Biased samples to study reservoir souring processes

Production water samples are commonly used to study reservoir souring process. The aim of this study is to examine the reliability of these samples by using a state of the art coupled Thermo-Hydro-bioChemical numerical model. The transport and growth of five different representative sulfate-reducing strains (SRSs) in a model subsurface environment are simulated numerically by considering various biofilm formation characteristics and injection flow rates. After one pore volume (PV) injection, and assuming no biofilm formation, for three injection flow rates corresponding to pore velocities of 5.58 × 10 (cid:0) 8 , 83.7 × 10 (cid:0) 8 and 167.4 × 10 (cid:0) 8 m/s, souring within the reservoir is partially or completely derived by two SRSs that have an optimal growth temperature of 28 and 39 ◦ C. However, the produced water taken after one PV is dominated by a SRS that has an optimal temperature of 82 ◦ C. For a higher pore velocity of 558 × 10 (cid:0) 8 m/s, without considering any biofilm formation, produced water sample contains the same SRSs as the reservoir. However, if half of the produced biomass by various SRSs participates in biofilm formation, even for the high pore velocity of 558 × 10 (cid:0) 8 m/s, the produced water sample cannot reveal the SRSs that derive souring in the reservoir. Therefore, utilizing produced water samples may be misleading in reservoir souring studies. The results presented in this work suggest that more accurate prediction of reservoir souring requires characterization of the major groups of sulfate reducing bacteria in the injection water and undisturbed formation brine, and understanding their biofilm formation behavior.


Introduction
Biologic production of hydrogen sulfide (H 2 S) by sulfate-reducing bacteria (SRB) in oil reservoirs usually happens as the consequence of seawater flooding and is referred to as reservoir souring (Veshareh and Ayatollahi, 2019).Due to the toxicity and corrosive characteristics of H 2 S, reservoir souring is undesirable both economically and environmentally (Jiang et al., 2016;Vance and Thrasher, 2005).Therefore, over the past few decades numerous research studies have been completed on biological aspects of reservoir souring.
Past endeavors can be categorized into both experimental and simulation studies.In the experimental studies commonly batch or flow experiments are performed to find the souring rate and sulfate-reducing microbial community (SRMC) (do Vale et al., 2020;Marietou et al., 2020;Prajapat et al., 2021).Reservoir souring simulations are commonly employed to utilize the laboratory scale observations for predicting the field scale responses (de Jesus and de Andrade Lima, 2021; Veshareh et al., 2021).The souring experimental studies regardless of their methodology are conducted on three types of inoculums: produced water (Chen et al., 1994;Gaspar et al., 2016;Hubert et al., 2005;Voordouw et al., 2009), backflow water from an injection well (Bødtker et al., 2009;Gaspar et al., 2014;Lysnes et al., 2009), and proxy inoculums (inoculums that are not taken from the reservoir, but are related to the reservoir) (Greene et al., 2003;Hubert and Voordouw, 2007;Hubert et al., 2009).Obviously, the reliability of reservoir souring simulation studies depends significantly on the quality and the relevance of experimental studies utilizing actual or analogous fluid and porous media samples of the reservoir.
In petroleum reservoirs, reservoir souring is a process that evolves in both time and space domains and is controlled by flow rates, rock mineralogy and heterogeneity, fluid compositions and importantly by the temperature (Li et al., 2017).Considering a reservoir with production and injection wells that undergoes injection of seawater with lower temperature than the reservoir temperature, the fluid samples can be obtained a single or multiple times from limited available sampling points (e.g.wells).These samples are used in reservoir souring experimental studies as representative fluid of the targeted reservoir (Agrawal et al., 2012;Bødtker et al., 2009;Jurelevicius et al., 2021;Okoro et al., 2014;Zahmatkeshan et al., 2021).The samples however, disregarding whether they are taken from an injection point or a production well, represent mainly a single temperature and pressure condition at a fixed time and location.It is questionable whether the microbial community of these samples is representative of the microbial community of the reservoir.In other words, the seawater and produced water samples at the time of sampling can be dominated by different bacteria than those active within the reservoir experiencing a broader conditions (Gao et al., 2015;Ren et al., 2015).Indeed, the seawater sample or the backflowed injection water sample gives some information about the microbiome in the injection well and the near wellbore.The produced water samples offer partial information about the evolution of the mixture of injected water microbiome and reservoir indigenous microbiome.In groundwater aquifers it has been shown that there is a discrepancy between the groundwater biota and samples taken from ground water wells due to the fact that the well condition can be very different than the aquifer condition (Korbel et al., 2017).Different conditions in the well and the aquifer support different biological communities.
In studies of contaminant biodegradation, biomass has been reported to coexist in the form of suspended biomass as well as attached to the sediments (Grösbacher et al., 2018).Some works have presented that the majority of bacteria (>99%) is attached to the solid phase (Griebler and Lueders, 2009).It is known that SRB are able to produce biofilm (White and Gadd, 2000).However, biofilm formation has often been neglected in reservoir souring simulations (Cheng et al., 2016;Coombe et al., 2004), or has been considered using simplified models (Sunde et al., 1993;Veshareh andNick, 2019, 2021).
To the best of our knowledge no previous research work has studied the variations of SRMC in time and space domain under nonisothermal flow conditions within a petroleum reservoir and how it can be affected by biofilm formation characteristics of SRB or operation parameters such as injection flow rate.Consequently, the conditions under which backflowed or produced water samples are complete for souring studies are unknown.In this work, a 1D non-isothermal reactive transport model is used.A representative microbial ecology for the seawater and the formation brine are used as the boundary and initial conditions of the model.Using this model, the succession of reservoir microbiome in space and time domains under varying temperature conditions with considering no biofilm, partial and extreme biofilm formation, is evaluated.It is gauged whether or not the samples taken from the production wells could represent the reservoir microbiome and how the succession of microbiome is controlled by the pore velocity and fluid temperature.At last, the requirements for better understanding of SRB community structure and prediction of the dynamic behavior of SRB in the subsurface environment and the ensuing produced water quality are highlighted.

