The interplay between microbial reservoir souring and barite scale formation in hydrocarbon reservoirs

The injection of seawater into a hydrocarbon reservoir (seawater flooding) as a secondary or tertiary oil recovery method is associated with two possibly significant challenges. First, the formation and deposition of various types of scale may happen due to incompatibility between the injection seawater and formation brine. Especially, the addition of sulfate ions may trigger the formation of various types of sulfate scales (e.g., barium sulfate, strontium sulfate, and calcium sulfate). Second, microbial reservoir souring may happen due to the activation of Sulfate Reducing Bacteria (SRBs), which reduce sulfate ions to hydrogen sulfide. This is mainly a result of a drop in temperature in the reservoir, the addition of sulfate from the seawater to the reservoir, and the presence of Dissolved Organic Carbon (DOC) coming from reservoir hydrocarbon. Since both these processes include the consumption of sulfate ions, a competition is expected to happen between them. Especially, there is a concern about whether an efficient mitigation strategy for souring (e.g., nitrate treatment) will result in less consumption of sulfate ions and in turn more formation of sulfate scales. This study tests this theory and investigates the effect of souring intensity and mitigation on the severity of barite scale formation inside the reservoir. In this study, a non-isothermal multi-component bio-chemical model to simultaneously simulate both the processes is developed. Several simulation cases in one and two dimensions are investigated in different conditions in order to study the effect of three influential parameters, namely sulfate ion concentration in the injection sweater, the DOC content of the reservoir hydrocarbon, and injection flow rate on barite scale formation, microbial reservoir souring, nitrate treatment, and the interplay among them. The results show that the effect of barite scale formation on reservoir souring is small (a maximum of 4 percent reduction in the total generated hydrogen sulfide) whereas reservoir souring and nitrate treatment significantly influence barite formation. Depending on the case, the presence of souring can cause a complete removal of barite scale especially around the production well (positive effect) or a maximum of 8 times increase in barite scale amount around the production well (negative effect). Moreover, in all cases, with a more efficient nitrate treatment, although less hydrogen sulfide is generated inside the reservoir (up to a full removal of souring), the generation zone moves closer to the production well. Therefore, an insufficient nitrate treatment may cause an earlier hydrogen sulfide production from the production well (up to twice as early). Several other trends observed in the set of results are also presented in this paper.


