# Physical processes occurring in tight gas reservoirs from Western Canadian Sedimentary Basin: Noble gas signature

Magali Pujol, Sander van den Boorn, Bernard Bourdon, Matthias Brennwald, Rolf Kipfer

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Magali Pujol, Sander van den Boorn, Bernard Bourdon, Matthias Brennwald, Rolf Kipfer. Physical processes occurring in tight gas reservoirs from Western Canadian Sedimentary Basin: Noble gas signature. Chemical Geology, 2018, 480, pp.128-138. 10.1016/j.chemgeo.2017.12.011. hal-02322955

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Accepted Manuscript

Physical processes occurring in tight gas reservoirs from Western
Canadian Sedimentary Basin: Noble gas signature

Magali Pujol, den Boorn, Bernard Bourdon, Matthias Brennwald,
Rolf Kipfer

<figure><img src="image_2.png" /></figure>

PII: S0009-2541(17)30692-7

DOI: https://doi.org/10.1016/j.chemgeo.2017.12.011

Reference: CHEMGE 18582

To appear in: *Chemical Geology*

Received date: 12 December 2016

Revised date: 4 December 2017

Accepted date: 17 December 2017

Please cite this article as: Magali Pujol, den Boorn, Bernard Bourdon, Matthias Brennwald, Rolf Kipfer, Physical processes occurring in tight gas reservoirs from Western Canadian Sedimentary Basin: Noble gas signature. The address for the corresponding author was captured as affiliation for all authors. Please check if appropriate. Chemge(2017), https://doi.org/10.1016/j.chemgeo.2017.12.011

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# Physical processes occurring in tight gas reservoirs from Western Canadian Sedimentary Basin: noble gas signature

Magali Pujol¹*, Sander Van den Boorn², Bernard Bourdon³, Matthias Brennwald⁴ and Rolf Kipfer⁴

¹ETH, Institut für Geochemie und Petrologie, Clausiusstrasse 25, 8092 Zürich, Switzerland

*Present day address: Total EP, CSTJF, Avenue Larribau, 64000 Pau, France

²Shell Projects and Technology, Kessler Park 1, 2288 GS Rijswijk, Netherlands

³Laboratoire de Géologie de Lyon, ENS Lyon, CNRS, and UCBL, Lyon, France

⁴EAWAG, Department of Water Resources and Drinking Water, Dübendorf, Switzerland

(Corresponding Author: magali.pujol@total.com)

Abstract 298 words

Main text 5737 words
**Abstract**

Noble gases have become a powerful tool to constrain the origin of fluids as well as the rates of fluid migration in sedimentary basins. The aim of this study was to apply these tracers to understand the genesis and the evolution of unconventional gas reservoirs, basin-centered gas reservoirs (also called tight-gas reservoirs). A natural laboratory for this study is the methane-rich gas field in Cretaceous tight sands from the Western Canadian Sedimentary Basin (WCSB). The selection of the WCSB was motivated by an easy access to wells that cover an extensive area from deep to shallow parts of the basin, as well as the relatively well documented geology and hydrology of the area. The elemental noble gas signature (He, Ar, Kr and Xe) of natural gas from 18 wells of the basin shows a mixture between the original low content noble gas signature of the hydrocarbon gas (after its charge into the reservoir) and water (trapped in intergranular volumes (IGV)), which is comparatively rich in noble gases. This difference in relative contents can be used to estimate the geographical position of the contact between the gas reservoir and the shallower IGV water. Furthermore, the 'original' noble gas signature, which is defined as the noble gases generated in the source, later transferred, and mixed with in situ produced noble gases in the reservoir, is mainly composed of radiogenic isotopes ($^{40}$Ar and $^{4}$He). The comparison of $^{4}$He/$^{40}$Ar ratios with an average value for potential source rocks and reservoir rocks production ratio (estimated with U, Th and K concentrations) allows us to understand how the gas was transferred from the source rock to the reservoir rock. These results, combined with the geological and hydrological knowledge of the WCSB, affords a new method to better understand the dynamics of unconventional gas reservoirs.
# 1. Introduction

The noble gases (He-Ne-Ar-Kr and Xe) are chemically inert and their properties vary gradually as a function of their atomic mass. In fact, the solubility of noble gases in water increases from He to Xe whereas it decreases in a gas phase with increasing atomic mass (Weiss, 1970a, 1971a; Crovetto et al., 1981; Smith and Kennedy, 1983; Smith, 1985; Kharaka and Specht, 1988; Harvey, 1998). Noble gases also have numerous isotopes, with some of them being produced by radioactive decay (Wetherill, 1953; Steiger and Jäger, 1977), which can be useful to trace the origin of fluids (Pinti and Marty, 1995; Kipfer et al., 2002). Due to their inertness and their volatility, noble gases hardly interact with most solid materials. Therefore, terrestrial noble gases tend to accumulate in the atmosphere (except for He), which is the largest noble gas reservoir on Earth (Ozima et Podosek, 2002). Furthermore, the atmosphere has a well defined composition (Basford, 1973) and is in equilibrium with surface waters. As a consequence, any deviation from this natural baseline (atmosphere or surface water) can be easily distinguished. Classically, noble gas composition in natural water is assimilated to Air Saturated Water (ASW) composition which is the noble gas content of water in equilibrium with air at a given temperature (Kipfer et al., 2002). One should note that the isotopic composition of the water (ASW) and air in these conditions are identical.

Over the past decades, numerous studies applied noble gas analyses to sedimentary basins. One of the most common applications is to determine the origin of gas compounds present in the reservoir (Oxburg et al., 1986; Ballentine et al., 1991; Jenden et al., 1993; Ballentine and Burnard, 2002; Zhou and Ballentine, 2004; Gilfillan et al., 2009; Prinzhofer et al., 2010). Also, as they reflect directly the physical processes, noble gases can also be used as a proxy to trace hydrocarbon migration from the source rock to the reservoir rock in sedimentary basins (Prinzhofer and Pernaton, 1997; Gilfillan et al., 2009).
The exploitation of unconventional reservoirs such as basin centered gas fields (BCG fields) by petroleum companies has significantly increased over the last decade. These reservoirs represent most of methane reserves in the world and the WCSB would represent 62% of the world reserves (Hiyagon and Kennedy 1992). To illustrate the main differences between Basin Centered Gas (BCG) field and a classical gas field, a simplified cartoon is presented in Figure 1. In the classical model, during gas migration from the source rock to the reservoir rock, gas migrates up through IGV (Intergranular Volume) filled by water. Water and gas are first mixed and are then organized by density (gas phase above water phase). In BCG fields, the porosity is extremely low in the reservoir rocks. During its migration, the gas pushes out main part of the water present in IGV creating a non equilibrated fluid column where the water phase is upper the gas phase (Tobin et al., 2010). This transitional state evolves through time, as the pressure difference decreases and the gas is slowly lost from the reservoir (Yuan et al., 2014 ; Amiri et al., 2015). To evaluate the evolution of such a reservoir, it is thus important to know the amount of gas is still contained in the reservoir and the importance of the water-gas contact zone, equivalent to the volume of gas impacted by water (Burnie et al., 2008).

