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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 Hyperbolic decline  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 into a finite-reseves reserves decline (possibly Exponential or Hyperbolic).

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

Harmonic and Hyperbolic declines  declines are both empirical.

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.

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