Introduction
Seawater flooding is a common strategy of improved oil recovery, during which seawater with a typical sulfate concentration of ~28 mM is injected into oil reservoirs to maintain reservoir pressure and sweep out oil (Cheng et al., 2018).The presence of sulfate ion (SO 4 2− ) in an oil reservoir may trigger two harmful mechanisms, namely microbial reservoir souring and sulfate scales deposition.Microbial reservoir souring is a process in which sulfate reducing bacteria (SRBs) consume sulfate and produce hydrogen sulfide (H 2 S), which is a hazardous and corrosive gas.Therefore, it may cause notable health and environmental risks (Fuller and Suruda, 2000;Jiang et al., 2016) and decrease the life expectancy of injection/production facilities, thus increasing capital and operational costs of oil and gas operations (Al-Janabi, 2020).To mitigate this problem, several methods have been proposed.One method is biocide injection, which directly kills the microorganisms (Xue and Voordouw, 2015).Furthermore, nitrate, nitrite, and perchlorate injection have been proposed to decline microbial activity through various mechanisms (e.g., bio-competition (Hubert and Voordouw, 2007), inhibition (Veshareh et al., 2021b), and H 2 S re-consumption by Nitrate Reducing Sulfide Oxidizing Bacteria (NRSOB) (Veshareh and Nick, 2019)).Scale formation, on the other hand, occurs in case of incompatibility between the injected seawater and the formation brine (Baraka-lokmane et al., 2021).Otherwise stated, wherever there is the possibility of mixing between the injected seawater and the formation brine, scale formation is possible.Deposition of scale inside the reservoir, especially around injection and production wells, and inside production and injection tubulars restrict the flow of fluids, thus reducing productivity or injectivity of the wells (Moghadasi et al., 2003).Various types of scale, including sulfate scales (e.g., BaSO 4 , CaSO 4 , and SrSO 4 ) form when, for instance, seawater, containing sulfate, mix with a Ba 2+ -rich formation brine.This causes barite (BaSO 4 ) scale precipitation in near-wellbore area, deep in the reservoir, and inside the tubulars (Civan, 2007;Merdhah and Yassin, 2009;Taheri et al., 2008;Tranter et al., 2020Tranter et al., , 2021a;;Younis et al., 2020).
There is the concern in oil and gas industry that the mitigation of reservoir souring may cause excessive sulfate scale deposition both in the reservoir and inside the production tubulars.That is because in the cases where souring and mitigation strategies as well as sulfate scale deposition are both possible, there may be a competition on the consumption of sulfate ions.SRBs consume sulfate and DOC to produce hydrogen sulfide.NRBs (Nitrate/Nitrite Reducing Bacteria) consume DOC and nitrate or nitrite, which may compete with SRBs on the consumption of DOC (bio-competition).Moreover, NRSOBs (Nitrate/Nitrite Reducing Sulfide Oxidizing Bacteria) may reduce nitrate/nitrite and oxidize hydrogen sulfide back to sulfate.The presence of nitrate may also have an inhibitory effect on SRBs' activity.The sulfate ions, on the other hand, may react with cations (such as barium ions) to produce scale in a reversible reaction (Fig. 1).
Notably, in the mixing zone of the injected seawater and reservoir brine, where scale formation is possible, such a competition occurs.Therefore, the concern that mitigating souring may provide higher concentrations of sulfate ions for the formation of sulfate scales (e.g., barite) arises.Hence, an inclusive simulation of all these processes is of paramount importance.To the knowledge of the authors, despite the extensive research on both the phenomena, there has been no study on the simultaneous effects of them.This study focuses on investigating the competition between microbial reservoir souring (including mitigation strategies) with barite precipitation on consuming sulfate ions.It is also worth noting that increased corrosion is another concern associated with the mitigation of souring using nitrate or nitrite, which is out of the scope of this study (Bybee, 2007;Iino et al., 2021;Lahme Sven et al., 2019;Nicoletti et al., 2022).
Over the last few decades, several numerical models have been developed and utilized to model reservoir souring and nitrate treatment.Coombe et al. (2004) 2019) then considered dissimilatory nitrate reduction to ammonium (DNRA) and sulfide oxidation to sulfur.Several studies have also addressed the kinetics of microbial souring (Veshareh et al., 2021a,b;Veshareh andNick, 2021a, 2021b).
On the other hand, several studies have investigated the rates and mechanisms of barite-water interaction (Gunn and Murthy, 1972;Mealor and Townshend, 1966;Murthy, 1994;Pina et al., 1998) and other studies have derived the reaction order of barite-fluid reactions using conductivity techniques (Nielsen and Toft, 1984;Taguchi et al., 1996;van der Leeden et al., 1992;Wat et al., 1992, p. 4) and activity methods (Bovington and Jones, 1970).Zhen-Wu et al. (2016) experimentally determined barite dissolution and precipitation rates as a function of temperature and aqueous fluid composition.Furthermore, Several modelling and simulation studies have been concerned with barite scale formation and precipitation in porous media and its effect on well productivity (Abouie et al., 2018;Chen and Shi, 2015;Delshad and Pope, 2003;Hu et al., 2015;Sorbie and Mackay, 2000;Tranter et al., 2020Tranter et al., , 2021b;;Xiong et al., 2020).
Despite the extensive efforts in studying barite precipitation and reservoir microbial souring separately, to the best knowledge of the authors, no work has yet investigated the effect of each one on the other one when both are possible.Specifically, during waterflooding oil and gas reservoirs, the addition of sulfate (through injection of seawater) to the reservoir and its mixture with a possibly barium-rich formation water may cause barite scale formation.At the same time, the addition of sulfate together with a drop in the reservoir temperature may provide a suitable environment for bacterial activities, especially microbial souring.To explain the interplay between microbial reservoir souring A. Mahmoodi and H.M. Nick and barite scale formation, this study investigates the impact of three related parameters, namely Dissolved Organic Carbon (DOC) content in the reservoir hydrocarbon, sulfate concentration in the injection seawater, and seawater injection rate on H 2 S production and barite deposition.Therefore, a better understanding of not only the extend of the competition between microbial reservoir souring and barite scale formation but also possible measures to prevent the threats associated with each of them is gained.However, more parameters, such as the temperature of injection seawater, biological properties of the bacteria, and biofilm formation properties could be of importance here (Veshareh and Nick, 2021c), which may be considered in the future research.It is worth noting that the presented model and the gained insight from this study could be useful in integrated studies of microbial activities in other areas of research, such as hydrocarbon-polluted groundwater and underground hydrogen, methane, and carbon dioxide storage (Henry et al., 2022;Hsia et al., 2021).

Methods
Coupling a commercial reservoir simulator with a component transport model and a chemical model enables reservoir-scale simulation of all these processes in one to three dimensions.The reservoir simulator can calculate three-phase (oil, water, gas) fluid flow in the porous media of a reservoir.Then, having the discharge of the fluids at the facets of the grid blocks, the component transport model calculates the concentration of all the components.In the cases of this study, 21 components exist in the system.Next, having the concentration of the components at each grid block, the bio-chemical model calculates the kinetics of the reactions (microbial and non-microbial) as well as phasepartitioning behavior of hydrogen sulfide and organic carbon among the phases in order to update the concentration of the components after the passage of a time-step.Finally, calculating the new porosity profile of the porous medium of reservoir using the volume of the deposited (or dissolved) barite, the new permeability profile is calculated and passed again to the reservoir model along with the new porosity profile for the calculation of fluid flow for the next time-step.
General assumptions for the model are as follow: -There is no interaction on molecular level between the probable deposited scale and biofilm.-There is no biofilm deposition.
-All the formed scale deposits immediately.
-Sulfate and barium ions are at equilibrium in the reservoir at the initial conditions.This implies that some barite may be present in the reservoir at the initial conditions.Therefore, in this work, the amount of barite in the medium is allowed to decrease below zero, meaning the reported barite amounts are relative to the amount of barite initially present in the medium.Alternatively put, negative numbers for barite amounts correspond to more dissolution than formation of barite.-Each guild of bacteria has uniform characteristics, namely growth rate and response to environmental changes.In other words, each guild consists of one strain (species) of bacteria.