To accurately build up a basin model, even for an unconventional play, several aspects have to be constrained (Hantschel and Kauerauf, 2009). First, the geological history needs to be known as precisely as possible; this includes how and when the sedimentary basin was formed, the diagenesis of the organic matter, the time of gas cracking, also the type of organic matter responsible for the oil/gas generation. This includes also the evolution of temperature and pressure in the basin, which are important drivers for fluid migration. Second, once the gas is formed, it is important to know the nature and pathways of the gas flow from the source rock (kitchen) to the reservoir(s). If all these parameters are well constrained, it is possible to accurately estimate how much and where the gas is stored in the reservoirs.
Noble gas studies are mainly applicable to the second aspect: the radiogenic noble gas signature of reservoir gas, compared to the source rock composition in U, K and Th (so the calculated production of ⁴He and ⁴⁰Ar), can provide insights into the migration process. The non-radiogenic noble gases of reservoir gas presumably come from a contact with an aquifer, so their composition can help determine the geographical limits of reservoir.

In this study, we analysed noble gases in unconventional gas reservoirs in Alberta with the goal of studying the physical properties and processes occurring in the basin, such as the position of the water-gas contact and the gas migration processes in a low porosity medium. Geophysical tools commonly used to determine the extensions of reservoirs or the position of faults can hardly be applied to unconventional reservoirs due to the low contrast of seismic signal between reservoir and cover rocks and also due to the lack of visibility of gas phase in seismic imaging (Meckel and Thomasson, 2008).

## 2. Basin geology

The geological history of Western Canada Sedimentary Basin has been intensively studied over more than four decades (Hichton (1968), Prather and Mc Court (1968), Masters (1979), Hiyagon and Kennedy (1992), Newson (2004), Webb et al. (2005) Ross and Bustin (2008) and references therein.) due to its petroleum and gas interest. It represents one of the largest natural gas reserves in the world and this natural gas contains more than 80% of methane. Nevertheless, this basin is considered as an unconventional reservoir as the gas reservoirs are different from the classical examples depicted in Figure 1, where an impermeable media overlying a reservoir with high porosity prevents gas escape. The Western Canadian Sedimentary Basin (WCSB) is a broad syncline fold. Its main axis is oriented N-S, on the eastern side of the Rocky Mountains, Alberta. These types of gas fields are called "basin centered gas" because the gas is located in the deepest central part of the syncline fold (and as a consequence there is an updip contact with the overlying aquifer), or "tight gas
reservoirs" due to the low porosity and low permeability of these reservoirs, the consequence of which is that it prevent the water infiltration in its deeper sections (Figure 2, modified from Masters, 1979).

The evolution of the WCSB can be split into two distinct phases (Hiyagon and Kennedy, 1992). The Paleozoic to Jurassic platformal series, dominated by carbonate rocks, was deposited on the stable craton adjacent to the ancient margin of North America. The overlying mid-Jurassic to Paleocene foreland basin series, dominated by clastic rocks, is contemporaneous to the formation of the Canadian Rocky Mountains. Reservoir rocks are mainly composed of Cretaceous siltstones/sandstones strata from the foreland basin. From West to East, the reservoirs are separated into three parts: (i) the disturbed zone, which is geologically complex represented by the central part of the syncline fold, under the Rocky Mountains, (ii) the highly pressurized zone (Intergranular Volume Pressure, $P_{IGV} >>$ hydrostatic Pressure, $P_{hydrostatic}$), where most of the gas is stored and, (iii) the underpressurized zone ($P_{IGV} \le P_{hydrostatic}$) which is close to the water-gas contact in the northeast. The source rocks have not been clearly identified and they could originate both from oceanic organic matter (Jurassic) or continentally-derived organic matter (Cretaceous). These source rocks mainly generated CH$_4$-rich gas (more than 80%), without any oil production (primary gas generation).

### 3. Sampling strategy

In order to evaluate the importance of gas-water interaction, sampled wells covered from the highly pressurized zone of the basin up to the underpressurized zone. The main issue was that each well could cross several reservoirs on the same vertical line. None of reservoirs is actually continuous throughout the basin; most reservoirs have the shapes of lenses (Figure 2) that are not necessarily in contact with each other. Thus, the gas sampled from the well represent a mixture between all reservoirs on the same vertical line (up to 8, as shown in
Figure 2), in which case the gas is said to be "commingled". The geographic location of the sampled wells is shown in Figure 3.

Source rock samples were taken from drill core of the high pressurized zone of the basin, stored in the core laboratory of Calgary. These were selected from different depths as an attempt to determine which source rock(s) is (are) responsible for gas production. Reservoir rock samples were also chosen. Noble gas signature, especially radiogenic noble gases, is supposed to reflect the source rock initial noble gas signature. Nevertheless, as reservoir rock volumes are more important than source rock volume, by a factor of about 20, and even if the radiogenic in situ production within reservoir rock is limited (poor K, Th and U content compared to source rock content), it is expected that the source rock noble gas signature is diluted and the "initial" gas measured in samples is actually a mixing between source and reservoir in situ produced noble gases.

