Effects of Aqueous Solubility and Geochemistry on CO2 Injection for Shale Gas Reservoirs

In shale gas reservoirs, CH4 and CO2 have finite aqueous solubilities at high-pressure conditions and their dissolutions in water affect the determination of the original gas in place and the CO2 sequestration. In addition, the dissolution of CO2 decreases the pH of connate water, and the geochemical reactions may thus occur in carbonate-rich shale reservoirs. The comprehensive simulations of this work quantify the effects of aqueous solubility and geochemistry on the performance CO2 huff-n-puff process in shale gas reservoir. Accounting for the aqueous solubility of CH4 increases the initial natural gas storage and natural gas production. The effect of the aqueous solubility of CO2 enables to sequester additional CO2 via solubility trapping. Considering the geochemical reactions, the application of the CO2 huff-n-puff process causes the dissolution of carbonate minerals and increases the porosity enhancing the gas flow and the gas recovery. Incorporation of geochemistry also predicts the less CO2 sequestration capacity. Therefore, this study recommends the consideration of aqueous solubility and geochemical reactions for the accurate prediction of gas recovery and CO2 sequestration in shale gas reservoirs during the CO2 huff-n-puff process.

www.nature.com/scientificreports www.nature.com/scientificreports/ However, they ignored some factors of considerable importance affecting the storage and transport of CO 2 and CH 4 during the CO 2 injection into the shale gas formation. The studies [10][11][12][13][14][15]17,[19][20][21][22][23][24][25][26][27][28][29] neglected the solubilities of CH 4 and CO 2 in the formation water, which affect the gas storage of CH 4 and CO 2 in shale gas reservoirs. In addition, the effect of the geochemical reactions on the EGR and CO 2 sequestration has not been investigated in the numerical studies [10][11][12][13][14][15]17,[19][20][21][22][23][24][25][26][27][28][29] . Experimental studies 22,[30][31][32] have explored the role of geochemical reactions in shale formations. The study 22 designed the characterization method consisting of optical microscope, X-ray diffraction, element analysis, low-pressure gas adsorption, and Fourier transform infrared spectroscopy to access geochemical changes when CO 2 was injected into carbonate-rich shale rock samples. It was observed that CO 2 dissolution in brine decreased the pH of brine resulting in mineral reactions and pore structure change. Another study 32 also observed carbonate mineral dissolution in the system of carbonate-rich shale/formation water/CO 2 by in-situ Fourier transform infrared spectroscopy. The experimental studies clarified the geochemical reactions in the system of carbonate-rich shale/formation water/CO 2 and observed the changes in physical properties of shale rock samples. However, the experimental studies have not quantified the effect of geochemical reactions on EGR and CO 2 storage during CO 2 injection for shale gas reservoirs.
Therefore, it is necessary to advance the understanding of CO 2 injection in tight shale reservoirs by implementing potential factors into the numerical simulations: (1) aqueous solubilities of CO 2 and CH 4 and (2) chemical reactions occurred in the system of gas/brine/shale formation. In this numerical study, an improved model of the CO 2 injection has been developed to account for the solubilities of CO 2 and CH 4 in formation water and geochemical reactions in the shale gas reservoirs. The effects of potential factors on the EGR and CO 2 storage have been analyzed with a series of runs with the developed model. The developed model is examined in the Eagle Ford shale gas reservoirs which have a high fraction of carbonate minerals. The Eagle Ford shale play is late Cretaceous in age and is located in the South Texas, USA 33,34 . It is 50 miles wide and 400 miles long and covers the 23 counties in South-Central Texas. Its depth varies between 2,500 ft and 14,000 ft and thickness ranges from 120 ft to 350 ft.

