© X. Zhang et al., published by IFP Energies nouvelles, 2020

1 Introduction

With the increasing exploitation of sour hydrocarbon reservoirs, a growing volume of acid gas, consisting primarily of carbon dioxide (CO₂) and hydrogen sulfide (H₂S), is generated. The conventional sulfur recovery method, which converts sulfur compounds to elemental sulfur and directly emits residual CO₂ into the atmosphere, can be adopted to dispose of acid gas. However, the recovered sulfur is below the commodity standard, making it difficult to sell and increasing the accumulation of hazardous waste. Furthermore, residual CO₂ emissions aggravate global warming. Consequently, Acid Gas Injection (AGI) into depleted oil and gas reservoirs is gaining increasing attention as an alternative to mitigate greenhouse gas emissions and to avoid the costs of desulfurization. Actually, acid gas injection operations have been approved worldwide (British Columbia Geological Survey, 2003; Carroll et al., 2009; Khan et al., 2013; Li et al., 2017; Miwa et al., 2002), and feasibility of AGI operations in China has been analyzed (Li et al., 2013; Liu et al., 2012). However, the implementation of acid gas injection requires a proper assessment of the effects induced by the presence of acid gas.

During acid gas injection, CO₂ and H₂S both displace and dissolve in the formation waters. Afterwards, the dissolved CO₂ and H₂S undergo hydrolysis reactions leading to the generation of weakly acidic solutions. Subsequently, acidic brine leads to the dissolution of the host rock minerals. Dissolved ions and minerals may also further react to precipitate carbonates and other secondary minerals (De Silva et al., 2015; Jia et al., 2016; Talman, 2015; Zhu et al., 2013). As a result, more exploration is needed in the pre-feasibility investigation phase on the potential impacts (including physical and geochemical properties) and the trapping evolution of acid gas (Bachu and Gunter, 2004; Cantucci et al., 2015; De Silva et al., 2015; Talman, 2015; Zhu et al., 2013).

Many investigations investigated the geochemical effects of acid gas injection. Knauss et al. (2005) evaluated the impacts of dissolved CO₂, as well as a mixture of dissolved CO₂ and H₂S, on a geological formation. In addition, Xiao et al. (2009) and Xu et al. (2007) developed models to estimate the gas-fluid-rock interactions, in which CO₂ was injected as a gas phase and H₂S was injected as an aqueous solute. As an analogue for CO₂ geological storage, the results suggest that the injection of additional H₂S is very similar to the injection of pure CO₂ (Knauss et al., 2005; Xiao et al., 2009; Xu et al., 2007). However, the presence of iron-bearing minerals leads to the precipitation of pyrite, which influences mineral trapping. Schaef et al. (2010) reported results from laboratory tests of various basalts reacted with water equilibrated with supercritical CO₂ containing 1% H₂S for 181 days. The results showed that very rapid precipitation of pyrite appeared to inhibit carbonate mineralization reactions. Schaef et al. (2013) continued the work of Schaef et al. (2010) by extending the duration of experiments up to 3.5 years. They found that permanent carbonate mineralization was not impaired by pyrite formation reactions, though pyrite appeared to coat the surface and halt carbonate formation in previous shorter duration tests.

The investigations mentioned above have provided significant insight into the geochemical effects of acid gas injection. However, the partitioning phenomena occurring after acid gas injection are neglected. Bachu and Bennion (2009) first carried out a series of laboratory experiments to examine the chromatographic partitioning of acid gas injected into deep saline aquifers. The experiments were conducted with H₂S as an impurity in the CO₂ stream, at 2%, 5% and 30% concentrations under static and dynamic conditions. They found that there is a time lag between CO₂ and H₂S appearing in the effluent gas. In addition, the higher the fraction of H₂S in the injection stream is, the smaller the time lag between the CO₂ and H₂S breakthroughs. Then, Bachu et al. (2009) carried out numerical studies to replicate the laboratory results, including the breakthrough of CO₂ appearing ahead of H₂S.

Many other studies have been undertaken to investigate both the physical and geochemical effects of acid gas injection. Zheng et al. (2010) and (2013) simulated the coinjection of H₂S with CO₂ into a deep saline aquifer to study the leakage of supercritical CO₂ and H₂S mixtures along a preferential pathway to an overlying fresh-water aquifer and to study reactions of the gas mixture with that aquifer. They concluded that there is some delay observed between the arrival times of CO₂ and H₂S into the shallow aquifer. Nevertheless, the effect does not continue very long in duration, and H₂S comigrating with CO₂ is predicted to enter the aquifer once this stripping effect ceases. If there was a sufficient amount of ferrous iron supplied in the aquifer, the precipitation of pyrite could sequester a large portion of the injected sulfide. Similarly, Zhang et al. (2011) performed numerical simulations to study the coinjection of H₂S and CO₂ in sandstone and carbonate formations. The chromatographic partitioning of acid gas was also observed. Moreover, they found that the presence of iron-bearing siliciclastic and carbonate was more favorable to H₂S mineral trapping. As a result, coinjection of H₂S in the CO₂ stream decreased the solubility and mineral trapping of CO₂ compared to the pure CO₂ injection case. Conversely, Bacon et al. (2014) found that co-sequestering H₂S along with CO₂ did not noticeably modify the predicted amount of CO₂ sequestered. Under this condition, up to 5% of H₂S is sequestered completely as pyrite.

