Microscopic Flow of CO₂ in Complex Pore Structures: A Recent 10-Year Review

1. Introduction

Because of the increasing greenhouse effect as well as acute global climate and environmental problems, countries worldwide have reached a consensus to actively respond to climate change and reduce greenhouse gas emissions [1,2,3,4,5]. As industrialization has continued since the industrial revolution, the use of fossil fuels has been increasing, and large amounts of CO₂ gas have been directly discharged into the air, which is one of the main reasons for the intensification of the greenhouse effect [6,7,8,9]. CO₂ emissions have caused a series of environmental problems, such as drought, glacier melting, and sea level rise, which have caused incalculable harm to the environment on which human beings depend [10]. At present, many technologies are available to control CO₂ emissions, such as improving the efficiency of fossil energy combustion, efficient development and utilization of green and clean energy, and carbon capture and storage (CCS) [11]. CCS refers to the use of separation and purification technology to collect a large amount of CO₂ from industrial waste gas and inject it into appropriate underground reservoirs for permanent storage [12,13], which is recognized as one of the effective methods to manage CO₂ [14,15,16,17]. The main storage geological layers include abandoned mines, unrecoverable coal seams, depleted oil and gas fields, deep saline aquifers, and the ocean [18,19,20]. The storage depth is generally below 800 m. CO₂ geological storage is the most important part of CCS, and the storage capacity and safety of geological storage bodies determine the effectiveness of CO₂ emission control [21]. However, the complexity [22], heterogeneity, and wettability of the pores directly affect the flow behavior of CO₂ in reservoirs. Therefore, investigating the CO₂ flow law and revealing the CO₂ microscopic flow mechanism have become key to evaluating the storage capacity and safety of geological storage bodies.

Numerous studies have been conducted on the flow of CO₂ in geological storage bodies. Lassen et al. [23] injected gaseous CO₂ into heterogeneous porous media at different rates, and the flow of CO₂ was monitored by sensors. The results showed that large-scale heterogeneity controlled the overall migration of gaseous CO₂ in porous media, whereas a smaller scale was important for gas saturation. The higher the injection rate, the larger the transverse diffusion of the gas phase. Zhang et al. [24] proposed that Darcy’s law can be used to describe two-phase fluid flow in porous media at the macroscopic scale. Saleem et al. [25] compared and verified the constructed two-phase flow model with field observation data, such as CO₂ eruption time, changes in sediment pH, gas leakage rate, the flow process, fluid interaction, and CO₂ dissolution in the CO₂ plume. The results showed that the CO₂ plume was formed and developed at a stable rate during the flow process, and the dissolution rate increased with an increase in the injection rate. These studies elucidated the flow of CO₂ from a macroscopic perspective. However, the flow behavior of CO₂ in a storage body is easily affected by its complex pore structures. In macroscale research, the complex pore structures of the storage body has not been accurately characterized. The research results are also based on macroscale flow and often ignore the effect of pore structure complexity. Therefore, an accurate description of the microscopic flow of CO₂ is crucial for determining the storage capacity and long-term safety [26,27,28].

X-ray Computed Tomography (CT) and Nuclear Magnetic Resonance (NMR), as non-invasive, non-destructive advanced imaging technologies [29,30], have the advantage of being able to reconstruct the complex pore structures of cores [31,32] and obtain key parameters, such as porosity, permeability, contact angle, and capillary number. Visualization and quantitative characterization of the complex pore structures at the microscopic scale can be realized [11]. Berg and Dalton et al. [33,34] obtained an accurate complex pore structures of sandstone and investigated the effects of permeability and wettability on CO₂ flow behavior. Liu et al. [35,36] first used a new reconstruction method to establish the fracture-controlled matrix unit then used the CT scanning technique to obtain the relevant parameters of the proposed fracture control matrix unit mass transfer model. The correctness of the model was verified by comparison with the experimental results of microscopic spontaneous imbibition. Liu et al. [37,38] studied the dynamic production process of a fractured reservoir and the influence of a complex pore structure on the imbibition recovery based on a fracture-controlled matrix unit. Liu et al. [39] performed microscopic spontaneous imbibition experiments, CT scans, and NMR tests on two mixed wetted core samples. The impact of mixed wettability on micro-spontaneous imbibition at the pore scale was investigated. The results showed that effective imbibition can be produced as long as water-wet walls are present in mixed wettability pores. Furthermore, a core-scale mixed wettability model was established by Liu et al. [40], and based on the phase-field theory, the influence of wettability on oil-water two-phase imbibition was studied. In addition, Liu and Song et al. [41,42] proposed two new modeling methods based on CT scanning: the finite volume element modeling method (Figure 1a) and the pore network model based on the maximum sphere algorithm (Figure 1b). The feasibility of the model was verified.