Mathematical Formulations
Adsorption. The multi-component adsorption from the gas phase on the reservoir rocks could be modeled based on an extended Langmuir isotherm model. The extended Langmuir isothermal model of CO 2 and CH 4 is a function of pressure and is described in Eq. 1.
where k and i indicate the component, e.g., CO 2 and CH 4 ; ω k denotes the moles of the adsorbed component k per unit mass of rock; ω k, max is the maximum number of moles of adsorbed component k per unit mass of rock; p is the pressure; y i, g is the molar fraction of the adsorbed component k in the gaseous phase; and B is a parameter of extended Langmuir isotherm model.

Solubility in water.
The gaseous components (CO 2 and CH 4 ) could dissolve in water at the high pressure condition. In shale gas reservoirs, a fraction of CH 4 might dissolves in formation water. Once the CO 2 is injected into the water-bearing gas reservoir, the CO 2 dissolves in the water as well. In this system, the aqueous solubilities of CO 2 and CH 4 are determined by equating their fugacities in the aqueous and gaseous phases (Eq. 2). While the Peng-Robinson equation of state (PR-EoS) determines the fugacities of gaseous components in the gaseous phase, Henry's law calculates their fugacities in the aqueous phase (Eq. 3). Introducing the Henry's law constant, it determines the amount of dissolution in the aqueous phase at specific temperature and pressure conditions (Eq. 4). Harvey 35 published the correlations of Henry's law constants for CO 2 and CH 4 (Eqs. 5 and 6). In addition, solubilities of CO 2 and CH 4 in aqueous phase are affected by the aqueous salinity. The relationship between solubility and salinity is formulated by introducing a salting-out coefficient (Eq. 7). The Henry's law constants of CO 2 and CH 4 at specific salinity are determined by incorporating their Henry's law constants in pure water and salting-out coefficients. The correlations predicting the salting-out coefficients of CO 2 and CH 4 are developed as shown in Eqs. 8 and 9 36 . Geochemical reactions. During CO 2 injection, a fraction of dissolved CO 2 in water may react with water.
It would produce H + and lower pH via aqueous reactions. Because the Eagle Ford reservoir has a high content of carbonate minerals, significant dissolution of carbonate minerals may occur at low-pH conditions. Therefore, it is important to consider the major geochemical reactions, including the aqueous and mineral reactions. The mathematical formulations and database of the geochemical reactions are referred from the works [36][37][38][39] . The aqueous reaction is a homogeneous reaction, thus implying that the reactions occur only in the aqueous phase. In aqueous reactions, ions may either form complexes with other ions, or aqueous complexes may decompose to form ions. Because the aqueous reaction is fast, it obeys the law of mass action introducing the ion activity product (Eqs. 10 and 11). The acitivity of ion, i.e., an effective concentration of ion, is defined as a function of acitivity coefficient and molality of ion (Eq. 12). The B-dot model is employed to calculate the acitivity coefficient incorporating ionic strength and charge of the ion (Eq. 13).
eq aq , where α denotes aqueous reaction; α K eq, is the equilibrium constant of aqueous reaction; Q α is the ion activity product of aqueous reaction; R aq is the number of reactions between components in aqueous phase; i indicates the component of aqueous reaction; n aq is the total number of components in the aqueous phase; n c is the number of gaseous components that are soluble in the aqueous phase; n a is the aqueous components that exist only in the aqueous phase; a i is the activity; i γ is the ionic activity coefficient; m i is the molality; I is the ionic strength; z i is the charge of the ion; a i is the ion size parameter; and γ A , γ B , and B are the temperature-dependent parameters. The mineral reaction of dissolution or precipitation is a heterogeneous reaction involving multiple phases, i.e., the solid and aqueous phases. Because the mineral reaction is a slow kinetic reaction, it requires enough time to achieve the equilibrium state in accordance with the rate law (Eqs. 14 and 15).
eq mn , www.nature.com/scientificreports www.nature.com/scientificreports/ where β denotes mineral reaction; r β is the mineral reaction rate; β k is the reaction rate constant of mineral reaction; β Â is the reactive surface area of a mineral; K eq, β is the solubility product constant of the mineral reaction; Q β is the ion activity product of the mineral reaction; R mn is the number of reactions between minerals and aqueous components; k indicates the component in mineral reaction; β n is the number of mineral components; a k is the activity of component k; and v kβ is the stoichiometric coefficient of the mineral reaction.
