Effects of Reservoir Heterogeneity on CO₂ Dissolution Efficiency in Randomly Multilayered Formations

Abstract

Carbon dioxide (CO₂) dissolution is the secondary trapping mechanism enhancing the long-term security of CO₂ in confined geological formations. CO₂ injected into a randomly multilayered formation will preferentially migrate along high permeability layers, increasing CO₂ dissolution efficiency. In this study, sequential Gaussian simulation is adopted to construct the stratified saline formations, and two-phase flow based on MRST is established to illustrate the spatial mobility and distribution of CO₂ migration. The results show that gravity index $G$ and permeability heterogeneity ${\sigma }_Y^2$ are the two predominant factors controlling the spatial mobility and distribution of CO₂ transports. The CO₂ migration shows a totally different spatial mobility under different gravity index and heterogeneity. When the permeability discrepancy is relatively larger, CO₂ preferentially migrates along the horizontal layer without accompanying the vertical migration. For the formation controlled by gravity index, CO₂ migration is governed by supercritical gaseous characteristics. For the medium gravity index, the upward and lateral flow characteristics of the CO₂ plume is determined by gravity index and heterogeneity. When the gravity index is smaller, permeability heterogeneity is the key factor influencing CO₂ plume characteristics. Permeability heterogeneity is the decisive factor in determining final CO₂ dissolution efficiency. This investigation of CO₂ mobility in randomly multilayered reservoirs provides an effective reference for CO₂ storage.

1. Introduction

Global warming is the greatest existential challenge facing humanity according to the Intergovernmental Panel on Climate Change (IPCC) Report [1]. Global warming may threaten human life security and social sustainable development [2]. Geological carbon sequestration is an effective measure against global climate change since it can mitigate climate impacts and reduce greenhouse gas emission [3,4]. Saline aquifers in deep geological formations are predominantly candidates for geological CO₂ sequestration given their hydrodynamic, geological, and thermal conditions [5,6]. It is estimated that geological reservoirs have a potential storage capacity between 8000 and 55,000 Gt of CO₂, representing a sufficient capacity to store over 200 years of current carbon dioxide emissions [7,8].

CO₂ is in supercritical state when injected into saline aquifers (the pressure and temperature of supercritical CO₂ are 7.382 MPa and 31.048 °C, respectively) [9]. CO₂ trapping mechanisms are mainly as follows: stratigraphic or structural, solubility, residual, and mineral trapping [10,11,12,13,14]. For structural trapping, supercritical carbon dioxide is confined as a buoyant immiscible phase within the reservoir, restrained by the structure and the seal rock. Due to residual pressure or capillary pressure, the immobilization of CO₂ occupies the small pores of the saline aquifer during CO₂ injection [15,16,17]. The fluid–rock interaction of the aquifers results in solubility trapping, reducing the amount of mobile CO₂ lying below the cap rock and ensuring the long-term security of CO₂ storage [18]. Furthermore, mineral trapping is considered to be the result of rock-fluid-CO₂ interaction, involving the geochemistry reactions of reservoir minerals such as calcite, dolomite, siderite, etc. Mineral trapping is the slowest but the most permanent and most safe process [19,20,21,22].

