DO is consumed rapidly in the columns with 70% of the DO measurements less than
336 0.5 mg L-1. The inhibition constant KI and the half-saturation constant KO only influence DO
337 concentration predictions in the first 5-10% of the columns, and thus have a relatively small
338 impact on the overall model accuracy. Similarly, the nitrate half-saturation constant, KN, is
339 limited to the range 0.01 – 1.0 mg-N L-1, but over 90% of the data has N concentrations greater
340 than 1 mg-N L-1.
341
342 Table 3. Estimated parameter values and parameter sensitivity indices for each model.

Model Parameter Estimate Sen. Index
Model 1 Vh1 2.5 1.112
(NO3-, DO, VO 20.0 0.975
& DOC) BO 0.12 0.901
Vh2 0.10 0.893
BN 0.49 0.476
KC 0.11 0.419
VN 0.17 0.291

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KI 0.1* 0.050
KN 0.2* 0.031
KO 0.1* 0.025

Model 2 Vh2 0.11 2.854
(NO3- BN 0.51 1.400
& DOC) VN 0.17 0.658
KC 0.10 0.434
KN 0.2* 0.066

Model 3 VN 0.15 2.202
(NO3- VO 16.54 0.306
& DO) KN 0.05 0.172
KI 0.1* 0.086
KO 0.1* 0.017

Model 4 VN 0.14 3.767
(NO3-) KN 0.05 0.298

Model 5 VN 0.13 3.839
(0 order)

343 Parameter estimates marked with ‘*” were insensitive, and fixed at the literature value. For
344 estimated values, units are the same as those listed in Table 1.

345

346 The k-fold validation test revealed that all of the models predicted nitrate concentrations with

347 similar median test RMSE (Figure 2, Table S3), and an ANOVA test found no significant

348 difference between the mean RMSE values of the different models (p = 0.886). Additionally,

349 there was no significant difference in RMSE values between the models for predicted DO (p =

350 0.682) and DOC (p = 0.937) concentrations. Model 1 (full model) may provide a more

351 mechanistic understanding of denitrification processes in woodchip reactors when nitrate, DO,

352 and DOC are considered, but may be unnecessarily complex when only nitrate concentrations are

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353 of interest. There is a direct relationship between model complexity and model error due to
354 variance.55 Given no significant difference in mean error between the models, the zero-order
355 model is preferred under the conditions tested because it is the least parameterized. Under
356 conditions not tested in this study (e.g., variable temperature), a more parameterized model may
357 predict nitrate concentrations with less error.
358 There are several possible explanations for why the zero-order model had similar prediction
359 error compared to the more complex models. First, DO inhibition may have a relatively minor
360 effect on denitrification rates in WBRs. Although DO may inhibit nitrate removal, DO is present
361 in a relatively small fraction of the column (< 10%) such that DO inhibition has little impact on
362 the overall nitrate removal rate. As HRT decreases, presumably DO will be present in an
363 increasingly larger fraction of the reactor and inhibition will introduce significant error to the
364 models that do not explicitly consider DO concentrations. Second, DOC concentrations also
365 appear to have a minor impact on nitrate removal rates. DOC concentrations increased along the
366 columns for all conditions tested, but no significant correlation between nitrate removal rates and
367 DOC production rates was observed (p = 0.95; Table S2). One possible explanation is that the
368 DOC released from woodchips is composed of a biodegradable and non-biodegradable fraction,
369 and the increasing DOC concentrations may represent the non-degradable fraction of DOC
370 accumulating in the column. This would also explain why DOC concentrations could be greater
371 than KC but the system is still carbon limited. Mean DOC concentrations only rose above 2 mg L-
372 1 (Figure S4.a) for the low flow/low influent nitrate test condition (N0 = 2 mg-N L-1, ν = 1.4 cm
373 h-1), where nitrate concentrations dropped below 0.5 mg-N L-1 mid-column (Figure 1.a). In
374 experimental conditions with the same flow rate but higher influent nitrate concentrations, mean
375 DOC concentrations remained below 2 mg L-1 (Figures S4.d and S4.g). The increase in DOC

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376 concentrations was likely caused by the release of unutilized degradable DOC once nitrate
377 became the limiting reactant. Lastly, the half-saturation constants, KO and KN, and the inhibition
378 constant, KI, were insensitive for all models, suggesting that modeling solute degradation with
379 Michaelis-Menten kinetics is unnecessary. When KN was explicitly estimated for Model 4, the
380 optimal value of 0.05 mg-N L-1 (Table 2) essentially transformed the Michaelis-Menten term into
381 a zero-order reaction rate.

