Color model – Core Flooding¶

The core flooding protocol is designed to mimic SCAL experiments where one immiscible fluid is injected into the sample at a constant rate, displacing the other fluid. The core flooding protocol relies on a flux boundary condition to ensure that fluid is injected into the sample at a constant rate. The flux boundary condition implements a time-varying pressure boundary condition that adapts to ensure a constant volumetric flux. Details for the flux boundary condition are available (see: https://doi.org/10.1016/j.compfluid.2020.104670)

protocol = "core flooding"

To match experimental conditions, it is usually important to match the capillary number, which is

$\mbox{Ca} = \frac{\mu u_z}{\gamma}$

where $\mu$ is the dynamic viscosity, $u_z$ is the fluid (usually water) velocity and $\gamma$ is the interfacial tension. The volumetric flow rate is related to the fluid velocity based on

$Q_z = \epsilon C_{xy} u_z$

where $C_{xy}$ is the cross-sectional area and $\epsilon$ is the porosity. Given a particular experimental system self-similar conditions can be determined for the lattice Boltzmann simulation by matching the non-dimensional $\mbox{Ca}$ . It is nearly awlays advantageous for the timestep to be as large as possible so that time-to-solution will be more favorable. This is accomplished by

use a high value for the numerical surface tension (e.g. alpha=1.0e-2)
use a small value for the fluid viscosity (e.g. tau_w = 0.7 and tau_n = 0.7 )
determine the volumetric flow rate needed to match $\mbox{Ca}$

For the color LBM the interfacial tension is $\gamma = 6 \alpha$ and the dynamic viscosity is $\mu = \rho(\tau-1/2)/3$ , where the units are relative to the lattice spacing, timestep and mass density. Agreemetn between the experimental and simulated values for $\mbox{Ca}$ is ensured by setting the volumetric flux

$Q_z = \frac{\epsilon C_{xy} \gamma }{\mu} \mbox{Ca}$

where the LB units of the volumetric flux will be voxels per timestep.

In some situations it may also be important to match other non-dimensional numbers, such as the viscosity ratio, density ratio, and/or Ohnesorge/Laplace number. This can be accomplished with an analogous procedure. Enforcing additional constraints will necessarily restrict the LB parameters that can be used, which are ultimately manifested as a constraint on the size of a timestep.

Color {
   protocol = "core flooding"
   capillary_number = 1e-4            // capillary number for the displacement
   timestepMax = 1000000              // maximum timtestep
   alpha = 0.005                      // controls interfacial tension
   rhoA = 1.0                         // controls the density of fluid A
   rhoB = 1.0                         // controls the density of fluid B
   tauA = 0.7                         // controls the viscosity of fluid A
   tauB = 0.7                         // controls the viscosity of fluid B
   F = 0, 0, 0                        // body force
   WettingConvention = "SCAL"         // convention for sign of wetting affinity
   ComponentLabels = 0, -1, -2        // image labels for solid voxels
   ComponentAffinity = 1.0, 1.0, 0.6  // controls the wetting affinity for each label
   Restart = false
}
Domain {
   Filename = "Bentheimer_LB_sim_intermediate_oil_wet_Sw_0p37.raw"
   ReadType = "8bit"              // data type
   N = 900, 900, 1600             // size of original image
   nproc = 2, 2, 2                // process grid
   n = 200, 200, 200              // sub-domain size
   offset = 300, 300, 300         // offset to read sub-domain
   voxel_length = 1.66            // voxel length (in microns)
   ReadValues = -2, -1, 0, 1, 2   // labels within the original image
   WriteValues = -2, -1, 0, 1, 2  // associated labels to be used by LBPM
   BC = 4                         // boundary condition type (0 for periodic)
}
Analysis {
   analysis_interval = 1000           // logging interval for timelog.csv
   subphase_analysis_interval = 5000  // loggging interval for subphase.csv
   visualization_interval = 100000    // interval to write visualization files
   N_threads = 4                      // number of analysis threads (GPU version only)
   restart_interval = 1000000         // interval to write restart file
   restart_file = "Restart"           // base name of restart file
}
Visualization {
   write_silo = true     // write SILO databases with assigned variables
   save_8bit_raw = true  // write labeled 8-bit binary files with phase assignments
   save_phase_field = true  // save phase field within SILO database
   save_pressure = false    // save pressure field within SILO database
   save_velocity = false    // save velocity field within SILO database
}
FlowAdaptor {
}