Gravity Effects

For large-scale applications it might be necessary to take gravity effects into account. Darcy’s law then applies when the gradient in hydraulic potential drives fluid movement in the porous medium. In this case Darcy’s law can be written as follows:

In this equation g is the vector of gravitational acceleration. The hydraulic potential in the equation comes from the pore pressure, p, and gravity, ρ g.

Furthermore, in the Subsurface Flow Module, g can be defined as using the elevation D according to

where g is the magnitude of gravitational acceleration. The direction of the elevation is defined as

If a reference position rref is specified the elevation is determined using

The choice of D has a significant impact on results and the physics involved. For example, if D is the vertical coordinate z and if the flow is entirely horizontal within the xy-plane, then the gradient in D vanishes and the driving force is caused by pressure gradients alone.