Although acid gas injection has been investigated extensively, those studies only consider the effects of an H₂S impurity in CO₂ storage, including the partitioning phenomena of impure CO₂ storage, geochemical effects by coinjected H₂S and CO₂ storage capacity influenced by H₂S. The H₂S concentration in the injected CO₂ stream is lower than 10%. However, the H₂S concentration in acid gas injection operations varies from 2% to 85% (British Columbia Geological Survey, 2003). Essentially, water in the porous media becomes saturated with more soluble gas more quickly. In addition, a higher fraction of H₂S in the acid gas results in an earlier breakthrough of both CO₂ and H₂S (Bachu and Bennion, 2009; Bachu et al., 2009). Additionally, more site-specific studies considering the variability and uncertainty of key hydrogeological and geochemical parameters are needed (Zheng et al., 2013). Thus, the feasibility of acid gas injection in the Tarim Basin is urgently needed that considers the effect of acid gas composition (59% CO₂ and 41% H₂S), mineral composition, formation water chemistry and reservoir physical conditions.

In the present study, a numerical simulation was conducted to investigate the feasibility assessment of acid gas injection in a carbonate formation of the Tarim Basin. Four aspects were mainly considered: (1) the distribution of the acid gas plume and partitioning phenomenon occurring between CO₂ and H₂S; (2) the pressure buildup due to acid gas injection; (3) the geochemical effects and corresponding effects on the porosity of the reservoir; and (4) the trapping evolution of injected acid gas, including the acid gas mixture, CO₂ component and H₂S component. Finally, we considered the uncertainty of key parameters, including the injection rate, permeability and porosity, and performed a sensitivity analysis to investigate their impact on the evolution of gas saturation, pressure buildup and entrapment of injected acid gas.

2 Geological setting

The Tarim Basin is the largest sedimentary basin in China, with an area of approximately 560 000 km². The formation and evolution of the basin can be divided into four main periods: Sinian-Cambrian, Ordovician, early Permian, and Cretaceous (Chen et al., 1997). As the largest petroliferous superposed basin in China, it has been well studied geologically (Chen et al., 1997; Gao et al., 2016; Jia et al., 2016; Shen et al., 2016), however, its potential as a site for acid gas injection has not yet been investigated. In this section, the geological setting of the Tahe oilfield is briefly addressed in Section 2.1 and the selected injection reservoir is presented in Section 2.2.

2.1 Tahe oilfield

The Tahe oilfield, located in the northern Tarim Basin (Fig. 1a), is in the southwest Akekule uplift in the Shaya uplift. It is surrounded by the Caohu sag to the east, the Halahatang sag to the west, the Manjiaer sag to the south and the Yakela uplift to the north (Fig. 1b). The origin of petroleum in the Tahe oilfield is mainly Cambrian-Ordovician source rocks. To date, the Tahe oilfield, with its 12 blocks (Fig. 1c), is the largest oilfield found in the Paleozoic marine carbonate rocks in China. Petroleum is recovered from the Ordovician carbonate rocks and the Carboniferous and Triassic sandstones (Yu et al., 2011).

2.2 Carbonate reservoir

The No. 2 United Station is located in Block 6 of the Tahe oilfield (Fig. 1c). It generates a large amount of acid gas as a byproduct during crude oil processing. To reduce greenhouse gas emissions and reduce the costs of desulfurization, the SINOPEC intends to dispose of acid gas in depleted oil and gas fields. A preliminary investigation led to the selection of well TH75CX as the injection well near the No. 2 United Station (Fig. 2).

A 5500 m deep borehole site investigation revealed that the Ordovician stratigraphic sequence in the well includes the Lower-Middle Ordovician Yingshan Group (O_1–2y). The Yingshan Group is the main oil and gas reservoir with a thickness of 51 m. As a carbonate rock reservoir, it mainly consists of open platform facies limestone. At present, the carbonate rock reservoir is in the end period of production and is considered the potential disposal site of acid gas.

3 Numerical approach

3.1 Numerical toolbox

A numerical simulation of this study was performed by the TMVR-EOSG (unpublished) simulator, which was developed from TMVOC-REACT (Zheng et al., 2010, 2013). As with TMVOC-REACT, the simulator links TMVOC (Pruess and Battistelli, 2002) and TOUGHREACT (Xu et al., 2012) by replacing the fluid and heat flow parts in TOUGHREACT with TMVOC. To analyze the coupling process occurring between flow and chemistry, gas partial pressures and fugacity coefficients calculated by the flow module (TMVOC) are passed to the geochemical module (TOUGHREACT). The routine GASEOS (Reagan, 2006) is also incorporated to calculate gas partial pressures and fugacity coefficients in gas mixtures. Temporal changes in porosity and permeability owing to mineral dissolution and precipitation are fed back to the fluid flow module by lagging one-time steps. Moreover, TMVR-EOSG additionally incorporates a new Equation of State (EOS), namely, Ziabakhsh-Ganji and Kooi EOS (Ziabakhsh-Ganji and Kooi, 2012) with binary interaction coefficients for CO₂–SO₂, CO₂–H₂S, CO₂–CH₄ and CO₂–N₂. The new EOS can simulate the impacts of gas mixtures including CO₂, SO₂, H₂S, CH₄ and N₂, and allow for an accurate and efficient modeling of the thermodynamic equilibrium of gas mixtures and brines.

3.2 Model setup

To investigate the potential physical and geochemical interactions occurring among acid gas, formation water, and rock minerals, a one-dimensional (1D) radial model (Fig. 3) was used in the simulation. According to the underground conditions of the Yingshan Group, the 1D model was set as a homogeneous carbonate formation with a thickness of 50 m. In the lateral direction, the model covered a 10 000 m radial distance and 130 radial grid elements with the grid spacing gradually increasing away from the injection well. The volume of the outer grid element is specified as a large value of 10³⁰ m³ to represent an infinite lateral extent.