In addition, experts have conducted several theoretical and numerical simulations on the flow mechanism of CO₂ at the macroscale. Krause et al. [43] carried out a numerical simulation study of CO₂-brine two-phase flow using the modified Carman-Kozeny equation. The distribution of CO₂-brine in the core was predicted. Theoretical studies and numerical simulations at the macroscale play a crucial role in revealing the flow mechanism of CO₂. However, the complex pore structures have a very important effect on CO₂ microscopic flow. The lack of mathematical and numerical models that consider the influence of pore structure complexity and may lead to bias in the conclusions.

Figure 1. The new modeling method based on CT images: (a) Images of reconstructed porous samples in finite volume elements of pore space (b) EPNMs of rock samples [41,42]^.

Figure 1. The new modeling method based on CT images: (a) Images of reconstructed porous samples in finite volume elements of pore space (b) EPNMs of rock samples [41,42]^.

To this end, we collated and analyzed relevant literature on the microscopic flow of CO₂. In particular, the complex pore structures substantially affected the CO₂ microscopic flow mechanism. At present, experimental methods, theoretical analysis, and numerical simulations are advanced owing to the pore structure complexity of geological storage bodies, which is difficult to accurately express in physical model reconstruction, mathematical model characterization, and numerical model construction. Therefore, it is challenging to clearly reveal the microscopic flow mechanism of CO₂ in a complex pore structure. To solve this problem, this study systematically reviews recent advances in the microscopic flow of CO₂ in complex pore structures in the last decade to provide some technical and theoretical support for CO₂ geological storage. Overall, this review article focuses on the effects of complex pore structures on the microscopic flow behavior of CO₂ through three aspects: experimental studies, theoretical studies, and numerical simulations. It aims to enhance the current understanding of the CO₂ microscopic flow mechanism. Finally, potential challenges and new research directions for future work are identified and elucidated.

2. Flow experiments of CO₂ in complex pore structures

A large number of experiments have been carried out to study the microscopic flow of CO₂ in pore structures, and fruitful results have been achieved. This section introduces the research progress of the microscopic flow mechanism of CO₂ from four different aspects through analysis of the relevant literature.

2.1. Traditional characterization of pore structures during CO₂ microscopic flow

Mercury intrusion porosimetry (MIP) [44,45,46], scanning electron microscopy (SEM) [47,48], and gas adsorption [49,50,51] have been used to characterize the pore structures of the storage body and further explore the flow of CO₂. Du et al.[52] used high-pressure mercury intrusion and permeation experiments to investigate the effect of CO₂ injected into coal. The results showed that the reaction between CO₂-water and coal led to an increase in pore space and greatly increased permeability, which increased the permeability area of CO₂ and improved the CO₂ storage capacity. Using SEM, Khather et al.[53] observed that the decrease in pH during CO₂ injection caused the dissolution and migration of minerals, which resulted in an increase in rock permeability and the flow capacity of CO₂. Pearce et al.[54] studied the physical properties of the reservoir after CO₂ injection by SEM and found that the movement of fine particles may result in opening or blocking of the pores during CO₂ injection, increasing or decreasing permeability, and affecting CO₂ injection capacity. Brattekas and Haugen [55] used high-resolution micro-positron emission tomography (micro-PET) and radiotracers to achieve CO₂ tracing during flow and capillary capture. The results showed that CO₂ mainly flowed into the outer part of the core with high permeability.

However, these techniques have many limitations in accurately characterizing the pore structure complexity in rocks. For example, MIP can only obtain the total porosity of the sample and cannot characterize the complexity of the pore distribution within the sample. SEM is an effective technique for generating 2D images of microstructures. However, it cannot provide 3D images, which are important for evaluating the pore structure complexity [11]. More importantly, traditional characterization methods cannot visualize and quantitatively describe the microscopic flow of CO₂. Therefore, to accurately reconstruct the 3D complex pore structures and visually and quantitatively study the microscopic flow mechanism of CO₂ in the geological storage body, it is necessary to use advanced techniques, such as CT scanning and NMR, to conduct in-depth analysis using multidisciplinary intersection research ideas.

