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| q(t)=q_0 \exp \left( -D_0 \, t \right) |
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| Q(t)=\frac{q_0-q(t)}{D_0} |
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| Q_{\rm max}=\frac{q_0}{D_0} |
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| D(t)=D_0 = \rm const |
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where
| Initial production rate of a well (or groups of wells) |
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model parameter coincides with a constant Production decline ratestays consant: | LaTeX Math Inline |
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| body | D(t) = D_0 = \rm const |
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| body | --uriencoded--\displaystyle Q(t)=\int_0%5et q(t) \, dt |
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| cumulative production by the time moment |
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| body | --uriencoded--Q_%7B\rm max%7D =\int_0%5e%7B\infty%7D q(t) \, dt |
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| Estimated Ultimate Recovery (EUR) |
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| body | --uriencoded--\displaystyle D(t) = - \frac%7Bdq%7D%7BdQ%7D |
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| Production decline rate |
It can be applied to any fluid production: water, oil or gas.
Exponential Production Decline has a physical meaning of producing from a the finite-volume reservoir with finite reserves | LaTeX Math Inline |
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| body | --uriencoded--Q_%7B\rm max%7D |
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under Pseudo Steady State (PSS) conditions, resulting in constant Production decline rate | LaTeX Math Inline |
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| body | D(t) = D_0 = \rm const |
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A typical example of various fitting efforts of Exponential Production Decline are brought on Fig. 1 – Fig. 3 with exponential fitting being a clear winner.
See Also
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Petroleum Industry / Upstream / Production / Subsurface Production / Field Study & Modelling / Production Analysis / Decline Curve Analysis
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