A sulfur and nitrogen cycle knowledgeable mannequin to simulate nitrate therapy of reservoir souring

To simulate the batch experiments, totally different batch fashions every comparable to a state of affairs (outlined and described within the strategies part, listed in Desk S1) are assessed primarily based on how correct they will match the experimental knowledge, i.e. how small is their Sum of sq. errors (SSE).

The least SSE (Desk S1) is calculated for the simulation outcomes of a batch mannequin comparable to a state of affairs that solely considers group A (a bunch representing heterotrophic nitrate and nitrite discount via DNRA pathway). With the intention to examine batch fashions, the relative distinction between SSE of every batch mannequin (in %) with the least SSE is calculated via RSSEi = ((SSEi − least SSE)/least SSE) × 100, the place RSSEi is the relative SSE for the ith batch mannequin.

Besides the state of affairs that solely considers group A (the primary state of affairs in Desk S1), eventualities together with group A with different teams (eventualities 2 to six) have considerably decrease SSE values in comparison with eventualities excluding group A (7 to 14). This commentary means that heterotrophic nitrate/nitrite discount (derived by NRB) via the DNRA pathway is the key accountable mechanism of nitrate discount, and the presence of NRSOB and the denitrification pathway isn’t important. Observe that the genetic algorithm on this work is constrained such that it may decrease a bunch impact, however it can’t take away the impact. That’s, in a case the place a bunch known as α is accountable, the optimization contemplating group α and one other group results in a SSE worth near, however not the identical as, a SSE worth the place solely α is taken into account. Due to this fact, a barely totally different SSE worth of the state of affairs contemplating group A solely (state of affairs 1 in Desk S1) than the SSE worth of different eventualities together with group A (alongside different teams, eventualities 2 to six) don’t end in an analogous likelihood, SSE. Determine 2a–d present the batch experiments knowledge and simulation outcomes comparable to essentially the most possible case (known as SIM1; the batch mannequin that considers the first state of affairs of Desk S1, Fig. 1c1). Within the case of sulfate, sulfide, nitrate and nitrite, SIM1 prediction is cheap (Desk S2 lists parameters of SIM1).

Determine 2Figure 2

(a–d) Profiles of nitrate, sulfate, nitrite and lactate for various preliminary nitrate concentrations. Experimental knowledge are proven by markers and simulation outcomes (SIM1) are proven by strong traces. (e,f) Evaluate sulfide and sulfate concentrations measured with SIM1, SIM2 (SIM1 with out contemplating inhibition impact, proven by dashed traces) and SIM3 (SIM1 with out contemplating NRB exercise, proven by dotted traces). Observe that lactate focus must be learn from the appropriate vertical axis, for different parts focus must be learn from the left axis.

It must be famous that, SIM1 can’t predict lactate traits with good precision. Determine 2b–d illustrate decline in lactate focus at zero nitrate, nitrite and sulfate focus, i.e. lactate consumption occurs with out presence of any electron acceptor. Thus, incidence of fermentation (along with SRB, NRB and NRSOB exercise) could also be a purpose why the present mannequin can’t match the lactate focus knowledge (as SIM1 doesn’t think about any response for fermentation).

Notable variations amongst SSE of assorted eventualities (reported in Desk S1) counsel that the classifications of microbial communities within the reservoir, and their metabolic pathways considerably affect the accuracy of simulations to foretell reservoir souring, and effectiveness of nitrate injection. Moreover, it reveals that by utilizing a genetic algorithm, a easy batch experiment knowledge set can be utilized to foretell nitrate discount pathways.

