This article reports recent developments and advances in the simulation of the CO2-formation fluid displacement behaviour at the pore scale of subsurface porous media. Roughly, there are three effective visualization approaches to detect and observe the CO2-formation fluid displacement mechanism at the micro-scale, namely, magnetic resonance imaging, X-ray computed tomography and fabricated micromodels, but they are not capable of investigating the displacement process at the nano-scale. Though a lab-on-chip approach for the direct visualization of the fluid flow behaviour in nanoscale channels has been developed using an advanced epi-fluorescence microscopy method combined with a nanofluidic chip, it is still a qualitative analysis method.
Peng Hou1, Yang Ju1,3, Feng Gao1,2, Jianguo Wang2, Jian He1
1State Key Laboratory for Geomechanics & Deep Underground Engineering, China University of Mining & Technology, Xuzhou 221116, China. 2School of Mechanics & Civil Engineering, China University of Mining & Technology, Xuzhou 221116, China. 3State Key Laboratory of Coal Resources & Safe Mining, China University of Mining & Technology at Beijing, Beijing 100083, China.
Revised: 17 November 2016 / Accepted: 1 December 2016 / Published online: 4 January 2017
©The Author(s) 2017
The lattice Boltzmann method (LBM) can simulate the CO2 displacement processes in a two-dimensional or three-dimensional (3D) pore structure, but until now, the CO2 displacement mechanisms had not been thoroughly investigated and the 3D pore structure of real rock had not been directly taken into account in the simulation of the CO2 displacement process. The status of research on the applications of CO2 displacement to enhance shale gas recovery is also analyzed in this paper. The coupling of molecular dynamics and LBM in tandem is proposed to simulate the CO2-shale gas displacement process based on the 3D digital model of shale obtained from focused ion beams and scanning electron microscopy.
CO2, as one of the greenhouse gases, plays a key role in the cause of global warming, and its accumulation in the atmosphere is still increasing (Allen et al. 2014). As a result, CO2 mitigation has attracted increasing attention (Edenhofer et al. 2014). CO2 capture and sequestration (CCS) technology is an alternative to effectively reduce the CO2 emission in the short term (IEA 2013). Popularly, brine or saline aquifers, oceans, depleted oil reservoirs, and coal beds are considered potential geological formations for CO2 storage. For example, Fujii et al. (2010) and Zahid et al. (2011) argue that saline aquifers are the most viable alternative to store CO2 because they possess the greatest potential for carbon storage and wide geographical spread. Other studies suggest that CO2 is a working fluid that can be used to enhance oil recovery (EOR) and natural gas recovery (EGR) (Hughes et al. 2012; Liu et al. 2015a, b; Middleton et al. 2015). Injecting CO2 into oil or gas reservoirs is promising because it can also offset the costs of CCS (Koide et al. 1992; Blunt et al. 1993; Gunter et al. 1997).
When CO2 is injected into a deep geological formation in the liquid or supercritical state, it will cause large volumes of formation fluids such as oil, water (brine) or natural gas to be physically displaced (Kazemifar et al. 2016; Wang et al. 2013; Zhang et al. 2011b). In the CO2 displacement process, the major concern is the primary CO2 plume migration, which is closely related to how much CO2 can be stored in the respective porous subsurface sedimentary formation, the displacement efficiency of the oil/gas and the security of the stored CO2 (Berg and Ott 2012; Chen and Zhang 2010; Song et al. 2014). Therefore, a better understanding of the displacement mechanisms of CO2 and formation fluids in porous media is essential to assess the CO2 leakage risks and predict the amount of CO2 that can be absorbed and the oil/gas production as well.
Predicting changes in the flow and transport properties of CO2 and formation fluids in porous rock is still a challenging issue owing to the multi-phase flow, complexity of the fluid–rock interactions and intrinsic heterogeneity of porous rocks (Garcia-Rios et al. 2015). Thus, the CO2 displacement process in porous media has attracted increasing attention. Extensive research on CO2 displacement has been performed over multiple spatial scales that range from a few nanometres to tens or hundreds of kilometres, and it is also clear that the appropriate methods to be employed vary between different scales. At the macro-scale, average properties must be employed, as an explicit description of the pore-scale phenomena is simply impossible.
