Pauline Humez

ucalgary.ca Florian Osselin

Wolfram Kloppmann

Bernhard Mayer

A geochemical and multi-isotope modeling approach to determine sources and fate of methane in shallow groundwater above unconventional hydrocarbon reservoirs

Keywords: Methane, groundwater, stable isotope ratios, geochemical modelling, shale gas, coalbed methane

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A geochemical and multi-isotope modeling approach to determine sources and fate of methane in shallow groundwater above unconventional hydrocarbon reservoirs

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Introduction

The recent expansion of the natural gas and oil industry into unconventional hydrocarbon reservoirs in North America and other parts of the world (e.g. Argentina, Poland, Russia) is currently transforming the global energy outlook (US EIA, 2015; US EIA, 2016). Shale gas exploitation has increased markedly in the past decade due to horizontal drilling and hydraulic fracturing which have allowed the exploitation of hydrocarbon resources trapped in very low permeability source rocks. The production of these resources, however, is often associated with environmental concerns regarding freshwater consumption and potential contamination of surface water and groundwater, the appropriate management and treatment of fracturing chemicals and produced fluids, as well as other issues including induced seismicity, noise, traffic, air quality and atmospheric emissions (e.g. [START_REF] Rivard | An overview of Canadian shale gas production and environmental concerns[END_REF].

One of the main concerns is the potential migration of natural gas (composed mostly of methane, CH 4 ) toward freshwater resources (e.g. [START_REF] Jasechko | Hydraulic fracturing near domestic groundwater wells[END_REF][START_REF] Lefebvre | Mechanisms leading to potential impacts of shale gas development on groundwater quality[END_REF][START_REF] Rice | Groundwater-quality hazards of methane leakage from hydrocarbon wells: A review of observational and numerical studies and four testable hypotheses[END_REF][START_REF] Bachu | Analysis of gas leakage occurrence along wells in Alberta, Canada, from a GHG perspective -Gas migration outside well casing[END_REF][START_REF] Cahill | Mobility and persistence of methane in groundwater in a controlled-release field experiment[END_REF][START_REF] Digiulio | Impact to Underground Sources of Drinking Water and Domestic Wells from Production Well Stimulation and Completion Practices in the Pavillion, Wyoming, Field[END_REF]Harkness et al., 2017;[START_REF] Nicot | Controls on Methane Occurrences in Shallow Aquifers Overlying the Haynesville Shale Ga s Field, East Texas[END_REF]Wolfe and Wilkin, 2017). According to the terminology of [START_REF] Milkov | Revised genetic diagrams for natural gases based on a global dataset of >20,000 samples[END_REF], methane in natural environments can have biotic or abiotic origins. Biotic CH 4 is derived from biologically produced organic matter while the numerous reaction pathways resulting in abiotic methane production from geological sources are gaining increasing attention (Sherwood Lollar et al., 1993;[START_REF] Glasby | Abiogenic origin of hydrocarbons: An historical overview[END_REF][START_REF] Etiope | Abiotic Methane on Earth[END_REF][START_REF] Etiope | Abiotic Gas: Atypical, But Not Rare[END_REF].

A C C E P T E D M A N U S C R I P T

Biotic CH 4 is produced either by microbial or thermogenic degradation of organic matter.

Microbial CH 4 (also often called biogenic) is formed in relatively shallow geological formations through the microorganism-mediated decomposition of organic matter via acetate fermentation or reduction of CO 2 . Thermogenic gas is generated by degradation reactions of organic matter in deeper geological formations under high pressure and temperature (Whiticar, 1999;[START_REF] Schoell | The hydrogen and carbon isotopic composition of methane from natural gases of various origins[END_REF]Schoell, 1983).

Different classification schemes and plots [START_REF] A C C E P T E D M A N U S C R I P T Bernard | Natural-gas seepage in gulf of mexico[END_REF][START_REF] Bernard | A Geochemical Model For Characterization Of Hydrocarbon Gas Sources In Marine Sediments[END_REF][START_REF] Schoell | The hydrogen and carbon isotopic composition of methane from natural gases of various origins[END_REF]Schoell, 1983;Whiticar & Faber, 1986) recently revised by [START_REF] Milkov | Revised genetic diagrams for natural gases based on a global dataset of >20,000 samples[END_REF] have been used to distinguish microbial gases from thermogenic gases even though post-genetic reactions may alter the initial chemical or isotopic signature of methane and higher alkanes.

Natural gas of primary microbial origin usually contains at most trace amounts (<0.05%) of higher alkanes (C 2+ ) such as ethane resulting in a dryness parameter (CH 4 /(∑C 2+ ) higher than 1000 [START_REF] Bernard | A Geochemical Model For Characterization Of Hydrocarbon Gas Sources In Marine Sediments[END_REF] although dryness ratios as low as 100 for microbial gases have been reported more recently [START_REF] Milkov | Revised genetic diagrams for natural gases based on a global dataset of >20,000 samples[END_REF]. Additionally, microbial gas has usually carbon isotope ratios of methane expressed as δ 13 C CH4 (in ‰ vs. the standard V-PDB) ranging from -120 ‰ to a traditional upper limit of -60‰ (Schoell, 1983) that was recently revised to a higher value of -50‰ [START_REF] Milkov | Revised genetic diagrams for natural gases based on a global dataset of >20,000 samples[END_REF]. Thermogenic natural gas typically contains > 2% C 2+ alkanes resulting in a dryness parameter of <500, and is usually characterized by δ 13 C CH4 values > -55‰ (Schoell, 1983) although more negative δ 13 C values for immature thermogenic methane have been reported [START_REF] Rowe | Low-temperature thermal generation of hydrocarbon gases in shallow shales[END_REF]Tilley and Muehlenbachs, 2011;[START_REF] Milkov | Revised genetic diagrams for natural gases based on a global dataset of >20,000 samples[END_REF]. [START_REF] Milkov | Revised genetic diagrams for natural gases based on a global dataset of >20,000 samples[END_REF] revised and enlarged the thermogenic gas field compared to the original diagrams of [START_REF] A C C E P T E D M A N U S C R I P T Bernard | Natural-gas seepage in gulf of mexico[END_REF][START_REF] Bernard | A Geochemical Model For Characterization Of Hydrocarbon Gas Sources In Marine Sediments[END_REF] and Schoell (1983) with overall δ 13 C values for thermogenic methane from -20‰ to -73‰, and the range of -55 to -73‰ characterizing early mature thermogenic gases (also referred to as immature gas). Such δ 13 C values for early mature thermogenic gas could be misinterpreted as pure microbial gases but may also constitute a mixture between microbial and thermogenic gas [START_REF] Milkov | Revised genetic diagrams for natural gases based on a global dataset of >20,000 samples[END_REF].

