Question $1$

Oil flow in the porous medium at isothermal conditions is developed based on two physics

concepts: conversation of momentum and conservation of mass. Those concepts can be

translated into a partial difference equation or flow equation, which are $.$

Derive and discretize the PDE for the following listed conditions.

i$.$ Fluid flow in a porous rectangular rock

ii$.$ The porous rock is fully saturated with oil

iii. Fluid flow in the horizontal plane

iv$.$ Fluid flow in the $x-$axis

v$.$ Fluid is incompressible