Analysis of CO 2 Migration during Nanofluid-Based Supercritical CO 2 Geological Storage in Saline Aquifers

Carbon dioxide (CO2) geological storage in deep saline aquifers is a key measure to mitigate global warming. However, it still faces a variety of technical challenges such as enhancing CO2 effective storage capacities. In this paper, a preliminary model is developed to simulate CO2 migration during nanofluid-based supercritical CO2 geological storage in saline aquifers. The main mechanisms, including Brownian motion, thermophoresis, thermal energy transfer, and interfacial tension, are included in the proposed conceptual model. Based on the high-resolution space-time conservation element and solution element (CE/SE) method, the model is used to simulate CO2 migration and distribution in the in-situ heterogeneous saline aquifer. It can be inferred that the involvement of nanoparticles decreases shear stresses opposing flow and enhances CO2 mobility in the flow boundary layer. In addition, nanoparticles increase shear stresses outside the boundary layer and retard CO2 velocity. These competitive mechanisms result in homogeneous migration of CO2 in the saline formation. One preliminary suggestion is that nanofluids enhance homogeneous CO2 transport in the reservoir and mitigate the negative effects of stratigraphic heterogeneity on migration and accumulation of the CO2 plume. CO2 effective storage capacity may be greatly elevated by means of nanofluid-based CO2 geological sequestration. The concept of nanofluid-based CO2 geological storage may be potentially conducive to large-scale commercial CO2 geological storage and useful for exploration of geothermal resources in deep-seated hot rocks. The effects of CO2 solubility and geochemical reactions on nanofluid flows may be considered in a future study.


INTRODUCTION
Carbon dioxide (CO 2 ) geological storage in deep saline aquifers is a new field of study associated with climate change and environmental protection and provides insight into strategies to mitigate greenhouse gas emissions (Pang et al., 2012).This approach still faces a variety of challenges, such as leakage detection (Li et al., 2009), capacity assessment, impact of heterogeneity on CO 2 migration underground, and pressure buildup induced by CO 2 injection (Zhou et al., 2011).There are four trapping mechanisms for CO 2 geological sequestration: dynamic fluid trapping, dissolution trapping, residual trapping, and mineral trapping (Bachu et al., 1994;Hitchon, 1996;Soong et al., 2004;Li, 2011;Shi et al., 2011;Zhang et al., 2012).These mechanisms ultimately determine CO 2 migration and its phase state and storage capacities in deep saline aquifers.The effects of formation heterogeneity on CO 2 migration and distribution have attracted more and more attention.Ambrose et al. (2006) found that formation heterogeneity dominates CO 2 saturation and storage capacity, as evidenced by the impacts of heterogeneity on CO 2 mineral trapping (Doughty et al., 2001), residual trapping (Mito et al., 2008), and CO 2 migration characteristics (Hovorka et al., 2004;Xue et al., 2005;Yang et al., 2012b).Lei and Xue (2009) concluded that sandstone heterogeneity dominantly controls CO 2 saturation and accumulation during CO 2 flooding.Measures to mitigate the effects of formation heterogeneity on CO 2 distribution and storage capacity are key scientific issues for CO 2 sequestration in deep saline aquifers.
A nanofluid is a mixture consisting of a base fluid and suspended nanometer-sized solid particles, which can be made by the surface-active agent or surface charge methods (Choi, 1995;Tang et al., 2002;Wang and Mujumdar, 2007;Timofeeva et al., 2011).Among their most promising characteristics, nanofluids greatly enhance thermal conductivity (Masuda et al., 1993).The mechanisms governing nanofluid flows involve inertial effects, Brownian diffusion, thermophoresis, diffusiophoresis, the Magnus effect, fluid drainage, and gravity effects (Buongiono, 2006;Nield and Kuznetsov, 2009).Cheng et al. (2008) investigated the phenomenon of nanofluid two-phase flows.Nanofluid flows in porous media have recently attracted more attention in research and applications.Based on the Oberbeck-Boussinesq approximation, assuming local thermal equilibrium and homogeneity, and without considering particle agglomeration or deposition on porous surfaces, Nield and Kuznetsov (2009, 2010, 2011) established conservation laws involving continuity, momentum, nanoparticle diffusion, mass transfer, and thermal energy.They analyzed the effects of thermophoresis and Brownian motion on double-diffusion convection in porous media saturated by a nanofluid and found a similarity solution which was referred to as the relationship parameter between stream function and similarity.Meanwhile, Bhadauria and Agarwal (2011) presented the convection stability of nanofluids in a porous medium.
As is well known, nanofluids have been found to be attractive for many engineering applications, including heat exchange, because of their enhanced thermal conductivity.Nanofluids are characterized by strong penetration capability (Krajnik et al., 2011) and effectively reduce the critical time scale of flow instability.In particular, nanofluids decrease the shear stress within the fluid boundary layer, promoting convection-diffusion of fluid systems (Murshed et al., 2008).Some concerns have been expressed about whether nanofluids can enhance CO 2 convection-diffusion in saline formations to promote homogeneous CO 2 transport in the reservoir and to mitigate the negative effects of heterogeneity on migration and accumulation of the CO 2 plume.It remains to be determined whether effective CO 2 storage capacity can be greatly elevated by means of nanofluids.
The goal of the present paper is to investigate the effects of nanofluids on CO 2 migration in deep saline formations, with the aim of establishing a preliminary mechanism for nanofluid-based CO 2 geological storage.Based on the classical nanofluid model, nanofluid convection-diffusion was first analyzed in porous media.Then, coupled with multiphase flow equations, the effects of nanofluids on CO 2 plume distribution were investigated for a pilot project involving CO 2 geological sequestration in an in-situ saline aquifer.As reported in this study, a CE/SE-based code was developed, and comparisons were made between its numerical predictions and CO 2 distributions from the literature (Yang et al., 2012).The proposed model for nanofluid-based CO 2 geological sequestration may be useful for fundamental studies of CO 2 trapping mechanisms, with possible applications to CO 2 storage in saline aquifers and nuclear waste deposition.The results of this study could potentially promote basic research on nanofluid multiphase flow in porous media and applications of nanotechnology to environmental protection.Streimikiene and Mikalauskiene (2010) analyzed the possibility of geological storage of CO 2 mixed with nuclear waste, in which the term "nanofluid" refers to a new class of fluids engineered by dispersing nanometer-size nuclear waste particles in supercritical CO 2 .Therefore, a new concept of nanofluid-based CO 2 sequestration underground (abbreviated as NCS) was proposed.In the present study, an NCS model was established for CO 2 geological storage in deep saline aquifers.The term "nanoparticle" refers to an innocuous nanometer-sized mineral or organic solids particle.Nanofluid-based CO 2 geological storage is defined as permanent sequestration of specific nanofluids in reservoirs such as depleted oil fields and deep saline aquifers.Certain assumptions are required: (1) the Boussinesq approximation is used; (2) local thermal equilibrium in porous media is assumed; (3) nanoparticle concentration is dilute; (4) the solute does not affect the transport of nanoparticles in porous media.

