A Geochemical Model of Fluids and Mineral Interactions for Deep Hydrocarbon Reservoirs

A mutual solubility model for CO2-CH4-brine systems is constructed in this work as a fundamental research for applications of deep hydrocarbon exploration and production. The model is validated to be accurate for wide ranges of temperature (0–250C), pressure (1–1500 bar), and salinity (NaCl molality from 0 to more than 6mole/KgW). Combining this model with PHREEQC functionalities, CO2-CH4-brine-carbonate-sulfate equilibrium is calculated. From the calculations, we conclude that, for CO2CH4-brine-carbonate systems, at deeper positions, magnesium is more likely to be dissolved in aqueous phase and calcite can be more stable than dolomite and, for CO2-CH4-brine-sulfate systems, with a presence of CH4, sulfate ions are likely to be reduced to S and H2S in gas phase could be released after S 2− saturated in the solution. The hydrocarbon “souring” process could be reproduced from geochemical calculations in this work.


Introduction
With the exploration and production of middle-shallow oil and gas reservoirs, the main oil/gas fields have come to the late stages of production.More and more intensive exploration work has been done on middle-shallow fields and it is not easy to achieve more breakthroughs.So, researchers are devoting more efforts in deep reservoirs (with depth more than 5000 m).In China, the depositional environment is quite complex and special, so abundant hydrocarbon resources are possible.From the drilling evidence, an effective hydrocarbon reserve was found at more than 7000 m depth in China [1].More and more research on deep layer hydrocarbon exploration has been carried out in recent years.
For deep hydrocarbon research, fluid-rock interaction is an important topic, as it will influence the fluid composition, physical and chemical properties, and transportation in porous media.The geochemical reactions are more active at locations with both gas and water, such as so-called gas-water transition zones [2,3].When gas and water contact, both gas components and mineral will be dissolved in water, and many geochemical reactions could be triggered.In Sichuan basin, H 2 S can usually be found from gas reservoirs.The existence of H 2 S can be a result of geochemical reactions of dissolved hydrocarbon and sulfates.It is called "souring" process in some literature [2].
Numerical modeling of geochemistry is a useful tool to understand the mechanism of fluid-mineral interactions in deep reservoirs.PHREEQC is one of the most popular geochemistry software packages in hydrological applications [4].The speciation in water associated with hundreds of chemical reactions can be dealt with.TOUGHREACT is a 3D reactive transportation simulator which is able to calculate geochemical reactions with similar database as PHREEQC [5].This simulator has been widely used in CO 2 geological storage and geothermal recovery projects.Both of the software programs are powerful for geochemical reaction analysis in porous media.However, for fluid-mineral interactions in deep reservoir, gas-brine phase partitioning and speciation should be carefully considered due to high temperature and pressure.In gas reservoirs, CO 2 usually exists with quite a bit amount of hydrocarbons.So, in this work, we establish a mutual solubility model for CO 2 -CH 4 -brine systems, which is accurate for a pressure range of 1 bar to 1500 bar, temperature range of 0 ∘ C to 250 ∘ C, and salinity range of 0 to 6 m.With the solubility calculated by the model, PHREEQC is used to calculate equilibrium of CO 2 -CH 4 -brine-minerals (carbonates and sulfates).