Additionally, the physical and chemical processes occur in discontinuous pore geometries and are controlled by interfacial processes, which have a large influence on the large-scale phenomena of the system and ultimately require a pore-scale perspective for obtaining a better understanding of the mechanisms (Blunt et al. 2013; Wildenschild and Sheppard 2013; Ferrari 2014; Morais et al. 2016). In the last decades, the pore-scale modelling of CO2-formation fluid displacement has been promoted by three factors: the recent advances in porous media characterizations by visualization techniques, some novel numerical theories, and advances in high-performance computing (Ferrari 2014). However, studies on the CO2-formation fluid displacement using these promising technical and theoretical approaches have not been systematically analysed in the published literature.
Thus, the objective of this contribution is to outline the recent developments and advances in the simulation and visualization of the CO2-formation fluid displacement process occurring at the micro-scale and nano-scale—also referred to here as the pore-scale—and to highlight perspectives for future research. In Sect. 2, some relevant important processes and characterizations of the CO2-formation fluid displacement are briefly discussed. In Sect. 3, several novel visualization techniques and numerical simulation methods for the CO2-formation fluid displacement are introduced in detail, including a discussion of their strengths and weaknesses. Finally, Sect. 4 provides a comprehensive overview of the applications of CO2 displacement to enhanced shale gas production including the status of research, challenges and possible solutions.
2 Characterizations of the CO2-formation fluid displacement
2.1 Viscous fingering
In porous media, viscous and capillary forces play key roles in impacting the CO2-formation fluid displacement. The injected CO2 viscosity is generally lower than that of formation fluids (Nordbotten et al. 2005), and the interfacial tension between the CO2 and formation fluids depends on the pressure, temperature, and other system conditions (Chiquet et al. 2007; Espinoza and Santamarina 2010). Two dimensionless parameters, namely, the capillary number (Ca) and viscosity ratio (M), are commonly employed to describe the various forces encountered by the two fluids during their displacement in the porous media. These two parameters are defined as
where μ1 and μ2 are the viscosity of the displacing fluid and the viscosity of the displaced fluid, respectively. V2 is the bulk velocity of the displacing fluid, γ is the interfacial tension between the two fluids, and θ is the fluid–fluid contact angle with the solid surface.
Fig. 1 Classification of displacement patterns based on Ca and M. The boundaries marked with blue lines are those noted by Lenormand et al. (1988), whereas those marked with red lines are those from Zhang et al. (2011a). Modified after Yamabe et al. (2015).
Based on the values of Ca and M, three displacement patterns can be identified, as shown in Fig. 1: viscous fingering, capillary fingering and stable displacement (Lenormand et al. 1988; Zhang et al. 2011a; Yamabe et al. 2015). In the CO2 displacement process, the fluid flow speed is low in subsurface rocks (Ca ≪ 1), and the viscosity ratio is considered to be less than 1 (M < 1) (Yamabe et al. 2015). Hence viscous fingering can commonly occur during the CO2-formation fluid displacement. Viscous fingering is the formation of special fingers with morphologically unstable interfaces of the invading fluid. A deep understanding of viscous fingering is essential for accurately predicting the migration and transport of the injected CO2 and formation fluids within the pore structure of the formations.
2.2 CO2–rock interaction
With a deep understanding of the CO2-formation fluid displacement process, the CO2–rock interactions intervene in more areas than initially anticipated, whereby certain areas have attracted less attention to date. When CO2 is injected into formations, scCO2 will dissolve, and interaction will occur between the CO2 and formation rock (Gaus 2010). As a consequence, these interactions will lead to changes in the pore structure of the formation rock, decreasing the porosity and permeability of the rock. These changes in the pore geometry of the formation rock will seriously impact the fluid transport in the CO2-formation fluid displacement. Thus, there are three key issues summarized in the review of Gaus (2010), that is, where do CO2–rock interactions occur, what are the drivers of CO2–rock interactions and what is their influence on the porosity and permeability, and how can the CO2–rock interactions be assessed.
