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Arp's model splits into three types based on the value of 

q(t)=q_0 \exp \left( -D \, t \right)

q(t)=q_0 \cdot \left( 1+b \cdot D \cdot t \right)^{-1/b}

q(t)=\frac{q_0}{1+D \, t} 

Q(t)=\frac{q_0-q(t)}{D}

Q(t)=\frac{q_0}{D \, (1-b)} \, \left[ 1-{\frac{q(t)}{q_0}}^{1-b} \right]

Q(t)=\frac{q_0}{D} \, \ln \left[ \frac{q_0}{q(t)} \right]

Q_{\rm max}=\frac{q_0}{D}

Q_{\rm max}=\frac{q_0}{D \, (1-b)}

Q_{\rm max}=\infty

Arps decline only work for Boundary Dominated Flow.

The Exponential and Hyperbolic decline are applicable for Boundary Dominated Flow with finite reserves

Since all physical reserves are finite the true meaning of Harmonic 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 Exponential or Hyperbolic decline.

Exponential Exponential decline has a physical meaning of declining production from finite drainage volume 

Harmonic and Hyperbolic declines are both empirical.

See Also

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Petroleum Industry / Upstream /  Production / Subsurface Production / Field Study & Modelling / Production Analysis / Decline Curve Analysis

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