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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- \left( \frac{q(t)}{q_0} \right)^{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 \cdot (1-b)}

Q_{\rm max}=\infty

The Exponential and  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 intoa finite-reseves decline (possibly Exponential or  or Hyperbolic).

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

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The DCA Arps do not cover all types of production decline, but their application is quite broad and mathematics is quite simple which gained popularity as quick estimation of production perspectives.

See Also

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

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