...
Driving equation | Initial condition |
|
---|
Homogeneous Aquifer reservoir with | Initial Aquifer pressure is considered to be the same as Net Pay Area |
|
LaTeX Math Block |
---|
| \frac{\partial p_a}{\partial t} = \chi \cdot \left[ \frac{\partial^2 p_a}{\partial r^2} + \frac{1}{r}\cdot \frac{\partial p_a}{\partial r} \right] |
| LaTeX Math Block |
---|
| p_a(t = 0, r)= p(0) |
| |
Inner Aquifer boundary | Outer Aquifer boundary is one of the two below: |
---|
Pressure variation at the contact with Net Pay Are | "No-flow" | "Constant pressure" |
LaTeX Math Block |
---|
| p_a(t, r=r_e) = p(t) |
| LaTeX Math Block |
---|
anchor | p1p_PSS |
---|
alignment | left |
---|
| \frac{\partial p_a}{\partial r}
\bigg|_{(t, r=r_a)} = 0 |
| LaTeX Math Block |
---|
anchor | pconst |
---|
alignment | left |
---|
| p_a(t, r = \infty) = 0 |
|
...
One can easily check that
LaTeX Math Block Reference |
---|
|
honours the whole set of equations
LaTeX Math Block Reference |
---|
|
–
LaTeX Math Block Reference |
---|
|
/ LaTeX Math Block Reference |
---|
|
and as such defines a unique solution of the above problem.
...