For CO₂ dissolution trapping mechanisms, CO₂ dissolution efficiency due to rock-fluid-CO₂ interaction is controlled by reservoir heterogeneity on all scales [23,24]. Many previous studies have extensively investigated the effect of the geological heterogeneity on CO₂ trapping by experiment, field data and numeral simulation. Kim et al. [25] carried out Darcy-scale multiphase flow experiments on a heterogeneous specimen to obtain CO₂ saturation during both drainage and imbibition. Sohal et al. [26] studied the effect of heterogeneous wettability distribution on CO₂ storage efficiency, which showed that both heterogeneously distributed wettability and higher temperature accelerated the vertical CO₂ migration significantly and reduced storage capacity. Singh et al. [27] investigated CO₂ dissolution and local capillary trapping in permeability and capillary heterogeneous reservoir, which suggested that vertical distance between the centers of mass of the supercritical CO₂ and dissolved CO₂ plumes is larger for heterogeneous reservoirs. Onoja et al. [28] investigated the relevance of representing relative permeability variations in the sealing formation, the results demonstrate that gradational changes at the base of the caprock could influence the pressure changes propagating vertically into the caprock from the saline aquifer. Mouche et al. [29] presented an upscaled model for the vertical migration of the CO₂ plume, the results illustrate that the upscaled saturation is controlled by the capillary pressure at the interface of the connected layers. Green et al. [30] studied the heterogeneity effect of vertical permeability on CO₂ long-term migration and showed that the heterogeneous formation with equivalent effective vertical permeability has a shorter breakthrough time in saline aquifer. Deng et al. [31] investigated the effect of multi-scale heterogeneity on storage capacity, designs of injection wells, injection rate, CO₂ plume migration, and CO₂ potential leakage. Kim et al. [32] and Paiman et al. [33] investigated the fracture heterogeneity, and revealed that fractures can significantly affect the predicted amount of trapped CO₂. Galkin et al. [34] adopted X-ray tomography and electron microscopy for description of rock pore space considering reservoir heterogeneity, considered to be an important method to introduce new methods for the development of complex reservoirs. Martyushev et al. [35,36,37,38] modified the geological and hydrodynamic model considering both horizontal and vertical permeability heterogeneities (anisotropy parameter), significantly improving the adaptation of both injection and production wells. Oh et al. [39] researched the injection-induced pressure and buoyancy force in a horizontally and vertically stratified core utilizing a core-flooding system with a 2-D X-ray scanner, concluding that CO₂ movement was primarily controlled by media heterogeneity. Rasmusson et al. [40] constructed strata alternating high and low permeability to investigate CO₂ migration, considering the coupled wellbore-reservoir flow. Although several studies have investigated the effect of heterogeneity on CO₂ migration, there are very limited researches regarding qualitative analysis of CO₂ dissolution efficiency considering small-scale variability in stratification permeability during GCS.

The main objective of this investigation aims to reveal the effect of permeability heterogeneity on CO₂ dissolution efficiency in reservoir-caprock system. The two-phase flow model is implemented in MRST (Matlab Reservoir Simulation Toolbox) [41], a finite-volume based method. It is very convenient to develop new features within MRST. The two-phase flow involves the dissolution of CO₂ into brine and evaporation of H₂O into the CO₂ gaseous state. Mathematical description and model implementation of the simulation model are illustrated in Section 2 and Section 3, respectively. Model validation and sensitive analysis of the CO₂ dissolution efficiency are depicted in Section 4. Finally, the conclusions are summarized in Section 5.

2. Mathematical Model

2.1. Extended Reaction System

There are three chemical components (CO₂, H₂O, NaCl) in the geological system. The chemical species is determined by the following equilibrium chemical reactions [42,43]:

$$H_{2}O\left(l\right)\iff H_{2}O\left(g\right), K^H=f_g^H/a_l^H$$

(1)

$${CO}_2\left(aq\right)\iff {CO}_2\left(g\right), K^C=f_g^C/a_l^C$$

(2)

where $K^H$ and $K^C$ are the equilibrium constants for H₂O and CO₂, respectively; $f_g^{\alpha }$ and $a_l^{\alpha }$ represent the fugacity and activity of the $\alpha$ component in gas or liquid state.

The equilibrium constants of CO₂ and H₂O relation equations are expressed as:

$$K^{\beta }=K^{\beta 0}exp\frac{\left(p_l-p_0\right)V_{\beta }}{R{T}_c}$$

(3)

with

$$K^{\beta 0}={10}^{a_{\beta }+b_{\beta }{T}_c+c_{\beta }{T}_c^2+d_{\beta }{T}_c^3}$$

(4)

where $R=8.314$ [J$·$K⁻¹$·$mol⁻¹] is a universal gas constant; $T_c$ is the temperature in °C; $V_{\beta }$ is the mean molar volume of the pure condensed species when pressure changes from $p_0$ to $p_l$; $a_{\beta }$, $b_{\beta }$, $c_{\beta }$ and $d_{\beta }$ are the equation parameters.