**4. Sampling and analytical methods**

The CH₄-rich natural gas samples were collected by field operators in ~500 cc stainless steel gas cylinders sealed at each end with bellow valves. From each individual well, samples were taken using two different sampling methods. In both cases, the cylinders, pre-evacuated by AGAT Company (Edmonton, Canada) to a pressure of 17mm Hg (i.e. 22.7 mbar), were attached to the sampling port located after the separator (which separates the gas from liquid components) on the well site. Once attached, one of the cylinders was filled with gas directly without purging, whereas for the other method, the cylinder was purged for 15 seconds with natural gas before taking the sample. It appeared all samples that were not purged were too polluted by air to be interpreted and this study reports only results from the purged samples (Gilfillan et al., 2008 ; Gyore et al., 2015 ; Barry et al., 2016). All gas samples were analyzed for noble gas composition at ETH Zurich (Switzerland) using the same method as that described by Beyerle et al. (2000) which was designed for noble gas
analyses in water samples. An additional purification step was included in the extraction line specifically for handling natural gas. As all samples contained >80% of CH₄, the first step was to remove most of the hydrocarbons before introducing the sample into the rest of the purification line. This was achieved by fluxing the gas over two chemical traps (getters). These getters consisted of titanium sponges with a very high adsorption capacity and surface area. They acted to break down molecules containing hydrogen (e.g. hydrocarbons, and H₂O), which is most efficient at high temperature, the best efficiency being reached between 600 and 700°C. The getters were operated one after the other for 10 minutes at high temperature (650±50°C) and 10 minutes at room temperature. At high temperatures, hydrogen radicals are released in the line, whereas the other molecules remained adsorbed on the Ti sponge. At room temperature the reactions are reversed and hydrogen radicals were adsorbed whereas the remaining molecules were released. The purification process is optimized by allowing the connection between the two getters to be open when the second one is at high temperature, such that that the released H radicals were trapped by the first getter which was at room temperature. These getters also trap CO₂, O₂ and N₂ which are common contaminants in many terrestrial gas samples.

Source and reservoir rocks were ground to powder and sent to SARM (Service d'Analyse de Roches et Minéraux, CRPG, Nancy, France). The chemical composition of these rocks was measured by ICP-AES for major elements and ICP-MS for trace elements. Table 1 reports U, Th and K compositions which are producing noble gases: ⁴He is produced by decay of U and Th while ⁴⁰Ar is produced by decay of ⁴⁰K.

## 5. Results

All the noble gas results are reported in Table 2. Ne isotopes were measured but are not reported because ²⁰Ne and ²²Ne contents were about 2 times the blank value. Except for ⁴He and ⁴⁰Ar, all noble gas contents were very low in the gas phase: Xe and Kr for example are
up to 1000 and 100 times respectively less concentrated than in the ASW composition.
Nevertheless, as a typical blank represents less than 1% (10% for Xe isotopes,) of the
content measured in a sample, the results reported in Table 2 are corrected for blanks.

As shown in Table 1, the four reservoir rocks show rather homogeneous concentrations in U,
Th and K (within a factor of 2). These reservoir rocks should be representative of the main
reservoir rocks composition. In contrast, the compositional variability of the source rocks is
quite large (up to a factor of 100). However, since the most productive source rock, if it really
exists, could not be identified, we used instead the average of these compositions.

6. Estimation of the "initial" gas signature in the reservoir

The noble gas analyses were used to constrain the state and evolution of the natural gas
from the WCSB. To achieve this goal, the noble gas signature of the gas contained in the
reservoirs (without any modification due to migration or contact with water) has first to be
characterized. The gas was generated in the source rock, then migrated to the reservoir rock
and noble gases from the source rock were diluted by noble gases initially present in the
reservoir, we call this signature "initial noble gas signature". Once this signature is
determined, it is possible to distinguish it from any secondary modification, and this, in turn,
can help understand the origin of these modifications.

As the gas sampled from each well is commingled see Figure 1), the noble gas signature
recorded in our samples must also reflect the mixture between different reservoirs. The gas
found in each reservoir could also have been derived from different underlying source rocks.
Thus, due to this mixing process, it is difficult to extract a source signature specific to a given
source rock. Nevertheless, a common trend is obvious in a plot of Kr versus Xe contents
(Figure 4 Left panel). There is a clear mixing line between a component depleted in heavy
noble gases and a component identified as representing the formation water. The component
depleted in heavy noble gases by a factor of 100 to 1'000 times relative to ASW must
represent the signature of the reservoir gas that has been preserved despite these low
contents. If we combine the quasi-absence of heavy primordial noble gas with the high $^4$He
content and the very low $^3$He/$^4$He ratios (Figure 4 Right panel), one infers that the noble gas
signature is highly radiogenic. This fact can be explained by an early loss of initial
atmospheric noble gas from the future source rock (and maybe also from the future reservoir
rocks) during diagenesis (due to their loss with increasing pressure and temperature). The
loss of noble gas in source rocks (and/or reservoir rocks) is compensated by enrichment in
radiogenic noble gas due to in situ production by radioactive decay of U, Th and K
(producing mainly $^4$He and $^{40}$Ar). Following this early noble gas loss, during the gas charge in
the reservoir, the water is pushed out of the reservoir, and only residual water and in situ
produced noble gas are mixed with the charged natural gas. The initial signature of the noble
gases measured in reservoirs is purely radiogenic (i.e. it can be attributed to the effect of
radioactive decay), and with this signature it is possible to discriminate the subsequent effect
of kinetic mass fractionation or mixing with water.

**7. Discussion**

As described before, noble gas can be used to examine the mode of gas transport by
comparing the theoretical radiogenic noble gas signature produced in source and reservoir
rocks. In addition, the non-radiogenic noble gases of the reservoir are highly sensitive to
interaction with water, such that their composition can help determine the geographical
position of the gas/aquifer interface.

**7.1. Non radiogenic noble gas signature: lateral extension of the reservoirs**

An important target of this study was to understand the contact between the gas reservoirs
and the aquifers. Theoretically, as the gas in the reservoirs has an almost pure radiogenic
noble gas signature, when the analysed gas is sampled closer to the water contact zone, the
fraction of noble gases coming from the updip aquifer such as $ ^{36}\text{Ar} $, Kr, or Xe should
increase. To investigate this, $ ^{36}\text{Ar} $ contents were plotted as a function of depth of a reservoir
formation present in all wells. As shown in Figure 2, the depth of this reservoir increases from
the NE to the SW. In Figure 5, a trend from the shallower part of the basin, enriched in $ ^{36}\text{Ar} $
compared with the deeper part which has low $ ^{36}\text{Ar} $ content can be observed. One should note
that four wells represent exceptions to this trend, as they are enriched in $ ^{36}\text{Ar} $ while being
located in the deeper part of the basin, this fact will be discussed in section 8.