The mineral reaction generates or consumes the aqueous species in water. The formation/consumption rate of the aqueous species depends on the mineral reaction rate (Eq. 16). In addition, the mineral dissolution or precipitation changes the pore volume of the reservoir. The change in the total moles of the mineral results in the change of the pore volume, i.e., porosity (Eq. 17). The increasing or decreasing porosity also affects the permeability of the reservoir (Eq. 18).
where β v k, is the stoichiometric coefficient of the mineral reaction; γ β k, is the consumption or production rate of ionic species in brine owing to the mineral reaction; φ 0 and φ are the porosities before and after mineral reaction; N 0 β and N β are the total moles of mineral per bulk volume before and after mineral reaction; ρ β is the mineral molar density; and k 0 and k are the permeabilities before and after mineral reaction.

Numerical Simulations
This study uses the GEM TM software, developed by CMG Ltd, to simulate multi-phase and multi-component flows coupled with aqueous solubility and geochemical reactions. The target reservoir is constructed based on the published studies of the Eagle Ford shale gas reservoir 11,[40][41][42] . A description of the reservoir is represented in Fig. 1. The reservoir's dimensions are 2,500 × 1,050 × 200 ft 3 . It is discretized with 50 × 11 × 1 grid blocks. The horizontal well and hydraulic fracturing technologies are simulated in the reservoir. A total of 10 sets of transverse fractures are induced in the reservoir along with the horizontal well. This study simulates only one stage of the hydraulically fractured stimulated reservoir based on symmetry to save computation time and storage. The properties of the system are described in Table 1. The size of the fractured width is assumed to be equal to 0.001 ft referring the Rubin's work 41 . The extended Langmuir adsorption model is used to describe the adsorptions of CH 4 and CO 2 on the rock surface. The parameters of the model are listed in Table 2 43 . www.nature.com/scientificreports www.nature.com/scientificreports/ The CO 2 huff-n-puff process is adopted as the CO 2 injection to enhance natural gas production from shale reservoir. Prior to the execution of the CO 2 huff-n-puff process, natural depletion process recovers the gas over a two-year period. When the gas production by natural depletion becomes negligible, the CO 2 huff-n-puff process is deployed for the next two-year period. The bottom-hole pressure of the producer is set to 1,875 psi. During the CO 2 huff-n-puff, the CO 2 is injected with 2 MMscf/day until the bottom-hole pressure of the injector reaches 9,000 psi. A total of 12 cycles of CO 2 huff-n-puff are designed. Each cycle comprises two processes for two months-CO 2 injection for one month and production for another month.

