Laurent André

Hélène Pauwels

Marie Christine Dictor

Marc Parmentier

Mohamed Azaroual

Laurent Andre
email: l.andre@brgm.fr

Experiments and Numerical Modelling of Microbially-Catalysed Denitrification Reactions

Keywords: denitrification, thermodynamic driving force, kinetics, micro-organisms

come

Introduction

Groundwater nitrate (NO 3 -) concentrations exceed human health criteria in many places as a result of anthropogenic inputs such as industrial emissions and synthetic fertilizers and manure used in agriculture [START_REF] Squillace | VOCs, pesticides, nitrate, and their mixtures in ground-water used for drinking water in the United States[END_REF][START_REF] Mccallum | Mixing-induced groundwater denitrification beneath a manured field in southern Alberta, Canada[END_REF]and references therein). Nitrate is now very commonly found in groundwater in Europe and North America [START_REF] Matĕjů | Biological water denitrification -A review[END_REF][START_REF] Rivett | Nitrate attenuation in groundwater: A review of biogeochemical controlling processes[END_REF]. This creates environmental problems and has even led to the halting of pumping in many well fields. Techniques to decrease nitrate concentrations include ion exchange, reverse osmosis and biological denitrification [START_REF] Matĕjů | Biological water denitrification -A review[END_REF]. Denitrification (or dissimilatory nitrate reduction) is recognised as being an efficient natural microbially-mediated nitrogen removal process in soils and waters [START_REF] Dahab | Treatment alternatives for nitrate contaminated groundwater supplies[END_REF][START_REF] Rivett | Nitrate attenuation in groundwater: A review of biogeochemical controlling processes[END_REF][START_REF] Aelion | Low sulfide concentrations affect nitrate transformations in freshwater and saline coastal retention pond sediments[END_REF]. Indeed, groundwater nitrate can be attenuated by denitrification processes that reduce NO 3 -according to a series of reactions mediated by micro-organisms under anaerobic conditions [START_REF] Knowles | Denitrification[END_REF][START_REF] Tavares | Metalloenzymes of the denitrification pathway[END_REF][START_REF] Rivett | Nitrate attenuation in groundwater: A review of biogeochemical controlling processes[END_REF]:

0 2 I 2 II 2 III 3 V N O N O N O N O N      
This has been widely observed in natural environments such as wetlands [START_REF] Bowden | The biogeochemistry of nitrogen in freshwater wetlands[END_REF][START_REF] Whitmire | Rapid removal of nitrate and sulfate in freshwater wetland sediments[END_REF][START_REF] Scott | Denitrification, dissimilatory nitrate reduction to ammonium, and nitrogen fixation along a nitrate concentration gradient in a created freshwater wetland[END_REF], hyporheic zones [START_REF] Duff | Denitrification in sediments from the hyporheic zone adjacent to a small forested stream[END_REF][START_REF] Jones | Nitrification in the hyporheic zone of a desert stream ecosystem[END_REF][START_REF] Sheibley | Numerical modeling of coupled nitrification-denitrification in sediment perfusion cores from the hyporheic zone of the Shingobee River[END_REF] and shallow and deep aquifers [START_REF] Lovley | Deep subsurface microbial processes[END_REF][START_REF] Pauwels | Field tracer test for denitrification in a pyrite-bearing schist aquifer[END_REF][START_REF] Pauwels | The fate of nitrogen and sulfur in hard-rock aquifers as shown by sulfate-isotope tracing[END_REF][START_REF] Pinay | Nitrogen Control by Landscape Structures[END_REF][START_REF] Molénat | Mechanisms of nitrate transfer from soil to stream in an agricultural watershed of French Brittany[END_REF][START_REF] Ruiz | Effect on nitrate concentration in stream water of agricultural practices in small catchments in Brittany: I. Annual nitrogen budgets[END_REF]. Denitrification, with either heterotrophic [START_REF] Her | Influence of carbon source and C/N ratio on nitrate/nitrite denitrification and carbon breakthrough[END_REF][START_REF] Aslan | Combined removal of pesticides and nitrates in drinking waters using biodenitrification and sand filter system[END_REF] or autotrophic bacteria [START_REF] Koenig | Kinetic model of autotrophic denitrification in sulphur packedbed reactors[END_REF][START_REF] Park | Biological nitrate removal in industrial wastewater treatment: which electron donor we can choose[END_REF], is also used to treat drinking water.

All of these nitrate bioremediation processes use denitrifying bacteria, which, like other micro-organisms in soil, water, sediments and oceans, play a major role in the biogeochemical cycles of major and trace elements (carbon, nitrogen, sulphur, phosphorus, iron, mercury, selenium, arsenic, etc.) [START_REF] Dommergues | Ecologie microbienne du sol[END_REF][START_REF] Stevenson | Cycles of soil: carbon, nitrogen, phosphorus, sulfur, micronutrients. 2 nd Edition[END_REF][START_REF] Madigan | Brock Biology of Microorganisms[END_REF][START_REF] Ehrlich | Geomicrobiology[END_REF]. Most of these bacteria are able to use the energy of redox reactions to proliferate under aerobic or anaerobic conditions [START_REF] Decker | Energy production in anerobic organism[END_REF][START_REF] Mitchell | Coupling of phosphorylation to electron and hydrogen transfer by a chemiosmotic type of mechanism[END_REF]. They act as a catalyst for reactions in which electrons are transferred from a donor to an acceptor species. This microbial activity also links electron transfer to proton transfer through the cell membrane, enabling the synthesis of adenosine triphosphate (ATP) from adenosine diphosphate (ADP) and intracellular phosphate ions (P i ). However, this reaction occurs only if the energy of the corresponding redox reaction is high enough to provide the energy for bacterial metabolism as an excess enthalpy [START_REF] Jin | Kinetics of electron transfer through the respiratory chain[END_REF].

Bacterial behaviour in natural aqueous systems is therefore closely linked to redox reactions [START_REF] Lindberg | Ground water redox reactions: an analysis of equilibrium state applied to Eh measurements and geochemical modelling[END_REF][START_REF] Keating | Reactive transport modeling of redox geochemistry: Approaches to chemical disequilibrium and reaction rate estimation at a site in northern Wisconsin[END_REF][START_REF] Michard | Chimie des eaux naturelles. Principe de Géochimie des Eaux[END_REF].

These observations highlight the connexions between chemical and biological processes and the need to take into account a coupled thermodynamic/kinetic approach in order to accurately predict the global behaviour of such systems. Many theoretical and empirical approaches have been developed to describe biogeochemical processes. These include the enzyme reaction kinetic model proposed by [START_REF] Michaelis | Die Kinetik der Invertinwirkung[END_REF] and the bacterial growth kinetics model proposed by [START_REF] Monod | The growth of bacterial cultures[END_REF]. The latter is used most often to describe the relationship between bacterial growth and substrate concentration [START_REF] Rittmann | Environmental Biotechnology: Principles and Applications[END_REF]. This approach, while very successful for batch systems, has significant limitations. It is suitable for irreversible reactions and conditions far from thermodynamic equilibrium where chemical energy is not a limiting factor [START_REF] Curtis | Comparison of approaches for simulating reactive solute transport involving organic degradation reactions by multiple terminal electron acceptors[END_REF][START_REF] Jin | The thermodynamics and kinetics of microbial metabolism[END_REF][START_REF] Torres | A kinetic perspective on extracellular electron transfer by anode-respiring bacteria[END_REF]. It cannot, however, correctly predict reaction rates when substrate concentrations drop below a substrate threshold value [START_REF] Lovley | Minimum threshold for hydrogen metabolism in methanogenic bacteria[END_REF][START_REF] Cord-Ruwisch | The capacity of hydrogenotrophic anaerobic bacteria to compete for traces of hydrogen depends on the redox potential of the terminal electron acceptor[END_REF][START_REF] Giraldo-Gomez | Influence of mass transfer limitations on determination of the half saturation constant for hydrogen uptake in a mixed-culture CH 4 -producing enrichment[END_REF]. Like other empirical rate laws, it does not consider that, close to thermodynamic equilibrium, there is not enough available energy to meet the needs of micro-organisms for microbial metabolism, maintenance and other cellular functions [START_REF] Jin | The thermodynamics and kinetics of microbial metabolism[END_REF].