Materials and methods
A pair of injection and production wells that are 200 m apart are considered.To simulate reservoir souring in this system, a reaction model, a reservoir souring kinetic model, a reactive transport model and a heat flow model as explained in the following are utilized.

Conceptual description
Fig. S1 represents the model schematically.The model is 1D and takes into account two phases, one of which is at residual saturation and therefore does not move.This simplified model can represent water injection process when oil saturation is equal to the residual oil saturation and stationary.The biofilm considered in the model is sufficiently thin so it is possible to assume that (i) the biofilm does not have a volume and (ii) the concentration of substrates within the biofilm is equal to the concentration of substrate in the bulk water phase.The model accounts for multiple species containing multiple bacteria and some substrates.To model biofilm, it is assumed that a fraction of total biomass for each bacteria at a given location attaches to the rock and forms the biofilm.For the sake of simplicity, it is assumed that this fraction (hereafter called β) is the same for all bacteria.Even though the suspended biomass may have a different activity than the biofilm biomass (Yu et al., 2001), here, it is assumed that the suspended biomass has the same activity as the biofilm biomass.This assumption is in agreement with previous reservoir souring models (Haghshenas et al., 2012;Hosseininoosheri, 2016).
Various studies have reported that two groups of oil organics, namely VFAs and labile hydrocarbons such as monoaromatics and alkanes, comprise the electron donor of souring process (Birkeland, 2005;Grigoryan and Voordouw, 2008;Grigoryan et al., 2008).VFAs are mainly in the water phase whereas labile hydrocarbons are mainly in the oil phase.Following Haghshenas et al. (2012) and Cheng et al. (2018), acetate and toluene are considered to represent VFAs and labile hydrocarbons, respectively.It is assumed that none of the bacteria inhibits any of the other bacteria.It is also assumed that bacteria have no dormancy.The growth yield may differ for different bacteria and at different concentration of substrates/products and for different temperatures (Smeaton and Van Cappellen, 2018).However, due to lack of experimental data, in agreement with previous literature on reservoir souring (Cheng et al., 2016(Cheng et al., , 2018;;Coombe et al., 2010;Delshad et al., 2009;Haghshenas et al., 2012;Hubbard et al., 2014;Wu et al., 2018), it is considered that all bacteria have the same growth yield and the growth yield stays constant over the course of metabolic reaction.