a) 3 b) 3 c) 3
2
NO-3 (mg-N L-1) Model 1 1

Model 2

2 Model 3 2

Model 4

Model 5

11

0 0 0 10 20 30 40 50
0 10 20 30 40 50 0 10 20 30 40 50 0

d) 6 e) 6 f) 6

NO-3 (mg-N L-1) 444

222

0 0 0 10 20 30 40 50
0 10 20 30 40 50 0 10 20 30 40 50 0

g)12 h)12 i) 12

NO-3 (mg-N L-1) 10 10 10

888

666
0 10 20 30 40 50 0 10 20 30 40 50 0 10 20 30 40 50

382 Distance (cm) Distance (cm) Distance (cm)

383 Figure 1. Calibrated models (colored lines) plotted against column nitrate profile data (blue dots)

384 for each experimental run. The conditions for each plot are: a) N0 = 2 mg-N L-1, ν = 1.4 cm hr-1,

385 b) N0 = 2 mg-N L-1, ν = 3.4 cm hr-1, c) N0 = 2 mg-N L-1, ν = 8.2 cm hr-1, d) N0 = 5 mg-N L-1, ν =

386 1.4 cm hr-1, e) N0 = 5 mg-N L-1, ν = 3.4 cm hr-1, f) N0 = 5 mg-N L-1, ν = 8.2 cm hr-1, g) N0 = 11
387 mg-N L-1, ν = 1.4 cm hr-1, h) N0 = 11 mg-N L-1, ν = 3.4 cm hr-1, i) N0 = 11 mg-N L-1, ν = 8.2 cm

388 hr-1.

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0.8RMSE
0.6
0.4-
0.23

0O

0.5N
0.4
0.3DOC RMSE DO RMSE
0.2
0.1
0.5
0.4
0.3
0.2

389 Model 1 Model 2 Model 3 Model 4 Model 5
390 Figure 2. Results of the k-fold validation test for each model. RMSE values are plotted by

391 species. The red line shows the median RMSE value, the blue box shows the first and third

392 quartiles, and the whiskers show the maximum and minimum values.

393 Under certain test conditions, the zero-order model appeared to either under-estimate nitrate

394 concentrations (Figures 1.a, 1.b, and 1.g), or over-estimates nitrate concentrations (Figures 1.d

395 and 1.h). When the zero order model was rearranged as ܰ଴ − ܰ = ܸே‫ ̅ݐ‬and ܰ଴ − ܰ was plotted
396 versus ‫ ̅ݐ‬for all the data where N > 2 mg-N L-1, these model biases were less apparent (Figure 3),

397 with residuals from the zero-order model not significantly different from a normal distribution (p

398 > 0.139; Table S4). However when all data were included, the residuals were significantly

399 different from a normal distribution (p < 0.001; Table S4). This suggests an alternative model

400 may be more appropriate when nitrate concentrations are less than 2 mg-N L-1. Robertson11 and

401 Warneke et al.56 similarly found zero-order rates apply to nitrate removal in WBRs aged over

402 two years, until nitrate is depleted to less than 1 mg-N L-1.

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403

5

4

N - N (mg-N L-1) 3

O 2

1

0

404 -1
0 5 10 15 20 25 30 35 40
HRT (h)

405 Figure 3. Concentration of nitrate removed (N0 – N) along the length of the column for data

406 where N > 2 mg-N L-1 (black diamonds) and the zero-order model (red line) versus HRT for all

407 conditions tested.

408 In some cases, modeling DO or DOC concentrations in WBRs may be desirable. For example
409 in applications with low influent nitrate concentrations or low HRTs, DO inhibition may impact
410 the overall nitrate reduction rate and DO concentrations could be included to increase model
411 accuracy. WBRs with large retention times and N-limiting conditions resulted in sulfide
412 formation and methyl mercury production,57,58 increased methane emissions,7,56 and increased
413 DOC export to receiving waters.6,11 Modeling effluent DOC concentrations may also be
414 important to predict and mitigate the harmful effects of DOC export from WBRs. The most
415 appropriate model therefore depends on the species of interest. If DOC and nitrate are of interest,
416 Model 2 may be selected. If only DO and nitrate are of interest, Model 3 may be selected. Future
417 research could include SO42- transport in the coupled model to estimate the formation of H2S.
418 Environmental Implications