MATHEMATICAL MODEL AND NUMERICAL VALIDATION
According to the volume-averaged Navier-Stokes equations (Whitaker, 1996) and the nanofluid model (Nield and Kuznetsov, 2011), a set of controlling equations can be formulated for the conservation of mass, momentum, thermal energy, and nanoparticles as follows: Continuity equation: Momentum equation: Solute transport equation: Nanofluid transport equation: Thermal energy equation: is the gravitational force, and F s represents the volume forces, e.g., the interfacial tension vector as defined in (Yang et al., 2011) in the case of immiscible multiphase flows.All nomenclature in the above governing equations is defined in the literature (Nield and Kuznetsov, 2011;Yang et al., 2011).It has been proved that the main physical factors, such as the advection term, the Forchheimer quadratic drag term, and surface tension in the momentum equation significantly affect CO 2 migration in reservoirs (Yang et al., 2011(Yang et al., , 2012b)).The surface-tension force is obtained by using the weighted integration surface-tension model (as shown in Fig. 1) coupled with the hybrid particle Level-Set function (Yang et al., 2011).The conservation equations given above are solved using the space-time conservation element and solution element (CE/SE) method with secondorder accuracy (Yang et al., 2009(Yang et al., , 2012a)).
For model testing, the study focused on the Cheng-Minkowycz problem (Nield and Kuznetsov, 2011).A doublediffusive nanofluid flow can be numerically simulated by means of the space-time conservation element and solution element (CE/SE) method (Yang et al., 2012a).In this case, the interfacial tension is neglected.The governing equation, parameters, and boundary conditions are as defined by Nield and Kuznetsov (2011).For the one-dimensional problem, the grid used is 102.Fig. 2 illustrates the relationship between the stream function and the variable similarities for a typical case of a double-diffusive nanofluid.The agreement between the numerical predictions and the analytical solutions was very good to excellent.For further validation and evaluation of the double-diffusive nanofluid, laboratory experiments should be carried out in a future investigation.Nevertheless, this case should be useful for fundamental studies on nanofluid multiphase flow using numerical methods.In particular, the CE/SE method can capture the main physical phenomena of nanofluid transport (e.g., convection-diffusion) in porous media.
Because the numerical model of CO 2 storage is new, a twophase flow comparison study was first performed to validate the numerical model without considering nanoparticles.In