3 Displacement simulation and visualization
3.1 Experimental visualization
Laboratory experiments on CO2-formation fluid displacement can provide valuable insights into processes that control the displacement process at the pore scale of porous media and improve our understanding of multi-phase flow. Pore-scale experiments also permit the evaluation of the constitutive relationships that are used in large-scale simulators (Dehoff et al. 2012). Roughly, there are three main visualization approaches to detect and observe CO2 displacement processes at the pore scale: magnetic resonance imaging (MRI), X-ray computed tomography (CT) (Shi et al. 2009, 2011a, b; Zhao et al. 2011a; Alemu et al. 2013; Berg et al. 2013b) and fabricated micromodels (Ferer et al. 2004; Cottin et al. 2010; Zhang et al. 2011a; Wang et al. 2013; Al-Housseiny et al. 2012). These methods are recognized as effective approaches to directly characterize the transport properties of the displaced fluid and displacing fluid at the pore scale.
3.1.1 X-ray CT
X-ray CT is a non-invasive and non-destructive imaging technique used to characterize the internal physical structure of the sample and allow for the three-dimensional (3D) in situ visualization of the fluid phases (Lindquist et al. 1996; Hunt and Bajsarowicz 1988; Wellington and Vinegar 1985, 1987; Schlüter et al. 2014). The theories and devices of X-ray CT are described by Wildenschild and Sheppard (2013) in details. In the last decades, X-ray CT has been widely used to investigate CO2-formation fluid displacement. For instance, Berg et al. (2010) investigated the miscible displacement performance of a CS2–nC10 system at 1.5 MPa and 25 °C using CT scanning. The authors concluded that the front fingering could affect the mixing zone area. Berg et al. (2013a) also studied the displacement and mass transfer between saturated and unsaturated CO2-brine systems in sandstone using CT, and 3D saturation patterns during the injection were obtained (Fig. 2). Seo (2004) and Seo and Mamora (2005) conducted the first experimental study of enhanced gas recovery by injecting CO2 through a dry carbonate core that was saturated with CH4 at 20–80 °C and 3.55–20.79 MPa.
Fig. 2 3D saturation patterns (CO2 in red/yellow), a unsaturated CO2-brine systems and b saturated CO2-brine systems. The rock matrix is visible as a semi-transparent background. The displacement shows the gravity over-run of CO2. (Berg et al. 2013a).
The distribution of CH4 and CO2 in the core was obtained using an X-ray CT scanner at the breakthrough time. The recovery of CH4 was 73%–87%, and the dispersion coefficient of CO2 was approximately 0.0–0.12 cm2/min. In addition to the above studies using real reservoir rock cores, some researchers chose sand packs as an experimental material for basic research on the displacement process. Liu et al. (2015b) investigated the CO2–CH4 displacement process in sand packs, and the displacement process was scanned with a resolution of approximately 34.2 mm by an X-ray CT scanner. Concurrently, the dispersion coefficients were obtained, and the effects of the temperature, pressure, CO2 injection flow rate and mean diameter of the glass beads were analysed. Through the X-ray CT scan, the detailed displacement process in the sand pack sample was obtained noninvasively, as shown in Fig. 3. The existence of the mixing zone was proven, and no interface appeared in the process of CO2–CH4 displacement.
Fig. 3 a CT scan images of the same vertical section in displacement in the BZ04 glass bead sand pack sample with time; b corresponding CT scan images of the same middle cross-section located on the red line of the vertical section of (a); The colour scale is set based on grey scale, with glass beads painted as white with edges that may be red or yellow, blue and dark blue are CH4, green represents CO2, and cyan indicates a mixture of CH4 and CO2. (For the interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) (Liu et al. 2015b).