When the chemical reaction is at equilibrium, the mole fractions of H₂O in gas $x_g^H$ and CO₂ in liquid $x_l^C$ are illustrated in Equations (3) and (4).

$$x_g^H=\frac{K^H{a}_l^H}{F^H{P}_{tot}}$$

(5)

$$x_l^C=\frac{F^C\left(1-x_g^H\right)P_{tot}}{55.508r_{{co}_2}^{\prime }{K}^C}$$

(6)

where $F^H$ and $F^C$ the fugacity coefficients of H₂O and CO₂ in CO₂-rich phase; $P_{tot}$ is the total pressure; $r_{{co}_2}^{\prime }$ is the activity coefficient that illustrates the relation between the solubility of aqueous CO₂ in pure water and brine.

The mutual solubilities can be expressed in the following formula:

$$x_g^H=\frac{1-B-x_l^S}{\frac{1}{A}-B}$$

(7)

$$x_l^C=B\left(1-x_g^H\right)$$

(8)

$$A=\frac{K^H}{F^H{P}_{tot}}$$

(9)

$$B=\frac{F^C{P}_{tot}}{55.508r_{{co}_2}^{\prime }{K}^C}$$

(10)

Mass fractions of H₂O in gas phase ($X_g^H$) and aqueous CO₂ in liquid brine phase ($X_l^C$) can be obtained in a concise formula [44]:

$$X_g^H=\frac{18.015x_g^H}{18.015x_g^H+44.01\left(1-x_g^H\right)}$$

(11)

$$X_l^C=\frac{44.01x_l^C}{18.015\left(1-x_l^C\right)\left(1+0.05844m_l^S\right)+44.01x_l^C}$$

(12)

where $m_l^S$ denotes the molality of NaCl in liquid state.

2.2. Mass Transport Equations

Based on the mass balances of the H and C components in the geological system, the component transport equations are given as:

$${\sum }_{\alpha =l,g}\left[\frac{\partial \left(\phi S_{\alpha }{\rho }_{\alpha }{X}_{\alpha }^H\right)}{\partial t}+\nabla ·\left(X_{\alpha }^H{\rho }_{\alpha }{q}_{\alpha }\right)-\nabla ·\left({\phi S_{\alpha }{\rho }_{\alpha }{D}_{\alpha }\nabla X}_{\alpha }^H\right)\right]-Q_g^H=0$$

(13)

$${\sum }_{\alpha =l,g}\left[\frac{\partial \left(\phi S_{\alpha }{\rho }_{\alpha }{X}_{\alpha }^C\right)}{\partial t}+\nabla ·\left(X_{\alpha }^C{\rho }_{\alpha }{q}_{\alpha }\right)-\nabla ·\left({\phi S_{\alpha }{\rho }_{\alpha }{D}_{\alpha }\nabla X}_{\alpha }^C\right)\right]-Q_g^C=0$$

(14)

where $\alpha =l$ and $\alpha =g$ represent the liquid brine and gaseous CO₂-rich phase; $\phi$ is the reservoir porosity; $S_{\alpha }$ is the saturation of the $\alpha$-phase; ${\rho }_{\alpha }$ is the density of the $\alpha$-phase (kg$/$m³); $X_{\alpha }^H$ and $X_{\alpha }^C$ indicate the mass fraction of H and C components in the $\alpha$-phase; $D_{\alpha }$ is the dispersion tensor (m²$·$s⁻¹); $Q_g^H$ and $Q_g^C$ are the source term (kg$·$s⁻¹); $q_{\alpha }$ is the fluid flux of the $\alpha$-phase associated with Darcy’s velocity:

$$q_{\alpha }=-\frac{{\kappa k}_{r\alpha }}{{\mu }_{\alpha }}\left(\nabla p_{\alpha }-{\rho }_{g}g\nabla \mathrm{z}\right)$$

(15)

where $\kappa$ is the intrinsic permeability (m²); $k_{r\alpha }$ is the relative permeability of the $\alpha$-phase; ${\mu }_{\alpha }$ is the viscosity (pa$·$s); $p_{\alpha }$ is the fluid pressure (pa); $g$ is the gravitational acceleration (m$·$s⁻²); $\nabla \mathrm{z}$ is the vertical distance (m).