Reservoir model
This model simulates multi-phase non-isothermal fluid flow in the reservoir using a commercial reservoir simulator.In this study, a black oil model in Eclipse100 commercial simulator has been used.One can use any other reservoir simulator for this purpose as long as the outputs match the inputs of the component transport model.Similar to Nick et al. (2013) the model employs a sequential non-iterative approach (SNIA) for solving flow and (bio)reactive transport in porous media.
As barite scale is formed in the medium, porosity decreases as follows: where, ∅ t+1 and ∅ t are the porosity of a grid block at the next and current timestep, respectively, V barite (cubic feet) is the volume of the formed barite during the timestep in that grid block, and V bulk (cubic feet) is the bulk volume of the grid block.The structure-property relations are used to calculate the absolute permeability of the medium in all directions as follows (Maheshwari et al., 2013;Mahmoodi et al., 2018).
where, k (md) is the permeability corresponding to the porosity of ∅, and k ref (md) is the reference permeability corresponding to the reference porosity of ∅ ref .

Component transport model
In this model, having the velocity field of all the phases, the concentrations of all the components (mainly ions) and their changes due to the flow of fluids is calculated.In this study, a finite volume scheme together with a direct solution to the linear set of equations has been used.Moreover, the phase-partitioning of two important components (hydrogen sulfide and DOC) among the three phases has been considered using phase-partitioning coefficients, based on the following equations: where, K OWi , K GWi , and K OGi (mole fraction/mole fraction) are the oilwater, gas-water, and oil-gas phase partitioning coefficients, respectively.It goes without saying that knowing two of the three phasepartitioning coefficients enables us to calculate the third one.Phase-partitioning coefficients can be roughly considered constant in some cases (e.g.K OWi ) whereas they considerably vary with pressure and temperature in other cases (e.g.K GWi ) (Burger et al., 2013).For the dependency of K GWi on temperature and pressure, interpolation between data points from the literature was used.In this study, the results from Burger et al. (2013) have been used for this purpose.

Chemical model
The chemical model calculates the kinetics of the reactions.The set of the reactions that has been used in this study are presented in Table S1.The microbial reactions are a simplified version of the work of Cheng et al. (2016).The reason the set of reactions have been simplified is that isotopes have not been used or investigated in this study for any purpose.Moreover, only nitrate has been considered here as the mitigation agent, not perchlorate.Therefore, the reactions associated with perchlorate and different isotopes where neglected.Furthermore, in terms of analysis of the results, having a complex set of reactions complicates understanding the trends.Hence, this work only considers better-known pathways.The set of reactions and the rate parameters are explained in the work of Cheng et al. (2016), which has already been validated with the experiments of Engelbrektson et al. (2014).
In Table S1, f e represents the portion of the electron donor that is coupled with the electron acceptor, i.e., the portion that is used for A. Mahmoodi and H.M. Nick energy (catabolic reaction).f s , on the other hand, is the portion of the electron donor that is coupled with cell formation, i.e., the portion that is synthesized (anabolic reaction) (Bruce E. Rittmann and Perry L. McCar fdty, 2001).SRB, NRB, and NRSOB are the representatives of the communities of sulphate reducing bacteria, nitrate reducing bacteria, and nitrate reducing sulfide oxidizing bacteria, respectively.It is worth noting here that in reality, the community of each of the guilds may consist of various species (strains) with different characteristics.For instance, one strain of SRB may have a totally different optimum growth temperature compared to another one (Cheng et al., 2018).However, in this work, for the sake of simplicity, a unified set of characteristics is assumed for all the bacteria in one community of each type.It is also worth noting that the reaction corresponding to barite in Table S1 is a reversible reaction, meaning both barite precipitation and dissolution are possible.
In order to calculate the kinetics of the microbial reactions, the reaction rates are calculated based on Monod equation (Cheng et al., 2016): where, r (mol/kgw/sec) is the reaction rate, a B , a eD , a eA , and a Inh (mol/ kgw) are the activities of biomass, electron donor, electron acceptor, and inhibitor, respectively, μ max (1/sec) is the maximum specific growth rate (in case of abundant substrates), K eD and K eA (mol/kgw) are the half saturation constants of electron donor and electron acceptor, respectively, K Inh (mol/kgw) is the inhibitor constant, and m (1/sec) is a decay and mortality constant.
The maximum specific growth rate can vary with temperature.To account for this dependency, the following relationship is used (Rosso et al., 1995): where, T ( • C) is the temperature at which the maximum growth rate is desired, T min ( • C) is the temperature below which there is no microbial activity (i.e.μ max = 0), T max ( • C) is the temperature above which there is no microbial activity (i.e.μ max = 0), μ opt is the highest possible maximum specific growth rate (i.e., at the optimum temperature), and η(T) is a multiplier that defines the maximum specific growth rate when the temperature is between T min and T max , which is calculated as follows: where, T opt ( • C) is the optimum temperature, at which η(T opt ) = 1.This means that at this temperature, the maximum specific growth rate is the highest, which is μ opt .
For the kinetics of barite precipitation and dissolution, the following equation has been used to calculate the reaction rate (Zhen-Wu et al., 2016): where, r (mol/kgw/sec) correspond to the reaction rate, k (mol/kgw/ sec) is the reaction rate constant, Ω barite (unitless) is the saturation state of the fluid with respect to barite, and n ′ is the reaction order.The reaction order of barite formation and dissolution was considered to be 1 and 0.2, respectively (Zhen-Wu et al., 2016).The saturation state of the fluid with respect to barite can be determined as follows: where, Q barite is the activity product for barite (i.e. the product of activities of barium and sulfate), a Ba 2+ and a SO 2− 4 (mol/kgw) refer to the activities of barium and sulfate ions, respectively, and K sp, barite represents the solubility product of barite (aka, equilibrium constant for barite dissolution or precipitation reaction).The solubility product is essentially the product of activities of barium and sulfate under equilibrium conditions.Note that the reaction rate constant (k in equation ( 9)) and the solubility product (K sp in equation ( 10)) may vary with temperature and the ionic strength of the solution.Moreover, the reaction order (n ′ in equation ( 9)) varies with whether the process is dissolution or precipitation (Zhen-Wu et al., 2016).Activities of the ions are calculated as follows: where, C i (mol/kgw) is the molal concentration of a component and γ i (unitless) is the activity coefficient, which can be calculated using Davies equation (Davies, 1938): where, A is a constant, z i is the electrical charge of the ion, and I is the ionic strength of the solution, which is defined as: It is worth noting that Davies equation works well for the ionic strengths of below 0.5, which is the case in this study.
An explicit numerical scheme with careful determination of timestep size was utilized to compute the concentration changes due to chemical reactions.In order to validate the numerical method, a batch case was defined in Reaktoro open-source chemical solver, and the results were used to validate the code written for this study.The flowchart in Fig. 2 shows a schematic of the whole model.

