Comments on the numerical tools
Various multiphase flow formulations and a solute transport module in porous media have been developed and implemented in COMSOL. The numerical tools have been verified through various benchmarks and are applied to model the dynamics of underground gas storage in chapters 3 and 4.
The highly flexible numerical framework of COMSOL provides a large number of options for the solution algorithm and scheme of the PDE systems. The platform is continuously updated ensuring the availability of state of the art numerical methods and solvers. It has a powerful pre and post-processing interface with strong meshing capabilities that helps the user to save time in setup and visualization; focusing in the analysis of results and implementation details. It has also a certified quality assurance process that promotes its industrial application. When modelling convection-diffusion processes the Galerkin FEM spatial discretization used in COMSOL could lead to an oscillatory behavior that can be balanced by numerical stabilization methods. Nevertheless, a tight control on the spatial discretization is recommended to avoid oscillations.
The multiphase flow formulations implemented has been proven to properly reproduce the migration of two fluid phases in the subsurface. A series of immiscible formulations are available and the one selected may depend on the processes reproduced in each application. The compositional formulation proposed maintains the same dependent variables throughout the model domain. Switching variables can be efficient to face phase disappearing; however, it affects the structure of the Jacobian matrix. Using the same dependent variables facilitates the integration of this formulation in modular reactive transport codes as iCP.
The component partitioning between the gas and liquid phase is expressed by a kinetic rate. The equilibrium can be simulated by imposing a high kinetic rate; however, other mass transfers can be accounted. This approach broads the possibilities of the code. Nevertheless, few experimental data on kinetic mass transfer between phases are available on literature.
A fully implicit scheme and direct solvers have been used in the application models presented in this thesis. This method is robust and unconditionally stable and no time step restriction controls the temporal discretization; however, the method is computationally expensive. To date only one phase one component systems have been simulated.
The component solute transport module in porous media is developed using the convective form of the equation, which is more stable in Galerkin FEM. The module facilitates the transfer of information between COMSOL and iCP and it has been successfully applied in dozens of models.
iCP maximizes the synergies between COMSOL and PHREEQC, inheriting the capabilities of both codes. It combines the flexibility and wide range of applications and couplings from COMSOL with the most widely used code for geochemical processes. The SNIA approach does not pose global convergence problems although a tight control on the time step is required. At every step COMSOL has to reconstruct the matrix system, leading to a computational time penalty. It is, then, a reactive transport code appropriate for coupled systems (e.g. THMC problems) with complicated geometries or complex physical processes, rather than models with simple geometries without process coupling. A summary of the capabilities of the code is given in Table 2-7. The table has the same fields than tables 1, 2 and 3 in Steefel et al. (2015) to allow the comparison with other reactive transport codes.
The coupling of the multiphase formulations with reactive transport through iCP would generate a useful tool for multiphase flow challenges in porous media. There are already some codes that can deal with such processes: HYTEC (Sin et al., 2017; Van der Lee et al., 2003), MIN3P (Mayer and MacQuarrie, 2010), eSTOMP (White and Oostrom, 2006), MoReS (Farajzadeh et al., 2012; Wei, 2012), TOUGHREACT (T. Xu et al., 2006), PFLOTRAN (Mills et al., 2007), HYDROGEOCHEM (Tsai et al., 2013), RETRASO-CodeBright (Saaltink et al., 2004), DUMUX (Ahusborde et al., 2015; Vostrikov, 2014) and COORES (Tillier et al., 2007). The flexibility of iCP would allow the representation of a large range of multiphase physical processes (e.g. thermal and mechanical processes could be account).
Other interesting field for future expansion of the numerical tools is the integration of surface water with groundwater phenomena. This tool could improve our understanding of the processes affection the surface and near-surface and the interaction of the hydrosphere with the biosphere (plants and microbial activity).
In respect to the multiphase flow, the definition of a specific interfacial area between phases, as proposed by Niessner and Hassanizadeh (2009, 2008) and Niessner and Helmig (2007); could capture additional processes. Hysteresis as well as a more accurate description of the mass transfer between phases could be reproduced.
Carbon capture and storage
Carbon dioxide storage in porous media
One of the most promising technologies to mitigate anthropogenic greenhouse gas emissions is carbon capture and storage (CCS) (Boot-Handford et al., 2014; Chu, 2009; Edenhofer et al., 2014; Haszeldine, 2009; Lackner, 2003; Metz et al., 2005; Oelkers and Cole, 2008). Deep saline aquifers in sedimentary basins are widely distributed and have a large potential storage capacity able to sequester much of the emitted CO2 from point sources (Bachu, 2003; Bradshaw et al., 2007; Firoozabadi and Cheng, 2010; Metz et al., 2005; Michael et al., 2010; Orr Jr, 2009; Szulczewski et al., 2012).
Most saline aquifers intend to maintain CO2 under supercritical state for an efficient use of the underground storage space. Under this condition, CO2 is less dense and viscous than the formation fluid and migrates upwards driven by buoyancy forces forming a gravity current. A well-sealed caprock is, therefore, needed to prevent the CO2 leakage from the storage formation to overlying formations. This storing mechanism is known as structural or stratigraphic trapping (Metz et al., 2005). Once at the aquifer top, free-phase CO2 will continuously extend following the caprock slope unless confined in a dome-shaped structure or retained by other physical and geochemical trapping mechanisms (Figure 3-1). During this migration, there is a risk of leakage through open faults or abandoned wells.
