...
| LaTeX Math Block |
|---|
|
q(t)=\frac{q_{i}}{ \, \left[1+b \,cdot D \,cdot t \right]^{\frac{1}{b}}}-1/b} |
where
| Initial production rate of a well (or groups of wells) |
| LaTeX Math Block |
|---|
| D=-\frac{1}{q}\frac{dq}{dt} |
|
decline decrement (the higher the the stringer is decline) |
| defines the type of decline (see below) |
...
Arp's model splits into four types based on the value of
coefficient:
| Exponential | Harmonic | Hyperbolic | Power Loss |
|---|
| b = 1 | b = 0 | 0 < b < 1 |
| LaTeX Math Block |
|---|
| D=D_{\infty} + \frac{t^{n-1}}{\tau^{n}} |
|
| LaTeX Math Block |
|---|
| q(t)=q_{i} \exp \big [ -D \, t \big ] |
| |
Q-q(t)}Harmonic | b = 01 | q(t)=\frac{q_{i}}{[1+b \, D \, t] |
|
} Q\frac{q_{i} \exp \big [ -D_{\infty}t- \bigg(\frac{t}{ |
|
D\ln ( |
| LaTeX Math Block |
|---|
| Q(t)=\frac{q_{i} |
|
}{)Hyperbolic | b = 0..1 | 003NFq[1+b \, D \, t]^{1}b |
| LaTeX Math Block |
|---|
| Q(t)=\frac{q_{i}}{D \, (1-b)}(q_{i}^{1-b}-q(t)^{1-b})
|
|
Power Loss | | LaTeX Math Block |
|---|
|
D=D_{\infty} + \frac{t^{n-1}}{\tau^{n}} |
| LaTeX Math Block |
|---|
|
q(t)=q_{i} \exp \big [ -D_{\infty}t- \bigg(\frac{t}{\tau} \bigg)^{n} \big]
Exponential decline has a clear physical meaning of pseudo=-steady state production with finite drainage volume.
...