Based on the acid gas injection project designed by the SINOPEC, the acid gas injection rate is 19 200 Nm³/d for 25 years. The original flue gas generated by the No. 2 United Station includes 0.19 mol% methane (CH₄), 0.05 mol% ethane (C₂H₆), 0.03 mol% propane (C₃H₈), 1.47 mol% nitrogen (N₂), 46.77 mol% CO₂, 42.3 mol% H₂S and 9.2 mol% water (H₂O). Multistage pressurization and dehydration caused water extraction prior to acid gas injection. The total percentage for CH₄, C₂H₆, C₃H₈ and N₂ is just 1.92 mol%, and thus, only CO₂ and H₂S are the dominant components considered in our numerical simulation.

Acid gas was injected at a constant rate of 0.229 kg/s for CO₂ and 0.160 kg/s for H₂S in the simulation. In the simulation, a continuous gas injection was applied for a period of 25 years, and the geochemical transport simulations were run for 10 000 years.

3.3 Initial conditions

The initial reservoir pressure is 600 bar, and the formation temperature is 128 °C at a depth of 5500 m. However, due to limitations of existing studies, the experimental data for H₂S solubility were within a relatively high temperature (321 °C) and low pressure (210 bar) (Zheng et al., 2010). As a result, the simulator is applicable at moderate temperatures (< 200 °C) and pressures (< 200 bar). The convergence will probably worsen if the simulation is run under high-temperature and high-pressure conditions. More importantly, the accuracy of the calculation will decrease, because the solubility of a component present in different phases that is currently implemented in TMVR-EOSG is only valid under low temperature and pressure (Zheng et al., 2010, 2013). According to the phase-equilibrium properties of the system (Bierlein and Kay, 1953), the critical temperature and critical pressure are approximately 57 °C and 82 bar, respectively. To ensure the supercritical state of acid gas, the pressure and temperature are set as 90 bar and 60 °C in the simulation, respectively.

The initial mineral composition was derived from laboratory studies of the Yingshan Group carbonate by X-Ray Diffraction (XRD) analysis. The reservoir comprises 97% volume calcite and 3% volume quartz. The hydrogeologic parameters used in the 1D radial model are listed in Table 1. Petrophysical properties such as porosity and permeability of rock formations were inferred from the statistical data summarized in the literature (Liang et al., 2016). The evaluation index for porosity is the cumulative amount of single well oil production (Tab. 2). Since the oil production of TH75CX is 13 668 t, the porosity is set at 0.2. The permeability is assumed to be the average value of 5 × 10⁻¹² m² in the simulation. Due to the lack of available data, other required hydrogeological parameters are specified according to the literature (Xu et al., 2007; Zhang et al., 2011).

Water chemical analysis results are available for the water samples taken from the injection well TH75CX. The Yingshan Formation water is dominated by CaCl₂, and the aqueous solution composition is shown in Table 3.

3.4 Kinetic parameters of mineral dissolution and precipitation

The reversible and fast geochemical reactions can be described properly by the chemical equilibrium model. However, a kinetic model is necessary to represent irreversible heterogeneous reactions, for instance, mineral carbonation (Marini, 2006). A kinetic model is adopted by TOUGHREACT based on the transition state theory, where the kinetic rate is expressed as (Lasaga et al., 1994):$${ r}_{\mathrm{n}}=\pm k_{\mathrm{n}}{A}_{\mathrm{n}}{|1-{\mathrm{\Omega }}_{\mathrm{n}}^{\theta }|}^{\eta }$$(1)where r_n is the kinetic rate (positive values denote mineral dissolution and negative values denote precipitation), k_n is the kinetic rate constant (mol m⁻² s⁻¹), A_n is the specific surface area (m² kg w⁻¹), and Ω_n is the kinetic mineral saturation ratio. The parameters θ and η are set to one in this study as in common practice.

The kinetic rate constant k_n is influenced not only by temperature, but also by different chemistry mechanisms (acid, neutral and base mechanisms). For many minerals, the kinetic rate constant k_n is summarized as (Lasaga et al., 1994; Palandri and Kharaka, 2004):$$k_{\mathrm{n}}=k_{25}^{\mathrm{nu}}\exp \left[\frac{-E_{\mathrm{a}}^{\mathrm{nu}}}{R}\left(\frac{1}{T}-\frac{1}{298.15}\right)\right]+k_{25}^{\mathrm{H}}\exp \left[\frac{-E_{\mathrm{a}}^{\mathrm{H}}}{R}\left(\frac{1}{T}-\frac{1}{298.15}\right)\right]a_{\mathrm{H}}^{n_{\mathrm{H}}}+k_{25}^{\mathrm{OH}}\exp \left[\frac{-E_{\mathrm{a}}^{\mathrm{OH}}}{R}\left(\frac{1}{T}-\frac{1}{298.15}\right)\right]a_{\mathrm{OH}}^{n_{\mathrm{OH}}}$$(2)where superscripts or subscripts nu, H, and OH indicate neutral, acid and base mechanisms, respectively. k₂₅ is the rate constant at 25 °C, E_a is the activation energy, R is the gas constant, T is the absolute temperature, a is the activity of the species, and n is the power term (constant). The dissolution rate is assumed to be equal to the precipitation rate for all minerals. In this study, the parameters for the kinetics of dissolution and precipitation listed in Table 4 are taken from the literature (Marini, 2006; Zhu et al., 2013).