CO 2 -CH 4 -Brine Mutual Solubility Modeling
We assume that there are two fluid phases (i.e., aqueous phase and nonaqueous phase) existing at given temperature, pressure, and feed composition.CO 2 or CH 4 always dominates nonaqueous phase.Their solubilities in water and H 2 O content in nonaqueous phase are desired to be accurately reproduced by a thermodynamic model.In equilibrium state, for each component in the system (e.g., component ), the chemical potential in each phase should be equal.Then we have, For nonaqueous phase, where  NA(0)  () stands for standard chemical potential of component , which is the ideal gas chemical potential at the pressure of 1 bar [6,7];   is mole fraction of component  in nonaqueous phase;   is fugacity and   is fugacity coefficient;  is the gas constant (8.31446J/K/mol);  is temperature in K; and  is pressure in bar hereafter.
For aqueous phase, where  AQ(0) is the standard chemical potential of species  in an ideal aqueous solution with a hypothetical unit molality [8];  sol is the molality (in mole/Kg water, molal for short hereafter) of salt in the aqueous phase;  is the mole number of 1 kg water (55.508);  is the mole fraction of species  dissolved in the aqueous phase;   is activity of component  in aqueous phase; and   is activity coefficient of component .
For equilibrium constants of CO where   = √     (1 −   ) and   are binary interaction parameters of species  and .Binary interaction parameters for CO 2 , CH 4 , and H 2 O can be found in Table 3 according to Søreide and Whitson [10].[11] was successfully used in gas-water-mineral modeling for high salinities in previous works [12][13][14][15].Cations, anions, and interaction between particle pairs are considered to influence the component activity behaviors in aqueous phase.The activity coefficient equations are as follows: ln where   is cation molality,   is anion molality, and  - ,  - , and  -- are parameters that are functions of temperature and pressure. - ,  - , and  -- are known as Pitzer parameters and they are usually estimated from gas solubility data from aqueous solutions with dissolved salts.In this work, Pitzer parameters are usually calibrated from gas solubility from NaCl solutions. -Cl − is assumed to be 0. As the approximation in Duan and Sun [14] and Duan et al. [16],  -monovalent and  -bivalent are estimated as  -Na + and 2 -Na + .All ternary parameters are estimated as  -Na-Cl .Pitzer parameters are listed in Table 4.

Model Validation.
The model performance is evaluated from comparison of model results and related experimental data of CO 2 -CH 4 -brine systems (including the subsystems).
For CO 2 -H 2 O-NaCl systems, the experimental studies [17][18][19] are sufficient, which cover temperature from 0 ∘ C to more than 250 ∘ C and pressure from 1 bar to more than 1500 bar.From our comparison, the average absolute derivations for most of the data points are less than 10%.Figures 1(a) and 1(b) show a comparison of CO 2 solubilities in pure water and NaCl solutions calculated from this model and related experimental data.We can find that the model solutions agree with the experimental data in the wide ranges of temperature, pressure, and salinity.Figure 1(c Experimental data of CH 4 -H 2 O-NaCl system are also sufficient with temperature from 0 to more than 250 ∘ C and pressure from 1 bar to more than 1500 bar [20].Figures 2(a  Compared with single gas (CO 2 or CH 4 )-brine systems, gas mixture (CO 2 and CH 4 existing at the same time)-brine systems have less experimental data.The existing data are also not systematic.Qin et al. [21] have studied phase equilibria for CO 2 -CH 4 -H 2 O system at 325 K and 376 K and with pressure from 100 bar to 500 bar.21 data points were generated in the work.We compared their results with our model.From the comparison (see Figure 3), we can conclude that the model can predict mutual solubilities for CO 2 -CH 4 -H 2 O system.
In summary, the comparison of the model solutions with existing experimental data shows that the model can well reproduce and predict mutual solubility data of CO 2 -CH 4brine systems in wide ranges of temperature, pressure, and salinity.The model is reliable to be used in gas-water-mineral equilibrium analysis.