Results
This study consists of two sections: (1) simulations incorporating aqueous solubilities of CO 2 and CH 4 and (2) simulations coupled with geochemistry. The first section of the simulations investigates the effect of aqueous solubility on the hydrocarbon production and CO 2 sequestration during the CO 2 huff-n-puff process. The second section quantifies the effect of the geochemical reactions-which is attributed to the CO 2 dissolution in wateron the performance of the CO 2 huff-n-puff process in the shale gas reservoir. co 2 huff-n-puff process and consideration of the aqueous solubility. The original gas in place (OGIP) is initially determined to be equal to 6.7 × 10 8 moles. This corresponds to 563.5 MMscf of which free and adsorbed gases respectively occupy 94.1% and 5.9% of OGIP. For a comparison to the simulation of the CO 2 huff-n-puff process, the primary recovery process of natural depletion is simulated for a period of four years. Figure 2 describes the cumulative gas production of CH 4 from the shale reservoir. The primary recovery process   www.nature.com/scientificreports www.nature.com/scientificreports/ recovers 70% of OGIP. During the pressure depletion, 21% of adsorbed CH 4 is produced and it corresponds to 1.7% of the total CH 4 production (Figs. 2 and 3A). Most of the gas production is attributed to the production of free CH 4 gas. Because the free gas production is relatively fast, the gas production rate significantly decreases after one year. The rapid decline in the early production initiates the CO 2 huff-n-puff process. Firstly, the simulation of the CO 2 huff-n-puff process neglects the aqueous solubility and it is the base case of the CO 2 huff-n-puff process. The CO 2 injection would pressurize the depleted reservoir and cause more desorption of CH 4 due to the increasing adsorption of CO 2 (Fig. 3). The CO 2 huff-n-puff process injects 734.5 MMscf of CO 2 (or equivalently 8.8 × 10 8 mol), and 10.1% of the injected CO 2 is adsorbed on the rock surface (Fig. 3B). As a result, the CO 2 huff-n-puff process produces a total 84.7% of OGIP, which corresponds to a 14.7% higher production of OGIP than the primary recovery process for four years (Fig. 2). The CO 2 huff-n-puff process introduces two effects of more CH 4 desorption and re-pressurization, thereby enhancing gas recovery over primary recovery process. The CH 4 desorption caused by CO 2 adsorption is responsible for 5.2% of the OGIP, and corresponds to 87.4% of the initial amount of the adsorbed CH 4 (Fig. 3A). Re-pressurization by CO 2 injection contributes enhanced gas production as much as 9.5% of the OGIP. The CO 2 huff-n-puff process is also effective in storing CO 2 in the depleted reservoirs. This simulation observes that 45.1% and 10.1% of injected CO 2 are sequestrated by geological and adsorption trappings, respectively (Figs. 3B and 4).
Generally, CH 4 can dissolve in water owing to high pressure condition. Because high-pressure conditions exist within the reservoir, ignoring the aqueous solubility of CH 4 leads to the underestimation of the initial OGIP in shale formations. When the initial gas storage process takes into consideration the mechanism of the aqueous solubility of CH 4 , the initial OGIP slightly increases by 1.9%. Because the dissolved CH 4 in water is gasified by pressure depletion, it can be recovered (Fig. 5A). The CO 2 huff-n-puff process is simulated in the system. The desorption of CH 4 does not change, regardless of the aqueous solubility of CH 4 (Fig. 3A). As a result, the CO 2 huff-n-puff process that has accounted for the aqueous solubility of CH 4 recovers 1.3% more CH 4 compared to the base case (Fig. 2). The increase in the production is fully attributed to an increase in the OGIP owing to the aqueous solubility of CH 4 (Fig. 5A). In addition, the aqueous solubility of CH 4 hardly influence the potential of CO 2 sequestration compared to the base case (Fig. 4B). www.nature.com/scientificreports www.nature.com/scientificreports/ CO 2 is also soluble in water. Its solubility is higher than that of CH 4 44 . When the aqueous solubility of CO 2 is accounted for in the simulation of the CO 2 huff-n-puff process, there is a negligible change in the total hydrocarbon production compared to the base case (Fig. 2). However, the capacity of CO 2 storage would be increased, and the less production of CO 2 is observed (Fig. 4B). In this simulation, 41.2% and 10.1% of the injected CO 2 are sequestrated in the geological and adsorption forms, respectively (Figs. 3B and 4A). In addition, 6.2% of