These chemical and isotopic properties of microbial and thermogenic gas form the basis for identifying the sources of methane in shallow environments and in particular shallow groundwaters. Many groundwater monitoring programs mandated by various states in the USA and provinces in Canada rely on these fundamental characteristics to differentiate microbial methane that may have formed in shallow environments from thermogenic fugitive methane. The However, chemical and isotopic fractionation occurring during gas migration and methane oxidation may hinder the isotopic and compositional identification of gas sources (e.g. [START_REF] Etiope | Natural gas seepage: the Earth's hydrocarbon degassing[END_REF][START_REF] Prinzhofer | Isotopically light methane in n atural gas: bacterial imprint or diffusive fractionation?[END_REF]. Solubilities of methane, ethane, and higher alkanes vary as a function of pressure and temperature [START_REF] Culberson | Phase Equilibria in Hydrocarbon-Water Systems III -The Solubility of Methane in Water at Pressures to 10,000 PSIA[END_REF]IUPAC-NIST, 2012). During the migration of fluids from hydrocarbon reservoirs at depths between 2 and 4 km, towards the Earth' surface, alkanes will exsolve into a free gas phase at different rates causing changes in the dryness parameter [START_REF] Mcauliffe | Solubility in Water of C1-C9 Hydrocarbons[END_REF], a process often referred to as solubility fractionation [START_REF] A C C E P T E D M A N U S C R I P T Mcintosh | A Critical Review of State-of-the-Art and Emerging Approaches to Identify Fracking-Derived Gases and Associated Contaminants in Aquifers[END_REF][START_REF] Milkov | Revised genetic diagrams for natural gases based on a global dataset of >20,000 samples[END_REF]. Some studies have reported 12 C enrichment due to diffusive migration effects in coal leading to more negative δ 13 C CH4 values in diffused CH 4 compared to its source [START_REF] Prinzhofer | Genetic and post-genetic molecular and isotopic fractionations in natural gases[END_REF][START_REF] Prinzhofer | Isotopically light methane in n atural gas: bacterial imprint or diffusive fractionation?[END_REF]. In addition, methane may undergo partial oxidation under aerobic (coupled with O 2 reduction) or anaerobic conditions (e.g. coupled with denitrification or bacterial sulfate reduction). During oxidation, the light isotopes 12 C and 1 H are preferentially metabolized, leaving the remaining methane enriched in 13 C and 2 H resulting in elevated δ 13 C and δ 2 H values in the remaining methane (Whiticar and Faber, 1986;[START_REF] Barker | Carbon isotope fractionation during microbial methane oxidation[END_REF]. In consequence, it is possible to find microbial but partially oxidized methane with δ 13 C values between -50 and -30 ‰, i.e. in the range of thermogenic methane. Such elevated δ 13 C values of microbial methane that has undergone partial oxidation is referred to as pseudo-thermogenic. These processes may hinder the accurate differentiation of thermogenic and microbial methane leading potentially to false claims of thermogenic gas occurrence in shallow environments, if the assessment relies on the interpretation of gas composition and gas isotope ratios alone [START_REF] Rice | Groundwater-quality hazards of methane leakage from hydrocarbon wells: A review of observational and numerical studies and four testable hypotheses[END_REF].

It is therefore essential to develop reliable approaches to differentiate truly thermogenic gases from pseudo-thermogenic methane, namely microbial methane that has undergone oxidation, to accurately detect migration of methane from deep geological strata into shallow aquifers. The incorporation of other aqueous species and their isotopic fingerprints such as dissolved inorganic carbon (DIC), sulfate, and nitrate (if present) in such an approach can reveal processes such as denitrification and bacterial sulfate reduction coupled with anaerobic or aerobic oxidation of methane impacting the concentrations and carbon isotope ratios of DIC and methane.

Determining concentration and isotope ratios for the relevant dissolved and gaseous compounds and subsequent joint interpretation of the results is therefore a highly promising approach to

A C C E P T E D M

A N U S C R I P T assess whether methane in groundwater has been affected by geochemical processes modifying its isotopic composition. The often complex and challenging interpretation of such data sets can be facilitated by the use of geochemical modeling programs. One of the most widely used thermo-kinetic codes is PHREEQC, developed by the US Geological Survey (USGS), able to simulate geochemical reactions between water, gas, and mineral phases in aqueous systems (Parkhurst and Appelo, 2009). Hence, PHREEQC could be a powerful tool for the quantitative assessment of the sequence and the extent of biogeochemical reactions potentially affecting the chemical and isotopic fingerprints of methane, provided that the associated isotope fractionations factors are taken into account. In this case, inverse geochemical modeling of aerobic or anaerobic methane oxidation processes would allow backtracking to the original sources and concentrations of methane in shallow groundwater.

The objective of this study was to develop a method for accurately determining the origin and fate of methane in groundwater by integrating chemical and isotopic monitoring data of dissolved gases and aqueous species into a stringent geochemical model. A multi-isotope PHREEQC module was written for this study and tested on a groundwater data set from aquifers in Alberta, Canada. The module describes generic concepts controlling methanogenesis and methane oxidation that can be transferred to other groundwater study sites, associated with coalbed methane and shale gas development.

Shallow aquifers in Alberta

Alberta is Canada's most important oil and natural gas producing province with large conventional and unconventional hydrocarbon reserves. The latter include crude bitumen in northern Alberta, shale gas and tight gas 1 in the northwest, and coal bed methane (CBM) in southcentral Alberta (AER, 2014). Since the exploitation of these resources is often associated with environmental concerns regarding water consumption and potential contamination of shallow aquifers, groundwater monitoring programs have been put into place to detect potential adverse impacts from resource development, initially implemented during the phase of rapid development of unconventional energy resources accessing coal bed methane (CBM) (e.g. AER Directive 35).

In the area that was targeted for CBM production, the Government of Alberta maintains a number of monitoring wells belonging to the provincial Groundwater Observation Well Network 1 defined as low permeability non-shale gas reserves by AER (2015) has collected water levels and chemical and isotopic water quality information for aqueous samples and dissolved and free gases from, on average, 60 monitoring wells per year (Humez et al., 2016a;Humez et al., 2016b).

A C C E P T E D M A N U S C R I P T (GOWN)
For this study, we selected 21 GOWN wells that were repeatedly (between 2 and 10 times)

sampled between 2006 and 2018 and are mostly located in the southern part of the Province of Alberta (Figure 1). [START_REF] Lyster | Geostatistical rendering of the architecture of hydrostratigraphic units within the Paskapoo Formation, Alberta[END_REF][START_REF] Culberson | Phase Equilibria in Hydrocarbon-Water Systems III -The Solubility of Methane in Water at Pressures to 10,000 PSIA[END_REF][START_REF] Hamblin | The Horseshoe Canyon Formation in Southern Alberta: Surface and subsurface stratigraphic architecture, sedimentology, and resource potential[END_REF]. The terrestrial fluvial Upper and Lower Horseshoe Canyon Formation is mainly composed of sand and coal, whereas the marine Middle Horseshoe Canyon formation consists predominantly of shale with bentonite and little sandstone or coal [START_REF] Culberson | Phase Equilibria in Hydrocarbon-Water Systems III -The Solubility of Methane in Water at Pressures to 10,000 PSIA[END_REF]. The Belly River Group formation consists of fluvial sandstone and siltstone with minor mudstone and coal. All these formations comprise heavily used aquifers in the prairie region of Alberta [START_REF] Grasby | Regional characterization of the Paskapoo bedrock aquifer system, southern Alberta Geological Survey of Canada Contribution 2008-0479[END_REF]. The coal zones with CBM potential are included in the Horseshoe Canyon and the Belly River formations. Thin coal seams also occur throughout the Paskapoo Formation. The reported aquifer lithologies often vary considerably within each well and from one well to the other, from sandstone to siltstone with intermittent coal or shale beds lenses, preglacial sand, or surficial sandy and gravelly lacustrine or moraine deposits, giving rise to complex multi-aquifer systems. More information about these geological formations can be found in [START_REF] Meyboom | Geology and groundwater resources of the Milk River sandstone in southern Alberta[END_REF], [START_REF] Rosenthal | Depositional cycles and facies relationships within the Upper Cretaceous Wapiabi and Belly River formations of west central Alberta[END_REF], Hamblin (1998), [START_REF] Hamblin | The Horseshoe Canyon Formation in Southern Alberta: Surface and subsurface stratigraphic architecture, sedimentology, and resource potential[END_REF], [START_REF] Culberson | Phase Equilibria in Hydrocarbon-Water Systems III -The Solubility of Methane in Water at Pressures to 10,000 PSIA[END_REF], [START_REF] Lyster | Geostatistical rendering of the architecture of hydrostratigraphic units within the Paskapoo Formation, Alberta[END_REF], [START_REF] Grasby | Regional characterization of the Paskapoo bedrock aquifer system, southern Alberta Geological Survey of Canada Contribution 2008-0479[END_REF][START_REF] Prior | Bedrock Geology of Alberta[END_REF].

