Variable | Formula |
---|---|
Density, \(\rho\) | \(\rho = {\rho_l}{s_l} + {\rho_v}(1 - {s_l})\) |
Darcy velocity, \(\vec u\) | \(\vec u = \varepsilon \vec V\), \(\vec V\) is the physical velocity |
Relative permeability of liquid phase and vapor phase, \({k_{rl}}\), \({k_{rv}}\) | \({k_{rl}} = {s_l}^3\), \({k_{rv}} = {(1 - {s_l})^3}\) |
Kinematic viscosity, \(\nu\) | \(\nu = 1/(\frac{{{k_{rl}}}}{{\nu_l}} + \frac{{{k_{rv}}}}{{\nu_v}})\) |
Relative mobility of liquid phase and vapor phase, \({\lambda_l}\), \({\lambda_v}\) | \({\lambda_l} = \frac{{\nu {k_{rl}}}}{{\nu_l}}\), \({\lambda_v} = \frac{{\nu {k_{rv}}}}{{\nu_v}}\) |
Mixture pressure, p | \(\nabla p = {\lambda_l}\nabla {p_l} + {\lambda_v}\nabla {p_v}\) |
Permeability, \(K\) | \(K = \frac{{d_p^2{\varepsilon^3}}}{{150{{(1 - \varepsilon )}^2}}}\) |
Kinematic density, \({\rho_k}\) | \({\rho_k} = {\rho_l}{\lambda_l} + {\rho_v}{\lambda_v}\) |
Specific enthalpy of fluid, \({h_f}\) | \({h_f} = [{\rho_l}{s_l}{h_l} + {\rho_v}(1 - {s_l}){h_v}]/\rho\) |
Kinematic enthalpy of fluid, \({h_k}\) | \({h_k} = {\lambda_l}{h_l} + {\lambda_v}{h_v}\) |
Total mass flux, \(\vec j\) | \(\vec j = - D({s_l})\nabla {s_l} + {k_{rv}}{\lambda_l}\frac{{K({\rho_l} - {\rho_v})}}{{\nu_v}}\vec a\) |
Capillary diffusion coefficient, \(D({s_l})\) | \(D({s_l}) = \frac{{\sqrt {K\varepsilon } }}{\nu }{\lambda_l}(1 - {\lambda_l})\sigma [ - J({s_l})^\prime]\) |
Leverett correlation [35], \(J({s_l})\) | \(J({s_l}) = 1.417(1 - {s_l}) - 2.120{(1 - {s_l})^2} + 1.263{(1 - {s_l})^3}\) |
Effective heat transfer coefficient of fluid, \({k_{feff}}\) | \({k_{feff}} = \varepsilon {k_v}(1 - {s_l}) + \varepsilon {k_l}{s_l}\) |
Effective heat transfer coefficient of solid, \({k_{seff}}\) | \({k_{seff}} = (1 - \varepsilon ){k_s}\) |