2.3. Constitutive Equation

To set up the multiphase flow simulation, we need the capillary-saturation relationship $P_c\left(S_w\right)$. Flooding experiments on core samples from the reservoir are used to develop the empirical relationship between $P_c$ and $S_w$. Leverett J-function is adopted to normalize the measured data [45,46,47,48]:

$$J\left(S_w\right)=\frac{p_c}{\sigma \cos \theta }\sqrt{\frac{K}{\phi }}$$

(16)

where $\sigma$ is the surface tension measured in the laboratory; $\theta$ is the contact angle; $\sqrt{K/\phi }$ is scaling factor proportional to the radius of pore-throat.

Van Genuchten model for the retention curve is used to express the effective liquid saturation of the brine system [49]:

$$S_{l\left(p_c\right)}=\left\{\begin{array}{cc}1,& p_c<0\\ {\left[1+{\left(\sqrt{\frac{k\overline{\phi }}{k_g\phi }}{{\alpha }_{p}p}_c\right)}^{n_p}\right]}^{{-m}_p}& , p_c\ge 0\end{array}\right.$$

(17)

where $S_l$ is the effective saturation; $\overline{\phi }$ and $k_g$ are the mean porosity and mean permeability of the reservoir, respectively; ${\alpha }_p$ is the scaling parameter for the retention curve.

The relative permeabilities for the liquid and gas phases can be expressed as follows:

$$k_{rl}=k_{rlm}·{\left(S_l\right)}^{{ϵ}_p}{\left[1-{\left(1-S_l^{1/m_p}\right)}^{m_p}\right]}^2$$

(18)

$$k_{rg}=k_{rgm}·{\left(1-S_l\right)}^{{\gamma }_p}{\left(1-S_l^{1/m_p}\right)}^{{2m}_p}$$

(19)

where $k_{rlm}$, $k_{rgm}$, ${ϵ}_p$ and ${\gamma }_p$ are the scaling parameters, the values of the main parameters are as shown in

Table 1. Values of the main parameters for relative permeability.

Parameter	Value	Parameter	Value
$k_{rlm}$	1.0	$k_{rgm}$	1.0
${\alpha }_p$	5.0	$m_p$	0.4
${ϵ}_p$	0.5	${\gamma }_p$	0.5

.

3. Numerical Implementation

Newton-Raphson Iteration

Liquid pressure ($p_l$), gas pressure ($p_g$) and bottom hole pressure ($p_{bh}$) are chosen as the independent variables during the numerical implementation. Newton-Raphson iteration method is adopted to solve the governing equations. The system of three equations is expressed in compact form:

$$F\left(x\right)=0$$

(20)

where

$$\left[F\right]=\left[\begin{array}{c}{F}_H\\ F_C\\ F_W\end{array}\right], \left[x\right]=\left[\begin{array}{c}{p}_l\\ p_g\\ p_{bh}\end{array}\right]$$

(21)

where $F_H$, $F_C$ and $F_W$ represent the equilibrium control equations for H₂O, CO₂ and injection wells.

The Newton-Raphson iteration of $x$ is expressed as:

$$J_t^{i+1,k}{\left[\delta x\right]}^{i+1,k}=-{\left[F\right]}_t^{i+1,k}$$

(22)

where the Jacobian matrix is:

$$J_t^{i+1,k}={\left[\begin{array}{ccc}\frac{\partial F_H}{\partial p_l}& \frac{\partial F_H}{\partial p_g}& \frac{\partial F_H}{\partial p_{bh}}\\ \frac{\partial F_C}{\partial p_l}& \frac{\partial F_C}{\partial p_g}& \frac{\partial F_C}{\partial p_{bh}}\\ \frac{\partial F_W}{\partial p_l}& \frac{\partial F_W}{\partial p_g}& \frac{\partial F_W}{\partial p_{bh}}\end{array}\right]}^{i+1,k}$$