In figure 5, the $ ^{36}\text{Ar} $ content represents a proxy for the exchange of gas in the reservoir with
aquifer. Indeed, when the water is in contact with the gas for the first time, most of $ ^{36}\text{Ar} $ from
the water phase is transferred into the gas phase, as the CH$_4$/water partition coefficient for
noble gases is much higher than 1 and decreases from light to heavy noble gases (Zartman
et al. 1961). However, if the same residual water, which has lost its noble gases by
interaction with CH$_4$, is one more time in contact with gas, this gas will not be enriched in
$ ^{36}\text{Ar} $, but will have a noble gas signature characterized by a larger abundance of heavy noble
gas than light ones and an overall low noble gas contents (noble gas poor water (NGP
water)). Thus, to fully highlight the effect of interaction with water on the noble gas
composition, the evolution line of $ ^{136}\text{Xe}/^{36}\text{Ar} $ and $ ^{84}\text{Kr}/^{36}\text{Ar} $ ratios with successive contacts with
water are illustrated in Figure 6. When plotting our data on the same diagram (Figure 7, Left
panel), it is obvious that the composition of five wells which were not enriched in $ ^{36}\text{Ar} $
followed the water “distillation trend”, which means that these wells were in contact with
water that has interacted repeatedly with gas. These wells with NGP water signature were
represented on a map in Figure 7, Right panel. Focussing on the north-eastern region of the
field area, which is the shallowest and underpressurized part of the basin close to the water-
gas contact, noble gas composition evolves gradually from the central part of the basin (with
no noble gas water signature in the gas) through the northeast (NGP water signature in the
gas) until an estimated position of the aquifer (not distillated water noble gas composition in
the gas). The two closest wells from the water-gas contact show a strong influence of a water signature (high ³⁶Ar), whereas the three wells located to the southwest of the water-influenced wells shows an influence of NGP water and then the two wells farther in the southwest direction show no influence of water. Combined with the general SW-NE direction of gas migration (Jones et al. (1985), Majorowicz et al. (2013)), this indicates that the gas was first formed in the deeper part of the basin, migrated upwards along a northeast direction, thereby pushing the water along a NW-SE trending contact.

In the southwest region of the basin which corresponds to the deepest reservoirs, the situation is obviously more complex. This can be explained by the complexity of water circulation in this area due to the presence of a faulting system (Masters, 1979). Indeed, closer to the syncline axe, there are different directions of water flows (Bacchu et al., 1999). In conclusion, there are updip contacts both in the northwest, and in the north. Concerning the observed water influence in the central part of the basin (wells #8 and #18), a downdip contact with an aquifer is suspected. Indeed, as the fluid column in BCG reservoirs is unstable, it tends to reorganize by densities (gas phase above water phase) (Weides et al., 2014; Tobin et al., 2010; Majorowicz et al., 1999).

## 7.2 Radiogenic noble gases signature

As explained in section 6, the noble gas composition of the generated gas in the reservoir is almost purely radiogenic. Thus, the study of the radiogenic noble gas composition provides information on what happened to the gas before any mixing process with water. One can infer the gas migration process (diffusive versus Darcy flow) and the apparent age of the gas.

First, it is possible to determine how the gas is transferred from the source rock to the reservoir rock in the low porosity / low permeability system. An estimation of the Peclet number (Pe) in the sedimentary basin is needed to determine if the mass transfer is preferentially diffusive or advective (Darcy flow). It is not possible to calculate Pe precisely
due to variations in the permeability and bad estimations of characteristic lengthscale.

Nevertheless, Bacchu et al. (1993) estimated a value of Pe<10 for methane transfer, which means that the preferential mode of mass transfer in the basin is molecular diffusion, as expected in tight environment. With the noble gas signature it is possible to distinguish for each well between an advective gas transport (i.e. Darcy flow corresponding in fact to the absence of differential transport between noble gas species) and a diffusive transport where the signature was subjected to kinetic mass fractionation.

For this purpose, the amounts of $ ^{40}\text{Ar*} $ were calculated and plotted in Figure 8, Left panel, showing $ ^{4}\text{He} $ versus $ ^{40}\text{Ar*} $ compositions for each well gas. This was then compared with the predicted trend for an in situ production in the source and in the reservoir itself, based on their respective averages of U, Th and K production ratios. Three different cases are possible. First, if $ ^{4}\text{He}/^{40}\text{Ar*} $ ratios are compatible with ratios typical for source rocks or reservoir rocks, or a mixture of both, it means that the initial signature was preserved and that the transport was mainly advective during the charge. Second, if $ ^{4}\text{He} $ is enriched relative to $ ^{40}\text{Ar*} $, the initial signature was not preserved and the effect of diffusion depleted the heavy gases (here Ar) compared to the lighter ones (He). Last, $ ^{40}\text{Ar*} $ can be enriched relative to $ ^{4}\text{He} $, this latter case meaning that the lightest isotopes were probably lost by leakage of the reservoir.

In Figure 8, Left panel, three groups of wells can be identified, corresponding to the three cases described above: the first group is characterized by a high $ ^{4}\text{He}/^{40}\text{Ar} $ ratio compared with the radiogenic production ratios estimated in the source and the reservoir, the second group fits with the radiogenic “production line” with $ ^{40}\text{Ar*}/^{4}\text{He} $ ratios ranging between the source and reservoir production ratio and the last group composed of two wells shows an apparent excess of radiogenic $ ^{40}\text{Ar*} $.

The radiogenic noble gas compositions from the first group enriched in $ ^{4}\text{He} $ can be explained by a diffusive transport from the source rock to the reservoir rock. Considering the low Péclet
number, it is not surprising to have a highly diffusive transport where the lighter elements migrate preferentially to the reservoir rock. Furthermore, the observation of a diffusive transport widely spread in the field proves that the source rock is clearly distinct from the reservoir rock (no in situ CH₄ generation).

The signature of the second group can be explained by advective transport. The data lie on a well defined trend intermediate between the average production ratio of source and reservoir rocks. Considering the numerous stacked reservoirs and the numerous potential source rocks in the basin, it is surprising to observed such an homogeneous trend. It can be taken as evidence for mixing of the gas from different reservoir rocks and/or of production by a single source rock formation. The wells which have a low content in both ⁴He and ⁴⁰Ar can also be explained by a diffusive transport combined with a loss of ⁴He*. It should be noted in this case that the loss in He has to match exactly the enrichment inherited from diffusion. This could seem as fortuitous, hence this interpretation is considered as ad-hoc.

