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@wikipedia
Arp's mathematical model of Decline Curve Analysis is based on the following equation:
(1) |
q(t)=q_{i} \, \left[1+b \cdot D \cdot t \right]^{-1/b} |
where
| Initial production rate of a well (or groups of wells) |
(2) |
D=-\frac{1}{q}\frac{dq}{dt} |
|
decline decrement (the higher the
D the stringer is decline) |
| defines the type of decline (see below) |
The cumulative production is then:
(3) |
Q(t)=\int_0^t q(t) dt |
Arp's model splits into four types based on the value of
b coefficient:
Exponential | Harmonic | Hyperbolic | Power Loss |
---|
b = 1 | b = 0 | 0 < b < 1 |
D=D_{\infty} + \frac{t^{n-1}}{\tau^{n}} |
(4) |
q(t)=q_{i} \exp \big [ -D \, t \big ] |
|
(5) |
q(t)=\frac{q_{i}}{[1+D \, t]} |
|
(6) |
q(t)=\frac{q_{i}}{[1+b \, D \, t]^{\frac{1}{b}}} |
|
(7) |
q(t)=q_{i} \exp \big [ -D_{\infty}t- \bigg(\frac{t}{\tau} \bigg)^{n} \big] |
|
(8) |
Q(t)=\frac{q_{i}-q(t)}{D} |
|
(9) |
Q(t)=\frac{q_{i}}{D}\ln (\frac{q_{i}}{q(t)}) |
|
(10) |
Q(t)=\frac{q_{i}}{D \, (1-b)}(q_{i}^{1-b}-q(t)^{1-b})
|
|
|
Exponential decline has a clear physical meaning of pseudo=-steady state production with finite drainage volume.
See Also
Petroleum Industry / Upstream / Production / Subsurface Production / Field Study & Modelling / Production Analysis