Because of the large number and the complexity of the elementary mechanisms involved, the numerical modelling of these processes requires the use of powerful and relevant theoretical approaches in the calculation codes. To enable us to progress in our understanding of the biogeochemical behaviour of ecosystems, robust numerical tools must consider not only chemical and thermodynamic processes (i.e. Gibbs free enthalpy of the redox reactions), but also biological phenomena (i.e. bacterial growth). Among the various patterns proposed to simulate these coupled processes, that of [START_REF] Jin | A new rate law describing microbial respiration[END_REF][START_REF] Aslan | Combined removal of pesticides and nitrates in drinking waters using biodenitrification and sand filter system[END_REF][START_REF] Jin | The thermodynamics and kinetics of microbial metabolism[END_REF] appears to be the most comprehensive because it considers both the chemical characteristics of the system (through electron donor/acceptor concentrations) and thermodynamic conditions (through the Gibbs free enthalpy of the redox reactions involved), which are the driving forces of the biogeochemical processes. The suitability of this approach (thereafter called "the Jin and Bethke approach‖) and the role of the thermodynamic potential factor have been demonstrated for degradation processes with the thermodynamic control of the respiration rate during arsenate reduction [START_REF] Jin | A new rate law describing microbial respiration[END_REF], methanogenesis or sulfate reduction [START_REF] Jin | Predicting the rate of microbial respiration in geochemical environments[END_REF]. In these examples, the respiration process is expected to cease, even if significant amounts of both electron donors and acceptors are still available for metabolization. The role of thermodynamics has also been described concerning the progress of enzymatic reactions like benzoate, crotonate and glucose fermentations [START_REF] Jin | The thermodynamics and kinetics of microbial metabolism[END_REF].

Because denitrification is a complex process mediated by micro-organisms, this coupled thermokinetic/biogeochemical approach would seem to be highly suitable for simulating the biogeochemical reactions occurring between nitrate and electron donors in water. Such a model could be useful for the management of natural environments, particularly to estimate denitrification rates in groundwater for long-term groundwater protection or for the implementation of corrective measures to decrease the impact of diffuse sources. We describe here a versatile model that does not oversimplify the biogeochemical system (overall reaction of nitrate to N 2 ) and is suitable for denitrification catalyzed by different microbial consortia.

This model includes a multi-step denitrification process that enables better control of the numerous thermokinetic parameters involved by considering all reaction products. This model tests the suitability of the Jin and Bethke approach for each individual mechanism (the -driving forces‖ of each process). It defines the limiting and weight parameters and we use it to investigate how natural consortia influence the dynamics of denitrification. The model also enables integration of different microbial communities having specific influence on denitrification process. This model allows for evaluation of the relationship between anabolism and catabolism for the heterotrophic micro-organisms under consideration and it enables estimation of the fraction of denitrification that is caused by autotrophic and/or heterotrophic bacteria. This work is based on laboratory denitrification experiments (batch and packed bed column done with inoculum from groundwater that contains both heterotrophic and autotrophic bacteria), and yields numerical simulations of the biogeochemical reactions involved in the denitrification processes. Its objectives were to (i) identify the main steps that control the kinetic rate of the denitrification process, (ii) highlight an approach using both batch and flow-through column experiments, (iii) characterize the role played by micro-organisms during each reaction, and (iv) develop a comprehensive biogeochemical model of denitrification.

Experiments and Modelling

Experimental approach

Choice of experimental conditions

Denitrification experiments conducted in this study were done with water and rock samples collected in the Coët-Dan catchment, 70 km SW of Rennes (Brittany), in western France, where low nitrate concentrations in groundwater have been attributed to advanced denitrification mechanisms [START_REF] Pauwels | Temporal variability of nitrate concentration in a schist aquifer and transfer to surface waters[END_REF][START_REF] Pauwels | The fate of nitrogen and sulfur in hard-rock aquifers as shown by sulfate-isotope tracing[END_REF]. The presence of pyrite in the aquifer rock contributes to a high-rate denitrification reaction [START_REF] Pauwels | Field tracer test for denitrification in a pyrite-bearing schist aquifer[END_REF] mediated by autotrophic bacteria according to the simplified reaction:

5 FeS 2 + 14 NO 3 -+ 4 H + → 7 N 2 + 10 SO 4 2-+ 5 Fe 2+ + 2 H 2 O (1)
Heterotrophic denitrification involving organic matter has, however, also been reported [START_REF] Pauwels | Temporal variability of nitrate concentration in a schist aquifer and transfer to surface waters[END_REF][START_REF] Pauwels | Nitrates concentration in wetlands: assessing the contribution of different water bodies from anion concentrations[END_REF].

Groundwater was collected with a submersible pump and stored in a sterile vessel after three well volumes of water had been purged. The well enabled the collection of water at a depth between 7 and 15 ma redox zone where there is denitrification [START_REF] Pauwels | Temporal variability of nitrate concentration in a schist aquifer and transfer to surface waters[END_REF].

Aliquots were filtered through 0.45 µm pore size for chemical analysis. The bacterial analysis done on a raw groundwater sample with the -Most Probable Number‖ method [START_REF] Halvorson | Applications of statistics to problems in bacteriology. I. A means of determining bacterial population by the dilution method[END_REF]) confirmed the presence of (i) heterotrophic denitrifying bacteria, (ii) Thiobacillus denitrificans (about 2,500 cells mL -1 ) and (iii) Acidithiobacillus ferrooxidans (fewer than 0.5 cells mL -1 ). Most of the population is able to reduce nitrate to nitrite (about 5,870 cells mL -1 ), whereas only a small fraction is able to reduce nitrate to N 2 (about 130 cells mL -1 ).

Only heterotrophic denitrification was considered for batch experiments, whereas by using schist, both heterotrophic and autotrophic processes were involved during the flow-through column experiment. Experiments were done in the presence of acetate (model organic compound). This enabled us to break down the global mechanism and quantify the kinetics of the various denitrification steps (Eqs. 2 to 4).

) 4 ( 2 1 2 1 4 1 4 1 : 3 ) 3 ( 2 1 2 1 4 5 4 1 : 2 ) 2 ( 2 1 2 1 4 1 4 1 : 1 2 ) ( 2 2 3 2 2 ) ( 2 2 3 2 2 ) ( 2 2 3 3 O H CO N H COO CH O N Step O H CO O N H COO CH NO Step O H CO NO H COO CH NO Step aq aq aq                        

Batch experiments

Batch assays were done in glass serum flasks (500 mL) supplemented with 150 mL (biotic flasks) or 300 mL (abiotic flasks) of sampled groundwater (Table 1). The headspace was flushed with CO 2 gas to remove oxygen from the flasks. CO 2 was chosen instead of N 2 or CO 2 + N 2 mixtures in order to avoid a secondary nitrogen source in a nitrogen-enriched medium. The flasks were sterilised by autoclaving at 120 °C for 20 minutes. The biotic flasks were inoculated with 150 mL of non-sterile groundwater. Six flasks were prepared -3 biotic flasks and 3 abiotic flasks. Ten millilitres (10 mL) of a 3,000-mg KNO 3 L -1 solution were added to the medium to give a final concentration of 50 mg NO 3 -L -1 and 50 mL of a 1476.4mg Na 2 CH 3 COO L -1 solution were added to give a final concentration of 50 mg acetate L -1 . A trace-element solution (0.25 mL) containing the following, in mg L -1 , was added to this: Water and gas samples were collected at regular intervals to monitor the reaction.

Flow-through column experiment

Denitrification was studied in a glass column (0.45 L) equipped with an external water jacket that maintained the temperature at 14 °C throughout the experiment (Fig. 1). The column had an internal diameter of 3.5 cm and was 32 cm high. It was packed with 599.3 g of crushed schist (200 µm, see Table 2 for mineralogical assemblage) and sterilised 3 times at 24-hour intervals by autoclaving for 1 hour at 121 °C.

After sterilisation, the column was inoculated with a denitrifying bacteria consortium specially prepared for this experiment. The enrichment culture, prepared with a groundwater sample, was made up in sterile 500 mL serum flasks containing a culture medium composed of 150 mg L -1 of KNO 3 , 5.66 mg L -1 of Na-acetate and 1 mL of the trace-element solution described above. The pH of the medium was adjusted to 6.5 with a 1 molar H 2 SO 4 solution.

The serum flasks were then flushed with N 2 gas to ensure anaerobic conditions. The enrichment culture was incubated for 3 weeks at 14 ± 2 °C. Aliquots were sampled periodically to monitor bacterial growth and the nitrate concentration in the flask.

The experiment was done with synthetic water prepared with chemicals reagents (Table 3).

The nitrate-bearing solution was injected into the column after the inoculum solution for 200 hours in two phases:

-Phase 1 (between 0 and 100 hours). The column was fed continuously with synthetic solution 1 (Table 3) in the up-flow mode by an adjustable peristaltic pump (flow rate = 0.25 mL min -1 ). The major element concentrations in the injected aqueous solution were similar to those of the groundwater (Table 1). Before it was injected into the column (Fig. 1), the synthetic medium was continuously sparged with CO 2 gas and placed in a thermostatic chamber (14°C).

-Phase 2 (between 100 and 200 hours). A carbon source (acetate) with a concentration of 10 mg C L -1 (Table 3) was added to the synthetic solution 2.

An automatic sampler (Gilson) was connected to the outlet column in order to periodically collect water samples.

The hydrodynamic characteristics of the column were determined by injecting a conservative tracer, NaBr, before the denitrification experiment began. A pulse of the tracer at a constant flow rate (0.25 mL min -1 ) was injected and the outlet concentration of bromide was monitored with time. Based on the bromide breakthrough curve, the mean residence time was estimated to be 12.5 hours. The dispersivity coefficient, 0.02 m, was determined by modelling the flow transport with PHREEQC [START_REF] Parkhurst | User's guide to PHREEQC (version 2): A computer program for speciation, batch-reaction, one-dimensional transport, and inverse geochemical calculations[END_REF]. A pore volume of 190 cm 3 , corresponding to a mean porosity of 35 %, was calculated from the residence time and the injection flow rate.