(23)

Taylor series is used to update the independent variables:

$${\left[x\right]}^{i+1,k+1}={\left[x\right]}^{i+1,k}+{\left[\delta x\right]}^{i+1,k}$$

(24)

4. Numerical Simulation

4.1. Model Validation

In order to validate the accuracy of the numerical method, the sharp interface is achieved by moving all of the gaseous CO₂ above the liquid brine, and the plume depth of the interface is given:

$$z\left(r\right)={\int }_0^h{S}_g\left(r,z\right)dz$$

(25)

Figure 1 and Figure 2 show saturation distribution of the gas phase and the comparison of the numerical result with the similarity solution of CO₂ injection in homogenous formation by Nordbotten. Nordbotten et al. [50] derived the similarity solution of carbon dioxide injected into confined aquifers, assuming that a clear interface separates the gaseous CO₂ and brine liquid, as illustrated in Figure 2.

4.2. Effect of Pressure

The problem of interest here is the injection of supercritical CO₂ through a fully penetrating vertical well beneath the caprock in the deep confined saline aquifer. Sequential Gaussian simulation (SGSIM) as a stochastic method has been developed to generate a series of models of possible reservoir rock heterogeneities [51]. This simulation technique produces equiprobable models of a continuous variable with the appropriate probability distribution and a spatial correlation function. The simplicity and flexibility of the SGSIM code make it particularly appropriate for simulating petrophysical properties such as permeabilities and porosities of the reservoir. The multilayered reservoir is composed of horizontally stratified layers with the sequential Gaussian simulation method by SGSIM code. The permeability is represented by the spatial variability of the intrinsic permeability, and the permeability is rescaled to obtain the reservoir statical property as follows:

$$Y\left(x\right)=\overline{Y}+{\sigma }_Y{Y}_{std}\left(x\right)$$

(26)

where $\overline{Y}$ is the intrinsic permeability of the reservoir; ${\sigma }_Y$ is the sqrt of variance ${\sigma }_Y^2$, indicating the heterogeneity coefficient of saline aquifers; and $Y_{std}\left(x\right)$ is the standardized Gaussian random field with a zero mean and unit variance.

There are two immiscible fluid phases, namely the water-rich brine phase and the CO₂-rich gaseous phase. The brine phase is mainly represented by a high-concentration of NaCl in water. The temperature is considered to be constant during CO₂ injection. The simulation system is represented by an axisymmetric model in the cylindrical system ($r$, $\phi$, $z$).

The multilayered formation system is initially saturated with the brine in a hydrostatic state, and the top and bottom boundaries are impermeable boundaries. The liquid pressure at the right boundary increases downward with a vertical gradient. Schematic of the simulation setup is shown in Figure 3. Logarithm permeability distributions of the reservoir beneath the caprock with three different variances ${\sigma }_Y^2$ are illustrated in Figure 4. The specified values of logarithm permeability distributions along the reservoir depth are shown in Figure 5. The larger the variance is, the more heterogeneous the multilayered formation is. The parameters listed in adopted for GCS are illustrated in

Table 2. Summary of the parameters adopted for GCS.

Parameters	Symbol	Units	Values
Domain size	(R, b)	[m]	(3000, 100)
Grid discretization	(Nr, Nz)	[–]	(100, 100)
Porosity	ϕ	[–]	0.1
Mean permeability	$k_g$	[m2]	10−13
Initial liquid pressure	pl	[bar]	150
Initial gas pressure	pg	[bar]	1
Well radius	rw	[m]	0.1
Total injection mass	Minj	[Mt]	2.5
Residual saturations	(Slr, Sgr)	[–]	(0.2, 0)
Hydrodynamic dispersivities	(αL, αT)	[m]	(5, 1)
Molecular diffusion coefficient	Dm	[m2⋅s−1]	10−9
Salinity	$m_l^S$	[molal]	0.1
Temperature	Tc	[°C]	60
Simulation time	t	[s]	3.15 × 107

.