A C C E P T E D M

A N U S C R I P T

Sampling, Methods and Obtained Results

Two highly trained teams of sampling specialists from Alberta Environment and Parks (AEP)

have collected aqueous and gaseous groundwater samples from GOWN wells since 2006 and the sampling campaigns are still ongoing. Groundwater samples repeatedly obtained from 21 GOWN wells selected for this study were analyzed for aqueous and gaseous geochemical compositions and isotopic compositions of various compounds using analytical procedures that are described in the Supplementary Information section and in previous publications (Humez et al., 2016a;Humez et al., 2016b). A total of 88 samples were analyzed for major ion chemistry including concentrations of Ca, Mg, Na, K, SO 4 , NO 3 , Cl, and dissolved inorganic carbon (DIC), and concentrations of dissolved gases including methane. In addition, the isotopic compositions of dissolved methane (δ 13 C CH4 , δ 2 H CH4 ), sulfate (δ 34 S SO4 , δ 18 O SO4 ) and DIC (δ 13 C DIC ) were determined. The analytical data obtained for these groundwater samples from the 21 wells constitute a comprehensive, long-term monitoring record of dissolved gas contents, aqueous compositions, and isotopic fingerprints.

The analytical results for major and minor ion concentrations and isotopic fingerprints for the GOWN groundwater samples utilized for this study are summarized in Tables SI-1 and SI-2. The major ion concentrations vary widely and the water-types comprise Ca-HCO 3 , Na-HCO 3 and Na-Cl facies. Average concentrations of calcium and sodium varied from 0.02 to 3 mmol/kgw (millimoles per kilogram water) and from 8 to 70 mmol/kgw respectively (Table SI-1), while average chloride concentrations ranged between 0.01 and 40 mmol/kgw (Table SI-1).

Groundwater samples were found to be in thermodynamic equilibrium with calcite present as cement in most of the studied aquifers [START_REF] Hamblin | The Horseshoe Canyon Formation in Southern Alberta: Surface and subsurface stratigraphic architecture, sedimentology, and resource potential[END_REF][START_REF] Grasby | Regional characterization of the Paskapoo bedrock aquifer system, southern Alberta Geological Survey of Canada Contribution 2008-0479[END_REF] resulting in buffered pH values of 7.6 to 9.2 and in alkalinity concentrations of 5.1 to 20 mmol/kgw (Table SI-1). In this pH range, the main inorganic carbon species is bicarbonate (HCO 3 -). Methane was found to be ubiquitous in the groundwater samples with concentrations varying from 2.9 10 -4 to 2.4 mmol/kgw. The highest concentrations of methane (>0.01 mmol/kgw) were found in the Na-

A C C E P T E D M A N U S C R I P T
HCO 3 and Na-Cl water-types where the sulfate concentrations are <1 mmol/kgw as previously reported by Humez et al. (2016a,b).

The δ 18 O and δ 2 H values for groundwater varied from -24.0 to -8.9 ‰ and from -191 to -94 ‰ vs. VSMOW respectively, indicating atmospheric recharge of groundwater (Humez et al., 2016b).

Average δ 34 S SO4 values of sulfate ranged between +37 and -10 ‰ vs. V-CDT and average δ 18 O SO4 values varied between -7.0 and +7.9‰ vs. VSMOW (Table SI-2). Groundwater samples with the highest sulfate concentrations were characterized by δ 34 S SO4 and δ 18 O SO4 values <0 ‰ indicating that sulfate is predominantly derived from pyrite oxidation [START_REF] Grasby | Influence of till provenance on regional groundwater geochemistry[END_REF]. values varied from -84 to -26 ‰ vs. V-PDB, the highest δ 13 C CH4 values being associated with the lowest methane concentrations (2.9 10 -4 mmol/kgw) suggesting methane oxidation.

δ
4.

5.

Model development

Model framework

The geochemical and isotopic evolution of the different species of interest was investigated using the geochemical modeling code PHREEQC [START_REF] Parkhurst | User's guide to PHREEQC (version 2) -a computer program for speciation, reaction-path, 1D-transport, and inverse geochemical calculations[END_REF] combined with the Thermoddem database [START_REF] Blanc | Thermoddem -A database devoted to waste minerals[END_REF]. The starting point of the modeling approach is the identification of the geochemical processes that can affect methane concentrations and isotopic compositions (see Supplementary Information). A key process is methane oxidation, which can occur when methane migrates into aquifer sections with more oxidizing conditions (half-reaction Eq. 1):

CH 4 + 3H 2 O = HCO 3 -+ 9H + +8e -(1)
This oxidation reaction can proceed with several electron acceptors present in the groundwater samples. Measured dissolved oxygen concentrations in the Alberta groundwater samples (Tables SI-1 and SI-2) are consistently <1.0 mg/L, indicating anoxic or post-oxic conditions [START_REF] Berner | New geochemical classification of sedimentary environments[END_REF] while iron and manganese are present as reduced iron Fe(II) and manganese Mn(II) and 2b and2c).

A C C E P T E D M A N U S C
Therefore, methanogenesis will be modeled exclusively using the CO 2 reduction pathway. It is interesting to note that the methane-poor groundwater samples (black label) are located outside of the fields of microbial methane production, suggesting that AOM may have occurred. Depending on the geochemical facies, the investigated groundwater samples can be separated in two zones named Zone 1 and Zone 2. The conceptual approach for distinguishing the two zones is summarized in Figure 3. The mass balance for sulfate content at time t+dt in an element volume of zone 1 can be expressed as: , this results in Equation 6:

n SO4 (t + dt) = n SO4 (t) + Q × {SO 4 } in × dt -Q × {SO 4 }(t) × dt -r CH4 × dt (
{𝑆𝑂 4 }(𝑡) = 𝑛 0 𝑉 - 𝑛 𝐶𝐻4 𝑉 (6)
with n 0 the initial quantity of sulfate in the considered element volume and n CH4 the total amount of methane added to the volume between t=0 and t. Equation ( 6) links the open system behavior to a hypothetical batch system (closed system) where the hypothetical initial quantities of sulfate ). This simplifies the modeling considerably as PHREEQC is designed to handle batch systems. In the following, the open system of zone 1 will be modeled as a closed system through the transformation defined in Equation 6.

Since the actual system is an open system, products of AOM and BSR are being flushed away from the considered volume by groundwater movements and the reactants are replenished. This process is similar to a Rayleigh distillation as shown in Equation 7for methane and Equation 8for sulfate:

δ 13 C CH4 = δ 13 C CH4-fugitive + ε DIC-CH4 ln f (7) δ 34 S 𝑆𝑂4 = δ 34 S SO4-initial + ε H2S-SO4 ln f (8) with f = [CH 4 ]/[CH 4 ] 0 (resp. = [SO 4 ]/[SO 4 ] 0 )
, the fraction of remaining methane or sulfate after oxidation with respect to the initial fugitive methane and sulfate concentrations in the zone.