2.2. Effects of porosity and permeability characteristics on the microscopic flow mechanism of CO₂

The influence of key parameters, including porosity and permeability, on CO₂ flow in geological storage bodies is very important. By simulating 2D fluid flow experiments, Kitamura et al.[56] found that the flow behavior of CO₂ is strongly influenced by the small-scale heterogeneity of the pore structures. However, the simulation results have some errors because the model is 2D and cannot fully describe the pore structure complexity. To investigate the effect of the reservoir laminar structures on the flow behavior of CO₂, Krishnamuthy et al.[57] used the CT scanning technique to observe the flow path of CO₂ by measuring the CO₂ saturation variation in the rock. The results showed that CO₂ would preferentially flow through the region with larger porosity and pass unevenly along the axial direction (Figure 2). However, seepage under in situ conditions was not considered, thus the pore distribution of reservoir cores under in situ conditions could not be obtained. To accurately study the CO₂ microcosmic flow. Wang et al.[58] injected liquid CO₂ into a brine-saturated core. Multiscale CT scanning of sandstone was conducted, and the distribution of porosity at different locations of the core under in situ flow conditions was obtained. The phenomenon of CO₂ preferentially passing through the locations with higher porosity was observed from the images. Al-Bayati et al.[59] conducted a displacement experiment on stratified core samples using the CT scanning technique, and Figure 3 shows 2D images of fluid distribution in the XY direction of the stratified samples before and after CO₂ displacement. As illustrated in the figure, CO₂ first bypasses the low-permeability layer, leaving a large amount of oil to preferentially enter the high-permeability layer. Owing to the occurrence of the cross-flow phenomenon, CO₂ is transferred from the high- to the low-permeability layer.

Figure 2. Vertical stacked cross-section slices of CO₂ saturation computed from CT data [57]^.

Figure 2. Vertical stacked cross-section slices of CO₂ saturation computed from CT data [57]^.

Figure 3. 2D images in the XY direction of fluid distribution before and after CO₂ flooding: (a) with cross-flow (b)without cross-flow [59]^.

Figure 3. 2D images in the XY direction of fluid distribution before and after CO₂ flooding: (a) with cross-flow (b)without cross-flow [59]^.

A clay interlayer, one of the typical representatives of a low-permeability layer, has an important influence on CO₂ flow. Using CT scanning, Xu et al.[60] studied the flow characteristics of CO₂ in a special sandstone containing multiple thin clay interlayers. The experiment demonstrated that the flow channel of CO₂ was mainly established in the sandstone, and the clay interlayer hindered CO₂ flow. However, the description of how the CO₂ flow was hindered by the clay interlayer was too vague. Therefore, Xu et al.[61] further monitored the flow process of CO₂ in the interior of the clay interlayer sample (Figure 4). When the injection direction was parallel to that of the clay interlayer, the clay interlayer separated the CO₂ flow (Figure 4a). When the injection direction was perpendicular to that of the clay interlayer, the clay interlayer hindered the CO₂ flow forward (Figure 4b).

Figure 4. Image of CO₂ distribution during sample drainage: (a) parallel injection (b) vertically injection [61]^.

Figure 4. Image of CO₂ distribution during sample drainage: (a) parallel injection (b) vertically injection [61]^.

2.3. Two-phase flow law in CO₂ microscopic flow

When CO₂ is injected into the deep brine layer, it enters the reservoir pore structures to displace the original fluid from the pore space, and the flow process is an immiscible two-phase flow [29]. However, it is difficult to observe the space-time variation of the two-phase interface between immiscible two-phase fluids in porous media. Therefore, immiscible two-phase flow must be understood from a pore-scale perspective, which is very important and extremely complex [62].

