Corey-Quad Model Tab

The Corey-Quad Model Tab allows for setting the parameters that define a system of conservation laws that models three-phase flow in a porous medium with each relative permeability mobility function being the square of the corresponding saturation (i.e., a quadratic Corey-type model).

The phases are called aqueous, oleic, and gaseous. The model parameters are the corresponding fluid viscosities, \(\mu_w\), \(\mu_o\), and \(\mu_g\); they are specified in "Corey-Quad Settings". With \(s_w\), \(s_o\), and \(s_g = 1 - s_w - s_g\) denoting the water, oil, and gas saturations, the flux functions are

\[f_w(s_w, s_o) = \lambda_w(s_w)/\lambda_{\text{tot}}(s_w, s_o),\]

\[f_w(s_w, s_o) = \lambda_o(s_o)/\lambda_{\text{tot}}(s_w, s_o),\]

where

\[\lambda_w(s_w) = s_w^2 / \mu_w,\]

\[\lambda_o(s_o) = s_o^2 / \mu_w,\]

\[\lambda_g(s_g) = s_g^2 / \mu_g,\]

\[\lambda_\text{tot} = \lambda_w + \lambda_o + \lambda_g.\]

After choosing flux parameters, you can compute an "optimal" speed range by clicking on "Optimize Speed Range". This speed range is an interval that includes the minimum and maximum values of the characteristic speeds over the domain and has "nice" endpoints.

TODO: Fix the following to document the possibilities for the viscosity matrix, such as the one derived from a capillary pressure model.

The four components of the constant viscosity matrix are specified in "Viscosity Params Settings".