In the geochemical reaction process, only a portion of the mineral surface can be dissolved. The surface area directly involved in mineral dissolution and precipitation by the solid unit mass is called the specific surface area. TOUGHREACT uses the following relationship to compute reactive surface areas of minerals (Xu et al., 2012):$$A_{\mathrm{r}}=\left(V_{\mathrm{frac}}{A}_{\mathrm{m}}+A_{\mathrm{prc}}\right)/C_{\mathrm{w}}$$(3)where A_r is the effective reactive surface area of minerals in units of m²_mineral/kg_water for input into the kinetic rate laws (Eq. (2)), A_m is the surface area in units of m²_mineral/m³_mineral, A_prc is the precursor surface area in units of m²_mineral/m³_medium, V_frac is the mineral volume fraction in m³_mineral/m³_medium and C_w is the wetted-surface conversion factor in units of kg_water/m³_medium. A_m, V_frac and C_w change during the course of a simulation as minerals dissolve and precipitate and as the liquid saturation of the medium fluctuates.

In terms of minerals in a rock, surface areas in units of cm²/g can be calculated from$$\mathrm{A\text{'}}=100/{\rho }_{\mathrm{m}}=100{\mathrm{AM}}_{\mathrm{m}}/V_{\mathrm{m}}$$(4)where A is the surface area in units of cm²/g, ρ_m is the mineral density in g/cm³, Mm is the molecular weight in mol/g, Vm is the molar volume in cm³/mol, and A’ is the specific reactive surface area specified in the simulation. In this study, A’ used in the simulations is based on the literature (Xu et al., 2007; Zhu et al., 2013), as shown in Table 4.

As a result of mineral precipitation and dissolution, the volume of the matrix changes. In TOUGHREACT, porosity changes are directly tied to volume changes and taken in the code as follows (Xu et al., 2012):$$\varphi =1-\sum _{m-1}^{\mathrm{nm}}{\mathrm{fr}}_{\mathrm{m}}-{\mathrm{fr}}_{\mathrm{u}}$$(5)where nm is the number of minerals, fr_m is the volume fraction of mineral m in the rock (V_mineral/V_medium, including porosity), and fr_u is the volume fraction of the nonreactive rock. As the fr_m of each mineral changes, the porosity is recalculated at each time step.

Several options are available in TOUGHREACT to calculate permeability changes as a result of mineral precipitation and dissolution. In this study, it is assumed that permeability does not change during the course of simulation.

4 Results

4.1 Similarity solution of the simplified radial flow

In the numerical simulation, 1D radial flow, infinite and uniform aquifer, and constant injection rate were specified. Under these conditions, the results are expected to be self-similar and can be plotted against the similarity variable r²/t. The self-similarity of the numerical results is a good method of assessing the space and time discretization (Pruess and García, 2002; Pruess and Müller, 2009). Figure 4 confirms that the gas saturation and pressure profiles at 1 year and 25 years are self-similar.

Figure 4 shows that there are two distinct regions. The inner region (r²/t < 1.35 × 10⁻⁴ m²/s) is a two-phase (liquid-gas) zone, and the outer region (r²/t > 1.35 × 10⁻⁴ m²/s) is a single-phase liquid condition. The maximum gas saturation is 0.27, which indicates that the injection of acid gas only partially displaces the resident formation brine. The minimum liquid saturation is 0.73. It is noted that the pressure change has the same transition point as the gas saturation at r²/t = 1.35 × 10⁻⁴ m²/s. The maximum pressure caused by acid gas injection is 90.28 bar. Pressure buildup occurs on a large scale when massive acid gas is injected into the formation, and the effect occurring in the two-phase zone is more pronounced than in the single-phase zone.

4.2 Acid gas migration

To better understand the process of acid gas migration, selected information is presented in graphical form as a function of radial distance from the injection wellbore at discrete time intervals of 0.01, 1, and 25 years during the injection period, and 100, 1000, and 10 000 years during the postinjection period. The evolution of gas saturation and mass fractions of the acid gas components (CO₂ and H₂S) in gas and aqueous phases is shown in Figures 5 and 6, respectively.

The formation is initially full of brine, and the injection of acid gas into the formation invades the pore space. Under the control of the pressure gradient and capillary forces, the resident brine located near the wellbore will be displaced and will migrate into the surroundings. The displacement is a drainage process in terms of the relevant displacement characteristics of acid gas and brine. The acid gas displacement fronts migrate approximately 6, 60, and 300 m at 0.01, 1, and 25 years, respectively, during injection, as shown in Figure 5; in the vicinity of the injection well, the maximum gas saturations reach 0.23, 0.26, and 0.27, respectively; correspondingly, the minimum liquid saturations during injection are 0.77, 0.74, and 0.73, respectively, which are much larger than the residual water saturation (s_lr = 0.3).

During the postinjection period, the main displacement is a mixing process of drainage and imbibition processes. On the one hand, acid gas migrates farther under the pressure gradient. At 100 years, the acid gas displacement front migrates approximately 343 m (Fig. 5). On the other hand, the capillary pressure serves as a driving force to induce a backflow of brine toward the injection point. In addition, the injected acid gas gradually dissolves in the formation water. Thus, the gas saturation decreases to 0.09 at 100 years. After 1000 years, the acid gas-displacement front stops progressing forward, and the main displacement occurring is the imbibition process. The system has a tendency to reach equilibrium when gas saturation decreases approximately to the residual gas saturation of 0.05.