Capillary or residual trapping immobilize CO2 in the pore space in disconnected ganglia due to interphase surface tension. During the migration of the gravity current, aquifer native fluid imbibes back areas previously occupied by CO2 isolating and fixing small CO2 blobs. Furthermore, due to differences in density and capillary pressure between the free-phase and the underlying fluid phase, a so-called capillary fringe or transition zone is formed (Golding et al., 2013, 2011; Nordbotten and Dahle, 2011). Capillarity reduces the risk of leakage, immobilizing the CO2 over a large area, shrinking and reducing the propagation speed of the free-phase plume and enhancing the CO2 dissolution (Doster et al., 2013; Hesse et al., 2008; Juanes et al., 2010, 2006; Kumar et al., 2005; Zhao et al., 2013).
Both residual and mobile CO2 gradually dissolve into aquifer native fluid. The resulting CO2-rich fluid is approximately 1% denser than ambient fluid (Ennis-King and Paterson, 2003; Garcia, 2001), preventing the buoyancy driven escape of CO2 to upper layers or to the atmosphere. CO2 dissolution is a key process for carbon storage. It increases storage safety by decreasing the CO2 fugacity, lowering the pressure of the supercritical CO2 and, thus, limiting the gas migration and pressure build up. Furthermore, dissolved CO2 promotes water-rock interaction that could mineralize the carbon (Audigane et al., 2007; Xu et al., 2005), further increasing the stability of the storage.
Figure 3-1. Schematic illustration of the CO2 evolution in a saline dome-shape aquifer. Time increases downwards. The migration of free-phase CO2 as well as its dissolution in the native fluid and the consequent convective mixing are depicted. Dots represent the edges of free-phase plume: the trailing edge (TE, red) and leading edge (LE, blue). When the plume splits, an interior trailing edge (ITE, green) and interior leading edge (ILE, black) are defined.
The presence of denser CO2-rich fluid above the less dense native fluid lead to gravitational instabilities. This instability promotes convection that carries the CO2-rich aqueous fluid downwards generating finger shape CO2-concentration profiles (Ennis-King and Paterson, 2003; Hidalgo et al., 2013; Kneafsey and Pruess, 2010; Riaz et al., 2006). As thermodynamic equilibrium is rapidly attained between supercritical CO2 and the native formation fluid, its dissolution is controlled by the fluid renewal rate. Fluid convection, therefore, can increase dramatically the CO2 dissolution rate. Recently, field evidence of these processes have been observed (Sathaye et al., 2014). Emami-Meybodi et al. (2015) reviewed recent advances in CO2 convective dissolution in saline aquifers through experiments, and theoretical and numerical models.
This chapter is divided into two sections. The first, focuses on the interaction between different CO2 trapping mechanisms in the subsurface. It evaluates the fate of CO2 in a syncline-anticline system with a large scale multiphase model. The second part of the chapter deals with the effects of chemical reaction in convective mixing, a critical process in carbon storage. It analyzes a short portion of a reservoir with a fully coupled reactive transport model.
Interactions of CO2 gravity currents, capillarity, dissolution and convective mixing in a syncline-anticline system1.
Despite the relevant role of convective dissolution in carbon underground storage, the interplay between free-phase plume migration and this process is not completely understood. The wide range of temporal and spatial scales involved in the problem (the long gravity plume and the detailed convective mixing), poses challenges in its simulation. Numerical models showing convective mixing have been typically conducted on small-scale (Emami-Meybodi et al., 2015), being rare the models able to reproduce this process in a large scale. Despite the coarse spatial resolution Audigane et al. (2007) were able to capture in an approximate way the effects of convective mixing with a reactive transport model of the Sleipner site. Upscaled dissolution by convective mixing have been incorporated into reservoir scale theoretical models (Gasda et al., 2011; MacMinn et al., 2011) and laboratory experiments (MacMinn et al., 2012; MacMinn and Juanes, 2013). Recently, Hidalgo et al. (2013) analyzed the impact of convective mixing on CO2 gravity plumes without taking into account capillary trapping. Elenius et al. (2015) performed a similar study on a tilted aquifer. These previous studies illustrate that convective dissolution may limit the extent and speed of the gravitational current. Sin (2015) compared analytical studies of plume migration and convection with a large scale model showing chromatographic effects due to differences in gas solubility.
Table of contents :
2 Numerical tools
2.1.1 Mathematical description
2.1.2 Numerical methods
2.2.1 Mathematical model
2.2.2 Numerical method
3 Carbon capture and storage Interactions of CO2 gravity currents, capillarity, dissolution and convective mixing in a syncline-anticline system.
3.2.2 Model Description
3.2.3 Results and Discussion
3.2.4 Concluding remarks
3.3.2 Model description
4 Underground hydrogen storage Quantitative assessment of seasonal underground hydrogen storage from surplus energy in Castilla-León (north Spain)
4.2.2 Problem definition
4.2.3 Mathematical Model
4.2.4 Results and discussion
5 General conclusions and perspectives