CO 2 /CH 4 -Water-Mineral Interactions in Deep Environments
In Sichuan basin, carbonates (such as dolomite or calcite) are the dominant minerals in some natural gas reservoirs; meanwhile sulfates (such as gypsum or anhydrite) and clay minerals are also commonly found [22,23].In Sichuan natural gas reservoirs, CH 4 is always accompanied with other components such as CO 2 , N 2 , or H 2 S [24].PHREEQC is a famous software package for water-mineral interaction calculations.Pressure effects can be considered using its third version [4].
With an accurate mutual solubility model of CO 2 -CH 4 -brine systems, geochemical reactions in CO 2 -CH 4 -water-mineral systems can be calculated by combining this model and the PHREEQC functionality.Through this research, we aim to find out (i) the influences on geochemical reactions in depth (i.e., temperature and pressure increase or decrease); (ii) sensitivity of gas components (i.e., CO 2 or CH 4 ) to water composition, mineral dissolution, or precipitation.
In this work, the calculations are based on Sichuan basin background.The hydrostatic pressure is assumed to be 100 bar/Km, and geothermal gradient is assumed as 25 ∘ C/Km according to a previous work [25] with surface temperature set as 25 ∘ C. The depth range of the research is from 3000 m to 6000 m.Relationships of depth, temperature, and pressure are shown in Figure 4. To clarify the influences from gas components, sodium chlorite is considered as the only salt that is dissolved in water as an initial solution.Geochemistry equilibrium of CO 2 -CH 4 -brine-dolomite, CO 2 -CH 4 -brinecalcite, and CO 2 -CH 4 -brine-gypsum/anhydrite systems is studied.Two gas compositions are considered, pure CH 4 or 10% CO 2 + 90% CH 4 , to evaluate CO 2 influences.
Table 5 lists the species of ions, minerals, and gases which get involved in geochemical reactions in CO 2 -CH 4 -brinecarbonate systems and CO 2 -CH 4 -brine-sulfate systems.4 -Brine-Carbonate Systems.For CO 2 -CH 4brine-carbonate systems, cases of fluid equilibrium with calcite and dolomite are studied, respectively.Figure 5 shows the molality of carbon (including HCO 3 − , CO 2 , CaHCO 3 + , CaCO 3 , CO 3 2− , MgHCO 3 − , and MgCO 3 ) dissolved in aqueous phase with different depths, gas compositions, and salinities.Figure 6 shows the molality of calcium (including Ca 2+ , CaCO 3 , CaHCO 3 + , and CaOH + ) and magnesium  (including Mg 2+ , MgOH + , MgCO 3 , and MgHCO 3 + ) that is dissolved in aqueous phase.From Figure 6, it is shown that CO 2 in the gas phase will promote calcite or dolomite dissolution.From the calculations, we find that, with CO 2 existing in the system, carbon concentration in aqueous phase increases with depth.From 3000 m to 6000 m, the carbon molality is almost doubled in Figure 5 at different salinities.However, compared with calcium, magnesium is more solvable and increases with depth.From our calculation, in fluid-dolomite systems, with an increase in temperature and pressure, more calcite precipitates.We can conclude that, in deep carbonate environments, calcium is more likely to precipitate and magnesium ion is more likely to be rich in aqueous phase and transport to shallower areas due to diffusion gradient.So, in general, calcite approaches being existing in deeper environments and dolomite is more likely to be existing in shallower environments.In this work, we perform several numerical experiments to evaluate the influence of gas composition and depth on fluid-mineral equilibrium.For gas composition, we considered three cases: pure CH 4 , 10% CO 2 + 90% CH 4 , and pure CO 2 .The calculations covered depth from 3000 m to 6000 m. Figure 7 presents S(−2) (i.e., sulfur dissolved in water with chemical valence −2, which can be S 2− , HS − , and H 2 S as ions) and S(+6) (i.e., sulfur dissolved in water in chemical valence +6, which can be SO 4 2− , HSO 4 − , CaSO 4 , and CaHSO 4 + ) concentration in equilibrium of gas-water-gypsum.From Figure 7, we can find the following:

CO 2 -CH
(1) With pure CO 2 in gas, S(−2) in water is extremely low, and more CH 4 is dissolved in water leading to higher S(−2) concentration.
(2) Higher CO 2 mole fraction in gas phase will lead to higher S(+6) concentration in water phase.CO 2 (g) (3) With higher depth, higher S(+6) concentration can be found, but depth influence on S(−2) concentration is not clear.
It is clear that CH 4 is the key component for S(+6) to be reduced to S(−2) species in water.The related redox geochemical reaction is When CH 4 and SO 4 2− are dissolved in water, the above reaction is triggered, and CH 4 is oxidized from C(−4) to C(+4).In the meantime, SO 4 2− is reduced to S 2− .Figure 8(a) shows the amount of calcite precipitation for different cases of geochemical equilibrium.Referring to Figure 8(a), in case of pure CO 2 in gas phase, there is no calcite precipitation; with higher CH 4 mole fraction in gas phase, more calcite can be precipitated; in deeper environments, more calcite can be precipitated.This phenomenon is also connected with sulfur reduction.With CH 4 dissolved in water, more sulfate is consumed and more calcium ions are dissolved in water.In this process, carbanions are generated because of the redox reaction.With more and more calcium  and carbanion in the solution, calcite becomes saturated and precipitates.Another product is H 2 S in gas phase.With more and more S(−2) generated in water, S 2− and H + approach combining with one another, and H 2 S becomes saturated and is released in gas phase.As shown in Figure 8(b), with more CH 4 in gas phase, more H 2 S will be generated in gas phase at equilibrium states.From this study, we can find that CH 4water-sulfate redox reaction could be a mechanism of H 2 S origin in gas reservoirs [2].From the figure, we can also find that, at higher depth, more H 2 S can be generated.This result agrees with the statement from Li et al. [2].

