The Thin Barrier multiphysics coupling uses the Extra Dimension tool to solve the equations for the pressure and saturations through the thin barrier structure’s thickness. The thin structure has its domain represented by the product space between the lumped boundary and the additional dimension for the thickness. Inside this product space, it is convenient to split the gradient operator into a tangential part and a normal part: ∇=∇t+∇n.

The following assumptions, used in deriving the Thin Barrier equations from the equations solved in the Multiphase Flow in Porous Media interface, justify the simplification ∇=∇n:

In addition, these assumptions imply that the effect of gravity on the phase transport can be neglected. This results in the following set of equations for the saturations si, (i ≠ ic) and the pressure :

Here εp (dimensionless) denotes the porosity and κ the permeability (SI unit: m2) of the porous material in the thin barrier. Further more ρi denotes the density (SI unit: kg/m3), μi the dynamic viscosity (SI unit: kg/(m·s)), pi the pressure field (SI unit: Pa), ui the (normal) volumetric flux (SI unit: m/s) and κri the relative permeability (dimensionless) of phase i, respectively.

Since the interfaces between the thin barrier and the adjacent domains are boundaries between a more permeable and a less permeable porous domain, conditions analogous to the Porous Medium Discontinuity Boundary Condition are needed to couple the equation Equation 7-66 for the saturations inside the thin barrier to the equations in the adjacent domains. These condition at the extremities of the extra dimension can be written as:

where the superscript t is used to indicate the saturation and capillary pressure inside the thin barrier (the low permeable side of the interface), and the superscript d indicates the domain adjacent to the downside of the thin barrier (the high permeable side), and

where the superscript u indicates the domain adjacent to the upside of the thin barrier (again the high permeable side) and where ds is the length of the extra dimension, or equivalently, the thickness of the thin structure.

The additional conditions are continuity of the fluxes for all phases and continuity of the pressure of the phase ic computed from the volume constraint. Note that this last condition assumes that this phase is present both inside the thin barrier and in the adjacent domains. Furthermore, this boundary condition assumes that the phase ic computed from the volume constraint is the wetting phase and it is necessary that the settings for the van Genuchten or Brooks and Corey capillary pressure model in the adjacent domains match this assumption.