Using the CT scanning technique, Kogure et al.[63] injected CO₂ into the Berea sandstone at different times in opposite directions, and the flow behavior of CO₂ in the Berea sandstone was observed. The images show several narrow pore throats that allow CO₂ flow. Despite injection from opposite directions, the distribution of CO₂ is essentially the same in the final stage of injection (Figure 5). Liu et al.[64] injected CO₂ into a glass bead bed in both the upward and downward directions, and a displacement saturated water experiment was conducted to investigate the distribution of CO₂ in the core. As shown in Figure 6, the displacement effect of CO₂ injected downward was substantially better than that of CO₂ injected upwards (Figure 6b). This is attributed to the "gas channeling" phenomenon when CO₂ is injected upward, but the cause of the "gas channeling" phenomenon was not discussed in depth. Lv et al.[65] combined the CT scanning technique and a micromodel to study the flow process of CO₂-brine in the pore structures at different injection rates under static and transient conditions. The results showed that a higher injection rate gives rise to a higher displacement efficiency but a lower sweep efficiency. Further, using NMR technique, Teng et al.[66] found that the different viscosities and densities of CO₂ and water caused the "gas channeling" phenomenon of CO₂, which led to the premature breakthrough of CO₂ and reduced the displacement efficiency. In addition, Zhang et al.[24] obtained the local porosity and saturation of Berea sandstone. The results showed that the forward movement of CO₂ on the capillary pressure is the main reason for the formation of the pathway of CO₂ flow. CO₂ preferentially passes through the large-sized pores, and the seepage zone gradually expands whereas the CO₂ saturation increases.

The influence of pore geometry on the microscopic flow mechanism of CO₂ cannot be ignored. Zhang et al.[67] used CT scanning to scan the displacement process of CO₂ and found that CO₂ was unevenly distributed in sandstone samples. A larger flow patch was formed during the flow process. Herring et al.[68] adopted the Bentheimer sandstone core and used the CT scanning technique to observe the displacement process of CO₂ at the pore scale. The images show that CO₂ invaded the pore space in a capillary fingering regime (Figure 7). Liu et al.[69] visualized and quantitatively analyzed the dynamic diffusion process of CO₂ in n-decane-saturated porous media. The results showed that the channels of the porous media hindered the diffusion of CO₂. The local diffusion coefficient of CO₂ gradually decreased with time along the diffusion path until it reached a steady state.

Figure 5. X-ray CT images of distribution of scCO₂ in Berea sandstone [63]^.

Figure 5. X-ray CT images of distribution of scCO₂ in Berea sandstone [63]^.

Figure 6. 3D image of CO₂ distribution in displacement process and analysis of up-and-down displacement efficiency [64]^.

Figure 6. 3D image of CO₂ distribution in displacement process and analysis of up-and-down displacement efficiency [64]^.

Figure 7. 3D, 2D and 2D closer view overlain on the original grayscale image of CO₂ within sandstone [68]^.

Figure 7. 3D, 2D and 2D closer view overlain on the original grayscale image of CO₂ within sandstone [68]^.

2.4. Microscopic flow of CO₂ in different phase states

In geological storage, appropriate CO₂ phase states, including gaseous, liquid, and supercritical, should be selected according to the specific conditions and requirements of the storage body for injection. The CT scanning technology has been used to conduct extensive research on the microscopic flow of CO₂ in different phase states. CO₂ bubbles, a typical representative of the gaseous state, have a stable state in porous media with a high resistance factor (i.e., good plugging capacity), which plays a very important role in the safety of long-term storage of CO₂ [70,71,72]. Xue et al.[73] found that microbubble CO₂ injection can minimize the content of free CO₂ in the reservoir compared with that of conventional CO₂ injection and can also efficiently utilize the pore space of the reservoir, which is conducive to the long-term safety of large-scale CO₂ storage. Patmonoaji et al.[74] and Zhai et al.[75] conducted displacement experiments in sandstone and found that microbubble flow has a stronger sweeping efficiency than that of conventional flow, which can improve the displacement efficiency and storage capacity of CO₂.

The experimental results proved that CO₂ foam can not only improve oil and gas recovery compared with conventional CO₂, but also improve pore space utilization and increase CO₂ storage in the reservoir. Accordingly, Du et al.[76] further investigated the seepage characteristics of CO₂ bubbles in porous media. However, the experimental object was self-made homogeneous porous media, whereas most of the actual reservoir is composed of heterogeneous rocks; thus, the experimental results have some limitations. For this reason, McLendon et al.[77] injected CO₂ with and without a surfactant into real Berea sandstone under high-pressure conditions to observe in situ bubble generation. The results showed that CO₂ tended to pass through the high-permeability reservoir without the addition of surfactant but resulted in a decrease in the sweep efficiency of CO₂. Du et al.[78] studied the dynamic bubble flow behavior in the entrance region of porous media and obtained dynamic three-phase saturation distributions along the sample core. The results showed that the CO₂ bubble could push most of the liquid phase into the latter part of the porous media, but the forepart was difficult to push, showing an obvious entrance effect.