the injected CO 2 is captured based on an aqueous solubility mechanism (Fig. 5B) that constitutes one of the CO 2 storage mechanisms 45 . Compared to the previous simulation that accounts for the aqueous CH 4 solubility, the simulation that accounts for the aqueous solubility of CO 2 leads to a smaller storage of CO 2 via geological and adsorption trappings (Figs. 3B and 4A), but stores additional CO 2 based on aqueous solubility (Fig. 5B). When the simulation of the CO 2 huff-n-puff process considers the aqueous solubilities of CH 4 and CO 2 , increasing CH 4 production and CO 2 sequestration are obtained comparing to the base case (Figs. 2, 3B, 4B and 5B). co 2 huff-n-puff coupling with geochemistry. Previous simulations investigate the effect of the aqueous solubility on the gas recovery and CO 2 sequestration during the CO 2 huff-n-puff process in the shale formation. Once the CO 2 dissolves in brine with a decreasing pH, geochemical reactions occur in carbonate-rich shale reservoirs. This section explores the role of geochemistry on the performance of the CO 2 huff-n-puff process in carbonate-rich shale reservoirs. Table 3 lists the geochemical reactions of the aqueous and mineral reactions for their implementations in the simulations. The reservoir is assumed to have 30% of carbonate minerals (calcite, dolomite, and magnesite) to represent a carbonate-rich shale reservoir. Simulations of the primary recovery and the CO 2 huff-n-puff processes are conducted for the shale reservoir once the geochemical reactions have been incorporated in the simulation framework. The findings are compared to those obtained from the base case, which is the simulation of the CO 2 huff-n-puff process based on the consideration of the aqueous solubility of CO 2 (but not based on geochemistry). Additional application of the CO 2 huff-n-puff process pertaining to the reservoir which has no carbonate mineral is simulated to quantify the role of the mineral. Lastly, the effect of the aqueous solubility of CH 4 is also confirmed when the CO 2 huff-n-puff process has accounted for geochemistry and is deployed in the carbonate-rich shale gas reservoir. www.nature.com/scientificreports www.nature.com/scientificreports/ First, the simulation results of the carbonate-rich shale reservoir are analyzed. Prior to the CO 2 huff-n-puff process, the precipitation of carbonate minerals mainly occurs during the natural depletion process (Fig. 6). The precipitation of carbonate minerals slightly decreases the pore volume of the reservoir, but the effect of the rock's compressibility owing to the pressure depletion overwhelmingly decreases the pore volume (Fig. 6). Once the CO 2 huff-n-puff process is initiated, the dissolution of CO 2 in water produces H + and decreases pH (Fig. 7A). In low-pH conditions, carbonate minerals dissolve. The mineral dissolution leads to an increase in the pore volume (Fig. 6). During the CO 2 huff-n-puff process, the pore volume of the reservoir is still lower than initial volume despite of re-pressurization. The dissolution of carbonate minerals enlarges the pore volume, i.e., the porosity (Fig. 7B). This is equivalent to a minor increase in the permeability of the matrix. The behaviors of adsorption and desorption of CH 4 and CO 2 hardly change regardless of geochemistry (Fig. 8). As a result, the simulation of the CO 2 huff-n-puff process incorporating geochemistry recovers additional amount of CH 4 by 1.7% compared to the base case (Fig. 9). The increase in the gas production is attributed to the dissolution of carbonate minerals   www.nature.com/scientificreports www.nature.com/scientificreports/ enlarging the porosity during the CO 2 huff-n-puff process. This can be confirmed by comparing these findings to the simulation findings of the CO 2 huff-n-puff process for the reservoir which contains no carbonate minerals. When the process is deployed into the reservoir, any increase in the cumulative production is not observed (Fig. 9). When the CO 2 huff-n-puff process incorporating the aqueous solubility of CH 4 as well as geochemistry is simulated in the carbonate-rich shale formation, the cumulative production of CH 4 is increased by 2.6% compared to the base case (Fig. 9). Because the geochemical reactions and aqueous solubility of CH 4 negligibly affect the adsorption and desorption of CO 2 and CH 4 (Fig. 8), an increase in hydrocarbon production is attributed to an increase in the initial OGIP owing to the solubilized CH 4 in water, and to the porosity changes owing to dissolution of carbonate minerals.
