\begin{equation} \begin{aligned} \frac{\partial \rho \phi}{\partial t} - \nabla\cdot \left[ \frac{\rho}{\mu}\mathbf{K_m} (\nabla p_m - \rho \mathbf{g}) \right] - q \delta_\Gamma = 0 \quad \text{in} \, \Omega \\ \frac{\partial \rho \phi}{\partial t} - \nabla_\tau\cdot \left[ \frac{\rho}{\mu}\mathbf{K_f} (\nabla p_f - \rho \mathbf{g}) \right] + q = 0 \quad \text{in} \, \Lambda \\ q = \zeta (p_f - p_m) \quad \text{and} \quad \Gamma = \Omega \cap \Lambda \end{aligned} \end{equation}