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Anchor
Current_rate_cumulative Current_rate_cumulative

Match the value of the current rate and cumulative 

LaTeX Math Inline
body --uriencoded--q%5e*(t=t_N) = q_N

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LaTeX Math Inline
body --uriencoded--Q%5e*(t=t_N) = Q_N

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The value of the model rate at the current time moment and decline pace are set to match both current rate 

This makes Exponential Production Decline and Harmonic Production Decline are fully set while Hyperbolic Production Decline has opportunity to vary one model parameter

q(t) = \frac{Q_N/\tau_0}{1-\exp(-t_N/\tau_0)}  \cdot \exp(-t/\tau_0) 

q(t) = \frac{(1-b) \cdot Q_N/\tau_0}{ 1 - \left( 1 + b \, t_N/\tau_0 \right) ^{-b/(1-b)}} \cdot \frac{1}{\left(1 + b\, t/\tau_0 \right)^{1/b}}

q(t)=\frac{Q_N/\tau_0}{\ln (1+ t_N/\tau_0)} \cdot \frac{1}{1+t/\tau_0}

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