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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

PDEs

Black oil equations with CO2 represented by gas phase/component and water represented by oil phase. CO2 can dissolve in water.

Constitutive relations

Fluid-matrix interaction

  • Capillary pressure:

For fine sands (ESF, C, D):

\begin{align*} p_c(S_{l}) = p_\text{entry}S_{l}^{-1/\lambda} \end{align*}

For coarse sands (E, F, G):

\begin{align*} p_c(S_{l}) = p_\text{entry}((0.999\times S_l)^{-\frac{10}{7}}-1)^{\frac{2}{3}} \end{align*}

  • Relative permeability:

\begin{align*} k_{r\alpha} =k_{r\alpha}^{max}S_{e\alpha}^{n_\alpha} \end{align*}

\begin{align*} S_{e\alpha}=max\left(0, \frac{S_\alpha-S_{r\alpha}} {1-S_{rCO_2}-S_{rWater}}\right) \end{align*}

Parameters

Parameter ESF C D E F G
Pentry 1471 294 98 50 45 40
Lambda 1 1 1 n/a n/a n/a
n_W 3 3 3 3 3 3
k_rW^max 0.71 0.93 0.95 0.93 0.72 0.75
S_rW 0.32 0.14 0.12 0.12 0.12 0.10
n_C 1.5 1.5 1.5 1.5 1.5 1.5
k_rC^max 0.09 0.05 0.02 0.1 0.11 0.16
s_rC 0.14 0.1 0.08 0.06 0.13 0.06

Phase composition: Applied equations of state

  • CO2 in liquid phase: \begin{align*} r_s^{sat,ref}=\frac{\rho_{w0}}{\rho_{c0}}\omega^{sat,ref}\ r_s^{sat}(p)=r_s^{sat,ref} \frac{p}{p_{ref}}\ r_s=\min\left(r_s,r_s^{sat}(p)\right)\ \end{align*}

\begin{align*} \omega^{sat,ref}=0.002 \frac{kg}{kg} \end{align*}

  • Water in gas phase:

Not accounted for

Density

  • Liquid phase:

\begin{align*} \rho_w(p,r_s)= \rho_{w0}\exp\left(c_w(p-p_{ref})\right) \left(1 +\frac{\Delta \rho_w^{sat}}{\rho_{w0}} \frac{ r_s}{r_s^{sat,ref}}\right) \end{align*}

Deltarho_w^sat/rho_w0= 1.6e-4 rho_w0=998 kg/m^3 c_w=0.458e-9 Pa^-1 p_ref=1e5 Pa

  • Gas phase:

\begin{align*} \rho_w(p,r_s)= \rho_{c0}\exp\left(c_c(p-p_{ref})\right) \end{align*}

rho_c0=1.815 kg/m^3 c_c=1e-5 Pa^-1

viscosity

  • Liquid phase: mu_w=1e-3 Pa s

  • Gas phase: mu_c=14.7e-6 Pa s

Solubility limit

2 kg/m^3

Temperature

~20C

Domain volume

Domain: 2.8m x 1.5m x 0.02m = 0.084 m^3

Spatial parameters

Please provide the relevant facies parameters as a csv file.
E.g. The parameters p_\text{entry}, \lambda, S_{lr}, S_{gr} for the different facies are given in spatial_parameters.csv.
Obviously, the number and type of parameters for your model might differ from the ones in the provided template.

Numerics

Coupling of flow and transport, temporal and spatial discretization

Fully coupled, fully implicit, cell-centered FV with TPFA. Default MRST set up for Black Oil

Linearization and Solvers

Newton with line search, direct matlab solver

Primary Variables

p_w, E.g. Dependent on local phase composition:

  • Both phases present: p_l, S_g...

Computational Grid

homogeneous rectangular grid 1cm x 1cm x 2cm, 150 x 280 x 1 = 42000

Performance

note that these are estimates from observing output rather than systematically calculating it

Indicator Average Min Max
time step size [s] 100 1 600
# nonlinear iterations per time step 10 3 25
# linear iterations per solve N/A N/A N/A