Simulation cases
A series of simulations are performed in 1D to illustrate how microbial souring and mitigation compete against scaling on sulfate consumption through the porous medium.Furthermore, a series of 2D simulation cases were performed to illustrate how flow properties in the reservoir can affect the processes.
Table S2 represents the common inputs for all the cases.Needless to mention, the optimum, minimum, and maximum temperatures for microbial activities are used in equation ( 8) to calculate the maximum specific growth rate.
Moreover, the phase partitioning coefficient of H 2 S between oil and water phases is assumed to be constant (K OW = 25) and between water and gas phases, which depends on pressure and temperature, follows the data of Burger et al. (2013).For the solubility product of barite versus temperature, data from Monnin (1999) were used.In order to use these data sets, linear interpolation between datapoints was utilized.
The concentration of the components in the injected seawater and the initial concentrations in the formation brine are represented in Table S3 (Cheng et al., 2016).
Table 1 represents the inputs of simulation for all the cases.In the 1D cases, a seawater injection well is located in the left side of the medium (grid 1) and a production well is located in the right side of the reservoir (grid 50).In the 1D cases, crossflows cannot be studied.In real world, one expects to see enhanced scale precipitation around the production well, where the flow of the formation brine and injected seawater collide (and mix) for a longer time around that specific location.Therefore, similar conditions and cases in 2D are also inspected.In the 2D cases, a seawater injection well is located in the left side of the medium and a production well is located in the right side of the medium as shown in Fig. 3.
Five different conditions were assumed in 1D and 2D in order to investigate the effect of each of the processes on the other one in different situations.Condition B represents when there is only barite precipitation happening with no microbial reactions (microbial reaction rates are imposed to be zero).Condition S denotes only microbial souring with no barite formation (barite reaction rates are imposed to be zero).Condition SB denotes the presence of both barite and souring reactions.In all the B, S, and SB conditions, no nitrate treatment is assumed, meaning nitrate injection concentration was set to be zero.Conditions SBN2, SBN10, and SBN50 consider all the processes (barite precipitation, microbial souring, and nitrate mitigation) for nitrate injection concentrations of 2, 10, and 50 mM, respectively.This type of naming is used in all the figures and hereafter in the text.All the results are presented at three different times.For the cases with different injection rates, the times have been changed to represent the same number of pore volumes of injection.Table 2 is a guide to the properties in each of the cases and the corresponding figure number.

Results and discussion
This section begins with the presentation of some of the results of a few hand-picked simulation cases that represent the most notable findings of this study.Then, the general trends in the full set of results (presented in Figs.S1-S32 in the supplementary material) is discussed.

