Arp's mathematical model of Decline Curve Analysis is based on the following equation:
(1) | q(t)=q_{i} \cdot \left( 1+b \cdot D \cdot t \right)^{-1/b} |
where
q_i = q(t=0) | Initial production rate of a well (or groups of wells) |
D=-\frac{1}{q}\frac{dq}{dt} | decline decrement (the higher the D the stringer is decline) |
0 \leq b \leq 1 | defines the type of decline (see below) |
The cumulative production is then:
(2) | 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 | ||||||||
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b=1 |
b=0 |
0<b<1 | D=D_{\infty} + \frac{t^{n-1}}{\tau^{n}} | ||||||||
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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 / Decline Curve Analysis
References
Arps, J.J.: “ Analysis of Decline Curves,” Trans. AIME,160, 228-247, 1945.