The evolution of the CO₂ and H₂S mass fractions in the gas and aqueous phases at different times is shown in Figure 6. In terms of the mass fractions dissolved in the aqueous phase, the distances of the maximum CO₂ mass fraction are 6.6, 65.3, and 323.7 m at 0.01, 1, and 25 years, respectively, and those of H₂S are 4.1, 43.6, and 216.3 m at 0.01, 1, and 25 years, respectively, during injection. During the postinjection period, the distance of the maximum CO₂ mass fraction dissolved in the aqueous phase is 363.3 m at 100 years, and the distance of the maximum H₂S mass fraction dissolved in the aqueous phase at 100 years is 229.1 m. Because the acid gas displacement front does not progress forward after almost 1000 years (Fig. 5), the distances of the maximum CO₂ and H₂S mass fractions dissolved in the aqueous phase remain at 384.9 and 229.1 m, respectively. The maximum dissolved CO₂ mass fraction is achieved at a longer distance than that of the maximum dissolved H₂S mass fraction. In other words, the displacement distance of CO₂ is longer than H₂S in the aqueous phase at any time.

For the mass fraction in the gas phase, the changing process has similar characteristics to the mass fraction in the aqueous phase. The distances of the maximum CO₂ mass fraction are 6.6, 65.3, and 323.7 m at 0.01, 1, and 25 years, respectively, and those of H₂S are 3.453, 38.8, and 192.9 m at 0.01, 1, and 25 years, respectively, during injection. During the postinjection period, the distance of the maximum CO₂ mass fraction in the gas phase is 343 m at 100 years, and H₂S is 204.3 m. The distance of the maximum CO₂ mass fraction and H₂S in the gas phase remains at 363.3 and 204.3 m, respectively, after 1000 years. Thus, the displacement distance of CO₂ is longer than H₂S in the gas phase at any time.

Additionally, the maximum CO₂ mass fraction in the aqueous phase is 0.04, and then decreases to 0.023 when the H₂S mass fraction increases to 0.043. The results indicate that the solubility of H₂S in formation water is two times higher than that of CO_2. In the gas phase, the maximum CO₂ mass fraction decreases from 1 to 0.59 (the CO₂ mass fraction in the injected acid gas) when the H₂S mass fraction increases to 0.41 (the H₂S mass fraction in the injected acid gas). This change occurs because there is a time lag in the breakthrough front between CO₂ and H₂S.

4.3 Pressure buildup

When acid gas is injected into deep formations, the invasion of acid gas in pore space will cause pressure buildup. Moreover, the pressure gradient that arises from acid gas injection has a tendency to drive acid gas to water-saturated pores. Thus, minor differences are observed in the evolution of pressure buildup (Fig. 7) and gas saturation (Fig. 5).

As with the evolution of gas saturation, pressure buildup has a significant increase at 6, 60, and 300 m, while acid gas is injected for 0.01, 1, and 25 years, respectively. The maximum pressure buildup is generated near the injection well at 0.25, 0.275, and 0.285 bar, respectively. However, an important difference is that pressure buildup is induced at a small value, although the gas saturation remains at zero before acid gas arrives.

During the postinjection time, pressure perturbations decrease gradually over time. The distance of sharp pressure buildup is 343 m at 100 years and then remains unchanged after 1000 years, which is in accordance with the distance of the gas displacement front. After 10 000 years, the pressure of the water-saturated region recovers to its original level, and the value of the two-phase region decreases to 0.08 bar.

4.4 Geochemical effects

After injection, acid gas dissolves in the formation water over time, and then undergoes hydrolysis reactions. For the acid gas system, those reactions and their associated equilibrium constants, logK_25°C,1bar, are (Xu et al., 2012):$$\begin{array}{c}{\mathrm{CO}}_2\left(\mathrm{aq}\right) + {\mathrm{H}}_2\mathrm{O} \leftrightarrow {\mathrm{H}}^{+} + \mathrm{H}{\mathrm{CO}}_{3^{-}} \log K_{25\mathrm{°}\mathrm{C},1\mathrm{bar}} = \log \left(\right[\mathrm{H}{\mathrm{CO}}_{3^{-}}\left]\right[{\mathrm{H}}^{+}]/(\left[{\mathrm{CO}}_2\right(\mathrm{aq}\left)\right]\left[{\mathrm{H}}_2\mathrm{O}\right]\left)\right)\\ = -6.58\end{array}$$(6)$$\mathrm{H}{\mathrm{CO}}_{3^{-}} \leftrightarrow {\mathrm{H}}^{+}+{\mathrm{CO}}_3^{2-} \log K_{25\mathrm{°}\mathrm{C},1\mathrm{bar}} = -10.62$$(7)$${\mathrm{H}}_2\mathrm{S}\left(\mathrm{aq}\right) \leftrightarrow {\mathrm{HS}}^{-} + {\mathrm{H}}^{+} \log K_{25\mathrm{°}\mathrm{C},1\mathrm{bar}} = -7.42$$(8)

Reactions (6)–(8) all involve H⁺ and then produce an acidic zone where the pH value tends to decrease. In a highly acidic environment, calcite may dissolve into formation water, consuming H⁺ as subsequent reaction, which partially buffers the system:$$\mathrm{Ca}{\mathrm{CO}}_3 + {\mathrm{H}}^{+} \leftrightarrow {\mathrm{Ca}}^{2+} + \mathrm{H}{\mathrm{CO}}_{3^{-}}$$(9)

During acid gas injection, the distributions of $\mathrm{H}{\mathrm{CO}}_{3^{-}}$ and HS⁻ concentrations in brine along the radial distance at different times are presented in Figure 8. Since pH value is the master variable in the system, we plot it as the right-hand axis on the plots.

