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| LaTeX Math Block |
|---|
|
q(t)=q_{i} \cdot \left( 1+b \cdot D \cdot t \right)^{-1/b} |
where
| Initial production rate of a well (or groups of wells) |
| LaTeX Math Inline |
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| body | D=-\frac{1}{q}\frac{dq}{dt} |
|---|
|
| decline decrement (the higher the the |
stringer |
| defines the type of decline (see below) |
The cumulative production is then:
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Arp's model splits into three types based on the value of
coefficient:
| Exponential | Hyperbolic | Harmonic |
|---|
| | |
| LaTeX Math Block |
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| q(t)=q_{i} \exp \left( -D \, t \right) |
|
| LaTeX Math Block |
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| q(t)=q_{i} \cdot \left( 1+b \cdot D \cdot t \right)^{-1/b} |
|
| LaTeX Math Block |
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| q(t)=\frac{q_{i}}{1+D \, t} |
|
| LaTeX Math Block |
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| Q(t)=\frac{q_{i}-q(t)}{D} |
|
| LaTeX Math Block |
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| Q(t)=\frac{q_{i}}{D \, (1-b)} \, \left[ q_{i}^{1-b}-q(t)^{1-b} \right]
|
|
| LaTeX Math Block |
|---|
| Q(t)=\frac{q_{i}}{D} \, \ln \left[ \frac{q_{i}}{q(t)} \right] |
|
Arps decline only work for Boundary Dominated Flow.
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