RESULTS: NANOFLUID-BASED CO 2 GEOLOGICAL STORAGE
A pilot-scale CO 2 geological sequestration project undertaken in the Jilin oilfield was selected as a test case for nanofluid-based CO 2 storage.Effects of nanoparticle involvement on CO 2 migration were investigated without considering solute transport.Based on analysis of log data from 196 wells, formation porosities varied from 4% to 18%, with an average of 11.4%.The permeability was calibrated (as shown in Fig. 4) by the regression equation K = 7.8 × 10 -8 e 66.7ε derived from in-situ data for sandstones.The 3D heterogeneous geological model was constructed using GSLIB.A mean permeability of 2.65 mD was assigned in GSLIB.The Gaussian model (the GSLIB function SGSIM) was used with a correlation length of 100 m.Fig. 5 depicts a visualization of the generated permeability field.
For further detailed information about the conceptual model, parameters (e.g., geothermal gradient), and mesh grids, the reader is referred to the literature (Yang et al., 2012b).The top and bottom boundaries were assumed to be impermeable walls, while other boundaries were kept permeable.The normal gradient of the nanoparticle volume fraction was set to zero for all boundaries.A constant temperature was imposed on the top and bottom boundaries.Zero heat and mass flux were respectively applied to temperature and solute concentration on all vertical boundaries.The depth profiles of hydrostatic pressure and temperature were specified initially according to in-situ observations (Yang et al., 2012b).The physical properties are summarized in Table 2. Thermal parameters were obtained from in-situ monitoring of specific sandstones.Here, it was assumed that (1) CO 2 and brine   Table 2. Thermophysical properties for a case simulation.

Physical properties
Silica nanoparticles Density (g/cm 3 ) 2.33 Specific heat(J/g•°C) 0.7 Thermal conductivity(W/cm•°C) 1.3 Thermal diffusivity(cm 2 /s) 0.8 was derived from the state equations; (5) CO 2 solubility and geochemical reactions were not considered; and (6) The solute transport mechanism was not considered, and the solute did not affect nanoparticle transport.Numerical analysis focused on CO 2 migration over short time scales, and the effects of nanofluid on CO 2 distribution in the heterogeneous saline formation were investigated.Numerical simulations were performed on an HP Z800 workstation with dual cores.Fig. 6 illustrates CO 2 migration and distribution in the saline formation.In the case of supercritical CO 2 injection (as depicted in Fig. 6(a), previous studies (Yang et al., 2012b)  dramatically compared to the case of supercritical CO 2 injection.CO 2 migrated primarily around the injection wells.The predominant flow path was unremarkable.CO 2 accumulation was characterized by a quasi-elliptical shape with an average diameter of 4 km, suggesting a reduction of heterogeneous effects.

