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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 

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 coefficient:

Exponential Production DeclineHyperbolic Production DeclineHarmonic 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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D(t) =\frac{D_0}{1+ b \cdot D_0 \cdot t}
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D(t) = \frac{D_0}{1+ D_0 \cdot t}
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\tau(t) = \tau_0 = \rm const
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\tau(t) = \tau_0 + b \cdot t
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\tau(t) = \tau_0 + t
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RPR(t) = \tau(t) \tau_0 = \rm const
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RPR(t) = \tau_0 + \frac{\tau_0 \, q_0 \, b /}{(1-b)} \, \frac{1}{q(t)}
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RPR(t) = \rm{not applicable due to infinite volume}

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