Gravity index $G$ is defined as the ratio of gravity force resulting from vertical permeability, density difference, and reservoir thickness to the viscose force:

$$G=\frac{2\pi \left({\rho }_l-{\rho }_g\right){\rho }_{g}g{k}_h{h}^2}{Q{\mu }_l}$$

(27)

where ${\rho }_l$ and ${\rho }_g$ are the density of the brine liquid and supercritical gaseous phases; $k_h$ is the vertical permeability of the reservoir; $h$ is the vertical thickness of the formation; and $Q$ is the injection rate of the gas phase.

The parameters listed in

Table 3. Gravity index calculations in different simulated cases.

Case	$\mathit{Q}(\mathit{M}\mathit{t}/\mathit{y})$	${\mathit{k}}_{\mathit{g}}\left({\mathbf{m}}^2\right)$	${\mathit{\sigma }}_{\mathit{Y}}^2$	$\mathit{G}$
1	7.5	10−13	0	0.6
2	2.5	10−13	0	1.8
3	0.8	10−13	0	5.6
4	0.8	10−13	0.3	5.6
5	0.8	10−13	1.0	5.6
6	0.8	10−13	4.0	5.6
7	2.5	10−13	0.3	1.8
8	2.5	10−13	1.0	1.8
9	2.5	10−13	4.0	1.8
10	7.5	10−13	0.3	0.6
11	7.5	10−13	1.0	0.6
12	7.5	10−13	4.0	0.6

includes different values of injection rate $Q$, variances ${\sigma }_Y^2$ and gravity index $G$. Note that gravity index $G$ and variances ${\sigma }_Y^2$ are dimensionless.

4.3. Spatial Mobility and Distribution of CO₂

Effective gas saturation $S_{ge}$ is adopted to interpret the CO₂ plume evolution during CO₂ injection:

$$S_{ge}=\frac{S_g-S_{gr}}{1-S_{lr}-S_{gr}}$$

(28)

where $S_{lr}$ and $S_{gr}$ are the residual liquid and gas saturation, respectively.

Dimensionless time variable $t^{\ast }$ is adopted to facilitate the interpretation of CO₂ dissolution efficiency:

$$t^{\ast }=\frac{t}{t_c}$$

(29)

$$t_c=\frac{\phi {\mu }_{l}h}{\left({\rho }_l-{\rho }_g\right)g{k}_h}$$

(30)

where $t_c$ is the characteristic time, an important indicator of the migration time from the bottom of reservoir to the top due to buoyant forces.

Figure 6 shows the spatial mobility and distribution of CO₂ over time. The plots in the first and second column in Figure 6 show the migration path for Cases 10 and 12, respectively. At the initial injection stage, the spatial mobility of CO₂ shows a quite different distribution behave for heterogeneous reservoirs when $t=0.01t^{\ast }$. For the smaller formation heterogeneity such as ${\sigma }_Y^2=0.3$, the upwind and lateral migration of the CO₂ plume is relatively more uniform around the injection well, compared with heterogeneity ${\sigma }_Y^2=4.0$. The variation difference between the logarithm permeability distributions along the reservoir depth is relatively larger for $\mathrm{C}\mathrm{a}\mathrm{s}\mathrm{e}$ 12, as illustrated in Table 2, and the mainly horizontal flow path is generated as the CO₂ migrates along the horizontal layer with the maximum permeability at time $t=0.01t^{\ast }$. While $t=0.05t^{\ast }$, CO₂ starts the migration along the layers with the relatively high permeabilities in the multilayered formation. Due to the big discrepancies in permeability as shown in Figure 5, there are certain relatively low permeability layers that restricts the upwind migration of CO₂ with heterogeneity ${\sigma }_Y^2=4.0$. It can be observed from the second column in Figure 6 that the CO₂ preferentially migrates along the horizontal layer, without accompanying the vertical migration. While for the first column in Figure 6, the CO₂ migrates along the horizontal layers in the early injection period ($t\le 0.4t^{\ast }$), and CO₂ continue to transport horizontally and gradually migrate upwind to the top of the reservoir due to buoyancy forces in the late injection stage ($t\ge 0.4t^{\ast }$). It is indicated that permeability heterogeneity is the primary factor influencing the spatial mobility and distribution of CO₂ injection.