The mineral dissolution influences the concentration of ions in water. It produces HCO 3 − in water buffering pH of in-situ brine. When the reservoir has no carbonate minerals, higher concentrations of H + and lower concentrations  www.nature.com/scientificreports www.nature.com/scientificreports/ of HCO 3 − are observed during the CO 2 huff-n-puff process (Fig. 10). The geochemical reactions also affect the CO 2 storage capacity. Precipitation of carbonate minerals contributes to the long-term CO 2 sequestration that constitutes one of the CO 2 storage mechanisms 45 . The dissolution of carbonate minerals observed in the CO 2 huff-n-puff process is  www.nature.com/scientificreports www.nature.com/scientificreports/ unfavorable to the CO 2 storage. In addition, the dissolved CO 2 in water via solubility trapping mechanism can exist in different forms of carbon dioxide complexes, e.g., HCO 3 − , CaHCO 3 + . As a result, the CO 2 huff-n-puff process with geochemistry sequesters a smaller amount of CO 2 in water (approximately 14.6%) compared to the base case (Fig. 11A). Because there is a negligible change in the adsorption of CO 2 (Fig. 8B), a smaller CO 2 storage in water mainly causes an increased CO 2 production of up to 8.6% (Fig. 11B). When the reservoir has no carbonate minerals, the sequestered CO 2 in water decreases by at most 13.2% compared to the simulation result with the carbonate-rich shale reservoir (Fig. 11A). A smaller production of CO 2 (up to 6.0%) is expected when the reservoir does not contain any carbonate minerals (Fig. 11B). Lastly, simulations investigate whether the aqueous solubility of CH 4 affects the CO 2 storage of CO 2 huff-n-puff process considering geochemistry or not. Because the aqueous dissolution of CH 4 has no impact on the geochemical reactions, it hardly affects the capacity of CO 2 sequestration (Fig. 11B).

Conclusions
This study assessed the hydrocarbon recovery and CO 2 storage during the CO 2 huff-n-puff process in shale gas reservoirs. It explored the roles of aqueous solubility and geochemistry on the performance of the CO 2 huff-n-puff process. The following conclusions have been drawn based on the findings of the numerical study.
(1) While most of the OGIP in the shale gas reservoir consisted of free gas and the adsorbed CH 4 , neglecting the aqueous solubility of CH 4 was shown to underestimate the OGIP by 1.9% and gas recovery by 1.3%. Because the dissolved CH 4 in water can be recoverable during the natural depletion and the CO 2 huff-npuff process, accurate prediction of the hydrocarbon recovery required the consideration of the aqueous solubility of CH 4 . (2) Consideration of the aqueous solubility of CO 2 did not affect the gas recovery of CH 4 from the shale formation. However, it sequestered additional 6.1% of injected CO 2 in the shale formation via the aqueous solubility. During the CO 2 huff-n-puff process, accurate prediction of CO 2 sequestration should consider storing CO 2 via forms of geological trapping, adsorption, and solubility trapping in depleted shale formation. www.nature.com/scientificreports www.nature.com/scientificreports/ (3) With the incorporation of geochemistry in the simulation of the CO 2 huff-n-puff process, the dissolution of CO 2 promoted the recovery of CH 4 from the carbonate-rich shale gas reservoir. Once the CO 2 dissolved in water, the pH of brine decreased and the dissolution of carbonate minerals occurred in low-pH condition. This resulted in a slight increase in the pore volume, i.e., porosity, and in a parallel increase in permeability, and then an increase in the hydrocarbon production of the order of 2.6% was obtained. Therefore, it is necessary to consider the effect of geochemistry for accurate prediction of shale gas production of CO 2 huff-n-puff in carbonate-rich shale formations. (4) Ignoring the geochemical reactions was associated with the risk of overestimating the CO 2 sequestration during the CO 2 huff-n-puff process. Because of the geochemical reactions, dissolved CO 2 can be sequestered into the forms of carbon dioxide complexes in water. Therefore, consideration of the geochemical reaction predicted a smaller potential of CO 2 sequestration by 14.6% during the CO 2 huff-n-puff process in the depleted shale gas reservoir.