The most notable findings
Unexpectedly, it is seen to be possible that nitrate treatment causes the souring zone in the porous medium to move away from the injection well and thus an earlier hydrogen sulfide production from the production well, despite a decreased total amount of generated hydrogen sulfide in the reservoir (see Fig. 4, Fig. 5, and Fig. 6, corresponding to cases 1D_01, 1D_01, and 2D_01, respectively).Such behavior is seen since higher concentrations of nitrate in the injection water postpone the consumption of sulfate ions.Therefore,

Table 1
Inputs of simulation for all the cases.sulfate is available at locations further away from the injection well (i.e., closer to the production well).Hence, more souring takes place closer to the production well and less souring takes place closer to the injection well.This may cause an earlier increase in the hydrogen sulfide content of the produced fluids (note the time at which hydrogen sulfide reaches the end of the medium in Fig. 5).However, postponing the consumption of sulfate ions results in a less total amount of generated hydrogen sulfide in the medium.On a more practical note, depending on when the production is planned to stop, nitrate treatment could possibly cause a more total produced hydrogen sulfide.
The second noticeable point in the results of the 2D cases is that higher souring may have a considerable impact on barite formation, especially around the production well.Such accumulation of barite around the production well is not evident in the 1D cases since it is highly dependent on the flow patterns.In the 2D cases, due to the fact that the flow of the formation brine and the injection seawater converge toward the production well and collide (and mix) for an elongated time, severe barite formation is possible.Remember that the injected seawater is rich in sulfate and the formation brine is rich in barium.However, the results of the 2D cases demonstrate that souring could result in either higher or lower barite formation (or dissolution) around the production well, i.e., souring can either worsen or mitigate scaling problem.Two of the extreme cases in that sense are compared in Fig. 7.
The difference between the two cases represented in Fig. 7 is the initial DOC content in the oil phase.In the case 2D_03, the DOC content is low whereas the case 2D_07 is a high-DOC case.Therefore, no noticeable difference is observed in the no-souring condition (condition B) as DOC content does not directly affect barite formation kinetics but indirectly affects it through souring.Nevertheless, where souring is not severe (due to low DOC content in case 2D_03, condition SB), an enhanced amount of barite is seen to form around the production well due to a delay in the consumption of barium ions deep in the reservoir and thus their movement toward the production well.This is contrary to where souring is severe (due to high DOC content in case 2D_07, condition SB), where as a consequence of full sulfate consumption through microbial souring, no sulfate is available around the production well and thus dissolution takes place there.On a more technical note, when the concentration of either sulfate or barium or both is very low, the activity product (10) is less than unity.Hence, the reaction rate (9) becomes negative, which means the barite formation reaction goes occurs in the opposite direction (dissolution).
The few cases discussed so far cannot be taken as the representative of all the cases.Hence, a summary of the results in all the studied cases is presented in Figs.S1-S32.Moreover, the general trends seen in the complete set of the results are discussed hereafter.From left to right, each profile corresponds to the case with a nitrate concentration of 0, 2, 10, and 50 mM in the injected seawater, respectively.The complete set of graphs for this case is represented in Fig. S1.

Trends in 1D simulation results
Fig. 6.The concentration profile of hydrogen sulfide (in mM) in the water phase throughout the porous medium for the simulation case 2D_01 at 2800 days for the 4 conditions that include souring.From left to right, each profile corresponds to the case that include souring and barite scaling with a nitrate concentration of 0, 2, 10, and 50 mM in the injected seawater, respectively.The complete sets of graphs for this case are represented in Fig. S25.-S12).These are the cases in which lower concentration of DOC is assumed to be initially present in the oil phase.Conversely, the effect of nitrate treatment on the total amount of generated hydrogen sulfide in cases 1D_05 to 1D_08 is less considerable (Figs.S5-S8 and graphs B1 to B3 in Fig. S13-S16), where DOC content of the oil is high.This suggests that in case of high DOC content in the reservoir hydrocarbon, nitrate injection might not be an effective solution.
• In all 1D cases, higher nitrate concentration results in a shift in hydrogen sulfide production zone toward the production well.This suggests that, contrary to the total amount of generated hydrogen sulfide inside the reservoir, more hydrogen sulfide is produced from the production well in the earlier stages of production in case of higher nitrate content (look at graphs B2 and B3 in Figs.S9-S16).This happens because higher nitrate means less sulfate consumption close to the injection well.Hence, more sulfate is available further away from the injection well (look at graphs E1 to E3 in all the conditions in Figs.S9-S16).• In all the 1D cases, especially the cases where souring is present, lower injection rates cause higher souring and less barite formation (or more barite dissolution) closer to the production well (look at Figs. S1-S8 and graphs B1 to B3 and C1 to C3 in Figs.S9-S16).This happens due to that DOC is for a bit longer supplied around the production well in these cases (Figs.S1-S8).Consequently, more souring takes place there and thus less sulfate is available for barite formation.• In the cases with low DOC content, not much change happens to the barite amount in the medium after breakthrough (compare graph C2 with C3 in Figs.S9-S12.).Nevertheless, in the cases with high DOC content, in conditions with souring (SB, SBN2, SBN10, and SBN50), still noticeable changes in barite amount happen way after breakthrough (compare graph C2 with C3 in Figs.S13-S16).This happens due to that souring is already finished (all the DOC has already been consumed as seen in Figs.S1-S4) in most of the cases with low DOC content before the final depicted time in each case.This doesn't happen in high DOC cases because there is more DOC (substrate) available for souring and thus higher potential for continuous souring for longer times.