Analytical procedure

Nitrate, nitrite and acetate concentrations were determined during the batch and flow-through column experiments by ion chromatography with a DIONEX IC3000-SP-EG-DC system equipped with an AS50 autosampler and a conductimetric detector. A gradient elution with sodium hydroxide, from 10 to 100 mM, was applied at 1 mL min -1 at 30 °C through an anionic column (DIONEX-AG19 and AS19 HC, 4 mm ID). An aliquot was sampled for bacteria counting using a Thoma cell by optic microscopy (Zeiss 400x). N 2 O in gas samples was analysed with a chromatograph (VARIAN 3800) equipped with a gas injection valve and an electron capture detector.

For the flow-through column experiment, the samples were collected in glass tubes previously flushed with nitrogen and sealed. The tubes were opened in an anaerobic glove box for analyses. One aliquot of raw sample was used for bacteria counting. pH and oxido-reduction potential (ORP) were measured on the raw sample and the remaining water was filtered at 0.45 µm for anionic analyses

(NO 3 - , NO 2 - , SO 4 2-
, Cl -, CH 3 COO -) by ion chromatography.

Numerical modelling approach

Micro-organisms affect the geochemical cycle of many chemical species by catalysing chemical reactions while the physicochemical properties of the environment control the activities of micro-organisms by providing habitats, nutrients, and energy [START_REF] Jin | The thermodynamics and kinetics of microbial metabolism[END_REF]. Physicochemical, thermodynamic/kinetic and biological phenomena must, therefore, be accurately predicted before we can determine the fate of chemical species (reactants and products), microbial population activity and microbial growth. Modelling requires a robust numerical model able to account for all of these strongly linked characteristics and the evolving properties.

Thermodynamic and biological coupling

Various kinetic rate laws and coupled models have been proposed to describe the thermokinetics of bacterial growth [START_REF] Hoh | A practical kinetic model that considers end product inhibition in anaerobic digestion processes by including the equilibrium constant[END_REF]Fennel and Gossett, 1998;[START_REF] Hunter | Kinetic modeling of microbially-driven redox chemistry of subsurface environments: coupling transport, microbial metabolism and geochemistry[END_REF][START_REF] Noguera | Unified model describing the role of hydrogen in the growth of Desulfovibrio Vulgaris under different environmental conditions[END_REF][START_REF] Kleerebezem | Kinetics of syntrophic cultures: a theoretical treatise on butyrate fermentation[END_REF][START_REF] Knab | Thermodynamic and kinetic control on anaerobic oxidation of methane in marine sediments[END_REF]. They are all based on Monod's equation and often add terms containing a thermodynamic factor (such as the reaction quotient Q/K, where Q is the ionic activity product and K is the equilibrium constant of the reaction) or a minimum free energy (G min ). However, most of these approaches were developed to describe specific physiological systems with constant G min values. The approach proposed by [START_REF] Jin | Kinetics of electron transfer through the respiratory chain[END_REF][START_REF] Curtis | Comparison of approaches for simulating reactive solute transport involving organic degradation reactions by multiple terminal electron acceptors[END_REF][START_REF] Aslan | Combined removal of pesticides and nitrates in drinking waters using biodenitrification and sand filter system[END_REF][START_REF] Jin | The thermodynamics and kinetics of microbial metabolism[END_REF] goes further and seems to be more suitable and flexible because it associates (i) a kinetic factor for an electron donor, (ii) a kinetic factor for an electron acceptor, (iii) a term for bacterial growth, and (iv) a thermodynamic factor. Furthermore, the Jin and Bethke approach makes it possible to propose a consistent reactive transport model for hydro-geochemical systems with kinetically dissolving/precipitating minerals for which the reaction quotient Q/K is used in the context of the Transition State Theory [START_REF] Lasaga | Chemical kinetics of water-rock interactions[END_REF][START_REF] Palandri | A compilation of rate parameters of water-mineral interaction kinetics for application to geochemical modeling[END_REF].

The Jin and Bethke approach is based on the relationship between chemical redox reactions and microbial growth under natural conditions. Redox reactions, which are often slow, can, in some rare cases, be at thermodynamic equilibrium or close to it [START_REF] Lindberg | Ground water redox reactions: an analysis of equilibrium state applied to Eh measurements and geochemical modelling[END_REF][START_REF] Keating | Reactive transport modeling of redox geochemistry: Approaches to chemical disequilibrium and reaction rate estimation at a site in northern Wisconsin[END_REF][START_REF] Michard | Chimie des eaux naturelles. Principe de Géochimie des Eaux[END_REF][START_REF] Stefansson | Redox reactions and potentials in natural waters at disequilibrium[END_REF]. In natural systems, the progress of redox reactions is usually catalysed by micro-organisms. During this process, bacteria use some of the released energy to synthesize adenosine triphosphate (ATP) from adenosine diphosphate (ADP) and the orthophosphate ion (intracellular PO 4 3-, denoted P i ) (Eq. 5):

                    D A A D D A i A D ATP m A D P m ADP m A D (5)
where  D  A  D+ and  A-are the stoichiometric coefficients of chemical species (D = donor, A = acceptor). The ATP serves as a chemical energy reserve (stock).

From this, [START_REF] Jin | Kinetics of electron transfer through the respiratory chain[END_REF] derived a comprehensive kinetic law (Eq. 6) that can account quantitatively for the thermodynamic driving force of redox reactions:

T A D F F F ] X [ k v ( 6
)
where v is the overall rate of microbial respiration (mol L -1 s -1 ), k is the intrinsic kinetic constant (mol g -1 s -1 ) and [X] is the biomass concentration (g L -1 ). F D and F A (ranging from 0 to 1, dimensionless) are kinetic factors accounting for the effects of the concentration of dissolved chemical species involved in redox reactions (Eqs. 7 and 8):

           D D D D D D D D ] D [ K ] D [ ] D [ F (7)            A A A A A A A A ] A [ K ] A [ ] A [ F (8)
where D ,  A ,  D+ ,  A-are exponents of reactant and product concentrations. Their values are not predicted by theory and depend on details of the electron transport mechanism [START_REF] Jin | A new rate law describing microbial respiration[END_REF]. K D and K A are constants for electron donor D and acceptor A.

F T (ranging from 0 to 1, dimensionless) is the thermodynamic potential of the overall reaction corresponding to the driving force of the reaction (Eq. 9):

              RT P G m redox G exp 1 T F (9)
where G redox is the free enthalpy of the reaction, G P is the phosphorylation energy, and  is the average stoichiometric coefficient of the overall reaction. The coefficient m is the number of synthesised ATP defined in the overall reaction (Eq. 5).

Numerical modelling approach

The Jin and Bethke approach was included in the geochemical code PHREEQC [START_REF] Parkhurst | User's guide to PHREEQC (version 2): A computer program for speciation, batch-reaction, one-dimensional transport, and inverse geochemical calculations[END_REF] to deal with denitrification in the presence of acetate. This approach requires, however, that the database used by the calculation code be modified. In its standard use, this code is based on chemical equilibrium calculations of aqueous solutions interacting with minerals and gases using general and extended thermodynamic databases, and aqueous redox reactions are considered to be at equilibrium. As this is rarely the case [START_REF] Stefansson | Redox reactions and potentials in natural waters at disequilibrium[END_REF], a kinetic term must be introduced for redox reactions. PHREEQC is a very flexible code for simulating chemical reactions in the aqueous phase and enables the re-writing of aqueous redox reactions to account for kinetic constraints. Since this study focuses on nitrate behaviour, all redox reactions involving nitrogen were re-written to take into account the kinetics of successive transformations (decreasing redox number: N(V)→N(III)→N(II)→N(I) →N( 0)). The chemical equilibria between nitrate-nitrite-N 2 O and N 2 were removed from the database and replaced by kinetic laws. Only aqueous complexing reactions of nitrate and nitrite with cations and vapour-liquid equilibrium for N 2 O and N 2 were kept.

Thermo-kinetic simulation of denitrification processes

The coupled thermodynamic-biogeochemical approach is applied to the reduction of (i) nitrate to nitrite (Eq. 2), (ii) nitrite to nitrous oxide (Eq. 3) and (iii) nitrous oxide to nitrogen (Eq. 4).

These reactions are kinetically constrained, whereas thermodynamic equilibria are retained between all other species in the aqueous phase including nitrogen species (ligand) complexing cations. The term F T in Eq. ( 9) was determined based on the following assumptions. The phosphorylation enthalpy (G P ) is roughly estimated to be 50 kJ mol -1 under typical physiological conditions [START_REF] White | The physiology and biochemistry of prokaryotes[END_REF], whereas  and m are reaction-dependent parameters.