What’s the dominant NT mechanism by NRB

To light up the impact of nitrite inhibition, a brand new simulation is taken into account (known as SIM2, Fig. 1c1) and is fitted to the experimental outcomes. SIM2 is SIM1 with out the inhibition coefficient, i.e. all parameters are the identical as SIM1 besides that the inhibition coefficient, I/(CNitrite + I), is eliminated. Thereafter, to check the impact of biocompetition, NRB reactions are eliminated (a mannequin that solely incorporates SRB reactions with kinetic parameters the identical as SIM1, known as SIM3, Fig. 1c1). In different phrases, SIM2 is SIM1 with out nitrite inhibition impact and SIM3 is SIM1 with out nitrite inhibition and biocompetition results. Determine 2e,f display sulfate and sulfide concentrations for these three simulations (SIM1, 2, three) in comparison with the experimental knowledge. We additionally calculated SSE for sulfide and sulfate (reported in Desk S3). From Fig. 2e,f and Desk S3 it’s clear that SIM2 is way much less correct and its deviation from experimental knowledge will increase by a rise in preliminary nitrate focus. SIM3 predicts roughly the identical focus profile for sulfide and sulfate as that of SIM2. Desk S3 knowledge confirms this interpretation since RSSE (for sulfate and sulfide) for SIM2 and SIM3 are about the identical (about four% relative distinction), and markedly totally different from SIM1. This means that in experiments by Xu et al.33, nitrite inhibition is the key mechanism that suppresses SRB exercise, whereas, biocompetition for a standard carbon supply doesn’t have notable inhibitory results. Due to this fact, we argue that if nitrite inhibition isn’t important, and NRB are the one accountable group for nitrate therapy, nitrate therapy won’t be efficient.

Simulation of the move experiments

Within the earlier sections it was discovered that nitrite inhibition is the principle mechanism via which heterotrophic nitrate and nitrite discount via DNRA pathway can inhibit SRB exercise in small scale batch experiments of Xue et al.33. Simulation of the batch experiments leaves two questions unanswered.


What’s the nitrate therapy main mechanism if nitrate discount happens via an autotrophic course of (somewhat than a heterotrophic)?


What’s the interaction between reactive processes and move?

To reply above talked about questions we use the move experiments of Hubert et al.13 the place nitrate therapy utilizing autotrophic NRSOB was evaluated via 1D area move experiments.

Determine three reveals the simulation outcomes of the reactive transport mannequin (described within the methodology part) fitted to outcomes of the move experiments utilizing the genetic algorithm (known as SIM4; Desk S4 reveals SIM4 mannequin parameters, Fig. 1c2). Observe that the one parameters which are fitted listed here are kinetic parameters of the reactions (a response representing SRB, and two reactions representing group B, Desk S5).

Determine threeFigure 3

Comparability between knowledge of the move experiments (blue markers), simulation of the Coombe et al.12 (the dashed line) and authors’ mannequin (the strong line). (a) Sulfide focus, 1st port; (b) sulfide focus, fifth port; (c) sulfate focus, 1st port; (d) sulfate focus, fifth port; (e), nitrate focus, 1st port; (f) nitrite focus, 1st port (the dotted line must be learn from the appropriate axis and reveals nitrate injection focus).