Mathematical description
2.1.2.1.Reservoir souring kinetic model.The Monod formulation characterizes the rate of reservoir souring derived by the i th member of a sulfate-reducing microbial community (e.g.Veshareh and Nick, 2019): Where i denotes the strain, r [ML − 3 T − 1 ] is the souring rate, μ [T − 1 ] is the growth rate at a given temperature under unlimited substrate availability, and K [ML − 3 ] is the half saturation constant.Subscript A and D refer to electron acceptor and electron donor, respectively.b is the endogenous Rosso et al. (1995) μ i at a given temperature can be calculated as follow: Table 1 Kinetic parameters of five SRSs.μ maxm and T opt values are based on values reported in (Cheng et al., 2018) and other values have been assumed. Strain M.J. Veshareh and H.M. Nick Where T[θ] is the temperature and for the i th strain, μ maxi [T − 1 ] is the maximum growth rate, T maxi [θ] and T mini [θ] are temperatures higher and lower than which the growth is zero, and T opti [θ] is the temperature at which the growth rate is maximum.It is obvious that reservoir souring rate, R [ML − 3 T − 1 ] is calculated as the summation of reservoir souring rate derived by each individual strain: Where n is the number of SRSs present in the SRB community.
In this study, five exemplary SRSs with distinct T opt values equal to 82, 63, 51, 39, and 28 • C, are considered.They are referred to as SRS 82 , SRS 63 , SRS 51 , SRS 39 , and SRS 28 , accordingly.Table 1 lists their parameters required for equations (1) and (2).Fig. S2 also illustrates the growth rate-temperatures dependency of the five SRSs.While SRS 82 , SRS 63 and SRS 51 are present initially in the reservoir formation brine, SRS 28 and SRS 39 are only present in the injection water.Note that seawater is considered as the injection water.

Reaction model.
Microbial metabolisms are formed from two individual reactions called catabolism and anabolism.For each mole of electron donor used, a portion is consumed to produce energy (f e ) and the rest (f s ) is used to synthesize biomass.Values of f e and f s depend on the metabolisms' electron donor and acceptor (McCarty, 1972).For the case that acetate is the electron donor of reservoir souring process, f e and f s are calculated to be 0.92 and 0.08, respectively, resulting in the following metabolic reaction (Veshareh and Nick, 2019): Similarly, if toluene is the electron donor the following metabolic reaction can be obtained: The values of maximum growth rate and optimum growth temperature for each SRS are taken from Cheng et al. (2018), (Table 1).

Reactive transport model.
To simulate reservoir souring, assuming that the fluid velocity is constant in time and space domains, for substrates and products, the following generalized reactive transport equation is utilized: Where i is reaction components, C iw [ML − 3 ] is concentration of component i in the water phase (w), V [LT − 1 ] is pore velocity of the water phase, D [L 2 T − 1 ] is diffusion/dispersion coefficient and S i is the source term to take into account the reaction.S i is equal to r i × v i , where v i is the stoichiometric coefficient of component i in the metabolic reaction.K i is the partitioning coefficient of component i.Note that the partitioning coefficient of all components except toluene is considered to be zero.Tables 2 and S1 list the initial condition, boundary condition and parameters of equation ( 3).
Biofilm evolution can be modeled by considering mechanisms such as attachment and detachment (Rosenzweig et al., 2014).Attachment is usually considered to be a linear function of suspended bacteria concentration, while detachment is driven by shear-derived erosion.For the sake of simplicity, here it is assumed that a constant fraction (1-β) of biomass is mobile and the remaining biomass (βC j ) is immobile and stays attached to the rock.The parameter β is called the biofilm fraction.The following equation is utilized to model the biomass transport of different strains in porous media: Where the index j represents different strains SRS 28 , SRS 39 , SRS 51 , SRS 63 and SRS 82 .Table 2 also lists the initial and boundary conditions for equations (4) and ( 5).Note that for β=1 this model is equivalent to the biofilm model of Sunde et al. (1993).

Heat flow in porous media
. By assuming a non-deforming medium that is fully saturated, and by assuming thermal equilibrium between the solid and fluid phases, the macroscopic energy balance equation can be written as (Saeid et al., 2014): Where ρ is the thermal conductivity and is calculated as follow: Where the suffix f refers to fluid, s refers to solid and φ is porosity.The volumetric heat capacity is calculated as follow: Tables 2 and S1 list the initial condition, boundary condition and other parameters required to solve equations ( 4)-(6).

Damköhler number
Damköhler number of component j (e.g.H 2 S) produced by the i th SRS is defined as (e.g.Bear, 2018): where t c,trans is a characteristic transport time and calculated as the system length (here 200 m) divided by the pore velocity and t c,react is a characteristic reaction time for production or consumption of component j by the i th SRS, and in this work is calculated as follow: where v j is the stoichiometric coefficient of component j in the metabolic reaction.