Conclusions
In this work, an accurate mutual solubility model is constructed with "fugacity-activity" method for CO 2 -CH 4 -brine systems.This model has a wide application range of pressure, temperature, and salinity, which can be used for fluid phase equilibrium in deep hydrocarbon reservoirs.
Combined with the mutual solubility model and PHREEQC, the equilibrium CO 2 -CH 4 -brine-mineral systems under deep reservoir conditions can be calculated.The mutual solubility model can be used to calculate the mole numbers of CO 2 /CH 4 dissolved in brine at given temperature, pressure, and salinity.With the dissolved mole numbers of CO 2 /CH 4 , PHREEQC is used to calculate the speciation between aqueous phase and mineral.
CO 2 /CH 4 -brine-carbonate (i.e., dolomite or calcite) and CO 2 /CH 4 -brine-sulfate (i.e., gypsum or anhydrite) equilibria were studied with the above methodology.From the study, we find the following: (1) For CO 2 /CH 4 -brine-carbonate (calcite or dolomite) systems, with an increase in depth, calcium is more likely to precipitate as calcite and magnesium is more likely dissolved in aqueous phase.In other words, dolomite could be rich in shallower position and calcite may approach being existing at deeper locations.
(2) With CH 4 present in the CO 2 /CH 4 -brine-sulfate (gypsum or anhydrite) systems, redox reaction is triggered and S(+6) is reduced to S(−2).H 2 S will be released when S(−2) becomes saturated in aqueous phase.This process could be one of the origins for H 2 S in gas reservoirs in Sichuan basin, China.
This work is an attempt to do preliminary fluid-mineral interaction calculations with a new established accurate mutual solubility model of CO 2 -CH 4 -brine systems combined with PHREEQC, version 3. The geochemical reaction parameters are still needed to be validated for high temperature and pressure.Also, more systematic research work of gas-water-minerals is still required in the future according to real depositional environments.
) shows the H 2 O solubility in nonaqueous (CO 2 -rich) phase of the model solutions and experimental data.From the figure, the model can well reproduce H 2 O solubility in nonaqueous phase.
) and 2(b) show the comparison of CH 4 solubilities in water and NaCl solutions of experimental data and this model.
Figure 2(c) shows the experimental data of H 2 O in nonaqueous (CH 4 -rich) phase and the related model solutions.From the comparisons, the experimental data can be well reproduced by the model.

Figure 1 :
Figure 1: Mutual solubilities of CO 2 -brine systems.Lines are calculated results from this model, and dots are from experimental data.(a) CO 2 solubility in pure water; (b) CO 2 solubility in NaCl solutions; (c) H 2 O solubility in CO 2 -rich phase.

Figure 2 :
Figure 2: Mutual solubilities of CH 4 -brine systems.Lines are calculated results from this model, and dots are from experimental data.(a) CH 4 solubility in pure water; (b) CH 4 solubility in NaCl solutions; (c) H 2 O solubility in CH 4 -rich phase.

Figure 5 :Figure 6 :
Figure 5: Molality of total carbon dissolved in water varying with depth at different salinities and gas compositions.Dashed yellow line represents the case of pure CH 4 of gas in the system.Blue lines represent results from fluid-calcite systems (with gas composition CO 2 : CH 4 = 1 : 9 in mole).Red lines with dots represent the result from fluid-dolomite systems (with gas composition CO 2 : CH 4 = 1 : 9 in mole).

Table 3 :
Binary interaction parameter in PR-EOS.