4.4. Effect of Heterogeneity and Gravity Index

Figure 7, Figure 8 and Figure 9 show the spatial distribution of the effective saturation ($S_{ge}$) and mass fraction of aqueous CO₂ in brine ($X_l^C$) at the end of the injection ($t=1.1t^{\ast }$). The influences of heterogeneity and gravity index on CO₂ migration are compared for the simulated cases.

For homogenous formation, the low viscosity CO₂ tends to migrate to the top of the geological structure due to the density difference between the CO₂ plume and the brine for Cases 1, 2, and 3. During the upward migration of the CO₂ plume, a large amount of gas phase migrates to the top of the aquifer due to buoyancy forces. The effective saturation at the top of the formation is relatively higher than that of the lower formation. It can be seen from Cases 1, 2, and 3 that mass injection rate or the gravity index has obvious influence on CO₂ plume migration. The higher the CO₂ injection rate, the farther the CO₂ plume migration. The CO₂ migration sketch is approximately proportional to the CO₂ injection rate. The variation of the mass fraction of aqueous CO₂ in brine shows a similar trend.

For the multilayered formation, gravity index and heterogeneity are the two predominant factors controlling CO₂ plume migration. For the bigger gravity index such as $G=5.6$, gravity index is the dominant factor controlling CO₂ migration, as illustrated in Figure 7. When the formation heterogeneity is relatively small (${\sigma }_Y^2\le 1$), the distribution and mobility of CO₂ migration are almost identical at the end of the injection. While ${\sigma }_Y^2=4$, there are some low permeability layers that impedes the vertical flow of CO₂ migration. The CO₂ migrates laterally along the preferentially high permeability layers away from the injection wells. The CO₂ migration distance is almost the same for Cases 3, 4, 5, and 6 at a relatively small injection rate. For the medium gravity index such as $G=1.8$, the influence of heterogeneity is increasing. When ${\sigma }_Y^2\ge 1$, the distribution and mobility of CO₂ migration is discontinuous due to the permeability heterogeneity. For smaller heterogeneity such as ${\sigma }_Y^2=0.3$, the effective gas saturation is almost the same as that of the homogenous formation. The gravity index and heterogeneity could influence the upward and lateral migration of the CO₂ plume at the medium injection rate. For the smaller gravity index such as $G=0.6$, formation heterogeneity is the key factor influencing CO₂ distribution. CO₂ migrates laterally along the high permeability layers, and the corresponding lower permeability layers obstruct the upward migration of the CO₂ plume. The farther the CO₂ migration, the bigger the permeability variance ${\sigma }_Y^2$. It is suggested that with the increase of heterogeneity variance ${\sigma }_Y^2$, horizontal flow paths are generated and the heterogeneity characteristics of effective saturation become more obvious. The existence of high permeability layers in the multilayered formation is conducive to CO₂ storage. The larger the permeability variance ${\sigma }_Y^2$ is at field level, the more CO₂ will be constrained underground during CO₂ storage.

4.5. CO₂ Dissolution Efficiency

Carbon dioxide dissolution efficiency $\eta$ is the mass quantification of CO₂ dissolved into brine with respect to the CO₂ injected into the formation per unit of time, as shown in:

$$\eta \left(t\right)=\frac{M^{\prime }\left(t+\mathsf{\Delta }t\right)-M^{\prime }\left(t\right)}{M\left(t+\mathsf{\Delta }t\right)-M\left(t\right)}$$

(31)

where $M^{\prime }\left(t\right)$ and $M\left(t\right)$ are the mass of the CO₂ dissolved into the brine and the total CO₂ injected into the well at time $t$, respectively; $\mathsf{\Delta }t$ is the time step. The CO₂ dissolved into the brine is indirectly calculated from the undissolved gaseous state as follows:

$$\eta \left(t\right)=\frac{Qt-\sum _i{\left[\phi V_i{S}_g{\rho }_g{X}_g^C\right]}^t}{Qt}$$

(32)

where $Q$ is the mass injection rate of CO₂; $V_i$ is the volume of the $i$-th grid cell; and $X_g^C$ is the mass fraction of CO₂ in gaseous state.