The above studies investigated the microscopic flow of single-phase CO₂. However, it is unusual that there is only CO₂ in the actual storage body, and two or multiphase may be present. Therefore, it is essential to further study the microscopic flow of CO₂ under the condition of polyphase coexistence (including miscible, near-miscible, and immiscible phases). Alhosani et al.[79] conducted an in situ study on immiscible-phase CO₂ displacement in oil-wet reservoirs. The images show that in strongly oil-wet rocks, the largest pore space was occupied by water, the smallest pore space was occupied by oil, and the medium-sized pore space was occupied by CO₂ (Figure 8a). CO₂ was distributed in a connected layer under near-miscible phase conditions (Figure 8b) and existed as separated "ganglia" in medium-sized pores under immiscible phase conditions (Figure 8c). Qin et al.[80] conducted a study on the wettability and spatial distribution of near-miscible phase CO₂ in oil-wet carbonate rocks under high temperature and pressure. The results showed that at the initial stage of injection, CO₂ had good connectivity with the oil phase and poor connectivity with the brine phase. With the continuous injection of CO₂, the wettability reversal process was triggered, resulting in a decrease in the oil wettability and an improvement in the CO₂ connectivity with brine. Hao et al.[81] conducted multiphase and multiple injection experiments. It was found that under the immiscible phase condition, the porous media showed remarkable gas coverage and flow stratification owing to gas buoyancy. The miscible-phase CO₂ injection eliminated the effect of buoyancy, thus expanding the storage area and flow range of CO₂.

The reliability of CO₂ geologic storage depends on the flow mechanism of CO₂ in reservoirs. With the help of advanced imaging techniques, such as CT scanning and NMR, in experimental studies, it is beneficial to study the microscopic flow mechanism of CO₂ in complex pore structures. However, few studies have used CT scanning and NMR technology to carry out real-time visualization and quantification research on the microscopic flow process of CO₂. In addition, microscopic flow studies of CO₂ in complex pore structures with multiphase are not sufficiently comprehensive, which is the focus of future research.

Figure 8. 2D and 3D images of a trapped water ganglion in a single pore: (a) segmented pore scale images (b) immiscible condition (c)near-miscible condition [79]^.

Figure 8. 2D and 3D images of a trapped water ganglion in a single pore: (a) segmented pore scale images (b) immiscible condition (c)near-miscible condition [79]^.

3. Theoretical model of CO₂ flow in pore structures

Theory is the cornerstone of all experiments and numerical simulations, and continuous improvement of the theory is the premise of studying the microscopic flow mechanism of CO₂. Darcy’s law [82] is one of the classical theories describing the macroscopic flow law of fluid in porous media, which is applicable to single- and multiphase fluid flow in loose sand columns, consolidated sandstone, and other dense porous media [83,84].

Zhang et al.[24] proposed Darcy’s law to describe two-phase fluid flow in porous media at the macroscopic scale:

$$q_{\alpha }=-\frac{k{k}_{r\alpha }}{\mu }(\nabla P)$$

(1)

where q is the flow flux, m³/s; k is the absolute permeability, m²; k_r is the relative permeability, μ is the viscosity of a fluid, Pa·s; ∇P is the pressure gradient, Pa; and α=1 and 2 are the two phases of a fluid.

Berg et al.[33] used Darcy’s law for two-phase flows to establish a mathematical model. The migration and mass transfer behaviors of saturated and unsaturated CO₂-brine system in sandstone were studied. The governing equations are as follows:

$$\phi \frac{\partial S_i}{\partial t}+\nabla \cdot \overrightarrow{v_i}=0$$

(2)

$$\overrightarrow{v_i}=-\frac{k_{r,i}}{{\mu }_i}K(\nabla p_i-{\rho }_i\overrightarrow{g})$$

(3)

Equation (2) describes the mass balance of CO₂ and water. The saturation of the wetting phase (water or brine, i=w) and the non-wetting phase (CO₂, i=nw) satisfies S_w+S_nw=1. The flux of the phases$\overrightarrow{v_i}$is described by Darcy’s law extending to two-phase flow, m/s; where φ is the porosity, K is the absolute permeability of the rock, m²; μ_i is the viscosity of the fluids, Pa·s; ρ_i is the density of the fluids, kg/m³; and g is the gravity constant, m/s².