Designed simulation scenarios
In order to study the coupled impact of temperature variation and biochemical reactions on the SRMC a detailed coupled Thermo-Hydro-bioChemical (THbC) numerical model (Veshareh et al., 2021) is used.The transport and growth of five different representative SRSs is simulated in a subsurface environment undergoing temperature alteration for an arbitrary injection volume of equal to three pore volumes of the modeled reservoir.To gain insight into the impact of the seawater injection rate on SRMC and reservoir souring, several simulations are conducted with four different injection/flow rates that are corresponding to velocity values ranging from 0.0048 to 0.48 m/day.To gauge the impact of biofilm formation, three β values of 0, 0.5 and 0.99 are considered.Table 3 lists the conditions for various simulated scenarios in this work.

Reservoir souring relationship with SRMC
Fig. 1b displays the modeled SRMC composition and Fig. 1f illustrates the rate profile of H 2 S production by each strain for a case that pore velocity (V) is equal to 83.7 × 10 − 8 m/s after 1 PV injection.Note that since H 2 S production rate is directly related to SRB growth, Fig. 1f can be used to compare the growth rate of each strain.Fig. 1b shows the modeled SRMC composition is dominated by either SRS 28 (L < 33 m), SRS 39 (33 < L < 75) or SRS 82 (L > 75 m), suggesting that SRMC is location dependent.At L = 130 m, H 2 S concentration is equal to 0.028 M for both V = 5.58 × 10 − 8 m/s (Fig. 1e) and 83.7 × 10 − 8 m/s (Fig. 1f) despite a significant difference in their SRMC (Fig. 1a and b).Therefore, reservoir souring is not only dependent on the SRMC.At V = 83.7 × 10 − 8 m/s, SRS 82 forms a significant portion of the modeled SRMC in many parts of the reservoir (L > 75).However, SRS 82 is active and  Note that temperature for growth of SRS 82 is favorable in locations > 50 m (Fig. 1b).However, the majority of the injected sulfate has been reduced by SRS 28 and SRS 39 such that there is no electron acceptor left for SRS 82 to grow after around 100 m from the injection well.

Impact of pore velocity on SRMC
By an increase in pore velocity, the location of maximum SRB concentration is pushed further into the reservoir (23, 95, 155 and 200 m, for V = 5.58 × 10 − 8 , 83.7 × 10 − 8 , 167.4 × 10 − 8 , and 558 × 10 − 8 m/s) as pore velocity controls the time available for SRB to convert sulfate in a given location range.Damköhler number (Da) demonstrates how the time available for each strain to derive souring changes depending on pore velocity.Higher Da values indicate that more time is available for a given SRS to derive souring.Comparing Figs.S3b and S3e shows that the Da of SRS 28 decreases by increasing pore velocity from 5.58 × 10 − 8 m/s to 83.7 × 10 − 8 m/s.For V = 5.58 × 10 − 8 m/s all the sulfate in the injected seawater is reduced in the vicinity of the injection well where the temperature is favorable for SRS 28 (L < 50 m, Fig. 1a).As a result, no sulfate reaches to the locations where temperature is favorable for SRS 39 , SRS 51 , SRS 63 , and SRS 82 .By increasing V to 83.7 × 10 − 8 m/s, the time available for SRS 28 to reduce the injected sulfate decreases (Fig. S3).Consequently, SRS 28 cannot reduce sulfate completely and a portion of the injected sulfate reaches the warmer sections of the reservoir where SRS 39 , SRS 51 , SRS 63 and SRS 82 are active (Fig. 1b).Fig. 1f shows that the remaining sulfate that passes the cold region dominated by SRS 28 is mainly reduced by SRS 39 .By further increase in the pore velocity to 167.4 × 10 − 8 m/s, the available time for SRS 28 and SRS 39 decreases (Fig. S3h) and as a result a higher fraction of sulfate stays unreduced and reaches to the location range that is favorable for SRS 82 , making SRS 82 the main sulfate reducer at this flow condition (Fig. 1g).Note that according to Fig. 1g (after 1 PV injection) the sulfate residual of the activity of SRS 28, 39, 51, 63 has a long enough residence time (Fig. S3h) such that the majority (95%) of the injected sulfate is reduced by SRS 82 in the location range of 110 < L < 181 m.However, increasing pore velocity to 558 × 10 − 8 m/s, the time available for SRB to reduce injected sulfate is lowered significantly (around 3 times) such that only 40% of the injected sulfate is converted to H 2 S (Fig. 1h) and mainly ahead of the temperature front (L > 140 m, where T = 90 • C).Therefore, by increasing the injection flow rate from 83.7 × 10 − 8 to 167.4 × 10 − 8 and 558 × 10 − 8 m/s, the maximum produced sulfide is reduced from 0.028 to 0.026 and 0.011 M, respectively.