For Eq. ( 2),  = 2 and m = 2/3. Two protons are transferred by electron pairs and three are required for ATP synthesis [START_REF] Jin | Predicting the rate of microbial respiration in geochemical environments[END_REF]. For Eqs. ( 3) and ( 4), few data are available in the literature. Consequently, the same values for and m were used for the three reactions (Eqs. 2 to 4) (Q. Jin, personal communication, August 2009). Gibbs free enthalpies of each reaction (G redox ), determined at each time step from the free standard enthalpy of each reaction are -140.12 kJ mol -1 , -248.92 kJ mol -1 and -314.43 kJ mol -1 for Eqs. ( 2) to (4), respectively [START_REF] Michard | Chimie des eaux naturelles. Principe de Géochimie des Eaux[END_REF].

In Eqs ( 7) and ( 8), the functions

     D D D ] D [ . K and      A A A ] A [ . K
are kinetic terms that replace the half-saturation constant in the Monod equation. In a first approximation, the kinetic term can be expected to be equivalent to the half-saturation constant only when the thermodynamic potential is close to 1 [START_REF] Jin | Predicting the rate of microbial respiration in geochemical environments[END_REF] or when, under appropriate geochemical conditions such as when the pH is buffered, there is a large substrate concentration and no build-up of metabolic products [START_REF] Jin | The thermodynamics and kinetics of microbial metabolism[END_REF]. In this study, as demonstrated below, the pH is buffered and the thermodynamic factor is close to 1 throughout the reaction. Consequently, the two kinetic terms are replaced by two half-saturation constants (K' D and K' A ). For step 1 of denitrification (Eq. 2), the values used are from Clément et al.

(1997): K' D = 1.20 mg L -1 and K' A = 0.66 mg L -1 . As no data are available for nitrite (Step 2 -Eq. 3) or N 2 O (Step 3 -Eq. 4), we used the same values for K' A and K' D as those determined for nitrate.

A growth yield of 0.13 mg-biomass/mg-NO 3 - [START_REF] Clément | Microbial growth and transport in porous media under denitrification conditions: experiments and simulations[END_REF] was used for step 1 (Eq.

2). For steps 2 and 3 (Eqs. 3 and 4), [START_REF] Clément | Microbial growth and transport in porous media under denitrification conditions: experiments and simulations[END_REF] did not give a value for growth yields. Values found in the literature indicate that the growth yield for nitrite is about three times that for nitrate [START_REF] Peyton | Nitrate reduction with Halomonas Campisalis: kinetics of denitrification at pH 9 and 12.5% NaCl[END_REF]: a value of 0.40 mg-biomass/mg-NO 2 -was therefore used. For nitrous oxide, as no literature data were found, the same value as the one for nitrate was chosen arbitrarily (0.09 mg-biomass/mg-N 2 O). For calculations, a conversion factor of 6.2 10 9 cells mg -1 biomass was used to convert experimental data (in cells mL -1 ) to input data for numerical model (in mg-biomass mL -1 ) [START_REF] Clément | Microbial growth and transport in porous media under denitrification conditions: experiments and simulations[END_REF].

Because denitrification by heterotrophic bacteria is studied, the model must also take into account the microbial growth using carbon from acetate and nitrogen from each nitrogenbearing species in solution. For the numerical simulations, the biomass is represented using a simplified generic form (C 5 H 7 O 2 N) and integrated into Eqs. ( 2

) ( 2 2 7 5 2 3 2 2 ) ( 2 2 7 5 2 3 2 2 ) ( 2 2 7 5 2 3 3 O H CO N O H C N H COO CH O N O H CO N O H C O N H COO CH NO O H CO N O H C NO H COO CH NO aq aq aq                           
These stoichiometric equations, which take into account the biomass growth (anabolism), were incorporated in the geochemical code. Although bacterial death obviously also affects the micro-organism population during the experiments, it was disregarded. We assumed that no significant nutrients (or chemical components) coming from dead bacteria are released into solution.

RESULTS AND DISCUSSION

Batch experiments

N-species

Batch experiments focused on measuring kinetic parameters for the entire denitrification reaction, from nitrate to N 2 . The abiotic flasks used as blanks show no denitrification during the entire experimental time. We know, therefore, that the nitrate attenuation observed in the biotic flasks is due to biological rather than chemical processes.

The results obtained on biotic flasks indicate a total denitrification in 40 days. Each experiment began with a period of about eight days during which the nitrate concentration did not vary (Fig. 2). Under our experimental conditions, micro-organisms seem to need time to adjust before denitrification begins. Nitrate reduction starts after 8 days with a decrease in nitrate correlated with the formation of nitrite in solution.

This first nitrate reduction reaction lasts about 30 days. At this time, nitrogen (+V) has been completely reduced to nitrogen (+III) and nitrite is the major aqueous nitrogen species. Only small and transitory amounts of N 2 O are found in solution. Significant quantities of this species appear in solution when nitrite begins to be reduced by micro-organisms. The N 2 O concentration then increases steadily before N 2 appears and nitrogen(I) is finally reduced to nitrogen(0).

Modelling is based on experimental constraints and the results obtained, using the Jin and Bethke approach, are described above. The kinetic constants for each reaction are:

-Nitrate to nitrite: An initial period (day 0 to day 8) during which no measurable microbial activity and no denitrification is recorded, is followed by a second period (day 8 to day 29) during which nitrate is reduced to nitrite consistent with a mean kinetic constant of 4.6 10 -7 mol N L -1 h -1 .

-Nitrite to nitrous oxide: A first period (day 0 to day 29), up to complete nitrate reduction, during which the nitrite reduction rate is assumed to be nil, is followed by a second period (day 30 to day 40) during which the nitrite reduction rate is about 2.3 10 -7 mol N L -1 h -1 .

-Nitrous oxide to nitrogen: The kinetic rate is highly dependent on nitrate and nitrite concentrations. Up to the total reduction of nitrate (day 0 to day 29), the nitrous oxide reduction rate is assumed to be nil, whereas thereafter (day 29 to day 60), a value of 2.1 10 -7 mol N L -1 h -1 provides a rather good fit of the observed results.

By coupling batch experiments and numerical modelling we were able to define the different steps of the denitrification process and determine the respective kinetic rates. The kinetic rate for the first reduction step (nitrate to nitrite) falls within the range reported in the literature (from 5.0 10 -7 to 2.0 10 -6 mol-N L -1 h -1 ) for denitrification with organic matter (Star and Guillham, 1993;Schipper andVojvodic Vukovic, 1998, 2000;[START_REF] Devlin | The effects of electron donor and granular iron on nitrate transformation rates in sediments from a municipal water supply aquifer[END_REF]. This experiment shows that the reduction of nitrite (and the formation of nitrous oxide) is related to nitrate consumption. As long as nitrate is present, nitrite increases and is measurable in solution. In natural environments, high nitrite concentrations are rarely observed, except in specific cases [START_REF] Kelso | Effects of carbon substrates on nitrite accumulation in freshwater sediments[END_REF]. In laboratory systems, this nitrite accumulation is often observed by the use of acetate as the electron donor. Carbon sources such as acetate and propionate cause nitrite to accumulate in the medium, which does not occur with butyrate, valerate or coproate [START_REF] Wilderer | Competition in denitrification systems affecting reduction rate and accumulation of nitrite[END_REF][START_REF] Van Rijn | Influence of volatile fatty acids on nitrite accumulation by a Pseudomonas stutzeri strain isolated from a denitrifying fluidized bad reactor[END_REF]. These authors assume that in the presence of acetate, nitrite accumulation is caused by differences in nitrate and nitrite reduction rates and by the competition between nitrate and nitrite reduction pathways for electrons. Our experiments confirm this hypothesis of competition between the two reduction processes in the presence of acetatenitrite reduction does not start until all of the nitrate has been consumed, favouring nitrate reduction before nitrite reduction and the nitrite accumulation.

pH pattern

The pH is initially stable or decreases slightly (during nitrate reduction to nitrite, up to day 29), and then increases during nitrite reduction (day 29 to day 40, Fig. 3). Calculated pH values fit the experimental data relatively well and the major trends are reproduced, except for some small discrepancies in the first part of the experiment. During nitrate reduction (Eq. 2), a small increase in pH is predicted by numerical calculations due to proton consumption, whereas experimental data show a slight decrease. The slopes of the curves for observed and simulated results are identical for the nitrite reduction reaction. Eq. ( 3) indicates that the proton consumption is higher than in the previous nitrate reduction reactionthe consequence of this being a change in the slope with a relatively greater increase in pH between day 30 and day 40. However, pH does not vary greatly due to the buffering capacity of the reactive aqueous solution.

Acetate as the electron donor

Acetate is the electron donor used by micro-organisms to promote the heterotrophic denitrification reaction. The concentration is constant during the first 8 days (when no nitrate is consumed) and then decreases sharply (Fig. 4). After 40 days, there is no longer any acetate (for 2 of the 3 replicates). The simulation correctly fits the observed data, except for one of the replicates, for which no explication can be found, since all of the other measured variables (nitrogen species concentration, pH, biomass concentration) are consistent for the three replicates. Numerical simulations confirm that all of the acetate is consumed during the experiment. It is used to synthesize CO 2 (catabolism) and biomass (anabolism) (Eqs. 10 to 12). When numerical modelling was done without taking the bacteria anabolism into consideration (Fig. 4 -dashed line) only about 30 mg of acetate are used to reduce 50 mg of nitrate (Eqs. 2 to 4).