Carbon and sulfur isotope enrichment factors between DIC and methane and between H 2 S and sulfate are ε DIC-CH4 andε H2S-SO4 . δ 13 C CH4-fugitive represents the carbon isotope ratio of the fugitive methane source prior to oxidation and δ 34 S SO4-initial is the initial sulfur isotope ratio of dissolved sulfate prior to methane intrusion.

However, the 34 S/ 32 S ratios of sulfate and 13 C/ 12 C ratios of methane are modified by isotope fractionation during bacterial sulfate reduction and methane oxidation, but also by the amount of fresh sulfate and methane being replenished by recharge waters and methane intrusion. This isotopic "dilution" is considered in this study by introducing an apparent enrichment factor 𝜀′ 𝑎-𝑏 = 𝜀 𝑎-𝑏 (1 -𝛽) which includes the intrinsic enrichment factor 𝜀 𝑎-𝑏 from the literature, and 𝛽 a recharge factor. The limiting values are 𝛽 = 1 (the net stream input is equal to the quantity of consumed sulfate and methane), and hence the sulfate and methane concentrations and stable isotope compositions remain constant, and 𝛽 = 0 (no flux, classical Rayleigh equation).

Finally, in such an open system the inorganic carbon pool is constantly renewed by the groundwater flow and to a lesser extent by calcite dissolution. Therefore, for zone 1 it is assumed that the isotopic composition of the DIC is imposed by the isotopic equilibrium between atmospheric CO 2 and calcite in an open system and is thus not affected by methane oxidation.

A C C E P T E D M

A N U S C R I P T Since the oxidation potential decreases along the groundwater flowpath, groundwater that accumulates methane may have a longer residence time [START_REF] Bates | Influence of groundwater flowpaths, residence times and nutrients on the extent of microbial methanogenesis in coal beds: Powder River Basin, USA[END_REF]. In such conditions, the groundwater flow is considered negligible, meaning that no recharge and flushing of the dissolved species (except for H 2 S) needs to be considered, contrary to zone 1. This implies that sulfur isotope ratios of sulfate will evolve following Equation 8 with the intrinsic sulfur isotope enrichment factor varying between -15 to -42‰ [START_REF] Krouse | Sulfur isotope studies and their role in petro leum exploration[END_REF][START_REF] Krouse | Sulphur isotopes in our environment[END_REF][START_REF] Aravena | Isotopes and Processes in the Nitrogen and Sulfur Cycles[END_REF] instead of the apparent isotope enrichment factor used in zone 1. Furthermore, the closed system implies that δ 13 C values of methane and DIC will not follow a Rayleigh distillation equation and therefore are best calculated with a mass balance equation.

Additionally, equilibrium with calcite will play a larger role than in zone 1 in the closed system of zone 2. Methane oxidation produces DIC, which triggers calcite precipitation. However, methanogenesis consumes H + as described in Eq. SI-6, which increases the pH. Since the solubility of calcite increases with decreasing DIC and decreases with increasing pH, methanogenesis has a non-trivial effect on calcite solubility and both dissolution and precipitation need to be considered in the modelling of zone 2b. Finally, since the carbon isotope ratio of the precipitated calcite and the remaining methane at a date t will depend on the DIC at that same

A C C E P T E D M

A N U S C R I P T time t, the whole process needs to be divided into infinitesimal steps that calculate the chemical and isotopic compositions of the solution at each time step. In practice, the calculation proceeds in 100 steps.

Zone 2a: Methanic conditions

For zone 2a, the evolution of the δ 13 C value of DIC in solution is described by Equation ( 9):

𝛿 13 𝐶 𝐷𝐼𝐶 (𝑖 + 1) =

𝛿 13 𝐶 𝐷𝐼𝐶 (𝑖){𝐷𝐼𝐶}(𝑖)+𝑑𝑛 𝐶𝐻4 (𝛿 13 𝐶 𝐶𝐻4 (𝑖+1)+𝜀 𝐷𝐼𝐶-𝐶𝐻4 )-dn 𝑐𝑎𝑙 𝜀 𝑐𝑎𝑙-𝐷𝐼𝐶 {𝐷𝐼𝐶}(𝑖+1)+dn 𝑐𝑎𝑙 (9) with {DIC} the molality of dissolved inorganic carbon and dn CH4 the quantity of methane oxidized between steps i and i+1, dn cal the quantity of DIC removed through calcite precipitation between i and i+1, and 𝜀 𝑐𝑎𝑙-𝐷𝐼𝐶 the carbon isotope enrichment factor for calcite precipitation.

For zone 2a, the isotope mass balance for carbon isotope ratios of methane depends on the proportion of methane that was oxidized and is calculated as follows:

𝛿 13 𝐶 𝐶𝐻4 (𝑖 + 1) = 𝛿 13 𝐶 𝐶𝐻4 (𝑖){𝐶𝐻 4 }(𝑖)-𝑑𝑛 𝐶𝐻 4 𝜀 𝐷𝐼𝐶-𝐶𝐻4 {𝐶𝐻 4 }(𝑖+1)+𝑑𝑛 𝐶𝐻4 (10)

Zone 2b: Methanogenic conditions

In contrast to zone 2a, methane is produced in-situ in zone 2b. Two reactions need to be considered: (1) methanogenesis via the CO 2 reduction pathway consuming DIC and producing methane with a specific carbon isotope enrichment factor through a specific microorganism consortium, and (2) oxidation of the produced methane coupled with bacterial sulfate reduction decreasing sulfate concentrations while adding to the inorganic carbon pool mediated by another specific microorganism consortium. In addition, the groundwater in zone 2b is considered to be in equilibrium with calcite. Figure 4 summarizes how CH 4 , DIC, SO 4 and calcite are interlinked and describes the conceptual scheme for zone 2b.

A C C E P T E D M A N U S C R I P T

Calculations of δ 13 C DIC values in zone 2b are performed in a similar fashion as described above for zone 2a while differentiating whether calcite is dissolving or precipitating. For calcite precipitation, the evolution for the δ 13 C value of DIC at a step i+1 is expressed as follows:

𝛿 13 𝐶 𝐷𝐼𝐶 (𝑖 + 1) = 𝛿 13 𝐶 𝐷𝐼𝐶 (𝑖){𝐷𝐼𝐶}(𝑖) + 𝑑𝑛 𝐶𝐻4 (𝛿 13 𝐶 𝐶𝐻4 (𝑖 + 1) + 𝜀 𝐷𝐼𝐶-𝐶𝐻4 ) -dn 𝑐𝑎𝑙 𝜀 𝑐𝑎𝑙-𝐷𝐼𝐶 -dn 𝑚𝑒𝑡ℎ𝑎𝑛𝑜 𝜀 𝑚𝑒𝑡ℎ𝑎𝑛𝑜 {𝐷𝐼𝐶}(𝑖 + 1) + dn 𝑐𝑎𝑙 + dn 𝑚𝑒𝑡ℎ𝑎𝑛𝑜 (11) with {DIC} the molality of dissolved inorganic carbon, dn cal the quantity of DIC removed from the solution by calcite precipitation (>0) between i and i+1, and dn methano the quantity of DIC removed by methanogenesis (>0).

