Transient flow in Radial Composite Reservoir:
| 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) |
|
| LaTeX Math Block |
|---|
| p_a(t, r=r_e) = p(t) |
|
| LaTeX Math Block |
|---|
| anchor | p1_PSS |
|---|
| alignment | left |
|---|
| \frac{\partial p_a}{\partial r} \bigg|_ {r=r_a} = 0 |
|
One can easily check that pressure from | LaTeX Math Block Reference |
|---|
|
honors the whole set of equations | LaTeX Math Block Reference |
|---|
|
–| LaTeX Math Block Reference |
|---|
|
and as such defines a unique solution of the above problem. | 