However, based on previous studies, the front fingering and the mixing zone of the displacement process can only be qualitatively analysed by the CT imaging and cannot be quantified. Moreover, the microscopic fluid state cannot be detected using medical CT scanners owing to the insufficiently high resolution (millimetre-scale) compared with the pore sizes, which could make the results of the experiments less credible. The resolution of nano-CT (50 nm)is high, but it takes a long time to collect one image unless fast synchrotron-based sources are used.
MRI is similar to X-ray CT in that non-invasive visualizations of the fluid movement and distribution can be obtained in the core. The differences are that unprecedented quantitative information about the distribution of fluid sand information about the rock structure corresponding to local regions within the porous media can be provided by MRI during the displacement processes (Song et al. 2012). Special features of MRI include its abilities to measure the fluid flow velocities and to distinguish between different liquids by the differences in their intrinsic MRI properties, which are difficult to obtain by other methods. It also has a shorter measurement time and is much less hazardous in comparison with X-ray CT (Xiong et al. 2016). Using the MRI technique, some studies were performed on the CO2-formation fluid displacement in porous media.
Suekane et al. (2005, 2006, 2009) used the MRI technique to directly visualize the distribution of supercritical CO2 (scCO2) in a bead-pack core containing water at a certain temperature and pressure that approximate aquifers at a depth of approximately 1000 m. Liu et al. (2011) analysed the immiscible and miscible CO2 displacement of oil in glass bead packs using MRI technology. In their study, the local Darcy velocities of CO2 were acquired based on the oil saturation data obtained from MRI images, and the effects of the capillary pressure, viscosity and buoyancy on the CO2 displacement process can also be evaluated using a special core flood analysis. Zhao et al. (2011a, b) proposed a method to calculate the average velocity of the CO2 front and implemented CO2–oil miscible displacement in a sand pack using MRI. The local Darcy phase velocities of the CO2 and oil were calculated with this method and are shown in Fig. 4. Song et al. (2012) studied the CO2-water displacement process in packed glass beads using high-resolution MRI.
MRI images of the CO2 displacement were obtained, and the effects of the displacement type, CO2 injection flow rate and effective porosity were considered. A summary of the results of the displacement experiments is shown in Table 1. Song et al. (2014) also analysed the in situ mixing zone performance of CO2-oil miscible displacement flows in a sand pack using MRI. The mixing zone length, CO2 frontal velocities, longitudinal dispersion coefficient and Peclet number were quantified based on magnetic resonance imaging. Yang et al. (2015) investigated the dynamic stability characteristics of fluid flow in CO2-oil miscible displacement using an MRI apparatus, and the CO2 frontal velocities and mixing zone length were visually quantified.
Although a number of studies have been conducted to investigate the CO2-formation fluid displacement in a sand pack using MRI, and some CO2-formation fluid displacement mechanisms have been clearly analyzed, there have been almost no studies on natural rocks owing to the harsh conditions of MRI against the experimental materials. As the geometry of the natural rock sample is more complex than that of the sand packs, the reliability achieved for the previous experimental results can be compromised.
3.1.3 Fabricated micromodels
The rock cores have an advantage in characterizing individual formations, but on the pore scale, the fluid flow is difficult to monitor since sophisticated and unique micro-tomographic facilities are needed to visualize the internal distribution of the fluids within the rock cores. The natural media also presents other challenges in that the porosity, pore size, connectivity, and wetting properties are unable to be independently manipulated. These limitations can be overcome by micromodels, which allow for the visualization of the fluid distribution using cameras with or without fluorescence microscopy. The subsequent quantification of the fluid transport and interfacial area may provide mechanistic insight into the physical fluid displacement process at the microscopic level. Experimental studies on the CO2-formation fluid displacement have been widely conducted in 2D micromodels to reveal the mechanisms of the fluid displacement.