Figure 10 shows the temporal evolution of CO₂ dissolution efficiency in brine during $t=1.1t^{\ast }$, and the effects of gravity index and heterogeneity on CO₂ dissolution efficiency are investigated. It can be observed from the first column in Figure 10 that the gravity index has a prominent influence on CO₂ dissolution efficiency. The higher the gravity index, the more CO₂ is dissolved in brine. CO₂ is more likely to dissolve in brines at a lower injection rate. For homogenous formation, the CO₂ dissolution efficiency is lower than that of the heterogeneous stratum at the same gravity index and the permeability heterogeneity is more conducive to CO₂ dissolution. When the gravity index is relatively bigger such as $G=5.6$, the formation is gravity controlled and the influence of permeability heterogeneity on CO₂ dissolution efficiency is not obvious. For bigger and medium gravity indices ($G\ge 1.8$), the CO₂ dissolution efficiency increases with the increase of heterogeneity coefficient ${\sigma }_Y^2$, and tends to achieve a stable value. As seen from $G=0.6$ in Figure 10, with the increase of the heterogeneity coefficient ${\sigma }_Y^2$, the curve of CO₂ dissolution efficiency is also gradually increasing at the same time. The second column in Figure 10 shows that the permeability heterogeneity is the decisive factor in determining the finial CO₂ dissolution efficiency. The dissolution curve shows a decreasing trend during CO₂ injection. During the initial injection period, the dissolution curve with the higher gravity index is relatively higher, and then the gaps between these curves become smaller and smaller, approaching a constant value. It should be noted that the CO₂ dissolution efficiency curve with the maximum gravity index ($G=5.6$) is slightly higher for CO₂ injection processes.

5. Conclusions

In this paper, sequential Gaussian simulation is adopted to construct the multilayered saline formations, and two-phase flow based on MRST is developed to investigate the spatial mobility and distribution of CO₂ being injected into the multilayered reservoir. The main conclusions are as follows:

(1)

The permeability heterogeneity is the primary factor influencing the spatial mobility and distribution of CO₂ injection. Heterogeneity variances ${\sigma }_Y^2$ is considered to be an ideal representation of reservoir permeability.

(2)

For the formation with the smaller heterogeneity, the upwind and lateral migration of the CO₂ plume is relatively more uniform around the injection well. For the bigger heterogeneity, CO₂ preferentially migrates along the horizontal layer without accompanying the vertical migration.

(3)

For the formation with the bigger gravity index, gravity index is the dominant factor controlling CO₂ migration. For the medium gravity index, the upward and lateral migration of the CO₂ plume is determined by the gravity index and heterogeneity. For the smaller gravity index, formation heterogeneity is the key factor influencing CO₂ distribution.

(4)

The dissolution curve shows a decreasing trend during CO₂ injection. The dissolution curve with the higher gravity index is relatively higher at the initial injection period and the gap difference between dissolution curves approaches to a constant value. The permeability heterogeneity is the decisive factor in determining the finial CO₂ dissolution efficiency.

(5)

From a practical point of view, most GCS field sites operate under $G\ll {\sigma }_Y^2$. It is suggested to store CO₂ in formations with relatively larger heterogeneity coefficient ${\sigma }_Y^2$.

(6)

Reactive 3-Phase flow model for geological sequestration is considered for future research. It will be a more sophisticated analysis of the GCS, incorporating the chemical reaction among aqueous species and rock-forming minerals, as well as the partition between gaseous CO₂ phase and liquid brine phase.