Trends in 2D simulation results
Figs. S17-S24 represent barite concentration profile and Figs.S25-S32 represent hydrogen sulfide concentration profile in the 2D simulations in eight different cases (low and high injection rates, low and high DOC content, and low and high sulfate concentration in the injection seawater) at 3 different times.
Looking at Figs. S17-S32, the following trends are seen: • In some of the 2D cases, excessive scale accumulation is vivid near the production well.This is the most notable difference between 1D and 2D cases that demonstrates the necessity of multi-dimensional simulations.Nevertheless, in some of the conditions (conditions SB, SBN2, SBN10, and SBN50 in Figs.S21-S24), this doesn't happen.
The excessive barite formation around the production well happens because after breakthrough, on the locations where simultaneous flow of the barium-rich formation brine and sulfate-rich injection seawater converge toward the production well, the two collide and mix for a longer time, and thus excessive amount of barite scale is formed.However, in the cases where souring consumes all the sulfate before reaching the production well, there is no sulfate available for barite formation around the production well.
• Despite what one may expect, in case of low DOC content in the reservoir oil and high sulfate concentration in seawater, in the conditions with more microbial souring, although less scale is formed deep in the reservoir, more scale accumulation is seen around the production well, (conditions SB, SBN2, and SBN10 in Figs.S19 and  S20).In such cases, no souring or a better souring mitigation expectedly shows less barite accumulation around the production well (conditions B and SN50 in Figs.S19 and S20).This happens because the concentration of the barium ions is the limiting factor in scale formation in these cases.Thus, when barium ions are less consumed deep in the reservoir (halfway between the injection well and the production well), they move toward the production well and accumulate there.Since there is a continuous supply of sulfate from the injected water, excessive barite scale precipitation is observed around the production well.Note that it only happens if a low DOC content limits souring, and also high sulfate concentration is present in the injection seawater.• In all the cases other than the ones mentioned in the last bullet point (Figs. S17 and S18,, the more souring the less barite formation occurs both deep in the reservoir and around the production well.That is because in the conditions with higher souring (condition SB compared to conditions B, SBN2, SBN10, and SBN50 in Figs.S17 and S18 and conditions SB, SBN2, SBN10, and SBN50, compared to condition B in Figs.S21-S24), in the cases were sulfate concentration is low (Figs.S17 and S18), all the sulfate is consumed close to the injection well.Similarly, in the cases with high DOC content (almost unlimited DOC) (Figs.S21-S24), no matter how much sulfate is present, most of it is consumed close to the injection well, and thus there is less sulfate left for barite precipitation.• In the 2D cases where there is no souring and sulfate concentration is low (condition B in Figs.S17, S18, S21, and S22), as injection rate increases, there is a small drop in the amount of barite precipitated around the production well.However, in the cases where there is no souring and sulfate concentration is high (condition B in Figs.S19, S20, S23, and S24), injection rate doesn't considerably lower the average amount of barite around the production well.• In the 2D cases where there is souring, the effect of injection rate on barite formation around the production well is very sensitive to each specific case and a general trend is not seen.However, this effect is notable in some of the cases (e.g., condition SB, and SBN50 in Figs.S19 and S20).• In all the 2D cases, the considerable barite formation or dissolution around the production well happens way after breakthrough.Hence, it is a matter of abandonment plan to decide whether the considerations discussed in this paper are necessary or not for a specific case.• In all the 2D cases, the higher souring results in a smaller radius of barite formation around the injection well (compare condition B with conditions SB, SBN2, SBN10, and SBN50 in Figs.S17-S24).
Nevertheless, the amount of precipitated barite in the close proximity to the injection well is not noticeably affected by souring.That is because there is a time lag from when the injection seawater enters the medium and when microbial community is large enough so that microbial souring starts to make a difference.During this time, the barium ions have already been washed away from around the injection well.This may change if there is considerable microbial activity inside the injection well, before the seawater enters the medium.
• The amount of barite scale precipitated around the injection well and deep in the reservoir is low enough in all the 2D cases that no considerable effect on flow patterns is observed.Conversely, around the production well is an important bottleneck in the liquid production from the reservoirs where scale precipitation may cause significant damages.Notice that, for the sake of comparability, the legend in Figs.S17-S24 goes up to only 8 mM and any number higher than that is depicted with the same color.The real maximum number of barite concentration in the grid where the production well is located could be much higher than that.The maximum barite concentration in the 2D cases as well as their corresponding porosity and permeability (using equation ( 2)) are represented in Table S4.This shows a maximum of around 0.5% porosity reduction, which corresponds to 1.8% permeability reduction (case 2D_01 illustrated in Fig. S17).It is worth noting that although these amounts are not considerable in the cases of this study, in tight reservoir with very low permeability, the permeability change corresponding to very small porosity changes could be considerable since scale fragment tend to block pore throats.Furthermore, the formed barite fragments could move and enter the well and thus create flow barriers somewhere in the production tubulars.• Presence or absence of barite formation does not have a considerable effect on reservoir souring.(Compare condition S with condition SB in all 2D cases.)• Similar to what is shown in Fig. 6, in all the 2D cases, a more effective nitrate mitigation (higher nitrate concentration in the injection seawater) causes a shift in the hydrogen sulfide production zone away from the injection well and toward the production well (Compare the hydrogen sulfide concentration profile in condition S and SB with conditions SBN2, SBN10, and SBN50 in Figs.S25-S32).This results in an earlier production of hydrogen sulfide from the production well, despite a less total amount of generated hydrogen sulfide in the medium.This is a result of a delay in the consumption of sulfate ions in the vicinity of the injection well.• The DOC content in the reservoir hydrocarbon has a considerable impact on hydrogen sulfide propagation in the medium.The low-DOC cases (Figs.S25-S28) show a noticeably more propagated plume of hydrogen sulfide compared to high-DOC cases (Figs.S29-S32).This happens because in the low-DOC cases, most of the DOC in the vicinity of the injection well is consumed fast and thus the injected sulfate can move further away from the injection well and react there.Complemented by the point of the last bullet point, the practical implication of this observation is that in a high-DOC case, doing nothing may be a better strategy than nitrate treatment, depending on whether the hydrogen sulfide plume would reach the production well before abandonment or not.• Injection rate is shown to have a considerable effect on the amount and movement of hydrogen sulfide inside the medium.Higher total amounts of hydrogen sulfide is generated in the medium in the cases with lower injection rates.Nevertheless, higher injection rates cause the plume of hydrogen sulfide to reach the production well earlier in terms of pore volume injected of seawater.(Compare Fig. S25