The δ 13 C values of marine carbonates vary between 0‰ and +2‰ (Gautschi et al., 1991) and we used δ 13 C calcite of 0 ‰ in this study. Since calcite dissolution is considered to be a nonfractionating process Equation ( 11) becomes:

𝛿 13 𝐶 𝐷𝐼𝐶 (𝑖 + 1) =

𝛿 13 𝐶 𝐷𝐼𝐶 (𝑖){𝐷𝐼𝐶}(𝑖)+𝑑𝑛 𝐶𝐻4 (𝛿 13 𝐶 𝐶𝐻4 (𝑖+1)+𝜀 𝐷𝐼𝐶-𝐶𝐻4 )+𝑑𝑛 𝑚𝑒𝑡ℎ𝑎𝑛𝑜 𝜀 𝑚𝑒𝑡ℎ𝑎𝑛𝑜 {𝐷𝐼𝐶}(𝑖+1)+dn 𝑚𝑒𝑡ℎ𝑎𝑛𝑜 (12) 6.

Application of the Model to Alberta Groundwater Data

Description of the modeling scenarios

A series of scenarios with different initial conditions were selected for zones 1 and 2a,b (Table 1).

In all the scenarios, incremental quantities of methane (from 10 -7 to 1 mol/kgw) were added to the batch system and the final geochemical and isotopic compositions of dissolved groundwater constituents were calculated with PHREEQC as described in the previous section. The variables considered were the isotopic composition of fugitive methane for zone 1 and 2a (δ 13 C CH4, fugitive ), the initial 34 S/ 32 S ratio of sulfate in groundwater (δ 34 S SO4,initial -indicative of pyrite oxidation), the intrinsic (ε H2S-SO4 , ε DIC-CH4 , ε methanogenesis ) or apparent (ε' DIC-CH4 ,ε' H2S-SO4 ) carbon and sulfur isotope enrichment factors, the initial concentration of sulfate (SO 4 initial reservoir ) for zone 1 and the initial Three different carbon isotope ratios for fugitive methane were chosen to represent a wide range of δ 13 C values indicative of microbial (-80‰, -110‰) and late mature thermogenic (-35‰) methane origin. Three apparent carbon isotope enrichment factors ε' DIC-CH4 = -10‰, -5‰ and -2‰ were also considered in order to take into account the recharge effect on DIC in zone 1.

Carbon isotope enrichment factors for bacterial methane oxidation (ε DIC-CH4 ) of -15, -10 and -5‰

were used for intrinsic enrichment factors in zone 2 (Whiticar, 1999). The apparent sulfur isotope enrichment factor (ε' H2S-SO4 ) for BSR was -5‰ in zone 1, while the intrinsic ε H2S-SO4 was chosen between -15 and -42‰ in zone 2 to represent the full range of literature values [START_REF] Krouse | Sulfur isotope studies and their role in petro leum exploration[END_REF][START_REF] Krouse | Sulphur isotopes in our environment[END_REF][START_REF] Aravena | Isotopes and Processes in the Nitrogen and Sulfur Cycles[END_REF]. Finally, in order to consider the effect of recharge on the sulfate balance, four initial sulfate concentrations were chosen at 0.2, 0.085, 0.008 and 0.002 mol/kgw.

The initial δ 13 C value of CO 2 in zone 2 was either -20 ‰ or -30 ‰ corresponding to the typical range of carbon isotope ratios for CO 2 in soils derived from C 3 plants [START_REF] Rightmire | Relationship between the carbon isotope composition of soil CO2 and dissolved carbonate species in groundwater[END_REF]. Three different initial DIC concentrations were considered at 0.02, 0.01 and 6.10 -3 mol/kgw and two different carbon isotope enrichment factors for methanogenesis (ε methanogenesis ) of -60‰ and -95‰ (Whiticar and Faber, 1986). By convention: all fractionation factors ε are defined as ε b-a =δ b -δ a where δ is the relative deviation of the isotopic ratios of a the reactant and b the product of reaction from an international standard.

6.2 Geochemical evolution of the CH 4 -calcite-SO 4 system

The intrusion of methane into the initially SO 4 -rich groundwaters of zone 1 depletes the systems in sulfate through the combined action of AOM and BSR. Figure 5 shows the modeling results as solid lines (scenarios A1, G1 and H1) and dashed lines (D1). An anti-correlation between sulfate and methane concentrations is observed (i.e. the higher the methane content, the lower the sulfate concentration) following a 1:1 ratio since one mole of sulfate reacts with one mole of methane as described by Equation 3. The grey line represents the boundaries of zone 1 (Figure 5).

A C C E P T E D M A N U S C R I P T

In zone 2a, the fugitive methane is penetrating a zone where redox conditions can allow its presence and persistence. However, a small proportion of the fugitive methane will still be oxidized coupled with bacterial reduction of the remaining residual sulfate. This results in a slight increase of the DIC content (blue lines in Figure 6 corresponding to the methanic zone 2a). The methane oxidation process is limited by the low availability of sulfate allowing large concentrations of methane (up to saturation) to build up.

For zone 2b, two competing processes are at play: (1) the main process of methanogenesis simulated by CO 2 reduction and (2) the limited reduction of the remaining sulfate present in low concentrations < 1 mmol/kgw coupled with the oxidation of the produced methane. Both anaerobic methane oxidation coupled with BSR and methanogenesis impact the DIC pool in the aquifer. However, considering the low to negligible sulfate concentrations, the effect of methanogenesis on the DIC pool will be dominant. Orange lines corresponding to zone 2b scenarios in Figure 6 show the impact of methanogenesis via DIC reduction on the carbonate equilibrium of the batch simulations. It is interesting to see that calcite dissolution does not compensate the DIC removal from solution by methanogenesis, because of the concomitant pH increase, which decreases calcite solubility.

Figure 6: Relationship between DIC and dissolved methane concentrations for zones 2a (blue lines) and 2b (oranges lines) for groundwater from the 21 monitoring water wells. A2, A3, B2, B3, C2 and C2 refer to scenarios explained in Table 1.

The different scenarios are adequately characterizing the data for GOWN groundwater samples with the exception of the samples shown in green where both sulfate and methane concentrations are low and plot below scenarios A, B and C (Figure 6). In contrast, groundwater from well #214 had an unusually high DIC content as shown on Figure 6, plotting on the right of scenarios C2/C3. This may be the result of a different geochemical reaction decreasing pH and allowing for more calcite dissolution.

A C C E P T E D M

A N U S C R I P T 6.3 Isotopic evolution of the CH 4 -calcite-SO 4 system

C isotope evolution of methane

Both methane oxidation and methanogenesis processes have a strong impact on the carbon (and hydrogen) isotope ratio of methane. For zone 1 and 2a, the fugitive methane arrives in the aquifer from below with a constant isotopic composition and is then oxidized. Since methane oxidation fractionates carbon isotopes favoring the lighter 12 C in the produced CO 2 , the remaining methane becomes progressively enriched in 13 C ( [START_REF] Barker | Carbon isotope fractionation during microbial methane oxidation[END_REF]. Figure 7 represents the evolution of δ 13 C of methane during AOM coupled with BSR. Scenarios A1, F1 and G1 represent the intrusion of microbial methane with δ 13 C values of -80 and -110‰ respectively, while E1

represents the intrusion of thermogenic methane with a δ 13 C value of -35‰.