Assuming conservation of mass, any consumption or manufacturing of sulfate is coincident with manufacturing or consumption of sulfide. That’s, the simulation outcomes for sulfide and sulfate within the first port (Fig. 3a,c), and the final port (Fig. 3b,d) are symmetric; subsequently, explanations for adjustments (extremum values) noticed in Fig. 3a,b, are additionally legitimate for adjustments noticed in Fig. 3c,d. Most important adjustments in sulfide and nitrate focus traits are marked in Fig. three and are known as CH1 to CH30. Flowrate is initially zero till the entire discount of sulfate occurs (via response one), after which preliminary flowrate of zero.5 ml/h is utilized. By imposing flowrate, vitamins go biomass sooner, so much less response time results in much less manufacturing of sulfide, and extra focus of vitamins out there for biomass. Due to this fact, a pointy drop in sulfide focus happens (CH1 to CH2, Fig. 3a), biomass begins to develop and sulfide manufacturing is steadily constructed up again to the earlier degree in a couple of days (CH2 to CH3, Fig. 3a). CH3 (Fig. 3a) is a results of the addition of two.5 mM of nitrate on the inlet. As a result of introduction of nitrate, some sulfide is oxidized to sulfate (reactions four and 5 in Desk S5) and results in a fast fall in sulfide focus. After this fast fall, two phenomena occur in parallel. First, progress of NRSOB results in the next diploma of sulfide oxidation to sulfate. Second, since there’s an extra quantity of lactate within the system, SRB biomass grows to scale back the produced sulfate. These two phenomena proceed collectively. Initially, the sulfide oxidation charge is larger, so sulfide focus is diminished (the development between CH3 and CH4, Fig. 3a). Nonetheless, by progress of NRSOB, nitrate and nitrite focus, which reaches to the primary port, is decreased. CH21 to CH22 (Fig. 3e) illustrates discount in nitrite within the first port. Due to this fact, at CH4 (Fig. 3a) charge of sulfide discount turns into equal to that of sulfide oxidation. Subsequently, sulfate discount charge will increase and causes a rise in sulfide focus. The rise in sulfide focus continues till the nitrate focus on the injection level is elevated. Once more, the identical habits is noticed; CH5 (Fig. 3a) is corresponding to extend of nitrate focus from 2.5 to five mM. After a gradual lower of sulfide oxidation charge (nitrite focus that reaches the primary port is decreased because of the progress of NRSOB, CH23 to CH24, Fig. 3e), and a rise of sulfate discount charge, these two charges develop into equal at CH6 (Fig. 3a). Then, sulfate discount continues to extend till the subsequent change in nitrate focus is utilized (CH7, Fig. 3a). For the subsequent improve in nitrate focus, after the sharp lower in sulfide focus (CH7 to CH8, Fig. 3a), we can’t see the interval wherein sulfide oxidation charge is quicker than sulfide discount charge. A small improve in sulfide focus is noticed (CH8 to CH9, Fig. 3a) because of the discount within the quantity of nitrite that reaches the primary port (CH25 to CH26, Fig. 3e). Rising nitrate focus on the injection level has a negligible impact on sulfide focus within the first port for 2 causes. First, nitrate focus is excessive sufficient to oxidize all sulfide anions between the injection level and the primary port. Second, nitrite focus that reaches the primary port is excessive sufficient to maintain the sulfate discount charge negligible. After the 60th day, at nitrate injection concentrations greater than 10 mM, nitrate and nitrite concentrations are not diminished (Fig. 3e,f). Since nitrate discount is the results of sulfide oxidation, which means for nitrate injection concentrations greater than 10 mM no sulfate discount (sulfide formation) happens between the injection level and the primary port.

Contemplating the 56 cm distance between the primary and the final ports, each change in focus on the first port is anticipated to happen on the final port roughly 1.55 days later (journey time of various parts if convection is dominant and no retardation because of, for instance, adsorption occurs). The change in sulfide focus because of rising injection move charge, because it was seen within the first port (CH1 and CH2, Fig. 3a), isn’t seen within the final port. It’s because, the 56 cm distance is lengthy sufficient for practically all injected sulfate to be diminished earlier than it reaches the final port, even for the best move charge. The remainder of the sulfide focus adjustments noticed within the first port (CH3 to CH9, Fig. 3a) are noticed within the final port after 1.55 days (CH10 to CH18, Fig. 3b). That’s, explanations given for CH3 to CH9, maintain true for CH10 to CH18, respectively.

Coombe et al.12 additionally simulated the move experiments utilizing STARS simulator. Of their work, for each ports, negligible souring is noticed till in regards to the 10th day. It isn’t clear why souring is sort of zero on this timeframe. Concerning injection between zero–23 days, Coombe et al.12 don’t present when the injection was utilized. Their mannequin provides a comparatively good illustration of the method for the final port; nevertheless, it can’t moderately correlate the information for the primary port. Contemplating the organic part of the sulfate discount course of and its inhibition by nitrate injection, focus adjustments (in sulfate and sulfide) are anticipated because of progress of microorganisms (an exponential development). Abrupt adjustments (somewhat than exponential) in sulfide and sulfate focus profiles within the simulation results of Coombe et al.12 don’t present this progress part. Moreover, fashions by Coombe et al.12 underestimate the impact of nitrate mitigation over many of the area. That is in all probability as a result of the impact of nitrite inhibition was uncared for, and consultant reactions for the governing organic processes weren’t thought-about.

Influence of move path size on the required nitrate injection focus

Contemplating Fig. three, nitrate injection concentrations within the vary of 10 to 15 mM (comparable to a timeframe between in regards to the 60th day and the 86th day) can inhibit souring within the first port (Fig. 3a), however not within the final port (Fig. 3b). With these injection concentrations, a ample quantity of nitrite is produced and current within the first port to inhibit SRB exercise. Nonetheless, because of the nitrite discount between the primary and final ports, nitrite focus can’t be maintained between these ports. Because of this, reservoir souring is inhibited within the first port however not within the final port. In larger nitrate injection concentrations (greater than 15 mM, comparable to a timeframe after the 86th day) nitrite focus is maintained at a fairly excessive worth all through the column between the injection level and the final port.