The third group composition depleted in ⁴He is composed of two wells from the northeastern part of the basin. This can be due to the loss of lighter elements from the reservoir. Nevertheless, it is important to point out that for both wells (Figure 8, Right panel), the ⁴⁰Ar/³⁶Ar ratio is just slightly above the atmospheric ratio and that the only reason for the high content of ⁴⁰Ar* is the high content of total Ar (100 times more than the average composition of wells). Thus, these wells did not lose He, but were enriched in Ar by the contact with an aquifer which would have brought at the same time important amounts of ³⁶Ar and ⁴⁰Ar.. Moreover, their geographic position in the northeastern part of the basin and the study of non-radiogenic noble gas (section 6.2) confirm a contact with an updip aquifer, presumably far from the atmospheric recharge area because of the slight enrichment in ⁴⁰Ar*. This slight enrichment is due to aquifer circulation through rocks containing K, after the time of atmospheric recharge.
Considering the geographical distribution of noble gas compositions (Figure 8, Right panel), a trend can be observed from the NE to the SW. In the lower pressured part of the basin (Meckel et Thomasson, 2008), well signatures are more and more depleted in $^4$He for a similar $^{40}$Ar* content. In the higher pressured deep basin, the charging system is dominantly advective in the NW area, and diffusive (to highly diffusive with no excess in $^{40}$Ar*) in the rest to this area.

## 8. General implications

First, the noble gas signature of the natural gas derived from the source rocks was shown to be purely radiogenic. This radiogenic signature bears some meaning about the evolution of the gas prior to contact with water. The diagram $^4$He as function of $^{40}$Ar* (Figure 8, Left panel) shows all wells have roughly the same $^4$He content around $5 \times 10^{-5}$ ccSTP/cc, except for three wells that are enriched in $^4$He up to a factor of 4. Using the average $^4$He content, it is possible estimate the time necessary to accumulate the observed $^4$He based on the measured U and Th contents in cores. A few assumptions needs to be made to estimate an apparent $^4$He age: (i) all $^4$He is sited in intergranular volume with a reservoir porosity of 5%, (ii) fluid pressure is about $5 \times 10^7$ Pa (hydrostatic pressure at 5000 m depth, corresponding to 3000m deep gas which had a 2000m uplift) and gas temperature is about 363 K, (iii) gas consists of pure methane and, (iv) reservoir rock density is about 2800 kg/m$^3$. Given all these assumptions, the accumulated $^4$He can be estimated following the equation (Craig and Lupton, 1976; Battani et al., 2011):

$$(^4\text{He}) = (3.115 \times 10^6 + 1.272 \times 10^5) [\text{U}] + 7.710 \times 10^5 [\text{Th}].$$

Where $(^4\text{He})$ is the He production rate in atoms.g$^{-1}$.y$^{-1}$, and [U] and [Th] are respectively uranium and thorium concentrations in $10^{-6}$.mol.g$^{-1}$
First, as the density of CH₄ changes with pressure due to its non negligible compressibility factor, and has to be estimated in the P and T conditions of the reservoir:

$$ \rho(CH_4) = \rho_0 \times \frac{P}{P_0} \quad \text{with } \rho_0 \text{ the density of CH}_4 \text{ at a pressure } P_0 \text{ of 1atm and } 0^{\circ}\text{C,} $$

Using the ideal gas law for He, with a deviation factor of 1.06 (representing an ideality deviation, calculated under standard temperature and pressure), one obtains 3.63 x 10⁻³ mol of ⁴He per kg of fluid. To convert it into mol per kg of rock, the following equation can be used:

$$ M_f / M_{tot} = \frac{\rho_f \phi}{\rho_f \phi + \rho_r (1 - \phi)} $$

with Mf and Mtot being the mass of fluid and total mass (fluid + rock), respectively, ρf and ρr being the density of the fluid and of the rock and Φ the porosity, respectively.

Applying this equation, the concentration of ⁴He is 3.75 x 10⁻³ mol/kg, which is equivalent to an approximate ⁴He age of 578 million years. This age is clearly higher than the age of the rock, which implies that ⁴He amount is not only due to the production in the source rock. Nevertheless, this result is realistic as the gas produced is charged in the reservoir rock mainly by diffusion. The estimated source rock is located between 0 and 500 m under the estimated reservoir rock. As a consequence, the gas has to cross a large amount of rock which contains some U, K and Th and which also produces some ⁴He that can be collected by the migrating natural gas (open system). Our suggestion is that this ⁴He produced in the thickness between the source rock and the reservoir rock above is carried in the gas stream during the gas migration to the reservoir (Figure 9). This hypothesis can be illustrated by the 3 wells enriched in ⁴He (wells #1, #7 and #8), which, due to their geographical position, traveled the longest way from the kitchen (producing source rock in the central part of the basin) to the limit of the reservoir close to the water contact. Wells #6, #2 and #18 do not
show ⁴He excesses presumably due to an exchange of ⁴He with the water phase as explained in section 7.2.

The wells located in the NW (wells #16, #14, #10, #17, and #5) are characterized by a similar radiogenic noble gas signature, even though many reservoirs and possible source rocks are involved, this indicate that there were a mixing within the reservoir possibly through a fault system.

To summarize, the wells in the field can be separated in three different geographical areas according to the behaviour of their noble gases (Figure 10): the NE area, the NW area and the S.

First, on the NE area, both radiogenic and non radiogenic noble gas signatures show a NE-SW trend. The main gas flow is estimated to be from the SW to the NE (Bacchu et al., 1999), which correlates with our observations, showing an increasing influence of water towards the NE. The gas was first generated in the central part of the basin and is flowing upward, pushing the water-gas interface towards the NE. The non-radiogenic noble gas composition of this first generated gas clearly shows a water influence. Moreover, there is a correlation between the type of transport (from radiogenic noble gases) and the degree of interaction with water (from non radiogenic noble gases) (Figure 10). In the NE part, a direct influence of water is associated with a preferential loss of ⁴He, compatible with noble gases exchange with water phase poor in ⁴He. This progressive loss of ⁴He disappears through the south west, combined with the decrease of water influence, which confirms the gas migration direction and the geographical position of the water/gas contact.

In the deeper part of the basin, there is no clear trend as in the north eastern part, but there is still a correlation between the type of transport and the degree of interaction with water. Focussing on the NW area, an interaction with water (normal or noble gas poor water) is linked to an advective transport. This can be explained by water flow along a fault system (hydraulic fracturation), and not necessarily by any water/gas contact.
In the southern part of the basin, well #18 (and probably also well #8) are sitting on a downward dipping aquifer in Lower Devonian terranes (Weides et al., 2014; Majorowicz et al., 1999). It is possible that the measured water influence is not a direct gas water contact but results from the diffusion/percolation effect of noble gases from this aquifer into the reservoirs (Burnie et al., 2008).