However, in the process of CO₂ displacement, it is difficult to accurately capture the spatiotemporal variation of the interface of an immiscible two-phase fluid in the pore structures. For this reason, Porter et al.[85] redefined the simple expression of pressure in the absence of CO₂ gas, considering the pressure drop caused by flow and heterogeneity, which can reliably predict the position of the single-phase to multiphase flow transition:

$$P_{cr}=P_{sat}+\frac{\mu q(L-Z_p)}{k_{eff}}$$

(4)

where P_cr is the critical pressure, Pa; P_sat is the hydrostatic pressure, Pa; μ is the viscosity of water, Pa·s; q is the injection rate of CO₂ saturated water, m/s; L is the location of the bottom of the porous media, mm; Z_p is the location of the top of the porous media, mm; and k_eff is the vertical (harmonic) averaged effective permeability, m².

So far, Darcy’s law has successfully solved many CO₂ geological storage safety problems [86,87,88]. However, it also has some limitations; for example, in the case of high velocity flow, high Reynolds number (Re), and nonlinear flow, turbulent flow will occur in the complex pore structures, and Darcy’s law is no longer applicable. Therefore, many scholars have proposed the use of the extended form or combined with the actual situation to appropriately modify Darcy’s law to study single-phase CO₂ flow, CO₂-brine, or other miscible or immiscible flow behaviors at the pore scale.

Kogure et al.[63] proposed the extended Darcy’s law to calculate the relative permeability of porous sandstone in the CO₂-water system at the sub-core scale, and the flow behavior of CO₂ was studied:

$$Q_i=k_{ri}{k}_{abs}\frac{A}{{\mu }_i}(\frac{\Delta P}{L}-{\rho }_{i}g)$$

(5)

where Q_i is the flow rate of each fluid, m³/s; k_ri is the relative permeability, k_abs is the absolute permeability, m²; A is the cross-sectional area of the sample, m²; L is the length of the sample, m; ΔP is the pressure difference of the sample, Pa; μ_i is the viscosity of the fluid, Pa·s; ρ_i is the density of the fluid, kg/m³; and g is the acceleration of gravity, m/s².

However, the above scholars first determined the permeability of a complex pore structure based on Darcy’s law, then the flow behavior of CO₂ in the complex pore structures was studied, a very complicated process. Therefore, Wang et al.[89] used the extended form of Darcy’s law to describe the flow behavior of CO₂-water in the pore structures:

$$v_{\alpha }=-\frac{K{k}_{r\alpha }}{{\mu }_{\alpha }}(\nabla p_{\alpha }-{\rho }_{\alpha }g)$$

(6)

where v denotes the Darcy velocity, m/s; K is the intrinsic permeability tensor, m²; k_r is the relative permeability of the fluid phase, μ denotes the viscosity, Pa·s; ρ represents the density, kg/m³; P represents the pressure of the fluid phase, Pa; and g is the gravity vector, m/s².

Besides Darcy’s law, the microscopic flow of CO₂ can be effectively calculated based on the Young-Laplace law and Navier-Stokes equation. Chapman et al.[90] used the Young-Laplace law to calculate the displacement sequence in the node of the pore network model for predicting CO₂ displacement. The governing equation is as follows:

$$P_c=2\gamma \cos \theta (\frac{1}{h}+\frac{1}{w})$$

(7)

P_c is the capillary pressure, Pa; γ is the interfacial tension, N/m; θ is the contact angle, °; h is the height of the channel, mm; and w is the width of the channel, mm.

Ovaysi and Piri [91] simulated the microscopic flow of CO₂ in a deep saline solution as follows:

$$\frac{Dv}{Dt}=-\frac{1}{\rho }\nabla P+\frac{\mu }{\rho }{\nabla }^{2}v+g$$

(8)

$${\nabla }^2=0$$

(9)

where v is the velocity vector, m/s; μ is the viscosity, Pa·s; ρ is the density, kg/m³; g is the gravity vector, m/s²; and P is the pressure, Pa.

Although many theoretical models have been used to reveal the flow mechanism of CO₂ in complex pore structures, some existing mathematical equations have weak universality. In particular, CO₂ reacts with other fluid phases and pore surfaces during the flow process, resulting in pore structures damage and changes in the flow of CO₂. In conclusion, theoretical models considering wettability and damage effects are rare; therefore, it is necessary to further study the flow theory of CO₂ considering wettability and damage theory in complex pore structures.

