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Q_{\rm max}=Q(t=\infty)=\int_0^\infty q(t) \, dt =\frac{q_0}{D_0 \cdot (1-b)} |
The RPR is defined as:
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RPR(t) = \frac{Q_{max}-Q(t)}{q(t)} |
Arp's model splits into three types based on the value of
coefficient:
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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| 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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| RPR(t) = \tau_0 + \frac{\tau_0 \, q_0 \, b /}{(1-b)} \, \frac{1}{q(t)} |
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anchor | RPR_harm |
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alignment | left |
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| RPR(t) = \rm{not applicable due to infinite volume} |
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