## 9. Conclusions

In conclusion, noble gases are a useful tool to understand the physical processes related to the evolution of unconventional gas reservoirs. This noble gas study in the intensive drilled area could afford useful information about how some natural gas can fill a tight reservoir (fault system vs. diffusion). Radiogenic noble gas, reflecting the initial signature of the source rock, showed the main transfer process in this basin is diffusion, proved by the relative enrichment in <sup>4</sup>He compared to <sup>40</sup>Ar*. Some advective transfers (Darcy flow) were also brought out and appeared to be systematically linked to the presence of water. Thus the interpreted gas flow fits with the regional water flow (Weides et al., 2014 and references therein). This can be explained by a hydraulic fracturation created by the water flow in the basin. It can be interested to confirm this hypothesis with hydrocarbon relative concentrations. If methane / ethane concentrations ratios, for instance, are higher in "diffusive transfer zones" than in "advective transfer zones", then it can prove that noble gas compositions are a good tool to spotlight hydraulic fracturation zones even if fractures are presently sealed.

After the gas charge into the reservoir, noble signature can be modified by an eventual leakage or by a contact with an aquifer. As noble gas solubility is much higher in gas phase than in water phase (Ballentine and Burnard 2002) and as noble gas initial content is in favour of water, unidirectional gas flux from water phase to gas phase can be approximated. Then noble gas water signature is superimposed on noble gas signature from gas phase which explains why the initial signature is not lost. In this case study, gas was sampled
randomly from different parts of the basin from the deepest central part of the basin up to
close to gas basin borders. This kind of sampling showed that the noble gas water signature
are situated close to basin borders, and even more that the closer to the aquifer the sampled
gas is, the more concentrated the noble gas water signature is. In conclusion, due to their
inertness, noble gases isotopic and elemental compositions appear to be a useful tool to
better constrain and understand physical transfer and exchanges in unconventional
reservoirs. Nevertheless, like most of other methods, it becomes powerful when it is
integrated with other geological and fluids understanding to build an accurate basin model.

Acknowledgements

We would like to thank first Larry Paulson, Shell Canada Upstream, Edson Field Office, for
his great help on the field, his constant good mood and all our cultural differences
exchanges. Then, Philip Benham, Shell Canada Energy, spend lots of time explaining us the
basin sedimentology. Finally, Volker Dickmann, Olaf Podlaha and all the organic
geochemistry team, Shell Projects and Technology, Rijswijk, thank you for all the fruitfull
exchanges during these 2 years of work, they showed how much the communication
between different scientific communities helps the global understanding.
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Table captions

Table 1: Chemical composition of source rocks and reservoir rock formations from the Cretaceous Mannville Group. The analyses were made at SARM (Service d'analyses de roches et matériaux, CRPG, Nancy, France).