4. Numerical simulation of CO₂ flow in pore structures

Numerical simulation experiments on complex pore scales have become an effective tool for studying the flow of CO₂ in pore structures, which can impose conditions that cannot be reached by experimental methods, provide insight into the main processes of multiphase fluid flow in the storage body, obtain complete parameters of the flow process, and conduct systematic and accurate analysis. By comparing the experimental results with theoretical analysis, more comprehensive and objective conclusions can be obtained. At present, a variety of pore-scale simulation methods have been developed for CO₂ flow in porous media, including the Lattice Boltzmann Method (LBM) and Pore Network (PN) model [92].

4.1. Numerical simulation based on LBM

Computational Fluid Dynamics (CFD) [93], a traditional numerical simulation method for simulating fluid flow in porous media, has received considerable attention because of its simple algorithm, good conservation, and ability to handle complex geometric shape problems [94,95,96]. However, the traditional CFD method has some problems, including a large computational volume, low computational accuracy, difficulty in dealing with complex equations, and simple boundary conditions. To solve these problems, scholars [97,98,99] proposed adopting the LBM method to conduct CO₂ microscopic flow numerical simulations. Compared with the traditional CFD method, the LBM method can be programmed on a computer system with parallel processing capability. It has the advantages of easy handling of complex boundaries, simple description of fluid interactions, high computational efficiency, and high numerical accuracy, making it suitable for simulating the CO₂ flow in porous media at the pore scale. Therefore, gradually replacing the traditional CFD method is a promising research method.

Various types of multiphase multicomponent LBM models, including color models and phase field models, have been developed based on the description of different component interactions. Liu et al.[92] improved the LBM color fluid model to simulate the displacement of CO₂ to water in a double-permeable pore network. It was found that the degree of directional flow and flow behavior of CO₂ depend on the capillary number, as shown in Figure 9, which is consistent with the experimental results of Chang et al.[100]. To improve the accuracy of the simulation results, Jiang and Tsuji [31] introduced color function thresholds, velocity fields, and Neumann boundary conditions to construct a novel LBM numerical simulation method for pore-scale CO₂ displacement simulations. The results showed that reducing the initial CO₂ connectivity and sphericity index can reduce the CO₂ mobility rate and improve the capillary trapping capacity of CO₂.

Figure 9. Final fluid distribution in a random heterogeneous system: (a) logCa=-4.36, (b) logCa=-4.16, (c) logCa=-4.06, (d) logCa=-3.59, (e) logCa=-3.36, (f) logCa=-3.06 [92]^.

Figure 9. Final fluid distribution in a random heterogeneous system: (a) logCa=-4.36, (b) logCa=-4.16, (c) logCa=-4.06, (d) logCa=-3.59, (e) logCa=-3.36, (f) logCa=-3.06 [92]^.

However, the disadvantages of the color gradient model are also obvious, because it is not applicable to heterogeneous pore structures with real density and viscosity ratio of CO₂-brine. Therefore, Fakhari et al. [101] developed a phase field-based LBM and verified that the model could accurately simulate the multiphase flow characteristics of heterogeneous porous media at the pore scale through experimental comparison. Bakhshian et al. [102] used a multiphase LBM model to simulate the flow of CO₂-brine in Tuscaloosa sandstone rock. The results showed that heterogeneous CO₂ wettability led to a more dispersed fluid distribution and more tortuous CO₂ flow paths (Figure 10), and the residual trap of CO₂ increased with the increase in CO₂-wet regions. Guo et al. [103] studied the effect of the surface contact angle of Bentheimer sandstone on two-phase flow in porous media after the completion of CO₂ displacement. The results showed that the heterogeneity of wettability has a substantial impact on the relative permeability of CO₂. An immiscible phase displacement process in the CO₂-water-rock system was simulated by Guo et al. [104] and Atia et al. [105]. The obvious local CO₂ and water redistribution phenomena were caused by the heterogeneity of the pore-scale surface wettability under low water-wetting conditions while enhancing the aggregation or diffusion behavior of CO₂.

In addition, Wang et al. [106] proposed the multi-relaxation time lattice Boltzmann method (MRT-LBM) to simulate the diffusion and miscible phase flow of a CO₂-oil system in porous media at the pore scale. The results showed that CO₂ could diffuse into the oil phase more easily from regions that are relatively attractive to CO₂ and repulsive to oil in porous media.

Figure 10. 3D distribution of CO₂ in heterogeneous samples with different wettability [102]^.

Figure 10. 3D distribution of CO₂ in heterogeneous samples with different wettability [102]^.