With the intention to present the impact of move path size extra clearly, we modified the size of SIM4 mannequin to 2 meters and carried out the simulation. The nitrate injection focus on this simulation for the interval of 94 to 110 days may be seen in Desk S6. For this simulation, Fig. 4a reveals sulfide focus at 6.5 cm, 50.5 cm and 199.5 cm from the inlet. These sulfide focus profiles for various distances display that nitrate injection focus of 10 mM is sufficient to inhibit souring inside a 6.5 cm distance from the injection level whereas 17.5 mM and 20 mM are wanted for 50.5 and 199.5 cm distances. This implies that when NT is utilized to a subsurface reservoir, nitrate injection focus must be set primarily based on the space between injection and manufacturing wells. That’s, to design a profitable NT course of, nitrate injection focus is really helpful to be decided via simulation for various injection wells individually such that nitrate focus is all the time maintained excessive sufficient all through the medium between injection and manufacturing wells.

Determine fourFigure 4

(a) Sulfide focus at varied places of a 1D system, reveals the dependency of required inhibitory nitrate focus to the space between injection and manufacturing wells; the strong inexperienced line reveals nitrate injection focus, and must be learn from the appropriate vertical axis. (b,c) Illustrates the impact of sulfur biking and nitrite inhibition on the general effectivity of the nitrate therapy technique by NRSOB for the primary and the final port, respectively. SIM4 is the simulation contemplating NRSOB reactions and nitrite inhibition impact, SIM5 is the simulation contemplating NRSOB reactions with out inhibition impact, and SIM6 is the simulation with out contemplating NRSOB exercise.

Analysis of NT mechanisms by NRSOB

On this part, SIM4 is used to discover the significances of various mechanisms of souring inhibition by NRSOB (nitrite inhibition and sulfur biking). Initially, nitrite inhibition impact within the mannequin is ignored (by eradicating the inhibition coefficient in eq. 1, this mannequin is known as SIM5, Fig. 1c2), after which NRSOB exercise is uncared for (solely contemplating SRB response, this mannequin is known as SIM6, Fig. 1c2). The distinction between the outcomes of SIM4 and SIM5 represents the nitrite inhibition impact and the distinction between the outcomes of SIM5 and SIM6 illustrates the impact of sulfur biking. Determine 4b,c point out the outcomes of those three fashions. SIM4 simulation outcomes present that sulfide formation is decreased considerably because of nitrate injection. Quite the opposite, SIM5 leads to a excessive sulfide focus that’s impartial of nitrate injection. In actual fact, the outcomes obtained by SIM5 and SIM6 have an roughly related development, indicating nitrate injection has a negligible impact on SRB exercise. The considerably totally different development of the outcomes of SIM4 in comparison with these of SIM5 and SIM6 means that nitrite inhibition by NRSOB is a major contributor to NT. The roughly related development of SIM5 and SIM6 outcomes means that sulfur biking by NRSOB isn’t a serious contributor to NT.

Observe that sulfur biking may be efficient provided that the electron donor for SRB is limiting, and it can’t be efficient if nitrate and nitrite are limiting. Contemplating the response representing the metabolism of SRB (Desk S5, response 1), for every mole of lactate, 1.27 moles of sulfate reduces to sulfide. Due to this fact, as a way to trigger the system described within the move experiments by Hubert et al.13 to expire of lactate, 31.87 moles of sulfate are wanted. Concerning the sulfur biking course of, 31.87 moles of sulfate implies that 31.87 moles of sulfide must be oxidized. The metabolism of NRSOB is described by reactions NRSOB1 and NRSOB2 (of Desk S5), suggesting that every mole of nitrate can oxidize zero.29 moles of sulfide straight, and might oxidize zero.86 moles of sulfide not directly (because of the manufacturing of nitrite). Thus, one mole of nitrate can oxidize 1.16 mole of sulfide; that’s, within the absence of nitrite inhibition, (mathrm.10,(1mathrm.27/1mathrm.16)) moles of nitrate is required to inhibit SRB exercise in a hypothetical system. This hypothetical system assumes that:


One mole of lactate presents because the electron donor on the inflow. In comparison with actual reservoir situations, this steady lactate inflow is taken into account to account for natural issues that both initially happen within the formation brine (risky fatty acids) or diffuse into the water section from the oil section, e.g. benzene, toluene, ethyl benzene and xylene.