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419 Assuming the use of aged woodchips (> 1 year of saturated conditions) and constant
420 temperature conditions, a zero-order model provided equally robust prediction of nitrate
421 concentrations using the least number of input parameters. An important implication of a zero-
422 order model is that the HRT controls reaction rates. For vertical flow systems, such as
423 stormwater infiltration basins or vertical flow wetlands, calculating the HRT may be
424 accomplished using tracer data to determine ν and D. For horizontal flow reactor beds such as
425 those used in agricultural runoff, determining the HRT can be much more complex. Horizontal
426 flow agricultural woodchip reactors experience fluctuating flow rates and saturation levels,59
427 which means the saturated volume is constantly changing. Additionally, flow in woodchip media
428 is not always laminar and Darcy’s Law may not apply.21 The Forchheimer equation proposed by
429 Ghane et al.21 is a promising method to describe flow in woodchip reactor beds; however, further
430 research is needed to characterize residence time in woodchip reactor beds for a wide range of
431 flow rates and saturation levels.
432 Other than residence time, a number of other factors may explain the wide range of nitrate
433 removal rates reported in the literature. Denitrification rates in WBRs are highly dependent on
434 temperature.13,14,23 Temperature alone explained 50% of the variability in a multi-parameter
435 study investigating woodchip denitrification rates, with other parameters including wood type,
436 wood grain size, surface area, and cellulose content.14 Although temperature variability was not
437 taken into account in this study, the zero-order model can be modified to include the effects of
438 temperature using a Van’t Hoff-Arrhenius function.17,20 Further research will determine whether
439 a zero-order model is appropriate over a range of environmentally relevant temperatures. DO
440 inhibition may become more significant at temperatures below 21 °C, both because DO has a
441 higher saturation at lower temperatures and the aerobic respiration rate may slow whereby DO

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442 inhibition may then influence the reaction. At temperatures above 21 °C, DOC production may
443 increase and the reaction may shift from carbon-limited to nitrate-limited.
444 Woodchip age may have a substantial impact on nitrate removal rates. A study of a 15-year-old
445 field reactor measured a 50% drop in reaction rates after the first year,16 and a meta-analysis of
446 WBRs by Addy et al.23 determined that beds less than 13 months of age had significantly higher
447 nitrate removal rates than those 13 months and older. However, after the first year of operation,
448 nitrate removal rates stabilize.9,10 This phenomenon was also observed in the woodchip columns
449 used in this study, but woodchips in the field are unlikely to age as evenly since saturation levels
450 in the reactors are constantly changing due to fluctuating flow rates. As a result, woodchips at the
451 bottom of a reactor age faster than those at the top.7 The uneven aging of woodchips may affect
452 the overall nitrate reduction rate of a field reactor, and should be taken into account. The models
453 in this study were only applied to woodchips saturated for over one year, which may represent
454 several years of actual field conditions. Modeling efforts can be expanded to incorporate how
455 saturation time affects nitrate removal rates. Lastly, packing density may be another important
456 factor. The packing density used in this study (180 kg m-3) was in the lower range of typical
457 WBRs60 using oven-dried woodchips (190-240 kg m-3). This may have caused lower nitrate
458 removal rates than what may be achieved in more densely packed reactors. Data presented by
459 Schmidt and Clark14 suggest that denitrification rates may be linearly correlated with the volume
460 of wood present in the column, but further research should be conducted to substantiate those
461 results.
462

463
464 ASSOCIATED CONTENT

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465 Supporting Information. The following files are available free of charge.
466 Figure of experimental setup, explanation of bromide tracer test and results, explanation of
467 sensitivity analysis, and figures of DO and DOC profile concentrations (PDF).

468 AUTHOR INFORMATION
469 Corresponding Author
470 *Phone: 650-721-2615; fax: 650-725-9720; e-mail: [email protected]

471 Funding Sources
472 This research was funded by the National Science Foundation Engineering Research Center Re-
473 inventing the Nation’s Urban Water Infrastructure (ReNUWIt) (NSF Grant Number CBET-
474 0853512) and the Water Environment Research Foundation (WRF Project Number 4567, EPA
475 Agreement Number RD-83556701)

476 ACKNOWLEDGMENTS
477 This work was supported by the National Science Foundation Engineering Research Center: Re-
478 inventing the Nation’s Urban Water Infrastructure (ReNUWIt) and the Water Research
479 Foundation through the Water Environment Research Foundation. We thank Chloe Cheok for
480 her help with collection and analysis of lab samples.

481 ABBREVIATIONS
482 WBR, woodchip bioreactor; DO, dissolved oxygen; DOC, dissolved organic carbon; HRT,
483 hydraulic residence time; RMSE, root-mean-squared error.

484

485 REFERENCES

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