4.2. Numerical simulation based on PN

The PN model [107,108] is designed to simplify the porous media model by connecting the pores with pore throats of the ideal geometry, which can improve computational efficiency. Benali et al.[109] developed a PN model with an extended visual field to study real-time bubble texture dynamics under high pressure. The results showed that continuous and rapid CO₂ injection can bubble with a low surface viscosity. A large number of bubbles remained on the pore surface of the storage body, which improved the flow of CO₂ in the pore structures. Liu et al.[110] developed a new two-phase steady-state model based on PN. The model considers the capillary and viscous forces in the pore structures and proved a stronger seepage effect of CO₂ than that of brine. Cao et al.[111] used a high-pressure microscopic model and a PN model to simulate the displacement phenomenon during CO₂ injection into a saturated brine reservoir. The results showed that CO₂ has a better injection efficiency and capillary trap capability in regions with larger porosity.

Wettability, an important factor controlling the flow of multiphase fluids in porous media, has a remarkable influence on the microscopic flow of CO₂ [112]. Hu et al.[112] used a PN model to study the effect of wettability on CO₂-brine displacement. The results showed that CO₂ has higher saturation, wider directivity, and a more compact displacement pattern under medium wetting conditions. In addition, the CO₂-brine interface is smaller, which inhibits the mutual mass transfer. Basirat et al.[113] developed a numerical model based on the phase-field method to study the effect of different wettability on the two-phase flow of CO₂ and brine at the pore scale. The results showed that the trapped wetting phase saturation and normalized interfacial area increase with decreasing contact angle. However, the wetting condition had no effect on the CO₂ breakthrough time and saturation.

The numerical simulations of the microscopic flow of CO₂ in complex pore structures have been extensively investigated. However, numerical simulation methods tend to simplify the pore structure complexity and wettability, which reflect the real in situ conditions of the geological storage body. Therefore, considering the pore structure complexity and complex mixed wettability conditions, the establishment of accurate numerical models of geological storage bodies, as well as the improvement of the numerical experimental computational rate and accuracy are the frontier issues in conducting CO₂ numerical simulations of microscopic flow in complex pore structures.

5. Conclusions and outlook

CO₂ flow is easily affected by reservoir complexity. The microscopic flow mechanism of CO₂ is the key to revealing the flow mechanism of CO₂ in the storage body, which is of great importance for evaluating the safety and effects of CO₂ geological storage. This article thereby provides a systematic and comprehensive review for the last decade on the microscopic flow of CO₂ in the complex pore structures by experimental research, theoretical research, and numerical simulation. Moreover, the understanding of the microscopic flow mechanism of CO₂ in the complex pore structures was improved. It can be elucidated that pore structure complexity substantially impacts the microscopic flow process of CO₂, and its influence on wettability and damage needs to be further explored.

By considering the real-time visualization technology, multiphase, multiscale, damage mechanism, and wettability, future research directions on the microscopic flow mechanism of CO₂ may be anticipated:

(1) Future studies should carry out real-time CT scanning experiments for CO₂ displacement in combination with the research and development of a CO₂ microscopic flow real-time CT scanning clamping device to realize real-time visualization and quantitative description of CO₂ flow behavior in complex pore structures.

(2) The flow mechanism of single-phase CO₂ in complex pore structures has been extensively studied, but few studies investigated the micro-flow mechanism of multiphase CO₂. It is suggested that more attention should be paid to the microscopic flow mechanism of multiphase CO₂ in complex pore structures in the future.

(3) CO₂ geological storage should meet the needs of long-term storage and wide range. It is suggested to explore the flow mechanism of CO₂ in complex pore structures at multiscale to realize the upgrading from micro, mesoscopic to macro scales, which is of great importance for evaluating the long-term safety of CO₂ geological storage.

(4) In the process of CO₂ flow, chemical reactions occur with the pore surface, and the dissolution or precipitation of minerals changes the pore structures, which has a non-negligible impact on the microscopic flow mechanism of CO₂. In the future, attention should be paid to the influence of changes in the pore structures caused by chemical reactions on the microscopic flow mechanism of CO₂. The effects of wettability and damage are considered in the theoretical model study.

(5) The characteristics of the complex pore structures and wettability model are simplified, which cannot reflect the actual in situ conditions of the geological storage body. In the future, attention should be paid to the pore structure complexity and complex mixed wettability conditions. In addition, an accurate pore network numerical model of the geological storage body should be established for numerical simulation. The calculation rate and accuracy of the numerical experiment should also be improved.