NRSOB are nitrate and nitrite reducers solely (there isn’t a NRB).


Sulfide oxidization charge by NRSOB is the same as or higher than the sulfate discount charge by SRB.

For instance within the case of the move experiments, contemplating presence of 25 mM of lactate within the system, whatever the system size, 27.56 mM of nitrate must be current to inhibit SRB exercise utterly. This provides a normal indication of how the Minimal Inhibitory Nitrate Focus (MINC) can guarantee SRB exercise is inhibited. Observe that MINC relies on the kind and focus of the electron donor, and it could be totally different for various reservoirs. Nonetheless, the intention of introducing a 27.56 mM focus of nitrate is to display that there is usually a MINC, above which, souring may be utterly inhibited. This nitrate focus additionally reveals that nitrite inhibition is critical, because it decreases the inhibiting nitrate injection focus from 27.56 (MINC) to 15 mM. 15 mM is the nitrate focus above which souring is inhibited within the presence of nitrite inhibition. We name this focus the Required Inhibitory Nitrate Focus (RINC).

Due to this fact, we recommend that within the move experiments nitrite inhibition is an important mechanism, in distinction with the interpretation of Hubert et al.13.

In regard with the move experiment, firstly, though nitrite inhibition impact has been claimed to be not essential, we recommend that nitrite inhibition is an important mechanism. We additionally counsel that the RINC is determined by the kind and focus of the carbon supply, in addition to the move path size. That’s, to have a profitable nitrate therapy challenge, injecting the MINC isn’t mandatory, and calculating the RINC for every particular person injection nicely in an oil discipline can scale back nitrate consumption.

Nitrite-nitrate discount charge ratio

Up to now, the outcomes spotlight the significance of nitrite inhibition in NT, particularly if the carbon sources within the system are in extra. Contemplating important quantities of natural compounds both within the water section or within the residual oil section, together with the power of microorganisms to make the most of an enormous spectrum of compounds as electron donors, nitrite inhibition impact on SRB seems to be a key issue for controlling the effectiveness of NT processes. The ratio of nitrite discount charge to nitrate discount charge (R) is likely one of the parameters that specifies focus of nitrite within the system. Increased R values are inclined to decrease nitrite accumulation, and in flip, decrease NT effectivity. To point out the significance of R on the souring inhibition functionality of NRB and NRSOB, batch and move simulations are carried out with a variety of R values.

To review souring inhibition functionality of NRB at totally different R values, simulations are carried out with an preliminary nitrate focus of 700 mg/l utilizing parameters listed in Desk S2. With the intention to set R, in line with the utmost progress charge of NRB1, most progress charge of NRB2 is chosen to meet the specified vary of R values. Determine 5a reveals that souring happens at a slower charge if nitrite discount occurs at a slower charge than nitrate discount.

Determine 5Figure 5

(a) Sulfide manufacturing underneath affect of NRB exercise for varied values of nitrite-nitrate discount charge ratio (R) using the mannequin parameters of SIM1 with nitrate preliminary focus of 700 mg/l. The strong, dotted, dashed and dashed-dotted traces are for R equals to 2.75, 1.5, zero.75 and zero.25, respectively. (b) Sulfide manufacturing affected by NRSOB exercise for various values of R within the final port utilizing the mannequin parameters of SIM4. (c) Nitrate focus comparable to totally different instances of (b). In (b) and (c) the dotted, dashed, and strong traces are for R equal to zero.eight, zero.four and zero.2, respectively. Observe that totally different R values are obtained by altering nitrite discount charge.

To research the consequences of R on the souring inhibition functionality of NRSOB, simulations are run over 94 days utilizing parameters listed in Tables S4 and S6. Just like the strategy used to guage NRB functionality, most progress charge of NRSOB2 was chosen in line with the utmost progress charge of NRSOB1 to span the specified vary of R values. Figures 5b,c present sulfide and nitrite concentrations within the final port for these three simulations, respectively. They present that nitrate inhibitory results noticed for top R values are usually not important. In different phrases, if NRSOB are the nitrate reducer group, R worth for this group must be low as a way to observe noticeable nitrate inhibition.

