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Exponential Production Decline | Hyperbolic Production Decline | Harmonic Production Decline |
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| q(t)=q_0 \exp \left( -D_0 \, t \right) |
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| q(t) = \frac{q_0}{ \left( 1+b \cdot D_0 \cdot t \right)^{1/b} } |
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| q(t)=\frac{q_0}{1+D_0 \, t} |
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| Q(t)=\frac{q_0-q(t)}{D_0} |
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| Q(t)=\frac{q_0}{D_0 \, (1-b)} \, \left[ 1- \left( \frac{q(t)}{q_0} \right)^{1-b} \right]
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| Q(t)=\frac{q_0}{D_0} \, \ln \left[ \frac{q_0}{q(t)} \right] |
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| Q_{\rm max}=\frac{q_0}{D_0} |
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| Q_{\rm max}=\frac{q_0}{D_0 \cdot (1-b)} |
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| Q_{\rm max}=\infty |
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| D(t) = D_0 = \rm const |
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anchor | D_hyper |
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alignment | left |
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| D(t) =\frac{D_0}{1+ b \cdot D_0 \cdot t} |
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anchor | D_harm |
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alignment | left |
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| D(t) = \frac{D_0}{1+ D_0 \cdot t} |
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anchor | tau_exp |
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alignment | left |
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| \tau(t) = \tau_0 = \rm const |
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anchor | tau_hyper |
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alignment | left |
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| \tau(t) = \tau_0 + b \cdot t |
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anchor | tau_harm |
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alignment | left |
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| \tau(t) = \tau_0 + t |
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anchor | RPR_exp |
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alignment | left |
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| \mathrm{RPR}(t) = \tau(t) = \tau_0 = \rm const |
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anchor | RPR_hyper |
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alignment | left |
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| \mathrm{RPR}(t) = \tau_0 \, \left[
1 + \frac{b }{(1-b)} \cdot \frac{q_0}{q(t)}
\right]
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anchor | RPR_harm |
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alignment | left |
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| \mathrm{RPR}(t) = \rm{not} \rm{applicable} \rm{due} \rm{to} \rm{infinite} \rm{volume} |
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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 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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