As represented in Figure 7, methane in zone 1 (black lines) is characterized by a significant 13 C enrichment of up to 60‰ compared to the carbon isotope ratio of the original methane during AOM coupled with BSR. When following the black lines of Figure 7 towards lower sulfate concentrations, the remaining methane concentration increases (Figure 5), and thus the δ 13 C CH4 values of the remaining methane approach asymptotically the initial δ 13 C CH4 value of the fugitive methane, corresponding to large amounts of methane and small amounts of sulfate. Even if black lines are theoretically only valid for zone 1, those scenarios have been prolonged for sulfate concentrations below 1 mmol/kgw, to show the effect of complete BSR coupled with oxidation of methane that intruded into an initially sulfate rich aquifer (Figure 7). The different scenarios are adequately characterizing the data for GOWN groundwater samples. Figure 8 Processes that impact the δ 13 C values of methane are similar in zone 2a compared to those in zone 1 (blue lines, Figure 7). The initial δ 13 C CH4 value from fugitive methane increases at first as a consequence of methane oxidation coupled with BSR and then decreases again toward the isotopic composition of the fugitive methane with increasing methane concentration in the system (Figure 7). The three scenarios A2, B2 and C2 differ only in the C isotope enrichment factor for bacterial methane oxidation (ε DIC-CH4 ) equal to -5‰, -10‰, and -15‰, respectively. Finally, in zone 2b, the model considers that methanogenesis is consuming DIC to produce methane while the reduction of low to negligible remaining sulfate oxidizes only a small quantity of the produced methane (see Figure 4 for the conceptual interplay). Scenarios describing methanogenesis are represented with orange lines in Figure 7 and show a very sharp increase of δ 13 C CH4 values up to >+25‰ for sulfate concentrations around 5.10 -6 mol/kgw as the remaining DIC substrate is getting enriched in 13 C.

Figure 8: Effect of apparent carbon isotope enrichment factors ε' DIC-CH4 during the methane oxidation process on fugitive methane δ 13 C CH4 values intruding zone 1.

S isotope evolution of sulfate

As bacterial sulfate reduction in the model is calculated as a Rayleigh distillation process in all 3 zones, scenarios plot as straight lines with slope ε(or ε')in the δ 34 S versus log(SO 4 ) concentration plot in Figure 9. As described in the model set-up, zone 1 is characterized by a lower apparent sulfur isotope enrichment factor for BSR due to the influence of the recharge of fresh sulfate-rich groundwater. As mentioned in section 5.2, sulfate renewal is not considered for zones 2a and 2b and the S isotope enrichment factor for BSR becomes equal to the intrinsic enrichment factor from the literature. Two different slopes for zone 2 are represented in Figure 9 with ε SO4-HS = -15‰ and -42‰ showing the full extent of the literature range [START_REF] Aravena | Isotopes and Processes in the Nitrogen and Sulfur Cycles[END_REF]. Scenarios are differentiated by their initial sulfate content and initial δ 34 S values.

The influence of these two parameters can be seen in Two characteristic δ 13 C values for DIC are represented at -13‰ and -20‰ (Figure 10) [START_REF] Rightmire | Relationship between the carbon isotope composition of soil CO2 and dissolved carbonate species in groundwater[END_REF][START_REF] Kloppmann | Residence time of Chalk groundwaters in the Paris Basin and the North German Basin: a geochemical approach[END_REF].

In zones 2a and 2b, the evolution of δ 13 C values of DIC is very different depending on the type of processes involved (Figure 10, orange and blue lines). In the methanic zone 2a, the δ 13 C value of DIC decreases slowly, following the small increase of DIC concentration (see Figure 6) as a result of methane oxidation coupled with BSR. In contrast, the δ 13 C value of DIC increases markedly during methanogenesis by up to +30‰ for low sulfate concentrations <10 -5 mol/kgw (Zone 2b, Figure 10, orange lines). As the pool of DIC becomes smaller due to the CO 2 consumption by methanogenesis, the remaining DIC becomes strongly enriched in 13 C resulting in a marked δ 13 C DIC increase during methanogenesis. The C isotope ratio of DIC can thus be a very clear marker of such process occurring in the groundwater.

Classification of groundwater from the monitoring wells

The geochemical and isotopic model results allow the attribution of groundwaters from the 21 wells to five categories and also enables the assessment of the initial isotopic composition of the

A C C E P T E D M A N U S C R I P T
methane they contain and of the processes which led to the measured groundwater composition (Table 2). The fifth category represents the groundwater samples with low sulfate and low methane concentrations as observed in wells #140 and #984 (green labels, Figure 5). The low sulfate and methane concentrations can either be explained by (i) initially sulfate and methane poor waters, or (ii) groundwaters subjected to BSR leading to negligible concentrations of sulfate. Evidence of BSR from δ 34 S SO4 is only visible for groundwater from well #140. The option that these groundwater samples are also affected by a small extent of in-situ production of methane is not excluded.

δ 13 C DIC Well > 1 m M < 1 m M > 0 . 0 1 m M < 0 . 0 1 m M > - 5 5 ‰ < - 5 5 ‰ > + 0 ‰ < - 1 0 ‰ 1a
7.

Conclusions and Outlook

The geochemical and multi-isotope modeling approach developed in this study reveals two main sources of methane and the following processes affecting the obtained groundwater samples: (i) in situ methanogenesis resulting in microbial methane for a subset of samples; (ii) migration of microbial methane into aquifers with various redox conditions for a subset of samples, followed enhanced by the PHREEQC modeling of the interplay between methane and redox sensitive species and minerals (e.g. calcite) in the affected shallow aquifers. While designed based on the conditions encountered in groundwater in Alberta (Canada), the modeling approach is applicable to other contexts provided that adaptations are made regarding the main geochemical processes involved. Using sulfate as a key constituent for investigating Alberta groundwaters is pertinent since most groundwaters in Alberta are sulfate-rich, but in aquifers of other regions of the world sulfate may not be the dominant electron acceptor species. Other redox species such as nitrate, iron and manganese oxides may need to be considered and included in the modeling approach depending on the groundwater characteristics of the investigated aquifers. Additionally, even if some hydrochemical concepts were developed in the model to consider inflow and outflow of reactants and products, the batch calculations cannot take into account the whole complexity of groundwater movements and mixing processes at the basin scale. Despite these limitations, the model appears to be sufficiently robust to describe most of the observed chemical and isotopic compositions of the investigated groundwater samples. Hence it provides a suitable tool for decision makers for identifying the origin and fate of methane in groundwater.

Since all the geochemical processes including methane oxidation, bacterial sulfate reduction, and methanogenesis are biologically mediated, an interesting approach to improve the quality of the prediction could be a microbiological and metagenomic analysis of the groundwater samples. The characterization of the microbial communities responsible for the inferred geochemical processes would help to test whether the predicted scenarios are realistic.

For environmental impact assessment associated with the development of hydrocarbon resources from unconventional reservoirs, it is of critical importance to be able to differentiate between microbial methane formed in shallow environments, deep thermogenic methane that may have migrated into shallow aquifers, and microbial methane that has undergone oxidation. The occurrence of the latter process in shallow aquifers often results in a pseudo-thermogenic carbon isotope fingerprint of the remaining methane that can be easily misinterpreted as an intrusion of thermogenic methane from deeper zones. Differentiating these methane sources and processes solely based on concentration and isotope measurements of methane is often impossible. To resolve potential ambiguities of isotope fingerprints of methane and the associated source and process information, the model presented here uses the concentrations and isotopic compositions of methane, DIC and sulfate. Identifying and quantifying redox processes like BSR coupled to methane oxidation is crucial for determining sources and fate of methane in shallow groundwaters. The new modeling approach has the important capability to differentiate truly thermogenic methane from microbial methane that has undergone methane oxidation resulting in pseudo-thermogenic signatures, and hence helps to avoid misinterpretation and false-positives allegations of thermogenic gas leakage. The methodology developed in this study can be adapted and extended to other sites worldwide.

  S C R I P T latter may potentially migrate either from the intermediate depth zone below the base of groundwater protection (BGP, Lemay 2008), or from deep hydrocarbon production zones.

Figure 1 :

 1 Figure 1: Location of the 21 groundwater monitoring wells selected for this study (ID and symbols). The red symbols refer to wells with groundwater having elevated concentrations of methane and black and green symbols refer to wells yielding groundwater with low concentrations of methane.