Practical implications of the results
Considering that microbial reservoir souring has a considerable effect on the severity of barite precipitation, this study suggests barite scale (and possibly all sulfate scale) studies should consider souring in their work if souring is possible in their case.This had never been considered to the best knowledge of the authors.On the other hand, it is suggested in this study that the effect of scale precipitation on souring is minimal.Therefore, it may not be necessary to consider the effect of barite formation on souring for souring studies.
In both 1D and 2D cases, nitrate treatment caused a shift in hydrogen sulfide generation zone inside the reservoir.In other words, although the addition of nitrate reduces the total amount of produced hydrogen sulfide inside the reservoir, it causes hydrogen sulfide generation to take place closer to the production well.Hence, an earlier increase in the hydrogen sulfide concentration in production wells is expected in case of the addition of an insufficient amount of nitrate to the injection water.This is in accordance with the findings of a recent experimental work (Mitchell et al., 2021) who observed that sub-optimal dosed nitrate treated bioreactors produced sulfide more rapidly than untreated controls.They also presented field data that questions the effectiveness of nitrate treatment.
The trends observed in the results are highly affected by all the three investigated parameters (DOC content, sulfate concentration in the injected seawater, and injection rate).This gives us the ability to control both reservoir souring and barite scale formation considering the DOC content in the reservoir hydrocarbon and manipulating sulfate concentration in the injected seawater (for example through sulfate removal (Robinson et al., 2010)) and injection rates.

Conclusion
Based on the trends observed in the results, the following general conclusions could be made.
• A non-isothermal multi-component bio-chemical model to simultaneously simulate souring, nitrate treatment, and barite scale formation in the porous media of a hydrocarbon reservoir has been developed.• Given that more barite precipitation is formed around the production well due to the simultaneous flow of barium-rich formation water and sulfate-rich injection water around the production well, it is necessary to investigate scale formation in multi-dimensional analysis rather than only one dimension.To elaborate, in one dimension, the crossflow of the formation water and injection water around the production well is not visible.• Reservoir souring has a considerable impact on the amount of formed barite (and possibly other sulfate scales), both deep in the reservoir and around the production well.Nevertheless, the effect is minimal around the injection well.Consequently, it is necessary to consider the effect of souring when studying barite scale formation in the reservoir.• Expectedly, the choice of the mitigation strategy and its effectiveness also considerably influence scale formation deep in the reservoir and around the production well.However, the intensity of the effect is very sensitive to the case.Therefore, although no general recipe could be proposed, considering the effect while designing a souring treatment strategy is vital.• Hydrogen sulfide production zone may shift with the efficiency of the mitigation strategy of choice.This may cause an earlier increase in the concentration of hydrogen sulfide in the production well in case of a higher nitrate concentration in the injection seawater.Therefore, doing nothing instead of a non-adequate nitrate treatment may be better in certain cases if the full prevention of souring is not practical.Hence, a full-scale study of souring in each case is vital to find the optimum nitrate concentration that results in the least amount of produced hydrogen sulfide from the production wells.