As described above, the CO₂ transport distance is longer than the H₂S transport distance in the aqueous phase at each time. Together with Reactions (6)–(8), the $\mathrm{H}{\mathrm{CO}}_{3^{-}}$ concentration increases rapidly to 0.93 mol/kg H₂O once the breakthrough front of CO₂ arrives. Then, due to the preferential dissolution of H₂S, the $\mathrm{H}{\mathrm{CO}}_{3^{-}}$ concentration decreases gradually to 0.56 mol/kg H₂O as HS⁻ increases to 1.17 mol/kg H₂O. The change in calcite abundance is so small (Fig. 10a) that the influence on pH value can be neglected. H₂S generates a weaker acidic solution than that of CO₂ since the equilibrium constant of Reaction (8) is smaller than that of Reaction (6). Consequently, the pH value decreases to 4.65 when the $\mathrm{H}{\mathrm{CO}}_{3^{-}}$ concentration increases to the maximum value and subsequently increases to 4.76 due to the weaker acidity of H₂S.

In the region close to the injection well, a small amount of calcite precipitation occurs after 1 year, reaching a peak value of 1.6% at a distance of 0.32 m at 25 years. Calcite precipitation remains constant within a distance of 0.45 m after 25 years; thus, there is an overlap in that region among the four curves of 25, 100, 1000, and 10 000 years (Fig. 10a). The reverse process of Reaction (9) has a tendency to generate H⁺ and lower the pH value. At 25 years, the $\mathrm{H}{\mathrm{CO}}_{3^{-}}$ concentration reaches 0.52 mol/kg H₂O and that of HS⁻ reaches 1.39 mol/kg H₂O when the injection ceases. A pH of approximately 4.57 is attained.

For the acid gas postinjection period, as shown in Figure 9, the distributions of $\mathrm{H}{\mathrm{CO}}_{3^{-}}$ and HS⁻ concentrations in the region of the displacement front are very similar to those during the injection period. The pH value and calcite dissolution also increased. However, in the area close to the injection well, the calcite precipitation region extends to a radius of 2.6 m (the curves at 10 000 years coincide with those at 1000 years on the whole domain). Correspondingly, at 100 years, the $\mathrm{H}{\mathrm{CO}}_{3^{-}}$ and HS⁻ concentrations increase significantly, and the pH value slightly decreases in that region. After that, the aqueous $\mathrm{H}{\mathrm{CO}}_{3^{-}}$ and HS⁻ concentrations decrease to 0.55 mol/kg H₂O and 1.23 mol/kg H₂O, respectively. Moreover, a pH of approximately 4.75 is attained.

Only a marginal increase in quartz content can be observed in Figure 10b, with a peak volume fraction of 10⁻⁵ at a distance of approximately 2.6 m (the curve at 10 000 years coincides with that at 1000 years). Additionally, the precipitation and dissolution amount of calcite are relatively small. Therefore, the variation in porosity is rather small after acid gas injection, as shown in Figure 11. There are irrelevant porosity changes in regard to the hydraulic or mechanical properties of the reservoir. Furthermore, the area where porosity varies is consistent with that of the acid gas plume. The irrelevant porosity change is probably a consequence of numerical oscillation.

4.5 Acid gas trapping evolution

As with the CO₂ trapping mechanism, the acid gas trapping mechanism can be divided into geological trapping, geochemical trapping and hydrodynamic trapping (De Silva et al., 2015; Talman, 2015). Geological trapping includes structural trapping and residual trapping, i.e., mobile acid gas trapped by the formation structure or caprock units and by capillary pressure forces in the pore space. Geochemical trapping is composed of dissolution trapping and mineral trapping, and is thus considered to be a secure trapping mechanism because acid gas can be permanently stored in the formation without leaking to the surface.

For the simulated case, calcite dissolution occurs in the acidic zone, which is caused by the hydrolysis reactions of CO₂ and H₂S in the region of the displacement front. Therefore, no CO₂ or H₂S is sequestered in mineral phases during the displacement process; instead, some CO₂ and H₂S are dissolved. Although calcite is precipitated near the injection well, the amount of precipitation is almost equivalent to that of dissolution. As a result, no CO₂ mineral sequestration occurs after acid gas injection. Similarly, no H₂S mineral sequestration occurs after acid gas injection. Thus, there are three trapping mechanisms for acid gas, including mobile gas trapping, residual gas trapping and dissolution trapping, as shown in Figure 12.

During acid gas injection, the ratio of dissolved to total injected H₂S remains at 62%. In contrast, the ratio of dissolved to total injected CO₂ fluctuates from 46% to 49%, respectively. The variation in dissolution trapping is in line with that of the distribution of $\mathrm{H}{\mathrm{CO}}_{3^{-}}$ and HS⁻ concentrations at different times during the injection period shown in Figure 8, which is a result of the preferential dissolution of H₂S over CO₂. As a result, the ratio of dissolved to total injected acid gas fluctuates from 53% to 54%, respectively. Similarly, 11.6% of H₂S is residually trapped, 18%~19% of CO₂ is residually trapped, and 15%~16% of acid gas is thus residually trapped during acid gas injection.

For the acid gas postinjection period, both the residual trapping and dissolution trapping gradually increase, as shown in Figure 12. After a 1000-year storage period, the percentages of dissolution trapping, residual trapping and mobile gas phases for H₂S are 84.8%, 13.7%, and 1.5%, respectively, and those for CO₂ are 71.0%, 2.7%, and 26.3%, respectively. Additionally, the percentages of total acid gas injection in solubility trapping, residual trapping and mobile gas trapping are 76.5%, 21.1%, and 2.4%, respectively.