Table 2: Noble gas composition for gas samples from sampled gas wells. Air composition is from Basfod et al. (1973) except for $^{40}$Ar/$^{36}$Ar ratio which was recalculated by Lee et al. (2006). ASW composition equilibrated with 10°C fresh water is from Kipfer et al. (2002).
<table><caption>Table 1: Chemical composition of source rocks and reservoir rocks</caption><thead><tr><th>Samples</th><th>Th<br>(x 10<sup>-9</sup> mol/g)</th><th>U<br>(x 10<sup>-9</sup> mol/g)</th><th>K<br>(x 10<sup>-5</sup> mol/g)</th></tr></thead><tbody><tr><td>Source Rock Obed</td><td>8.54</td><td>4.32</td><td>1.06</td></tr><tr><td>Source Rock Obed</td><td>46.9</td><td>26.6</td><td>35.4</td></tr><tr><td>Source Rock Obed</td><td>37.4</td><td>15.3</td><td>35.2</td></tr><tr><td>Source Rock Obed</td><td>28.6</td><td>17.1</td><td>12.5</td></tr><tr><td>Source Rock Obed</td><td>28.2</td><td>12.8</td><td>15.1</td></tr><tr><td>Source Rock Obed</td><td>4.71</td><td>3.85</td><td>0.425</td></tr><tr><td>Source Rock Obed</td><td>1.50</td><td>0.584</td><td>0.212</td></tr><tr><td>Source Rock Obed</td><td>3.34</td><td>2.46</td><td>1.17</td></tr><tr><td>Source Rock Sundance</td><td>43.0</td><td>17.6</td><td>30.6</td></tr><tr><td>Source Rock Sundance</td><td>45.2</td><td>37.9</td><td>29.1</td></tr><tr><td>Source Rock Sundance</td><td>60.6</td><td>22.7</td><td>45.4</td></tr><tr><td>Source Rock Sundance</td><td>21.7</td><td>30.3</td><td>14.7</td></tr><tr><td>Source Rock Gething</td><td>43.2</td><td>15.4</td><td>32.9</td></tr><tr><td>Source Rock Notikewin</td><td>13.5</td><td>15.4</td><td>6.16</td></tr><tr><td>Average source rocks:</td><td>27.6</td><td>15.9</td><td>18.6</td></tr><tr><td>Cadomin Formation</td><td>6.13</td><td>4.22</td><td>4.25</td></tr><tr><td>Cadomin Formation</td><td>4.25</td><td>3.54</td><td>3.08</td></tr><tr><td>Blue sky Formation</td><td>5.08</td><td>2.72</td><td>4.78</td></tr><tr><td>Blue sky Formation</td><td>6.51</td><td>3.21</td><td>6.26</td></tr><tr><td>Average reservoir rocks:</td><td>5.49</td><td>3.42</td><td>4.59</td></tr></tbody></table>
<table><caption>Table 2 : Noble Gas composition for gas samples from sampled gas wells</caption><thead><tr><th>Sample</th><th><sup>4</sup>He x10<sup>-6</sup><br>(ccSTP/cc)</th><th>1σ</th><th>R/Ra</th><th>1σ</th><th><sup>36</sup>Ar x10<sup>-8</sup><br>(ccSTP/cc)</th><th>1σ</th><th><sup>40</sup>Ar/<sup>36</sup>Ar</th><th>1σ</th><th><sup>40</sup>Ar* x10<sup>-8</sup><br>(ccSTP/cc)</th><th>1σ</th><th><sup>84</sup>Kr x10<sup>-9</sup><br>(ccSTP/cc)</th><th>1σ</th><th><sup>136</sup>Xe x10<sup>-10</sup><br>(ccSTP/cc)</th><th>1σ</th></tr></thead><tbody><tr><td>1</td><td>20.10</td><td>0.016</td><td>0.0195</td><td>0.0005</td><td>3.49</td><td>0.03</td><td>666</td><td>14.3</td><td>1281.49</td><td>30.11</td><td>5.54</td><td>0.13</td><td>0.53</td><td>0.07</td></tr><tr><td>2</td><td>5.52</td><td>0.024</td><td>0.0437</td><td>0.0008</td><td>159.75</td><td>1.51</td><td>307</td><td>4.71</td><td>1341.90</td><td>24.19</td><td>44.22</td><td>0.23</td><td>7.56</td><td>0.21</td></tr><tr><td>3</td><td></td><td></td><td></td><td></td><td>3.67</td><td>0.03</td><td>301</td><td>1.06</td><td>8.81</td><td>0.09</td><td>9.67</td><td>0.05</td><td>1.62</td><td>0.03</td></tr><tr><td>4</td><td></td><td></td><td></td><td></td><td>2.80</td><td>0.03</td><td>388</td><td>43</td><td>250.27</td><td>27.83</td><td>2.06</td><td>0.03</td><td>0.97</td><td>0.03</td></tr><tr><td>5</td><td>4.12</td><td>0.010</td><td>0.0725</td><td>0.0014</td><td>700.00</td><td>6.63</td><td>296</td><td>0.2</td><td>0.00</td><td>0.00</td><td>140.40</td><td>0.57</td><td>15.23</td><td>0.22</td></tr><tr><td>6</td><td>6.04</td><td>0.015</td><td>0.0205</td><td>0.0007</td><td>149.31</td><td>1.41</td><td>306</td><td>1.2</td><td>1104.87</td><td>11.31</td><td>51.19</td><td>0.35</td><td>9.41</td><td>0.22</td></tr><tr><td>7</td><td>10.79</td><td>0.026</td><td>0.0246</td><td>0.0006</td><td>3.13</td><td>0.03</td><td>517</td><td>10.9</td><td>684.54</td><td>15.78</td><td>1.30</td><td>0.08</td><td>0.42</td><td>0.03</td></tr><tr><td>8</td><td>17.13</td><td>0.013</td><td>0.0676</td><td>0.0006</td><td>89.77</td><td>0.85</td><td>310</td><td>0.65</td><td>1023.36</td><td>9.90</td><td>46.21</td><td>0.17</td><td>16.02</td><td>0.26</td></tr><tr><td>10</td><td>6.56</td><td>0.016</td><td>0.0195</td><td>0.0006</td><td>1.09</td><td>0.01</td><td>630</td><td>15.4</td><td>361.88</td><td>9.40</td><td>0.63</td><td>0.01</td><td>0.23</td><td>0.02</td></tr><tr><td>11</td><td>4.59</td><td>0.011</td><td>0.0238</td><td>0.0008</td><td>0.48</td><td>0.01</td><td>804</td><td>22.7</td><td>244.27</td><td>7.35</td><td>0.33</td><td>0.01</td><td>0.14</td><td>0.02</td></tr><tr><td>12</td><td>6.75</td><td>0.017</td><td>0.0237</td><td>0.0006</td><td>2.16</td><td>0.02</td><td>331</td><td>55.9</td><td>70.05</td><td>11.85</td><td>0.55</td><td>0.03</td><td>0.18</td><td>0.04</td></tr><tr><td>13</td><td>6.07</td><td>0.015</td><td>0.0312</td><td>0.0007</td><td>1.29</td><td>0.01</td><td>411</td><td>13</td><td>144.50</td><td>4.77</td><td>0.41</td><td>0.50</td><td>0.13</td><td>0.00</td></tr><tr><td>14</td><td>5.58</td><td>0.021</td><td>0.0209</td><td>0.0011</td><td>2.08</td><td>0.02</td><td>328</td><td>40</td><td>61.22</td><td>7.49</td><td>0.53</td><td>0.01</td><td>0.14</td><td>0.01</td></tr><tr><td>16</td><td>6.97</td><td>0.017</td><td>0.0364</td><td>0.0013</td><td>508.20</td><td>4.81</td><td>299</td><td>0.24</td><td>203.28</td><td>1.93</td><td>115.53</td><td>0.45</td><td>14.83</td><td>0.20</td></tr><tr><td>17</td><td>5.59</td><td>0.014</td><td>0.0107</td><td>0.0004</td><td>0.49</td><td>0.00</td><td>951</td><td>54.3</td><td>320.90</td><td>18.53</td><td>0.31</td><td>0.02</td><td>0.10</td><td>0.02</td></tr><tr><td>18</td><td>5.01</td><td>0.013</td><td>0.0152</td><td>0.0005</td><td>36.46</td><td>0.34</td><td>295</td><td>2.46</td><td>0.00</td><td>0.00</td><td>7.30</td><td>0.05</td><td>0.86</td><td>0.03</td></tr><tr><td>19</td><td>4.70</td><td>0.012</td><td>0.0118</td><td>0.0009</td><td>0.67</td><td>0.01</td><td>337</td><td>34.7</td><td>25.76</td><td>2.66</td><td>0.19</td><td>0.01</td><td>0.07</td><td>0.01</td></tr><tr><td>20</td><td>5.45</td><td>0.014</td><td>0.0139</td><td>0.0008</td><td>1.11</td><td>0.01</td><td>361</td><td>38.6</td><td>69.46</td><td>7.46</td><td>0.33</td><td>0.02</td><td>0.11</td><td>0.01</td></tr><tr><td>AIR</td><td>5.20E-07</td><td></td><td>1.00E+00</td><td></td><td>3.12E-05</td><td></td><td>298.6</td><td></td><td></td><td></td><td>6.50E-07</td><td></td><td>7.71E-09</td><td></td></tr><tr><td>ASW</td><td></td><td></td><td></td><td></td><td>1.20E-06</td><td></td><td></td><td></td><td></td><td></td><td>4.82E-08</td><td></td><td>1.09E-09</td><td></td></tr></tbody></table>
Figure captions

Figure 1: Schematic cross sections showing the main differences between a classical field and a basin centered field in terms of pressures and fluid column organisation.