Acetate is the source of both the electrons and the carbon needed by bacteria to proliferate. This is highlighted by the two simulations. One considers only catabolism, while the other takes into account both the anabolism and the catabolism of the micro-organisms (Fig. 4).

Results using the first scenario do not match the measured acetate concentrations, whereas those using the second scenario agree with the observed acetate consumption data. This second scenario indicates that about 40 % of the carbon from acetate is used for anabolism and 60 % is used for catabolism. From Eqs. (10) to ( 12), the calculated mass-balance confirms that 41 % of the carbon coming from acetate is used for biomass production, in agreement with literature data. For aerobic degraders, [START_REF] Greskowiak | Modeling of carbon cycling and biogeochemical changes during injection and recovery of reclaimed water at Bolivar, South Australia[END_REF] proposed a value of 60 % for anabolism, meaning that 40 % of the carbon is converted to CO 2 . However, for anaerobic denitrification in the presence of acetate, this ratio is reversed. [START_REF] Clément | Microbial growth and transport in porous media under denitrification conditions: experiments and simulations[END_REF] defined a biomass growth yield of about 20 %, whereas [START_REF] Odencrantz | Stimulation of biologically active zones (BAZ's) in porous media by electron-acceptor injection[END_REF] and [START_REF] Istok | A thermodynamically-based model for predicting microbial growth and community composition coupled to system geochemistry: Application to uranium bioreduction[END_REF] have proposed values of 37.5 % and 41 %, respectively.

Biomass growth

Fig. 5 shows the evolution of the biomass in the batch experiment. The bacterial population increases rapidly (day 0 to day 8) before decreasing and then increasing once again. It stabilizes after 40 days (i.e. the end of nitrite reduction). The bacterial growth model, based on nitrate, nitrite and nitrous oxide reduction, produces results that are in relatively good agreement with experimental data. The overall trend and the final biomass concentration are in agreement with observed data. The only discrepancy concerns the first period (day 0 to day 8). Some bacterial activity, independent of the denitrification process since nitrate reduction and acetate oxidation are nil (or extremely low) during this period, is assumed to influence the biomass population and probably pH during this period. The batch experiments were done with groundwater initially containing both heterotrophic and autotrophic bacteria. Autotrophic bacteria (very active in the field) might develop during the experiment in the aqueous solution. These use the mineral carbon (bicarbonate), and their activity might explain the biomass peak and the slight decrease in pH (Fig. 3). This is hypothetical, however, and since it does not play a major role in the overall denitrification process, it was disregarded in the numerical calculations.

The measurements of biomass concentration in the three replicates also show that the bacterial growth stabilizes after 40 days, in correlation with the total consumption of electron donors and acceptors. Acetate and nitraterather than the bioavailability of other elementsseem to be the limiting factors of bacterial activity. As an example, a simple calculation of the amount of phosphorus needed shows that, assuming a classical formulation C:N:P106:16:1 for dry biomass [START_REF] Sigg | Chimie des milieux aquatiques; chimie des eaux naturelles et des interfaces dans l'environnement[END_REF], a few µmol P L -1 are necessary to generate the concentrations of biomass measured in the three replicates. The calculated P concentration and the limit of quantification have the same order of magnitude. We therefore assume that the natural groundwater used for these experiments provides enough trace elements (such as phosphorus) for the growth of the bacterial community.

Remarks on the Thermodynamic Potential Factor

One objective of this study was to determine the relative weight of kinetic factors influencing global denitrification. The thermodynamic potential factor (F T ) remains constant (and equal to 1) throughout the experiment (Figs. 6 and7). For denitrification in the presence of acetate, the thermodynamic factor has no affect on denitrification. For step 1 (i.e. reduction from nitrate to nitrite -Eq. 2), the denitrification process is governed by the kinetic factor (F A ) related to the electron acceptor concentration (i.e. nitrate), whereas for step 2 (i.e. reduction from nitrite to nitrous oxide -Eq. 3), the kinetics of denitrification is limited by F A (i.e. nitrite concentration) and mainly F D factors (i.e. acetate concentration). For denitrification in the presence of acetate (Figs. 6 and7), the thermodynamic factor can be disregarded and the global kinetics of denitrification are governed mainly by the concentrations of electron donors/acceptors. The model proposed by Jin and Bethke is, however, entirely suitable for simulating bacteriamediated changes in the redox state of a complex biogeochemical system.

Flow-through column experiment

Flow-through column experiments should help us better understand the influence of flow on water chemistry, in particular on the denitrification process. [START_REF] Tarits | Oxido-reduction sequence related to flux variations of groundwater from a fractured basement aquifer (Ploemeur area, France)[END_REF] have demonstrated the influence of hydrodynamic factors on water chemistry. They point out that denitrification is activated by pumping in the aquifer. In columns and, more generally, in consolidated porous media, microbial communities can also develop in biofilms, creating locally variable redox conditions and processes [START_REF] Yu | Stratification of microbial metabolic processes and redox potential change in an aerobic biofilm studied using microelectrodes[END_REF][START_REF] Bishop | A microelectrode study of redox potential change in biofilms[END_REF].

Our column experiment provides an opportunity to observe whether the denitrification kinetic rates determined using batch experiments are always valid and can be used as is in transport experiments. The breakthrough curves for nitrate and nitrite are given in Fig. 8 and for chloride and sulphate in Fig. 9.

The nitrate concentration increases until it reaches a constant value equal to the input concentration (50 mg L -1 ). The nitrite concentration is lower than 2 mg L -1 (Fig. 8). The synthetic solution 1 (Table 3) has lower chloride and sulphate concentrations than the inoculum solution initially introduced in the column. This explains the decrease in the outlet concentrations of these two ions during the first hours of the experiment (Fig. 9). Between 50 and 100 hours, the outlet concentrations for chloride, sulphate and nitrate are the same as the inlet concentrations: the system reaches a steady state. No denitrification occurs in the column during this period despite the presence of bacterial inoculum in the system and of pyrite in the schist (Table 2).

At time = 100 hours, phase 2 of the experiment begins with the input of a carbon source. A solution containing nitrate (50 mg L -1 ), acetate (10 mg L -1 ) and sulphate (33.78 mg L -1 ) is injected into the column (synthetic solution 2, Table 3). The nitrate concentration at the outlet of the column decreases immediately and the nitrite concentration increases. About 50 % of the injected nitrate has been reduced to nitrite and to reduced nitrogen species after 190 hours (Fig. 8). Nitrate removal is not in a steady state. It is more rapid between 100 and 130 hours than during the period between 130 and 200 hours. Nitrite concentrations followed the opposite trend with a sharp increase between 100 and 130 hours and a smoother variation thereafter (130 to 200 hours). The chloride concentration does not vary when the injected solution changes, whereas the sulphate concentration does. Since synthetic solution 2 contains less sulphate than synthetic solution 1, a decrease in the sulphate concentration was expected.

Although a small drop was observed, the outlet concentration of this species was always greater than the injected concentration, as opposed to what occurred during the previous phase (0 to 100 hours). Sulphates are therefore produced within the column, and we conclude that dissolved sulphates come from an interaction between the aqueous solution and minerals.

Considering the mineralogical assemblage of the constituting rock (pyrite-bearing schist), the sulphur production is attributed to the dissolution/oxidation reaction of pyrite. During this stage (100 to 200 hours), two electron donors impact on the denitrification processacetate (Eqs. 2 to 4) and pyrite (Eq. 1).

Based on the results of the column experiment, we assume that the bacterial inoculum used to colonize the schist was composed mainly of heterotrophic bacterial species. The specific medium, enriched in acetate and used to develop this inoculum, probably favours the growth of heterotrophic bacteria [START_REF] Tranvik | Bacterial Growth in Mixed Cultures on Dissolved Organic Carbon from Humic and Clear Waters[END_REF], which have a specific growth rate higher than that of autotrophic micro-organisms [START_REF] Tsai | Estimating biomass of heterotrophic and autotrophic bacteria by our batch tests[END_REF]. [START_REF] Marchand | Influence of heterotrophic microbial growth on biological oxidation of pyrite[END_REF] also show that heterotrophic microbial growth could have an impact on the behaviour of autotrophic populations, in particular on the biological oxidation of pyrite. They suggest that the development of heterotrophic micro-organisms might inhibit the rate and the extent of sulphide mineral oxidation. This experiment highlights the major role played by heterotrophic bacteria in the denitrification process since it is initiated by the addition of organic matter to the injected solution.