SRMC of produced water samples
Fig. 2a-d illustrates the concentration of different strains together with the temperature in the production well (L = 200 m).Indeed, Fig. 2a-d represents the information obtained through sampling the produced water.For V = 5.58 × 10 − 8 m/s the concentration of all SRSs is negligible in produced water samples taken at any given time.This is because V = 5.58 × 10 − 8 m/s is sufficiently low such that sulfate reduction only happens in a location range close to the injection well by SRS 28 (Fig. 1a) and after that a high transport time leads to complete decay of the produced biomass.For higher V values since sulfate becomes available for all SRSs, SRMC of the produced water (depending on its temperature) first is dominated by SRS 82 and then by SRS 28 and SRS 39 (Fig. 2b-d).The result shown in Fig. 2 at 1 PV is considered to gauge whether or not the extent of souring and/or bacteria contributing to souring after 1 PV can be predicted by sampling the produced water.Produced water taken after 1 PV does not contain any SRS (Fig. 2a) for V = 5.58 × 10 − 8 m/s and contains 78% and 85% SRS 82 for V = 83.7 × 10 − 8 and 167.4 × 10 − 8 m/s, respectively (Fig. 2b and c).At 1 PV, for V = 558 × 10 − 8 m/s SRS 28 and SRS 39 each form 50% of the SRMC (Fig. 2d).Fig. 2e-h shows the activity of SRSs found in the produced water sample as well as the degree of souring.This is because at V = 558 × 10 − 8 m/s sulfate reduction happens only ahead of the temperature front (where T = 90 • C) and due to the low residence time of sulfate, there is ample amount of sulfate available for SRS 82 activity and therefore it is not subjected to decay.

SRMC dynamics
Fig. 3 shows the SRMC structure of the reservoir subjected to different injection flow rates at three different time steps of 0.5, 1 and 1.5 PV.Fig. 3a-c reveals that for a low V of 5.58 × 10 − 8 m/s the SRMC in all time steps consists of only SRS 28 and SRS 39 , and the structure of the community stays relatively unchanged.On the contrary, for higher V values, the SRMC structure changes with time are more significant.For example, for V = 167.4× 10 − 8 m/s in the location range of 90-110 m, at the first time step, SRMC is dominated by SRS 82 (Fig. 3g), however, in the next time steps the fraction of SRS 82 decreases and the fraction of SRS 28 and SRS 39 increases (Fig. 3h and i).In order to quantify the degree of changes in SRMC structure (within the shown time steps) the following indicator can be used: Where C i,j is the concentration of the j th strain in the SRMC in the i th grid.Fig. S4 shows that the indictor DS of SRMC grows around 12 times (from 0.43 to 5.4 mM) with increasing V from 5.58 × 10 − 8 to 111 × 10 − 8 m/s.A further increase in V causes reduction in DS, e.g.increasing V from 111 × 10 − 8 to 558 × 10 − 8 decreases DS around 2 times (from 5.4 to 2.4 mM).The dynamic of individual scaled H 2 S production rates is illustrated in Fig. S5.It is clear that the rates are controlled by the temperature and availability of substrates.One could also use dynamic Damköhler number (Fig. S3) calculated based on the coupled simulations to explain the succession of reservoir modeled SRMC and reservoir souring.Da values of strains with higher T opt increases for higher flow rates as the required substrates become available in the region where the reservoir temperature is more favorable.This is different for the lowest flow velocity case as Da values of the high temperature strains are nearly zero due to lack of the substrate availability in the high temperature region of the reservoir.cases without biofilm formation.Comparing Figs. 4 and 5, it is clear that for the higher flow rates than 5.58 × 10 − 8 m/s, biofilm formation creates a greater discrepancy between the composition of modeled SRMC composition in the produced water and that of the reservoir.Hence, in cases with higher biofilm formation, the produced water is less likely to be representative of SRMC composition in the reservoir.