4.6 Sensitivity analysis

To investigate the numerical model sensitivity to the reservoir parameters porosity, permeability and injection rate, six different cases were considered based on the reservoir parameters. In the first two cases, we changed the injection rate from 19 200 Nm³/d (Base Case) to 38 400 Nm³/d (Case 1) and to 9600 Nm³/d (Case 2). According to the acid gas composition of the project, acid gas mixtures were injected at a constant rate of 0.458 kg/s CO₂ + 0.320 kg/s H₂S in Case 1 and 0.1145 kg/s CO₂ + 0.080 kg/s H₂S in Case 2. In Cases 3 and 4, the permeability values were changed from 5 × 10⁻¹² (Base Case) to 5 × 10⁻¹¹ (Case 3) and to 5 × 10⁻¹³ (Case 4). Finally, two cases with different porosities, 0.1 and 0.3, were performed (Cases 5 and 6, respectively). The total volume of acid gas injected in the reservoir is equivalent. Thus, the injection times of Case 1 and Case 2 are changed to 12.5 years and 50 years, respectively. In all other cases (Cases 3–6), the injection time was set as a value of 25 years, which was the same as the Base Case. Furthermore, in all cases, the time of geochemical transport simulations was set to 10 000 years.

Figure 13 shows the effect of the injection rate on the gas saturation and pressure buildup at three selected times as well as the evolution of acid gas trapping. The selected times include 1 year during the injection period and 10 000 years during the postinjection period in the three cases. The third selected times are 25, 12.5 and 50 in the Base Case, Case 1 and Case 2, respectively. Figure 13a shows that the gas saturation and migration distance increase during the injection period as the injection rate increases. At the end of acid gas injection, gas saturation is higher with a higher injection rate. However, the migration distances are almost the same. At 10 000 years, both the gas saturation and migration distances are the same at the three injection rates. The effect of the injection rate on the pressure buildup is consistent with that of the gas saturation (Fig. 13b). In terms of acid gas trapping, the percentage of dissolution trapping is smaller during the injection period when the injection rate is increased (Fig. 13c). However, the dissolution trapping rate is relatively higher after injection occurs at a higher injection rate. The differences in the rate of dissolution trapping for the different injection rates result from the differences in saturation distributions observed at the end of acid gas injection. At higher injection rates, much more acid gas is in the free gas phase. At 10 000 years, the same amounts of dissolution trapping are reached at the three injection rates. As shown in Figure 13c, the injection rate has little effect on the residual trapping.

Figure 14 illustrates the effect of permeability on the gas saturation and pressure buildup at three selected times as well as the evolution of acid gas trapping. Gas saturation, pressure buildup and acid gas trapping are significantly affected by permeability. Acid gas will be able to flow through more easily with a higher permeability. Thus, with a higher permeability, the gas saturation is lower and the migration distance is farther. The farther migration distance leads to a larger contact volume between the acid gas and formation water. As a consequence, the dissolution trapping ratio is relatively high at the end of the simulation with high permeability (Fig. 14c). The effect of permeability on pressure buildup is consistent with gas saturation and migration distance (Fig. 14b).

Figure 15 reports the effect of porosity on the gas saturation and pressure buildup at three selected times as well as the evolution of acid gas trapping. Acid gas moves farther when the porosity is reduced (Fig. 15a). The porosity has little effect on the gas saturation and pressure buildup. Additionally, as shown in Figure 15c, the same amounts of dissolution trapping are reached at the three porosities after acid gas injection.

5 Discussion

As investigated in the literature (Meng et al., 2015; Pruess and García, 2002; Pruess and Müller, 2009; Zhao and Cheng, 2017), salt precipitation is caused at the dry-out region near the injection well where liquid saturation is lower than the residual water saturation. The formation porosity and permeability may be reduced by solid salt precipitation. Injectivity impairment will eventually occur after salt accumulation. Under the condition of acid gas injection in this study, the minimum liquid saturation is 0.73, which is much larger than the residual water saturation (S_lr = 0.3). Thus, there is no dry-out region observed in the reservoir. More importantly, the distribution of liquid saturation is beneficial to engineering operations.

After acid gas injection, the evolution of the CO₂ and H₂S mass fractions in the gas and aqueous phases indicates that the leading gas front consists of CO₂ due to the preferential dissolution of H₂S in the aqueous phase. This partitioning phenomenon is consistent with current research (Bachu and Bennion, 2009; Bachu et al., 2009; Zhang et al., 2011; Zheng et al., 2010, 2013). In engineering operations, the quicker breakthrough of CO₂ can provide an advanced warning of a potential breakthrough of acid gas. Thus, immediate action should be taken once pure CO₂ is detected along the potential leakage pathway.

The pressure buildup region extends further than that of the acid gas plume, which is in agreement with existing research results (Birkholzer et al., 2009; Liu et al., 2018; Meng et al., 2015). In response to acid gas injection, the fluid pressure in the storage formation reached maximum values of approximately 0.285 bar near the injection zone. According to current practices for the underground injection control of liquid wastes, the maximum allowable injection-induced pressure increase should be limited to reduce the risks of seismic events and geomechanical damage (Bandilla and Celia, 2017; Birkholzer et al., 2009, 2015; Zhou et al., 2010). For example, the regulated injection pressure is limited to 0.181 bar/m in the Illinois Basin. Correspondingly, the allowable pressure increase needs to be less than 65% of the preinjection pressure (Bandilla and Celia, 2017; Zhou et al., 2010). In comparison, the maximum pressure buildup of 0.285 bar that was observed in the simulation corresponds to 0.32% of the preinjection pressure. Consequently, the pressure buildup due to acid gas injection is insignificant to the reservoir.