The absence of denitrification due to the oxidation of pyrite by nitrate during the first period (0 to 100 hours) was not expected since microbial denitrification had been observed at the site where the samples were collected [START_REF] Pauwels | Field tracer test for denitrification in a pyrite-bearing schist aquifer[END_REF]. However, these authors did not specify whether the autotrophic micro-organisms were chemolithotrophic bacteria (which use inorganic carbon as a carbon source and non-carbon compounds as an electron source, Chapelle 2001) or chemoorganotrophic bacteria (which use inorganic carbon as a carbon source and carbon compounds as an electron source, Chapelle 2001). From field measurements, they simply identified the preponderant role of autotrophic bacteria compared to that of heterotrophic bacteria. The results of our experiment show that chemoorganotrophic bacteria had been fostered by the acetate-enriched medium used to develop the inoculum, whereas chemolithotrophic bacteria, probably present in the inoculum but in low numbers, were not active enough to initiate the denitrification process. Consequently, the low population of chemolitotrophic micro-organisms and the absence of organic matter for chemoorganotrophic bacteria prevented any decrease in the nitrate concentration during this first period.

The column experiment was modelled with PHREEQC using a 1D column (discretised into 10 sections, each 3 cm long) with hydrodynamic characteristics determined using the bromide tracer (see paragraph 2.1.2). The simulation complies with the two-phase experiment: injection of a nitrous solution without organic carbon (synthetic solution 1, Table 3) during the first 100 hours, followed by injection of a nitrate/acetate solution (synthetic solution 2, Table 3) from hour 100 to hour 200. A constant injection flow rate is imposed at the inlet of the column and a Cauchy boundary condition is assumed at the outlet. A biomass concentration of 1.6 10 7 cells mL -1 is assumed at the beginning at the experiment.

For the biogeochemical part of the simulation, the kinetic parameters determined in batch systems with acetate were used without modification (Eqs. 10 to 12). However, in this flowthrough column experiment, the kinetic rate for reaction 1 (i.e. pyrite oxidation, Eq. 1) had to be estimated (3.2 10 -7 mol N L -1 h -1 ) based on field data [START_REF] Postma | Nitrate reduction in an unconfined sandy aquifer: water chemistry, reduction processes and geochemical modeling[END_REF][START_REF] Pauwels | Field tracer test for denitrification in a pyrite-bearing schist aquifer[END_REF]. To our knowledge, there is no literature data for the parameters used to calculate the thermodynamic factor of reaction 1 (Eq. 1). Only the free enthalpy can be calculated: -456 kJ mol -1 [START_REF] Michard | Chimie des eaux naturelles. Principe de Géochimie des Eaux[END_REF]. This value is high (of the same order of magnitude as that of acetate), and in batch experiments it was demonstrated that the thermodynamic factor is close to 1 with such a high G 0 . In a first approximation, for this calculation, the thermodynamic factor is assumed to be 1. A Monod approach is then used for reaction 1 (Eq. 1). This is justified due to the high free enthalpy of the reaction and the excess of pyrite in the schist [START_REF] Pauwels | Field tracer test for denitrification in a pyrite-bearing schist aquifer[END_REF].

The kinetic rates used for each reaction make it possible to reproduce the experimental values for nitrate, nitrite (Fig. 8) and sulphate (Fig. 9). The outlet sulphate concentrations, calculated from the inlet SO 4 concentration and the number of moles of pyrite oxidized by nitrates (Reaction 1, Eq. 1), are in good agreement with the observed data (Fig. 9). A small difference between measured and calculated sulphate concentrations is observed at 120 hours. Numerical modelling predicted a small peak in sulphate that is not observed. In the column experiment, the autotrophic bacteria have a short time lag, which is not considered in the numerical approach since the two bacterial processes (heterotrophic and autotrophic) are activated at the same time. This simultaneous activation might explain the punctual over-estimation of the sulphate concentration.

The numerical simulation of the second part of the experiment (between 100 and 200 hours) also confirms that the bacteria active in the column are, for the most part, heterotrophic since the outlet nitrate concentration starts to decrease when acetate is co-injected with nitrate.

However, heterotrophic denitrification alone cannot explain the measured decrease in the nitrate concentration. Autotrophic denitrification must also be involved to match the observed data. The two autotrophic processes (chemoorganotrophic and chemolithotrophic) are also assumed to be active in this experiment. Indeed, the addition in the injected solution of a carbon source (acetate) can activate the chemoorganotrophic mechanism. Moreover, heterotrophic bacteria produce alkalinity (mainly as dissolved CO 2 ), due to acetate degradation for their catabolism. According to the reactions described in Eqs. ( 10) to ( 12), 1 mole of nitrate induces the formation of about 1.8 moles of CO 2,aq . This increase in alkalinity could explain the increased activity of chemolithotrophic bacteria. All of these processes are assumed to be active in the column experiment.

The absence of any source of organic matter, therefore, prevents the development of chemoorganotrophic activity. The low alkalinity of the injected solution also stops the activity of chemolithotrophic bacteria. With the addition of acetate, the heterotrophic bacteria are activated and produce alkalinity, which is immediately used by chemolithotrophic microorganisms. We also assume that chemoorganotrophic bacteria are activated by the carbon availability. However, neither the data nor the model can explain the relative weight of each autotrophic community. This simultaneous heterotrophic/autotrophic denitrification has been described for nitrate removal from high-nitrate wastewater [START_REF] Gommers | Simultaneous sulfide and acetate oxidation in a denitrifying fluidized bed reactor-II. Measurements of activities and conversion[END_REF][START_REF] Aminzadeh | Salt inhibition effects on simultaneous heterotrophic/autotrophic denitrification of high nitrate wastewater[END_REF]. These authors emphasize the high efficiency of such a treatment, which enables the removal of sulphide, acetate and nitrate in natural and synthetic wastewater in fluidized bed reactors. [START_REF] Oh | Nitrate removal by simultaneous sulfur utilizing autotrophic and heterotrophic denitrification under different organics and alkalinity conditions: batch experiments[END_REF] calculated that the reduction of 1 mg of nitrate nitrogen, with methanol, generates 3.57 mg of CaCO 3 . According to these authors, the two processes are linked and a lack of any organic source can decrease the performance of denitrification treatment.

Modelling of both heterotrophic and autotrophic processes correctly reproduces the observed outlet concentrations of nitrate, nitrite and sulphate. The outlet nitrate concentration after 200 hours is close to 30 mg L -1 (for an inlet concentration of 50 mg L -1 ), which means that the two species of bacteria are able to remove about 40 % of the initial nitrate. A comparison of two calculations (results not shown here), one done with and the other without considering the autotrophic mechanism, indicates that 80 % of the nitrate consumption is due to heterotrophic denitrification and the remainder is due to autotrophic processes. The numerical results for the nitrite concentration are in good agreement with the observed data. As the modelling approach considers only the production of nitrite by the heterotrophic process, we deduce that autotrophic denitrification does not release any nitrite into solution (or that the kinetic rate of nitrite production equals the kinetic rate of nitrite consumption). This absence of nitrite accumulation (via pyrite oxidation) has been observed in NO 3 --reducing cultures [START_REF] Van Beer | Redox processes active in denitrification[END_REF][START_REF] Weber | Microbially catalysed nitrate-dependent oxidation of biogenic solid-phase Fe(II) compounds[END_REF].

The experimental results of this flow-through column experiment show no time lag when acetate is injected into the column. In batch experiments, there is no heterotrophic microbial activity during the first 8 days (Fig. 2). In the field, [START_REF] Pauwels | Field tracer test for denitrification in a pyrite-bearing schist aquifer[END_REF] -The flow rate through the column is low compared to the flow rate in field studies where transport processes have a greater impact on denitrification [START_REF] Pauwels | Field tracer test for denitrification in a pyrite-bearing schist aquifer[END_REF]. Moreover, the column experiment is done using crushed schist. Consequently, the exchanges, the contact surface and, therefore, the interactions between aqueous solution, mineral (in particular pyrite) and micro-organisms are probably more favourable, decreasing the time lag.

CONCLUSIONS

This study focuses on heterotrophic and autotrophic denitrification processes, i.e. the reduction of nitrate (NO 3 -) to nitrogen (N 2 ). Although denitrification in soils and aquifers is studied extensively for water quality, diffuse pollution transfer, and remediation, there is still an on-going debate in the scientific community concerning the contribution of organic matter as an electron donor when other mineral electron donors (i.e. pyrite) are available. The main goals of this study were therefore:

-to better understand denitrification processes in complex systems (water-rock-organic matter-microorganisms) using experiments and numerical modelling of elementary processes and, -to conceptualize numerical modelling based on a decoupled thermodynamic database that enables the integration of the new thermo-kinetic approach of [START_REF] Jin | Kinetics of electron transfer through the respiratory chain[END_REF], clearly splitting available energy in terms of three driving forces, i.e. catabolism, anabolism and a surviving reserve.

This new, comprehensive thermokinetic rate law based on energetic approaches takes into consideration both the thermodynamic driving force and biogeochemical processes. This approach is applied successfully to the heterotrophic denitrification processes in the presence of acetate coupled with the autotrophic contribution based on pyrite oxidation.