DISCUSSION
Generally, local temperature, nanoparticle fraction, and concentration gradients strongly affected the velocity field through the gravitational term in the momentum equation.In addition, the gradient of the nanoparticle volume fraction significantly influenced energy transfer.Meanwhile, Brownian motion and thermophoresis influenced nanoparticle convection-diffusion. Local temperature gradients strongly affected mass transfer.Therefore, the velocity field was influenced by Brownian motion and thermophoresis.In consequence, because the concentration field was coupled with the velocity field through convective terms in the species balance, the concentration field was affected as well.The change in mass transfer finally affected the local nanoparticle concentration at the interface and thus the interface tension gradient.An interfacial flow was induced because the system tends to lower its free energy in expanding regions of low interfacial tension (Wegener et al., 2009), which in turn affected both CO 2 and brine water adjacent to the interface.
The velocity was highly sensitive to shear stresses induced at the interface between CO 2 and brine water.The tangential flows at the interface lowered the relative velocity between the two phases.The inner chaotic flow patterns resulted in an increase in shear stress at the interface and therefore a reduction in fluid velocity.However, as nanoparticle transfer continued, the shear stresses in the fluid boundary layers decreased, and the relative velocity between the two phases increased.Meanwhile, nanofluid instability promoted significant mass transfer in the boundary layer.Under the influence of these competing mechanisms, CO 2 tended to migrate homogeneously.
Nanoparticle involvement decreased the shear effect within the fluid boundary layer and enhanced CO 2 mobility throughout the shear layer.Furthermore, the nanoparticles increased the interior shear stress in fluids.Thus, nanofluids finally promoted homogeneous migration of CO 2 in the saline aquifer.These observations suggest that nanofluids mitigate the effects of stratigraphic heterogeneity on migration and accumulation of the CO 2 plume.The effective storage capacity for CO 2 may therefore be greatly elevated by means of nanofluid-based CO 2 geological storage.
Compared with the density derived from the theoretical state equations for CO 2 , the proposed model overestimated CO 2 density by up to 35% due to the assumptions of local thermal equilibrium and the noninvolvement of CO 2 solubility and geochemical reactions as well as to matrix deformation.Further evaluation and validation of this model should be carried out through laboratory experiments.
A reliable governing equation for nanofluid dynamics in porous media is still in its infancy.The conservation equations established by Nield and Kuznetsov (2009, 2010, 2011) were based on the NS equation on a macroscopic level, which involved various dominant factors including Brownian motion and thermophoresis.The Oberbeck-Boussinesq approximation was used.This study has extended ideas from the literature (Nield and Kuznetsov, 2011) into the nanofluid two-phase flow problem and has preliminarily established a mechanism for nanofluid-based CO 2 geological sequestration.Surface tension was assumed to be that of CO 2 /brine water and does not reflect the physical properties of the surface tension of nanofluids.The surface tension model for nanofluids is as yet unclear.The proposed model involved the effect of nanoparticle concentration and considered the mechanism of heat transfer (e.g., Brownian motion), but the effects of nanoparticle size on flow was not taken into account.
The present study has focused on the impact of nanoparticle fraction on nanofluid dynamic behavior.Further research is needed on the effects of nanoparticle coalescence on permeability change in porous media and the impacts of nanoparticle microscale motion on nanofluid multiphase flow in porous media.

SUMMARY
Preliminary macroscopic balance equations for nanofluid multiphase flow in porous media have been developed.Three-dimensional versions have been solved numerically using a CE/SE-based numerical code.The numerical predictions were compared to experimental results, and good agreement was evident for the benchmark problems.The effects of nanoparticles on CO 2 migration in the in-situ heterogeneous saline formation were investigated numerically.The main physical mechanisms such as Brownian motion, thermophoresis, and interfacial tension were taken into account.
This research has suggested that inner chaotic flow patterns resulted in an increase in the shear stress at the CO 2 /brine water interface and therefore in a reduction in fluid velocity.As nanoparticle transfer continued, the shear stresses in the fluid boundary layers decreased, and the relative velocity between the two phases increased.Nanofluid instability enhanced mass transfer significantly in the boundary layer.Because of these competing mechanisms, CO 2 tended to migrate homogeneously.The nanofluids appeared to mitigate the effects of stratigraphic heterogeneity on CO 2 migration in the saline reservoir.
Due to the lack of laboratory and in-situ monitoring data, the mechanism of the proposed nanofluid-based CO 2 geological storage has not been verified.Further model validation should be carried out for future examination.In this case study, the initial nanoparticle fraction was 5%.Future research should consider the effects of different nanoparticle fractions on CO 2 migration for a pilot project.The effects of CO 2 solubility and geochemical reactions on nanofluid flows may also be considered in a future study.Nevertheless, the advanced ideas and information described here may be fruitful for enabling readers to find a sustainable solution for CO 2 geological sequestration.

Fig. 1 .Fig. 2 .
Fig. 1.Relationship between stream function and similar variables (dots denote analytical solutions, while the line represents the CE/SE calculated results.)

Fig. 3 .
Fig. 3. (a) Predicted plume migration of the solute, and (b) temporal evolution of average drop concentration without nanoparticles.Dots denote the experimental data observed (Wang et al., 2008), and the line represents the calculated results.

Fig. 4 .
Fig. 4. Regression relationship of permeability to porosity of sandstones.water were viscous, incompressible, and immiscible; (2) the formation consisted of heterogeneous porous media with inclusion of surface-tension effects; (3) the fluid-fluid interface did not resist nanoparticle transfer; (4) CO 2 density

Fig. 6 .
Fig. 6.Evolution of CO 2 migration in the saline formation at different time instants in the case of (a) supercritical CO 2 injection (Yang et al., 2012b) and (b) nanofluid injection.The color scale means CO 2 density.

Table 1 .
Nondimensional parameters in the case of mass transfer.