Only a small increase in quartz is observed after acid gas injection because quartz is relatively stable at pH values of 2.0–8.5 and below 250 °C (Li et al., 2016; Xu et al., 2007). In addition, the amounts of calcite precipitation and dissolution are relatively small. Consequently, the porosity is almost unaffected by chemical reactions.

Carbonate rocks have little trapping capacity for CO₂ because equilibrium is reached quickly from the accumulation of Ca²⁺ and $\mathrm{H}{\mathrm{CO}}_{3^{-}}$ ions through congruent reactions (Gunter et al., 2000; Zhu et al., 2013). In fact, no CO₂ mineral sequestration occurred after acid gas injection in this study. When H₂S is injected into iron-rich formations, mineral trapping of H₂S is achieved after pyrite reactions occurred (Li et al., 2016; Talman, 2015; Xu et al., 2007). Due to the lack of iron-rich formations in carbonate reservoirs, mineral reactions induced by H₂S are not considered and no observed H₂S mineral sequestration occurs after acid gas injection. Eventually, there are three trapping mechanisms for acid gas including mobile gas trapping, residual gas trapping and dissolution trapping.

During acid gas injection, the gas saturation and pressure buildup increased considerably with increasing injection rate. As a result, the percentage of the mobile gas phase is larger at a higher injection rate. However, the rate of the mobile gas phase reduced to a minimum is higher. Thus, the injection rate can be increased to facilitate acid gas trapping, which could be used as guidance for acid gas injection.

In the present study, only a 1D model is considered for simplicity in the numerical simulations. In the future, a fully 3D model will be needed for practical storage scenarios.

6 Conclusion

The possible impact of acid gas injection has been successfully evaluated through numerical modeling of a conceptual model with the hydrologic properties and mineral compositions of the target Tarim Basin reservoir, the possible impact of acid gas injection has been successfully evaluated. The major conclusions are as follows:

1. The maximum gas saturation of 0.27 is achieved at the end of injection, which is beneficial to engineering operations. At 10 000 years, the gas saturation tends to reach 0.05. In addition, the preferential dissolution of H₂S delays its breakthrough compared to that of CO₂ both in the gas and aqueous phases, and the maximum CO₂ mass fraction is almost 1. This finding has great implications for detecting and providing advanced warning of the potential leakage of acid gas.

2. During the injection period, the maximum pressure buildup is generated at 0.285 bar near the injection well at 25 years, and a slight increase in pressure is observed at the region where the acid gas has not yet arrived. After 10 000 years, 0.08 bar of pressure buildup is achieved within the distance at which acid gas arrives, and pressure is recovered to the original level out of that distance. The maximum pressure buildup of 0.285 bar that was observed in the simulation corresponds to 0.32% of the preinjection pressure. Consequently, the pressure buildup that occurred due to acid gas injection has little effect on the reservoir.

3. At the displacement front, the amount of calcite precipitation is small enough to neglect. The concentration of $\mathrm{H}{\mathrm{CO}}_{3^{-}}$ first increases and then decreases due to the preferential dissolution of H₂S. Because H₂S generates a weaker acidic solution than CO₂, the pH value decreases to 4.65 and subsequently increases to 4.76. In the region close to the injection well, a small amount of calcite precipitation occurs during the acid gas injection, and thus, a minimum pH value of approximately 4.57 is attained. The calcite precipitation region near the injection well extends largely after the acid gas injection ceases, and thus, there is a slight reduction in pH value in that region at 100 years. At the end of the simulation, a pH of approximately 4.75 is attained. In addition, the variation in porosity is relatively small after acid gas injection due to the small changes in calcite and quartz in the volume fraction.

4. There are three trapping mechanisms: mobile gas trapping, residual gas trapping and dissolution trapping. As a secure trapping mechanism, the ratio of dissolved H₂S to total injected H₂S is higher than that of CO₂ during acid gas injection. At the end of acid gas injection, 54% of acid gas is trapped by dissolution trapping, and 76.5% is trapped at the end of simulation.

5. There is a higher rate of mobile gas phase decreasing to the minimum amount with a higher injection rate. The injection rate can be increased to facilitate acid gas trapping, which could be used as guidance for acid gas injection.

6. The porosity has little effect on the gas saturation, pressure buildup and trapping mechanism. However, gas saturation, pressure buildup and acid gas trapping are significantly affected by permeability. Under a higher permeability, the gas saturation is lower and the migration distance is farther. Correspondingly, the mobile phase ratio is lower at the end of the simulation.

In summary, the distribution of acid gas is beneficial to acid gas injection. Moreover, the pressure buildup is under the allowable pressure increase. Additionally, the porosity change is negligible due to small changes in calcite and quartz in the volume fraction. In conclusion, our simulation indicates that acid gas injection is feasible in the carbonate formation of the Tarim Basin.

Acknowledgments

The authors wish to thank Prof. Simon Mathias of Durham University for his improvements in grammar and readability. The authors also wish to thank the two anonymous reviewers for their constructive suggestions for improving the quality of the manuscript. Special thanks to Guizhen Liu for her map illustration. This work was partially supported by the National Natural Science Foundation of China (Grant Nos. 41872210, 41274111) and SINOPEC Northwest Oilfield Branch (Grant No. 34400007-17-ZC0607-0172)

References

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