Reservoir souring relationship with SRMC
Considering Fig. 1 b and f, one can conclude that SRMC does not represent the present rate of reservoir souring rate alone.The observed current SRMC in the reservoir depends on the history of SRB growth rate over a period of time, i.e. the SRMC manifests the souring history rather than souring status at a given time.Therefore, in order to incorporate SRMC data in souring studies, the temperature dependency of each SRS should be available together with the temperature map of the reservoir.

Impact of reservoir heterogeneity on SRMC
In this study various multicomponent bio-reactive transport simulations with several simplifying assumptions are used.Geological heterogeneities could affect the results by influencing flow distribution and the reactions.Such heterogeneities include fractures (e.g.Kadeethum et al., 2019;Salimzadeh et al., 2019), and sedimentary features (e.g.Crooijmans et al., 2016;Ziabakhsh-Ganji et al., 2019).Their influence on SRMC mainly depends on the connectivity of main flowing pathways between the injection and the production wells.The analysis of Fig. 1 and the dependency of SRMC on pore velocity can be extended to souring studies that include natural or induced fractures connecting the producers to the injectors forming short circuits.It is postulated that presence of short circuit fractures results in an SRMC similar to that of observed for the high flow rate (Fig. 1d).
The extent of the temperature front in the reservoir depends on the degree of mixing in the reservoir which is mainly controlled by the reservoir heterogeneity at different scales and the velocity field.The parameters such as the size of the cold front region, injection temperature, the growth rate of the SRSs together with the availability of sulfate restrict the growth of some of the SRSs.It is visible in Fig. 1f and g that SRS 63 is active only for the pore velocity values between 83.7 × 10 − 8 m/s and 167.4 × 10 − 8 m/s.As a result of the interplay among the above-mentioned parameters, some of the SRSs may not form a significant part of the SRMC during the operation of an oilfield.

SRMC from produced water samples
For V = 5.58 × 10 − 8 m/s, Fig. 1e shows that after 1 PV seawater injection, SRS 28 activity leads to the complete sulfate conversion to H 2 S.However, this is not predictable by monitoring the production well (Fig. 2a) since the concentrations of various SRSs are negligible.For V = 83.7 × 10 − 8 m/s, Fig. 1b illustrates that souring is derived by SRS 28 , SRS 39 , SRS 82 .However, evaluation of the produced water (shown in Fig. 2b), may overlook the importance of SRS 28 and SRS 39 .The results indicate that SRMC observed in the production wells varies depending on the operational condition and the contrast between the initial reservoir temperature and injected seawater temperature.It is evident that the observed SRMC in the production wells can be very different than the active SRMC in the reservoir.Nonetheless, reservoir-scale souring studies typically rely on samples from production wells that are taken after H 2 S production is observed (Marietou et al., 2020;Veshareh et al., 2021;Vigneron et al., 2017).
The difference between the SRMC of the reservoir and that of the production water sample can be because of the decay that happens for two reasons.First reason is when a grown strain in colder conditions moves to warmer conditions where it cannot grow.The second reason for the decay is the absence of sulfate.Note that the results are based on the assumption that there is no dormancy (in reality a lower decay is expected due to dormancy).Due to the decay, the biomass concentration observed in the produced water (Fig. 2a-c) can be significantly less than the biomass concentration within the reservoir (Fig. 1a-c).The decay also depends on the pore velocity.Due to a complete decay for V = 5. 58 × 10 − 8 m/s (Fig. 2a), the biomass concentration in the produced water after 1 PV injection is zero.By increasing V to 83.7 × 10 − 8 and 167.4 × 10 − 8 m/s (Fig. 2b and c), the biomass concentration is not zero anymore due to a partial decay.By a further increase of V to 558 × 10 − 8 m/s, the biomass concentration in the produced water sample is not affected by the decay.This can be seen by comparing Figs.1d and 2d.
It is clear that microbial measurements of produced water samples give information only about a specific point of the reservoir and there can be a significant difference between the SRMC observed in the production well and that of the reservoir.Microbial count of the produced water, or injection well backflow samples, commonly utilized in many previous studies (Gittel et al., 2012;Gittel et al., 2009;Voordouw et al., 2009), may be a poor indicator for the reservoir souring extent.Also the results of laboratory scale souring studies on the produced water may not be necessarily scalable to the reservoir.Therefore, relying on the information obtained from produced water samples can be misleading and may not be enough for an accurate characterization of reservoir souring in mature oil fields.These findings indicate that an analysis of the initial SRMC condition of the reservoir should be part of a production deployment strategy.