Figure 2

 2 Figure 2: a) Plot of δ 2 H(CH 4 ) vs. δ 2 H(H 2 O) values and methanogenesis pathways boundaries from Whiticar (1986); b) δ 13 C(CH 4 ) vs. δ 2 H(CH 4 ) diagram from Milkov and Etiope (2018); c) δ 13 C(CO 2 ) vs. δ 13 C(CH 4 ) diagram from Milkov and Etiope (2018) with isotopic compositions of methane, CO 2 and H 2 O from this study added.

Figure 3 :

 3 Figure 3: Conceptual description of initial hypotheses and geochemical and isotopic calculations in zones 1, 2a and 2b as developed in PHREEQC for this study.

  S C R I P TBecause of the comparativey low residence time of these waters, the quantity of available sulfate for AOM gets constantly replenished by lateral groundwater flows, while products of the AOM/BSR coupling such as DIC and sulfides are flushed from the methane intrusion point (= open system). If the recharge sulfate flux is larger than the intruding methane flux, the methane is oxidized and the zone remains sulfate-rich. In contrast, if the recharge sulfate flux is smaller than the intruding methane flux, the zone becomes more and more reducing with decreasing sulfate concentrations and potentially shifting to methanic or methanogenic conditions (zone 2, see section 4.2.2).

  4) with 𝑛 𝑆𝑂4 the amount of SO 4 in the system [mol], 𝑄 [m 3 /s] the constant water flow through the considered element volume V[m 3 ]. Multiplied by SO 4 concentrations, it corresponds to the SO 4renewal/inflow flux and flushed SO 4 /outflow flux. {𝑆𝑂 4 } 𝑖𝑛 is the concentration in the inflow[mol.m -3 ] and 𝑟 𝐶𝐻4 [mol.s -1 ] the reaction rate of BSR coupled with AOM, considered to be constant. If the system is considered to be in steady state conditions (i.e. 𝑡 → ∞), Eq. (4) can then be reduced to: {𝑆𝑂 4 }(𝑡) = {𝑆𝑂 4 } 𝑖𝑛sulfate in the system during the steady-state is the difference between the constant renewal/recharge of sulfate and the constant methane input. If we define {𝑆𝑂 4

  n CH4 ) can be derived from the actual fluxes of the open system ({𝑆𝑂 4 } 𝑖𝑛 and 𝑟 𝐶𝐻4 𝑄

Figure 4 :

 4 Figure 4: Interplay between methanogenesis via CO 2 reduction and bacterial oxidation of produced methane coupled with bacterial sulfate reduction.

  initial ) for zone 2 as well as the initial carbon isotope composition of DIC (δ 13 C DIC ).

Figure 5 :

 5 Figure 5: Evolution of sulfate versus dissolved methane concentrations in simulations and in groundwater from the 21 monitoring water wells.

  displays the effect of different C isotope enrichment factors for methane oxidation for zone 1 with scenarios A1, B1 and C1 representing respectively apparent enrichments factors of -2‰, -5‰, and -10‰, respectively. The apparent enrichment factor affects the steepness of the Rayleigh distillation curve, with a steeper curve for higher ε values; values in the range of -5 and -2‰ seem more realistic for the groundwater samples.

Figure 7 :

 7 Figure 7: Evolution of δ 13 C values of methane versus sulfate concentrations during the simulations of zones 1 (black label), 2a (blue lines) and 2b (orange lines). Scenarios names fromTable 1 are indicated on the Figure.

Figure 9 :Figure 9

 99 Figure 9: a) Evolution of δ 34 S values of sulfate versus sulfate concentration (log(SO 4 )) in zones 1, 2a and 2b. The black lines represent the scenarios of zone 1 and the red lines the undifferentiated zones 2a and 2b; b) Conceptual scheme of the impact of the presence/absence of SO 4 renewal and dilution processes on sulfur isotope enrichment factors ε H2S-SO4 and δ 34 S.

Figure 10 :

 10 Figure 10: Evolution of the δ 13 C DIC values versus sulfate concentrations [log] in zones 1 (black lines), 2a (blue lines) and 2b (orange lines).

  by methane oxidation coupled with bacterial sulfate reduction in sulfate-rich aquifer zones causing a pseudo-thermogenic isotopic fingerprint for the remaining methane. No evidence of thermogenic methane migrating from deep hydrocarbon reservoirs into shallow aquifers was indicated by the model. The accurate detection of contamination of groundwater with fugitive methane, potentially associated with exploitation of conventional and unconventional energy resources, is greatly A C C E P T E D M A N U S C R I P T

Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10

 12345678910 Figure1

  that is comprised of monitoring wells completed in various shallow aquifers throughout the province that are usually screened only in a single formation. The GOWN consists currently of over 250 active observation wells with most of them located in CBM production areas in the southeastern part of the province, while only a few GOWN wells exist in the regions with shale gas development in the northwest. A comprehensive monitoring program conducted since 2006

  34 S SO4 values >0‰ for individual samples are associated with the lowest sulfate concentrations suggesting that bacterial sulfate reduction may have occurred. Despite a narrow range in DIC

concentrations, some δ 13 C DIC values were as high as +13.8 ‰ vs. V-PDB and 13 C-enriched DIC was observed in samples with the highest methane concentrations (>1.2 mmol/kgw). The δ 13 C CH4

  R I P T have generally low concentrations (below 0.01 mmol/kgw). Nitrogen is present almost exclusively as ammonium (NH 4 + ) at concentrations of around 0.01 mmol/kgw while nitrate is negligible (<0.005 mmol/kgw, Table SI-1). As a result, the main electron acceptor in the groundwater samples is sulfate with concentrations as high as 10 mmol/kgw. Therefore, methane oxidation in the shallow aquifers in Alberta proceeds almost exclusively coupled with bacterial

	sulfate reduction (Humez et al., 2016b); Eq. 2 combined with Eq. 1 gives the reaction Eq. 3:
	SO 4	2-+ 10H + +8e -= H 2 S + 4H 2 O (2)
	CH 4 + SO 4	2-+ H + = HCO 3	-+ H 2 S + H 2 O (3)

Both processes are bacterially mediated and referred to as Anaerobic Oxidation of Methane (AOM) and Bacterial Sulfate Reduction

(BSR)

. In this study, methanic conditions describe redox conditions where all electron acceptors have been consumed leading to the inhibition or considerable slowdown of AOM. Under these redox conditions, methane is stable and methane concentrations can build up. Additionally, lacking competition from sulfate reducers, methanogens can thrive and in-situ production of methane by microbial methanogenesis may become energetically favourable. Microbial methanogenesis proceeds via acetate fermentation or CO 2 reduction. These pathways are characterised by distinct carbon and hydrogen isotope fractionation and can be identified using cross-plots of δ 13 C CH4 and δ 2 Η CH4 or δ 13 C CO2 and δ 13 C CH4 values. According to the traditional plot of

Whiticar et al. (1986)

in Figure

2a

, methane in the groundwater samples of this study was predominantly formed via the CO 2 reduction pathway, confirmed by the more recent plots from

[START_REF] Milkov | Revised genetic diagrams for natural gases based on a global dataset of >20,000 samples[END_REF]

(Figures

Table 1 :