The thermodynamic and kinetic parameters incorporated in the geochemical code PHREEQC reproduce the concentrations of nitrate-bearing species during the entire duration of the batch experiment. This computer code is robust enough to model the behaviour of chemical species (electron donor, electron acceptor, pH, etc.), biological aspects (anabolism and catabolism of the biomass population) and energy conditions (thermodynamic factor linked to the reaction energy). The comparison of model and observed results confirms that each step of nitrate reduction in the presence of acetate is governed mainly by kinetic factors and not limited by thermodynamic constraints. The energies of the reactions (in the presence of an electron donor like acetate) are too high compared to the energy needed by micro-organisms to proliferate. Consequently, this factor is not limiting and nitrate reduction is complete if there is an excess of electron donors.

Nevertheless, although this thermodynamic approach is not useful for denitrification with acetate, it cannot be applied to all denitrification processes in the presence of other electron donors. The main factor influencing the thermodynamic factor is the free enthalpy of the reactionsthe reactions with acetate and pyrite are very energetic (several hundreds of kJ mol -1 ) whereas the free standard enthalpy of reactions with goethite or amorphous iron hydroxides are low (several tens of kJ mol -1 ). This approach should, therefore, be of value for dealing with denitrification involving goethite or amorphous oxides as electron donors. This work, which uses both batch and column experiments, shows that these two approaches are complementary. The kinetic data set determined at the batch scale (similar to literature data) is sufficiently well constrained to simulate nitrate, nitrite and biomass concentrations.

The numerical simulations indicate that during the heterotrophic denitrification reaction, about 40 % of the carbon from acetate is used for anabolism, whereas 60 % is used for catabolism. Moreover, this set of parameters, fitted with results from batch experiments, can be successfully used to model the column experiment, a 1D system. The heterotrophic denitrification in the column and batch experiments can be explained by the same process, which is promising for application to field studies. Numerical modelling is therefore a useful tool for managing natural environments when the numerous thermo-kinetic parameters are known.

Figure Captions

  observed an autotrophic metabolic lag of about 40 hours. The absence of a microbial adjustment period can be attributed to the experimental protocol: -During the first phase of the experiment (the first 100 hours), the microbial population was accustomed to a NO 3 --containing solution, thus limiting the beginning of microbial activity, when acetate was added.

Fig. 1 .

 1 Fig. 1. Schematic representation of the flow-through column Fig. 2. Evolution with time of the concentration of N-bearing species. Symbols correspond to experimental data with error bars. Lines represent modelling results Fig. 3. Evolution with time of pH. Points and dashed lines correspond to measured data of the three replicates. The solid line represents calculated pH values Fig. 4. Evolution with time of acetate concentration. Points with dotted lines correspond to measured data of the three replicates . The bold lines represent calculated values: dashed bold line = calculation without considering the bacterial anabolism; solid bold line = calculation with anabolism and catabolism Fig. 5. Evolution with time of biomass concentration. Points and dotted lines correspond to measured data for the three replicates. The solid line represents calculated values. Fig. 6. Variations of kinetic factors (F D , F A ) and the thermodynamic factor (F T ) for nitrate reduction (Eq. 2) versus nitrate concentration Fig. 7. Variations of kinetic factors (F D , F A ) and the thermodynamic factor (F T ) for nitrite reduction (Eq. 3) versus time Fig. 8. Nitrate and nitrite concentrations at the outlet of the column. Symbols represent experimental data and lines correspond to numerical simulation results.

Fig. 9 .

 9 Fig. 9. Evolution of sulphate and chloride concentrations. Symbols represent Cl -and SO 4 -concentrations in the aqueous solution at the outlet. Dashed and dotted lines correspond to Cl -and SO 4 --concentrations in the solution at the inlet. The solid line represents calculated sulphate concentration at the outlet of the column.

Table 1 : Chemical composition of the groundwater (in mmol kg -1 H2O )

 1

	Chemicals	pH	Eh	Alk	Ca	Mg	Na	K	Cl	NO 3	SO 4	Fe	DOC
			(mV)
	Concentration	6.68	179	0.77	0.38	0.36	0.80	0.03	0.78 < LOQ 0.33 0.13	0.058

LOQ = Limit of Quantification

Table 3 Chemical compositions and concentrations of the synthetic solutions

 3

		Concentration (mg L -1 )
	Chemical species	Synthetic solution 1	Synthetic solution 2
	Ca 2+	11.60	11.60
	Mg 2+	11.40	8.60
	K +	1.10	1.10
	Na +	30.40	40.00
	Cl -	21.60	21.60
	-CH 3 COO -HCO 3 2-SO 4 -NO 3	30.50 45.10 50.00 /	30.50 33.80 50.00 24.80

ACKNOWLEDGEMENT

We thank C. Crouzet and S. Touzelet (BRGM/Metrology, Monitoring and Analysis Division) for their assistance with experiments and chemical analyses, and S. Kremer (BRGM/Water Division) for her help modifying geochemical databases. The authors also thank two anonymous reviewers for helpful comments and suggestions.


S Godet

É Tournier

O Llopis

An integrated phase noise measurement bench for on-chip characterization of resonators and VCOs

Keywords: Phase noise, Built-in-self-test (BIST), integrated circuit, phase detection, SMR resonator

A phase noise measurement bench is integrated on a 3.6 mm 2 silicon chip. The bench includes a splitter with quadrature outputs, a phase detector, a low noise baseband amplifier and, if necessary, a synthesized source. Applications to the characterization of frequency sources and BAW resonators are discussed.

I. INTRODUCTION

A phase noise measurement bench is generally a costly laboratory equipment, based on active references or long delay lines, including low noise amplifiers and phase detectors. The ability to include on a single silicon chip the elements of such a measurement bench allows the measurement and the monitoring of this critical parameter in small size systems, and probably also the correction of the sources phase noise using active loops. The device under test may either be a frequency source (ex : a VCO) or a two port system, such as an amplifier, a digital circuit… In the first case, the phase noise measurement bench must include a frequency reference element, either passive (resonator, delay line) or active (reference source). In the second case, it is mainly based on a low noise phase detection process.

A special case of two ports devices characterization is the measurement of piezoelectric resonators noise, which is very difficult to perform using conventional phase noise measurement techniques on 50  load. Indeed, these devices need different impedances conditions to take benefit of their series or parallel resonances. While realized on a chip, the input and output impedances can be controlled and the resonator is characterized in the same conditions it experiences when it is included in a circuit.

Such an approach can be part of a Built-In-Self Test system [START_REF] Veillette | On-chip measurement of the jitter transfert function of charge-pump phase locked loops[END_REF][START_REF] Khalil | A self calibrated on chip phase noise measurement circuit with -75 dBc single tone sensitivity at 100 kHz offset[END_REF][START_REF] Valdes-Garcia | Built-in Self Test of RF Transceiver SoCs : from Signal Chain to RF Synthesizers[END_REF][START_REF] Cathelin | Circuit électronique comprenant un dispositif de mesure du bruit de phase d'un dispositif oscillant et/ou résonant[END_REF], and used for reliability applications. As an example, the ability to measure the phase noise degradation in an embedded system allows to switch from the noise degraded device (oscillator, amplifier…) to another device, thus maintaining the system performance at its best.

Various elements of a phase noise bridge have thus been designed using an integrated circuit foundry (ST Microelectronics, BiCMOS7RF 0.25 m). The system has been firstly designed to measure the phase noise of integrated BAW resonators using an SMR technology (CEA-LETI). However, the replacement of one of the resonators by a short line results in an enhancement of the detection of the frequency fluctuations of the source, and thus in the realization of a narrow bandwidth frequency discriminator. This discriminator is able to measure the phase noise spectrum of any type of LC resonator based VCOs.

II. PHASE NOISE MEASUREMENT SYSTEM

Figure 1 represents the typical circuit topology of such a phase noise measurement bench. The main device is a phase detector, generally realized with a mixer with the two signals (LO and RF) maintained close to the phase quadrature (±90°). The phase detector is followed by a baseband amplifier, which should feature an equivalent input low frequency noise lower than the output noise of the phase detector.

Resonator Source

Figure 1 : Typical topology of a phase noise measurement bench, in the configuration for source measurement (frequency discriminator). The residual phase noise measurement system is the same, with the resonator substituted by the device under test If the purpose of the measurement bench is to characterize the frequency source, the resonator is used as the frequency reference element, and is part of the measurement bench. It allows, thanks to its large phase to frequency slope (d/df), the conversion of the frequency fluctuations of the source into phase fluctuations, which are then detected by the phase detector.

If the purpose of the measurement bench is to measure the residual phase noise of two ports devices, such an amplifier, the device under test (DUT) replaces the resonator, but a frequency source should be available in the system. This oscillator must be tunable and, above all, must feature low AM and FM noise. The AM noise is the most critical specification in this case [START_REF] Cibiel | AM noise impact on low level phase noise measurements[END_REF], because the FM noise is simply removed by equilibrating the delay in the two arms of the phase detector. In the case of a resonator measurement, the problem of the parasitic FM noise detection of the source is solved by measuring two identical resonators, one in each arm of the phase detector, thus canceling the delay caused by one resonator. The resulting phase noise is the addition of the phase noise of the two resonators, i.e. a phase noise increased of 3 dB compared to a single resonator, if the resonators are identical. Finally, in the case of the measurement of frequency conversion devices (frequency dividers, multipliers…), once again two identical devices must be used, in order to reach the same frequency on the RF and LO ports of the mixer.