Caveats and future work
In this study, only one type of scale (BaSO 4 ) has been studied.However, other types of sulfate scale, such as SrSO 4 and CaSO 4 , may also play a role in the competition on sulfate ions.Depending on the composition of the formation water in each case, it is possible that considering all types of sulfate scales have a more considerable effect on souring compared to when we consider only one of them.Furthermore, since the generation of S 2− ions during reservoir souring is possible, the possibility of FeS scale generation is also present.Moreover, in this work, it is assumed that the formed scale is immobile.However, considering the detachment of scale from the rock surface could affect the results.
Additionally, one could use a more comprehensive presentation of microbial reactions for more precise simulations.However, for such a complex system of microbial activity in the environmental system, a comprehensive understanding of the system may never be possible.
Furthermore, the interplay between scaling and microbial souring with corrosion and scale precipitation inside the wellbore and surface tubulars is an interesting topic to be studied.Especially, corrosion in the production tubulars could be heavily affected by the composition of production liquids, which is defined by both souring and scale formation in the reservoir and tubulars.
Moreover, since the location of hydrogen sulfide generation zone inside the medium is seen to be shifting with the efficiency of the chosen mitigation strategy, one could investigate whether this could make an inadequate mitigation plan even worsen the souring problem.This could be done by looking at the concentration of hydrogen sulfide in the produced fluids instead of the porous media of the reservoir.
The presence of heterogeneity in the porous medium could also be an important factor to affect crossflows anywhere inside the reservoir or around the wells.Therefore, studying various geometrical flow shapes and their effect on scaling behavior may result in interesting insight.

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.
employed microbial growth and metabolite production in the STARS reservoir model to simulate laboratory continuous up-flow packed-bed bioreactor tests.Their model assumes nitrate is directly reduced to N 2 and sulfide is oxidized to sulfate.Haghshenas et al. (2012) implemented a biological model based on the UTCHEM model only considering the reduction of nitrate to nitrite without further reduction of nitrite and without oxidation of sulfide back to sulfate.Cheng et al. (2016) simulated the experimental work of Engelbrektson et al. (2014) using TOUGHREACT considering denitrification pathway for nitrate reduction by NRBs and NRSOBs assuming sulfide is only oxidized to sulfate.Veshareh and Nick (

Fig. 1 .
Fig. 1.Illustration of chemical and microbial pathways showing the possible interplay among sulfate scale formation, microbial reservoir souring, and nitrate or nitrite treatment.

Fig. 2 .
Fig. 2. The flowchart of the reactive transport model utilized in this study.The model uses a sequential non-iterative approach for solving flow and (bio)reactive transport in porous media.After each time step of solving multicomponent transport, it invokes a reactive solver to calculate reactions and update the concentration of each component.

FigFig. 3 .
Fig. S1 to Fig. S16 represent simulation results in 1D for eight different cases (low and high injection rates, low and high DOC content,

Fig. 4 .
Fig. 4. The concentration of hydrogen sulfide (in mM) in the water phase throughout the porous medium for the simulation case 1D_01 at 2800 days for all the 6 conditions (B: only barite scaling, S: only souring, SB, SBN2, SBN10, and SBN50:: barite scaling and souring plus 0, 2, 10, and 50 mM of nitrate concentrtion in the injected seawater.The complete set of graphs for this case is represented in Fig. S9.

Fig. 5 .
Fig.5.The concentration of hydrogen sulfide (in mM) in the water phase throughout the porous medium in time for the simulation case 1D_01 for the 4 conditions that include souring and barite scaling.From left to right, each profile corresponds to the case with a nitrate concentration of 0, 2, 10, and 50 mM in the injected seawater, respectively.The complete set of graphs for this case is represented in Fig.S1.

Fig. 7 .
Fig. 7.The concentration profile of barite (in mM) in the water phase throughout the porous medium and the vertical average concentration of barite against reservoir length at 10000 days for the simulation case 2D_03 (left) and case 2D_07 (right) for two conditions (top: condition B (barite scaling without souring), bottom: condition SB (barite scaling and souring)).The complete sets of graphs for these cases are represented in Fig. S19 (case 2D_03) and Fig. S23 (case 2D_07).

Table 2
Guide to the properties in each of the simulation cases and the corresponding figure number in supplementary materil.
). and low and high sulfate concentration in the injection seawater) through time.Looking at Figs. S1-S16, the following trends are seen: • At all times, a lower amount of barite scale is formed (or a higher amount of barite is dissolved) as more microbial reservoir souring takes place in cases 1D_01 to 1D_04, where DOC content of the oil is low (Figs.S1-S4 and graphs C1 to C3 in Figs.S9-S12).The presence of barite scaling does not considerably reduce microbial reservoir souring, i.e., the amount of generated hydrogen sulfide (compare condition S with SB in Figs.S1-S8 and graphs B1 to B3 in Figs.S9-S16).That is due to that the total amount of barium ions is limited in the formation brine.Hence, a limited amount of sulfate ions is consumed during scale formation.Therefore, the amount of barium ions controls the intensity of sulfate consumption for barite formation.One would expect this effect to be more noticeable in case of lowered sulfate ion concentration in the injected seawater.However, the difference is not considerably evident in the results (lowsulfate cases are presented in Figs.S1, S2, S5, S6, S9, S10, S13, S14).• Higher nitrate concentrations in the injection seawater effectively lowers total hydrogen sulfide generation in the medium in cases 1D_01 to 1D_04 (Figs.S1-S4 and graphs B1 to B3 in Figs.S9