OGS
[case] ComponentTransport

# ComponentTransport process

## Governing equations

The flow process is described by

$\phi \frac{\partial \rho}{\partial p} \frac{\partial p}{\partial t} + \phi \frac{\partial \rho}{\partial C} \frac{\partial C}{\partial t} - \nabla \cdot \left[\frac{\kappa}{\mu(C)} \rho \nabla \left( p + \rho g z \right)\right] + Q_p = 0,$

where the storage $$S$$ has been substituted by $$\phi \frac{\partial \rho}{\partial p}$$, $$\phi$$ is the porosity, $$C$$ is the concentration, $$p$$ is the pressure, $$\kappa$$ is permeability, $$\mu$$ is viscosity of the fluid, $$\rho$$ is the density of the fluid, and $$g$$ is the gravitational acceleration.

The mass transport process is described by

$\phi R C \frac{\partial \rho}{\partial p} \frac{\partial p}{\partial t} + \phi R \left(\rho + C \frac{\partial \rho}{\partial C}\right) \frac{\partial C}{\partial t} - \nabla \cdot \left[\frac{\kappa}{\mu(C)} \rho C \nabla \left( p + \rho g z \right) + \rho D \nabla C\right] + Q_C + R \vartheta \phi \rho C = 0,$

where $$R$$ is the retardation factor, $$\vec{q} = -\frac{\kappa}{\mu(C)} \nabla \left( p + \rho g z \right)$$ is the Darcy velocity, $$D$$ is the hydrodynamic dispersion tensor, $$\vartheta$$ is the decay rate.

For the hydrodynamic dispersion tensor the relation

$D = (\phi D_d + \beta_T \|\vec{q}\|) I + (\beta_L - \beta_T) \frac{\vec{q} \vec{q}^T}{\|\vec{q}\|}$

is implemented, where $$D_d$$ is the molecular diffusion coefficient, $$\beta_L$$ the longitudinal dispersivity of chemical species, and $$\beta_T$$ the transverse dispersivity of chemical species.

The implementation uses a monolithic approach, i.e., both processes are assembled within one global system of equations.

## Process Coupling

The advective term of the concentration equation is given by the confined groundwater flow process, i.e., the concentration distribution depends on Darcy velocity of the groundwater flow process. On the other hand the concentration dependencies of the viscosity and density in the groundwater flow couples the H process to the C process.

Note
At the moment there is not any coupling by source or sink terms, i.e., the coupling is implemented only by density and viscosity changes due to concentration changes as well as by the temporal derivatives of each variable.