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Please stick to the headings and their order. Don't modify the words in bold. Your input is required at each occurrence of "e.g." and "...".
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Physics

We used the HPC porous media code PFLOTRAN https://www.pflotran.org/documentation/index.html for our modeling. We also used FEHM initially (https://fehm.lanl.gov/) and got similar results. We have since then continued to use PFLOTRAN.

PDEs

E.g. One mass balance per component water and CO2.

Mass balance of the component i is in the form: \frac{\partial}{\partial t} \left(\varphi \sum_{\alpha} s_\alpha \eta_\alpha x^{\alpha}{i} \right) + \nabla \cdot \sum\alpha \boldsymbol{F}^{\alpha}_{i} = Q_i,

Here, \alpha is a fluid phase, the flux {\boldsymbol{F}}_i^{\alpha} is given by: {\boldsymbol{F}}i^{{\alpha}}= {\boldsymbol{q}}{{\alpha}}^{}\eta_{{\alpha}}^{} x_i^{{\alpha}} - \varphi s_{{\alpha}}^{} D_{{\alpha}}^{} \eta_{{\alpha}}^{} {\boldsymbol{\nabla}}x_i^{{\alpha}}, x_i^{\alpha} denotes the mole fraction of species i satisfying \sum_i x_i^\alpha=1,.

See https://www.pflotran.org/documentation/theory_guide/mode_mphase.html#governing-equations for more details.

Constitutive relations

Fluid-matrix interaction

  • Capillary pressure: Linear curves were used

  • Relative permeability: Linear curves were used

Phase composition: Applied equations of state

  • CO2 in liquid phase: Duan, Zhenhao, and Rui Sun. "An improved model calculating CO2 solubility in pure water and aqueous NaCl solutions from 273 to 533 K and from 0 to 2000 bar." Chemical geology 193.3-4 (2003): 257-271.

  • Water in gas phase:

Density

  • Liquid phase: International Formulation Committee of the Sixth International Conference on Properties of Steam (1967)

  • Gas phase: Span, Roland, and Wolfgang Wagner. "A new equation of state for carbon dioxide covering the fluid region from the triple‐point temperature to 1100 K at pressures up to 800 MPa." Journal of physical and chemical reference data 25.6 (1996): 1509-1596.

Solubility limit

1.67 kg/m3

Temperature

20 C throughout

Domain volume

Total domain volume: 0.08184 m3 Total pore volume: 0.03578m3

Spatial parameters

Parameters can be found in spatial_parameters.csv.

Numerics

Coupling of flow and transport, temporal and spatial discretization

  1. Flow and transport are spatially discretized using two-point flux finite volume. Backward Euler was used for temporal discretization with adaptive time-stepping.
  2. In case of tracer tests flow and transport are coupled sequentially.
  3. For CO2 flow/transport, full two-phase two-component mass balance equations are solved in a fully coupled fashion.

Linearization and Solvers

Newton outer loop with FGMRES linear solver along with CPR pre-conditioning was used.

Primary Variables

Computational Grid

Tri Delauney elements are converted to Voronoi Number of voronoi cells: 24748

Performance

Indicator Average Min Max
time step size [s] 6 6.e-6 6
# nonlinear iterations per time step 1 1 1
# linear iterations per solve 2 2 5