Er et al. (2010) investigated the porous matrix and fracture interaction during CO2 injection into a glass micromodel initially saturated with oil, demonstrating the importance of the CO2–oil interaction near the matrix-fracture interface. Chalbaud et al. (2009) visualized the scCO2 displacement of water in glass micromodels, but the saturations of the fluids could not be quantified owing to difficulties in distinguishing between the fluids. Riazi et al. (2011) simulated CO2-oil and CO2-water displacement processes in an etched glass micromodel, and the results showed a faster CO2 breakthrough in the micromodel saturated with oil than that with water. The above studies were all limited to qualitative visualizations of the fluid flow during the displacement process, and quantitative information about the interfacial areas and fluid saturations was not acquired.
The study of Zhang et al. (2011b) was the first to quantitatively evaluate the influence of the capillary forces and porous media heterogeneity on the liquid CO2-water displacement in a dual-permeability pore network micromodel using fluorescence microscopy. Wang et al. (2013) simulated the effects of the injection rates and injection methods on the scCO2 displacement of water in a homogeneous micromodel, and the results of the simulation are quantitatively compared using the obtained fluorescent images. Kazemifar et al. (2016) quantified the flow dynamics of the scCO2 displacement of water in a 2D porous micromodel by combining fluorescence microscopy and microscopic particle image velocimetry (PIV).
Unfortunately, micromodels lack the complex geometry of real media, which often have multiscale and random characteristics that will dictate the fluid and solute transport. In addition, these experimental studies used simple two-dimensional porous media. To overcome the above limitations, Ju et al. (2014a) incorporated several advanced technologies, such as CT scan, three-dimensional (3D) reconstruction (Gomi et al. 2007; Geiger et al. 2009; Hajizadeh et al. 2011; Zhang et al. 2013; Birk et al. 2014; Ju et al. 2014b), and 3D printing, to produce a physical model representing the natural rock. A 3D digital image can be obtained to represent the real rock structure based on the high-resolution X-ray CT imaging and the reconstruction, and then its three-dimensional micromodel using transparent material can be generated using a 3D printer. This novel idea offers a very good opportunity to accurately investigate the properties of complex flows.
These experimental simulation methods greatly promote our understanding of the CO2-formation fluid displacement mechanism. However, it is worth noting that these simulation experiments are performed based on the pore geometric characteristics of a convention formation that has a minimum pore size on the micrometre scale. The pore sizes and pore throat radii of unconventional gas reservoirs range from 1 to 300 nm, which are much smaller than those of conventional reservoirs with pore sizes in the range of 1–100 μm (Cipolla et al. 2009).
These popular experimental simulation methods are thus not able to investigate fluid flow at the nano-metre scale because the maximum precision of these techniques is on the micro-meter scale in general. Special characteristic features that can be produced at the nanometre scale include a high capillary pressure, low porosity, and high wetting phase residue saturation (Wu 2014). Other transportation mechanisms may also occur. The displacements of two-phase flow in nano-pores are poorly understood. Wu (2014) developed a lab-on-chip approach for the direct visualization of the fluid flow behaviour in nanoscale channels using an advanced epi-fluorescence microscopy method combined with a nanofluidic chip. This method is expected to improve the understanding of the CO2 displacement behaviour on the nano-scale. However, it is still a qualitative analysis method and cannot quantifiably reflect the displacement process.
3.2 Numerical simulation
A large number of the porous media studies on fluid displacement have been numerically performed, and numerical simulations can provide an economical and efficient pathway to explore the influences of the flow and physical parameters in various complicated porous media. Pore-scale simulations provide a level of information on flow characteristics that cannot be obtained in laboratory experiments, for example, the full pressure and velocity fields and the position of the interface. Modelling approaches of multiphase flow at the pore scale can be divided into two categories: direct simulations, in which the flow equations are directly solved on a discretized pore space obtained from images of rock cores, and network modelling, in which simplified flow equations are solved in an idealized pore network extracted from the real geometry (Blunt et al. 2013).