Importance of biofilm formation on SRMC dynamic
The results from the biofilm modeling by considering both mobile and immobile biomass hint at the importance of these features on the dynamics of sulfide generation and SRM sub-community assembly.The biofilm model used in this study can be improved, for example, by solving multi-component diffusion in biofilm as this allows the development of multiple chemical (e.g., substrates) gradients within biofilm.In addition one can include variability in growth yield within the biofilm accounting for accumulation of waste products and limited space within a biofilm.Even though improving the biofilm model could represent a more realistic system, it has little impact on the main conclusions of this study.

A prospect for reservoir souring studies
The dynamic of SRMC depends on the operational conditions.In all models, decreasing the injection velocity decreases the relative contribution of temperature changes on SRMC variation.Based on the results shown in this work, the extent of biofilm formation, reservoir temperature variation and substrate availability control SRMC dynamics.In order to provide a better understanding of reservoir souring, unbiased samples including the injecting seawater and unpolluted formation brine (formation water that has not been polluted by the injecting water) should be analyzed to characterize the initial SRB and their growth dynamic.These can help to improve the predictive capability of reservoir souring models.Such predictive models would then allow engineers to optimize reservoir development and mitigation plans by adjusting operational parameters such as injecting flow rate and temperature or inhibitor concentration.

Conclusion
In this study, a multiphase reactive transport model that simulates a representative microbial community is utilized to study the reservoir souring process.The main findings of this study are as follows: • There is a significant variation in the SRMC observed in production wells due to injection of low temperature seawater into hot reservoirs.
• Operational parameters such as injection rate and temperature and biologic characteristics of sulfate reducing bacteria such as biofilm formation properties control the degree of H 2 S production as well as the ecology of sulfate reducing microorganisms.• Flowback and produced water samples in reservoir souring studies may be biased.• This bias depends on factors such as degree of biofilm formation and flow velocity.• Unbiased samples including the injecting seawater and unpolluted formation brine should be utilized for reservoir souring studies.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 1 .
Fig. 1. a to d are profile of SRS concentration (left vertical axis) together with temperature (right vertical axis) and e to h are profile of H 2 S production rate by each strain (left vertical axis) in addition to H 2 S concentration (right vertical axis) after 1 PV seawater injection for V values of 5.58, 83.7, 167.4 and 558 × 10 − 8 m/s, respectively, for the case with β = 0.

Fig. 2 .
Fig. 2. a to d: SRS concentrations and total biomass (left vertical axis) and temperature (black dashed line, right vertical axis) at L = 200m; e to h: individual H 2 S production rate by each SRS and the total H 2 S production (left vertical axis), and H 2 S concentration (right vertical axis) in the production well (L = 200m) over a period of 4 PV seawater injection for V values of 5.58, 83.7, 167.4 and 558 × 10 − 8 m/s, respectively, for the case with β = 0.

Fig. 4 ,
Fig. 4, Fig. S6 and 5 illustrate similar results as shown in Fig. 1 a to d, e to h and Fig. 2 a to d, respectively, but with different biofilm fractions of 0.5 and 0.99.Fig. 4 a to c shows that biofilm formation does not influence the modeled SRMC composition for the low injection rate of 5.58 × 10 − 8 m/s.For the higher flow rates, the presence of biofilm leads to accumulation of SRSs closer to the injection well (Fig. 4 d to l).It is also evident from Fig. S6 d to l that H 2 S production rates, due to the presence of biofilm, can be two or three times more than those of the

Fig. 3 .
Fig. 3. Normalized fraction of SRB community formed from each SRS (left vertical axis) together with the total biomass concentration shown by the solid black line (right vertical axis), for the case with β = 0; at three time steps of 0.5, 1 and 1.5 PV, for four different pore velocity of 5.58, 83.7, 167.4 and 558 × 10 − 8 m/s.

Fig. 5 .
Fig. 5.Total SRS concentrations (biofilm and suspended) and total biomass (left vertical axis) and temperature (black dashed line, right vertical axis) at L = 200 m over a period of 4 PV seawater injection for V values of 5.58, 83.7, 167.4 and 558 × 10 − 8 m/s and β values of 0, 0.5 and 0.99.

Table 2
Initial and boundary conditions.

Table 3
Conditions of the simulated scenarios.