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| Exponential Production Decline | Hyperbolic Production Decline | Harmonic Production Decline |
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| q(t)=q_0 \exp \left( -D \, t \right) |
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| q(t)=q_0 \cdot \left( 1+b \cdot D \cdot t \right)^{-1/b} |
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| q(t)=\frac{q_0}{1+D \, t} |
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| Q(t)=\frac{q_0-q(t)}{D} |
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| Q(t)=\frac{q_0}{D \, (1-b)} \, \left[ 1- \left( \frac{q(t)}{q_0} \right)^{1-b} \right]
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| Q(t)=\frac{q_0}{D} \, \ln \left[ \frac{q_0}{q(t)} \right] |
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| Q_{\rm max}=\frac{q_0}{D} |
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| Q_{\rm max}=\frac{q_0}{D \cdot (1-b)} |
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| Q_{\rm max}=\infty |
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The Exponential and Hyperbolic decline are applicable for Boundary Dominated Flow with finite reserves
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| body | --uriencoded--Q_%7B\rm max%7D \leq \infty |
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while
Harmonic decline decline is associated with production from the reservoir with infinite reserves
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| body | --uriencoded--Q_%7B\rm max%7D = \infty |
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. In other words the
Harmonic decline decline is very slow.
Since all physical reserves are finite the true meaning of Harmonic decline decline is that up to date it did not reach the boundary of these reserves and at certain point in future it will transform into a finite-reserves decline (possibly Exponential or Hyperbolic).
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Petroleum Industry / Upstream / Production / Subsurface Production / Field Study & Modelling / Production Analysis / Decline Curve Analysis
[ Exponential Production Decline ][ Hyperbolic Production Decline ][ Harmonic Production Decline ]
References
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Arps, J. J. (1945, December 1). Analysis of Decline Curves. Society of Petroleum Engineers. doi:10.2118/945228-G
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