In abstract, no matter the kind of nitrate reducers (NRB or NRSOB), R is a crucial issue that influences the success of nitrate mitigation methods, i.e. If R is nice (~1) for the nitrate reducer group of a reservoir, NT course of for that reservoir appears to be not environment friendly.

Comparability of simulation and discipline observations

Determine 6 illustrates NO2− and H2S concentrations in a number of manufacturing wells of the Halfdan oil discipline which have been subjected to NT18. This determine reveals NO2− focus of wells for which nitrate therapy was not profitable (nice H2S concentrations), or was profitable (small H2S concentrations). Due to this fact, it signifies a correlation between nitrate therapy success and NO2− focus. Using our interpretations from the simulation outcomes mentioned in earlier sections, and the information reported by Vigneron et al.18, we current two explanations for NO2− and H2S focus traits noticed in these wells.


Inadequate nitrate has been injected via the injection nicely, i.e. nitrate injection focus has been lower than RINC or MINC. Due to this fact, nitrate and nitrite concentrations have develop into insignificant sooner or later between the injection and manufacturing wells. Subsequently, SRB exercise or souring has remained untreated from that time to the manufacturing nicely (Area A in Fig. 6).


Enough nitrate has been injected, i.e. nitrate injection focus has been equal or higher than RINC/MINC. Thus, nitrite focus has been maintained between the injection and manufacturing wells. As a result of presence of nitrite inhibition alongside the complete distance between injection and manufacturing wells, SRB exercise and in flip H2S focus has been saved low (Area B in Fig. 6). We declare that nitrite inhibition has been the dominant mechanism as a result of important concentrations of risky fatty acids (VFA) is noticed in manufacturing water of wells in area B, that means sulfur biking and biocompetition couldn’t have been efficient. Observe that, the space between injector and producer wells within the Halfdan oil discipline is about the identical. Nonetheless, the three producer wells in area B of Fig. 6, are linked to the injectors via direct fractures. Presence of fracture reduces the journey time (time that nitrate and nitrite are uncovered to nitrate reducers), and subsequently, the nitrate focus required to forestall reservoir souring.

Determine 6Figure 6

The connection between NO2− and H2S concentrations measured in a number of manufacturing wells of the Halfdan oil discipline reported by Vigneron et al.18. Excessive H2S focus is noticed for low concentrations of NO2− (area A). Considerably decrease H2S focus is noticed for top concentrations of NO2− (area B). Wells proven in area B are linked via direct fractures.

An identical development (a reverse relationship between NO2− and H2S concentrations) may be seen in Fig. 2 within the work of Agrawal et al.7 the place nitrite focus breakthrough is coincident with the tip of H2S manufacturing. Within the work of Agrawal et al.7, souring management and nitrite breakthrough isn’t obtained via improve in nitrate injection focus, somewhat by a lower in nitrite discount because of the removing of toluene. Which means when nitrate injection is began, the focus of NRB favourite electron donors is excessive. Thus, nitrite discount occurs after nitrate discount (Fig. three within the work of Agrawal et al.7 reveals that nitrite accumulation happens if nitrate exists). Nonetheless, as time proceeds there are usually not sufficient electron donors to scale back nitrite because of the dilution of electron donors. So nitrite is maintained and sulfide manufacturing is inhibited.

In 2004, for a discipline within the North Sea, Sunde et al.34 reported that altering the mitigation technique from biocide injection to nitrate injection precipitated 1000 occasions lower in SRB inhabitants, 50% lower in noticed corrosion, and lesser H2S manufacturing. The effectiveness of this NT course of is cited in different works35,36,37,38. Nonetheless, Mitchell et al.39 reinvestigated the identical discipline in 2017 and found that the H2S degree within the discipline for many of the wells elevated after 2004. Due to this fact, Mitchell et al.39 prompt that the lower in H2S manufacturing earlier than 2004 was not because of nitrate therapy, concluding that NT didn’t have a fascinating impact. Contemplating our simulation along with earlier discipline critiques (Vigneron et al.18 and Agrawal et al.7), we argue that ineffectiveness of NT within the Gullfaks oil discipline reported by Mitchell et al.39 won’t be because of the ineffectiveness of NT, however because of injecting an inadequate focus of nitrate all through the sector.

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