 1 Parameters of the different scenarios used for simulating carbon and sulfur isotope

	evolution in Zone 1, 2a and 2b.
			Zone 1: Fugitive methane in post-oxic/SO 4 -rich groundwater
	Scenario	SO 4 initial	δ 13 C CH4, fugitive	ε' DIC-	δ 34 S SO4,initial	ε' H2S-SO4
		reservoir		CH4
		mol/kgw	‰	‰	‰	‰
	A1	0.2	-80	-5	-25	-5
	B1	0.2	-80	-10	-15	-5
	C1	0.2	-80	-2	-5	-5
	D1	0.002	-80	-5	-15	-5
	E1	0.2	-35	-5	-15	-5
	F1	0.2	-110	-5	-15	-5

Table 2 :

 2 Definition of the different categories based on the modeling approach.

	ory	Categ	Description	SO 4 conc.	CH 4 conc	δ 13 C CH4

  Methane oxidation coupled with BSR is also evidenced by the δ 34 S values of sulfate trending toward more positive values (Figure9) even if the low apparent S isotope fractionation factors and the large sulfate pool limits the overall enrichment of 34 S in the remaining sulfate. evolution near the sulfate concentration of 10 -3 mol/kgw (Figures7 and 10), the pathways between zones 2a and 2b have not yet clearly diverged so that an attribution of groundwaters to one of the two sub-zones is ambiguous. #333 which are characterized by a strong enrichment of 13 C in DIC in the groundwater samples of all three wells, with δ 13 C DIC as high as +20‰. Groundwater form well #991 has similar characteristics to samples from wells #214, #310/311 and #333 in terms of sulfate and methane concentrations and δ 34 S values of sulfate. However, the DIC is not as 13 Cenriched as in groundwater from the other three wells. This may be due to additional controls on the carbon isotope ratios of DIC from other DIC sources through mixing, dilution, or water-rock interactions.

		initial water did not
		have high sulfate
		concentrations
	4	Advanced	214,310/311,
	methanogenesis in Category 4 comprises the groundwater samples that indicate strong evidence of methanogenesis 333, 991
	a groundwater within the aquifer. Methanogenesis is particularly obvious for groundwater from wells #214,
	Intrusion of showing little #310/311 and	114,148,229,
	microbial methane into a sulfate-rich zone; Methane oxidation coupled with BSR is a key processes Same as category 1, but with higher methane concentration variability evidence of BSR, indicating an initially sulfate-poor groundwater Groundwater with low concentrations of sulfate and methane The first category includes groundwater from wells #114, #148, #229, #234, #381, #398, #481, 234,381,398, 481 1b 126,144, 373 M A N U S C R I P T 5 140, 984 #126, #144 and #373. The geochemical and isotopic model shows that these groundwater samples M A N U S C R I P T
	2 3 conditions. Category 2 contains groundwater from wells #438, #439, #982 and Category 3 Intrusion of microbial methane into a sulfate-poor zone; the low initial sulfate concentration was originally caused by BSR 438, 439, 982 Intrusion of microbial methane A C C E P T E D have been impacted by the migration of microbial methane with δ 13 C CH4 values varying from -110‰ to -80‰ into a SO 4 -rich groundwater (zone 1). The subsequent oxidation of methane increased the initial δ 13 C values of methane by 50 to 70‰ to δ 13 C values of -55 to -25‰ (Figure 7) resulting in a misleading pseudo-thermogenic C isotope signature of the remaining methane. Categories 2 and 3 describe migration of microbial methane into favourable reductive aquifer A C C E P T E D
	into a sulfate-poor contains groundwater from well #456. The characteristic low sulfate concentrations of these
	zone. The sulfur groundwater samples can either be due to: (i) continuous BSR combined with methane oxidation
	isotope ratios of along the groundwater flowpath (Category 2 with a strong 34 S enrichment of the remaining sulfate
		sulfate indicate
		only minor BSR,
		suggesting that the

due to BSR) or (ii): initially sulfate-depleted groundwater (Category 3), potentially due to the absence of pyrite oxidation. It is possible that groundwaters obtained from these wells have been subjected to a limited extent of methanogenesis. Indeed at the beginning of the geochemical

Acknowledgements

This research was conducted as part of the G-Baseline project, co-funded by the French Research Agency (ANR-14-CE05-0050 grant) and a Natural Sciences and Engineering Research Council of Canada strategic project grant (NSERC grant n° 463605). Additional financial support from the Alberta Government through Alberta Environment and Parks (AEP), the Alberta Ingenuity Water Innovation Program (AI-WIP), and a NSERC discovery grant to B. Mayer is also gratefully acknowledged. We would like to thank both reviewers for their pertinent comments that helped to improve this paper.

Supplementary data

Supplementary material

A C C E P T E D M

A N U S C R I P T Hamblin, A.P., (1998). Detailed outcrop measured section of the St. Mary River Formation, Oldman River, west of Monarch, southern Alberta. Geological Survey of Canada, Open File 3613 (12 pp.). Harkness, J.S., Darrah, T.H., Warner, N.R., Whyte, C.J., Moore, M.T., Millot, R., Kloppmann, W.,

A C C E P T E


Vanessa Riffet
email: vanessa.riffet@lct.jussieu.fr

Vanessa Labet

Julia Contreras-García

Topological study of chemical bonds under pressure: solid hydrogen

Introduction

H 2 is the simplest molecule and as any molecular solid, hydrogen is expected to polymerize under pressure. The comprehension of the mechanism by which this polymerization occurs is the main motivation for the work presented here. For that, we used a topological approach to reveal the process of polymerization using the NCI topological tool. ➢ The NCI topological tool is therefore a very useful tool for the analysis of bonding transformation.

[1] J. Am. Chem. Soc. 132, 6498 (2010).

➢

  [1] The current best plausible structural candidates for hydrogen under pressure were investigated theoretically in Refs [23H 2 molecules confined in a ring ➢ imposed D 3h symmetry ➢ the d distance adjusted to model the effect of pressure ➢ Wigner-seitz radius and d relationship: 2πd = 6(2r s a 0 ) ➢ molecular motif contained in C2/c and Cmca-12To have a better understanding of this chemical bond transformation, we decided to computationally study the following molecular model: vdW interactions (ρ = 0 to 0.006 a.u.) ➢ V(λ 2 < 0) increase and reach its maxima at r s = 1.58 ➢ this is correlated with the strengthening of the vdW interactions Repulsion for 1.58 < r s < 0.88: ➢ the intermolecular interactions strengthen and the covalent bonds become weaker under pressure. ➢ V(λ 2 < 0) decreases which is correlated with the fact that the vdW interactions progressively transform into covalent bonds. ➢ V(λ 2 > 0) continues to increase up to r s = 0.99 and then decreases Complete polymerization for r s ≤ 0.88: ➢ the NCI peaks 1 and 2 are superposed ➢ the interactions 1 and 2 become equivalent ➢ the model system has polymerized ➢ In dense hydrogen; each H 2 molecule or hydrogen interacts mainly with the nearest neighbors ➢ Our analyses focuses on the solid phases using the first coordination spheres of each non-equivalent hydrogen. r s (3H 2 ) and P can be used (results not shown here).➢ H 2 solid phases and the polymerization process can be understood thanks to the 3H 2 molecular model. ➢ Three transition regimes were highlighted: dipolar attraction, repulsion and complete polymerization.Evolution of sign(λ 2 )ρ values of NCI peaks Volume integrations within the NCI region ➢ The polymerization process starts in the repulsive region.

  [2] Nature Physics 3, 473 (2007). [3] Phys. Rev. Lett. 106, 165302 (2011).

  ρ) = 0.2 a.u. ; color scale: -0.2 < sign(λ 2 )ρ < 0.05 a.u. **s(ρ) = 0.1 a.u. ; color scale: -0.2 < sign(λ 2 )ρ < 0.2 a.u.