Figure 2: SE-NW cross section of Alberta, modified from Masters, 1979. This geological section is equivalent to the sampling area. Up to eight stacked reservoirs are present in the same well.

Figure 3: Geographic location of sampled wells. The apparent NW-SE alignment of wells is representative of the geological steepening of layers within the basin. Different signs and colors are used to represent each well. They will be fully explained through the discussion part.

Figure 4: Upper panel: Kr versus Xe contents in ccSTP/cc. ASW stands for Air Saturated Water (Porcelli et al., 2002). Air composition is taken also from Porcelli et al. (2002). The compositions of well gas plot on a single mixing line between ASW and an initial signature with a low content in non radiogenic gases (i.e. $^{20}$Ne, $^{36}$Ar, $^{3}$He, Kr and Xe). Lower panel: He content in ccSTP/cc vs. $^{3}$He/$^{4}$He ratio. $^{4}$He content is high in the gas samples, higher than He content in the air. Combined with Figure 4, upper part, the gas signature appears to be almost only radiogenic.

Figure 5: $^{36}$Ar versus depth. As depth increases from NE to SW, this diagram represents the geographical variation of $^{36}$Ar from the low pressurized shallow part of the basin (NE) to the high pressurized deeper part (SW). There is a clear trend from the shallow part with a high $^{36}$Ar to the deeper part with a low $^{36}$Ar, except for 4 wells in the deeper part which have high $^{36}$Ar content (see text for explanation).

Figure 6: Conceptual time evolution (from A to D) of $^{136}$Xe/$^{36}$Ar versus $^{84}$Kr/$^{36}$Ar on the left part and corresponding map of phases interaction. This conceptual model represents a water distillation process seen from the interacted gas composition evolution in the 3 isotope diagram. The gas composition registers not only an interaction with water, but also the intensity of water previous exchanges with former gas generations. $G_x$ stands for gas phase and $W_x$ stands for water phase after x phases interactions. $G_0$ and W are the initial phases composition before any interaction. $G_n$ and $W_n$ are phases composition after the Nth interaction. It represents the effect of distillation due to repeated interaction between gas and water. If water is in contact with the gas, most of noble gases will be partitioned into the gas phase, as noble gases are more soluble in the gas phase than in water, and the effect increases with the decrease of noble gas mass (light noble gases partition preferentially into the gas phase). If the same batch of water, which is already depleted in noble gases, interacts again with a new batch of gas, the gas phase will not become enriched in $^{36}$Ar, but will be slightly enriched in heavy noble gases (Kr, Xe) compared to $^{36}$Ar as heavy noble gas will be more soluble in the water phase compared to the light ones.

Figure 7: Left panel: $^{84}$Kr/$^{36}$Ar versus $^{136}$Xe/$^{36}$Ar diagram showing the evolution of different gas samples interacting repeatedly with the same amount of water as modelized in Figure 6. The gas becomes enriched through the “distillation” of water in heavy noble gases (Kr and Xe) which are more soluble in the water phase than Ar. Black dots, squares and triangles represent samples with a high $^{36}$Ar ($G_1$, Figure 6). Grey dots and squares represent samples which were in contact with “distilled” water (no clear excess in $^{36}$Ar but slight enrichment in Kr and Xe, $G_2$ to $G_n$, Figure 6). Open dots and squares stand for samples without any influence
of water (G₀, Figure 6). Right panel: Map of the sampling area. The results from the left panel were reported on the map to see the geographical position of water influence.

Figure 8: Left panel: ⁴He versus ⁴⁰Ar* contents in ccSTP/cc. ⁴He are considered to be only radiogenic and ⁴⁰Ar* was calculated based on ³⁶Ar/⁴⁰Ar ratio compared to the atmospheric composition. These two radiogenic isotopes were mostly present in the source rock and were a part of the initial signature defined in section 6). Variations in He/Ar ratio provide information on what happened to the gas before any contact with water. The three types of samples defined in comparison with the estimated initial production ratio (relative to the slopes of source rock and reservoir rock) represent an advective transport (Darcy flow - open squares), a diffusive transport (open circles) or a leakage of the reservoir (open triangles). right panel: Map of the sampling area. The results established based on the type of transport (left panel) are reported on the map.

Figure 9: Schematic diagram showing the evolution of ⁴He contents measured in gas from reservoir layers. Stage 1: before gas generation, ⁴He is produced mainly in the source rock (S) during diagenesis. Stage 2: first gas generation, most of the ⁴He produced is removed from the source rock and transferred into the reservoir layer (R), some ⁴He is taken up during the pathway from some rocks similar in terms of composition to reservoir rocks. Stage 3: continuous gas generation, gas produced in the source rock still migrates to the reservoir layer with a much lower ⁴He content corresponding to the rate of gas migration. Gas in the reservoir is pushed by the following generations through the porous reservoirs previously filled by water. Stage 4: Mixing in the reservoir. As there is not a large difference (only a factor of 2) of ⁴He content between the border and the central part of the basin, there must be a mixing of ⁴He in the reservoir layer, at least a partial mixture.

Figure 10: Map summarizing all the results obtained in this study, integrated in a modelized view of the basin.
<figure><img src="image_3.png" /><figcaption>Figure 1</figcaption></figure>
<figure><img src="image_4.png" /><figcaption>Figure 2</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Figure 3</figcaption></figure>
<figure><img src="image_6.png" /></figure>

<figure><img src="image_7.png" /><figcaption>Figure 4</figcaption></figure>
<figure><img src="image_8.png" /><figcaption>Figure 5</figcaption></figure>
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<figure><img src="image_13.png" /><figcaption>Figure 6</figcaption></figure>
<figure><img src="image_14.png" /><figcaption>Figure 7</figcaption></figure>
<figure><img src="image_15.png" /><figcaption>Figure 8</figcaption></figure>
1. Before gas generation

<figure><img src="image_16.png" /></figure>

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2. First gas generation

<figure><img src="image_19.png" /></figure>

<figure><img src="image_20.png" /></figure>

<figure><img src="image_21.png" /></figure>

3. Continuous gas generation

<figure><img src="image_22.png" /></figure>

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4. Reservoir leakage

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<figure><img src="image_27.png" /><figcaption>Figure 9</figcaption></figure>
<figure><img src="image_28.png" /><figcaption>Figure 10</figcaption></figure>