One of the devices depicted in Figure 1 is very difficult to integrate : the phase shifter. It is realized on a macroscopic phase noise measurement system with a stretched line, which allows phase rotations of generally more than 180° at all the frequencies of interest. Such a wide control of the phase is difficult to get on integrated circuits. However, in the integrated world, the phase is generally well known and does not shift too much on the small lines used in a silicon chip. We thus propose a solution to this problem which avoids the realization of this phase control.

Finally, the output signal is analyzed on a low frequency spectrum analyzer. We have not integrated on a chip such a complex system, although it would be possible to do it. In our case, the final analysis is still performed out of the chip. However, it would be easy to integrate a power measurement on a given frequency bandwidth, which would allow to get an estimate of the phase noise at a given frequency offset carefully chosen for the application foreseen.

We will now describe all the elements of this system and the way they have been effectively integrated on silicon, starting with the input stages and ending with the phase detector stage.

A. Synthesized frequency source

An integrated synthesizer has been realized, and is depicted in

B. Input stage : splitter and quadrature output

The problem of the phase quadrature at the mixer input can be solved very easily in an integrated circuit approach with a power divider delivering signals already in quadrature. If the phase shift in the DUT is small, or if it can be compensated using two identical devices, the phase quadrature is maintained down to the mixer stage, and the phase detection is performed at its maximum sensitivity.

To realize this function, a digital frequency divider by two has been used. This circuit, depicted in Figure 3, is based on D flip-flop cells and generates four output signals which are all in phase quadrature (0°, 90°, 180° and 270°). However, such a digital circuit located at a critical stage of the phase bridge can be the main noise source of the system. Our goal has thus been to optimize the phase noise of this circuit [START_REF] Godet | A low phase noise and wide-bandwith BiCMOS SiGe:C 0.25um digital frequency divider for an on-chip phase-noise measurement circuit[END_REF], in order to get a very low residual phase noise divider. This has been performed using the phase noise simulation capabilities of Cadence TM , and particularly the ability of this software to isolate the main noise source of the circuit. An important optimization work has been focused on the D flip-flop topology, and more precisely on the current source of this differential element. More details on this process can be found in reference [START_REF] Godet | A low phase noise and wide-bandwith BiCMOS SiGe:C 0.25um digital frequency divider for an on-chip phase-noise measurement circuit[END_REF].

C. Phase detector

Phase detectors are classically realized with four balanced diodes mixers. Such phase detectors are very reliable and can work on a large frequency range. However, the main drawback of this approach lies in the need for a sufficient LO power to drive the mixer (typically 7 dBm) and on the conversion losses of passive mixers. It is therefore interesting to investigate on active mixers for phase detection. The residual phase noise of some bipolar transistor, when loaded and biased properly, is as low as the residual phase noise of schottky diodes silicon mixers, and these devices can lead to a substantial improvement of the phase detection coefficient. Various active phase detectors have thus been designed, based on Gilbert cell mixer and using bipolar devices. Two versions of this circuit have been realized, one based on resistive loads (Figure 5) and featuring a phase detection coefficient of 350 mV/rad, and another one based on active loads and featuring a phase detection coefficient of 970 mV/rad. Up to now, only the first circuit has been measured and used in the integrated phase noise bench, although the other circuit features a better simulated phase noise performance. When this second mixer will have been fully characterized, it will be the purpose of a dedicated publication. However, the resistive loads mixer is already particularly interesting because it features a phase detection coefficient higher than passive mixers and works on much lower level signals. Moreover, its phase noise is low, as it can be deduced from the overall system phase noise measurement presented in section III (Figure 9).

D. Low noise amplifier

The low noise amplifier must feature an equivalent input noise level lower than the output noise of the phase detector. Using the resistive loads mixer, the phase detection coefficient is (a little higher but) close to the phase detection coefficient of a passive mixer, and the amplifier performance should be as close as possible as the one of the best operational amplifiers. Such metrological amplifiers feature an equivalent voltage noise floor in the range of 1 nV/√Hz, and a 1/f noise corner frequency lower than 1 kHz. Our goal has thus been to integrate an amplifier with similar performances.

Our first attempt with a conventional differential topology first stage has led us to noise performances in the range of 20 nV/√Hz or more at the amplifier input. The strategy to improve the amplifier performance has been based on the duplication of the bipolar transistors involved in the first differential stage and, also, in the gain stage. Indeed, setting in parallel many transistors reduces the equivalent noise (at a cost of an input impedance reduction, which is not mandatory here) because the noise sources of each device are added incoherently meanwhile the current (the information) is added coherently. The result of this study has been the realization of a state of the art low noise amplifier, featuring a noise floor of 1.05 nV/√Hz and a noise corner frequency in the kHz range. This is particularly interesting, taking into account the small size (640 m X 227 m) and, above all, the low power consumption of this circuit : 2.5 V, 18 mA (45 mW).

Figure 6 represents the circuit realized, and Figure 7 the measured low frequency noise of this amplifier. The noise measurement is in perfect agreement with the simulated noise, and demonstrates that the design goals have been fulfilled. More details on the noise optimization process for this circuit can be found in reference [START_REF] Godet | A baseband ultra-low noise SiGe: C BiCMOS 0.25 um amplifier and its application for an on-chip phase-noise measurement circuit[END_REF].

E. Overview of the whole integrated circuit

These elements of the circuit are then put together on a single silicon chip. The final circuit is represented in Figure 8, and its size is in the range of 1.67 mm X 2.17 mm. The central part is dedicated to the DUT (case of residual phase noise measurement) or the resonators (BAW) and lines, which are reported on the circuit using a flip-chip technology. As the input stage provides four outputs in quadrature, we use these four outputs in order not to lose power, and the mixer is also designed with four inputs. The signal at the output of the low noise amplifier is then analysed on a FFT spectrum analyser. The system noise floor is measured using four identical short lines in place of the resonators. Unlike many passive microwave resonators, BAW resonators may induce a 1/f noise component in the circuit. As an example, we have measured some years ago on a conventional phase noise bridge a 1/f phase noise component in FBAR resonators [START_REF] Gribaldo | Experimental study of phase noise in FBAR resonators[END_REF], and the measured phase noise level in these devices was sufficient to be the main noise contribution to an oscillator realized with one of these resonators. However, the same measurements performed in the same conditions on some new SMR resonators have given results much too close from the measurement noise floor to conclude on the noise contribution of these devices. This is due not only to the absolute level of phase noise (or more precisely to the fluctuation of the resonator centre frequency) but also to the fact that a proper impedance must be used to get an observable resonance with these devices.

We have thus used our integrated phase noise bench to measure the residual phase noise of those SMR resonators, the resonators being realized at CEA-LETI in Grenoble (France). More details on these resonators and their applications can be found in reference [START_REF] Reinhardt | Acoustic Technologies for Advanced RF Architectures[END_REF]. Four identical resonators have thus been mounted using flip-chip technology on the silicon circuit. Unfortunately, some contacts problems due to differences in metals pads between the two devices have prevented the measurement of this integrated circuit. We have thus used the separated elements to assemble a partially integrated phase noise test bench, and we have obtained the data depicted in Figure 9. The measured noise is the one of the four devices (incoherent addition of the noise of each device), which is effectively higher than the noise floor. The phase noise of a single resonator can be deduced from this plot by subtracting 6 dB to this curve. Apart from the resonators residual phase noise, this measurement demonstrates a relatively good phase noise floor for our system. The phase noise floor is close to the measured phase noise of the input stage (frequency divider by two), with a bump on the spectrum added around 100 Hz offset, which is probably due to a contribution from the phase detector noise.

IV. CONCLUSION

A phase noise measurement bench integrated on a silicon chip has been presented. This bench may be used either for residual phase noise measurements, or for oscillator phase noise measurement in the frequency discriminator configuration, with a BAW resonator as frequency reference. Some of the elements of this bench are at the state of the art for integrated circuits functions in terms of noise performance (low noise amplifier, frequency divider). An application to the measurement of the noise properties of some BAW-SMR resonators is also presented.

Figure 2 .

 2 Figures 2a and 2b : Synthesized frequency source (6.8 GHz to 8 GHz) based on a digital prescaler PLL ; circuit topology (a) and photograph of the chip (b)

Figure 3 :Figure 4 :

 34 Figure 3 : Input power divider and frequency divider by two, featuring four outputs in phase quadrature

Figure 5 :

 5 Figure 5 : Active phase detector, with resistive loads

Figure 6 :Frequency

 6 Figure 6 : Photograph of the low noise output amplifier

Figure 7 :

 7 Figure 7 : Measured equivalent input voltage noise of the amplifier

Figure 8 :

 8 Figure 8 : Overview of the integrated phase noise bench

Figure 9 :

 9 Figure 9 : Measured phase noise of the four SMR resonators, and phase noise floor of the measurement bench

ACKNOWLEDGMENTS

We would like to thank A. Reinhardt and J.B. David from CEA-LETI for integrated resonator realization. This work has been performed in the frame of the contract "MOBILIS" which was part of the European FP6-IST program.