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Both Harmonic and Hyperbolic declines are empirical while Exponential decline has a physical meaning.
Exponential Production Decline has a physical meaning of declining production from finite drainage volume 

LaTeX Math Inline
bodyV_e
with constant BHP
LaTeX Math Inline
bodyp_{wf}(t) = \rm const
 (a specific type of Boundary Dominated Flow under Pseudo Steady State (PSS) conditions).

There are few approaches to match the Arps decline to the historical data which are covered in DCA Arps Matching @model.

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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Exponential Production Decline ][ Hyperbolic Production Decline ][ Harmonic Production Decline ][ Production Decrement ] 

[ DCA Arps Matching @model ]


References

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Arps, J. J. (1945, December 1). Analysis of Decline Curves. Society of Petroleum Engineers. doi:10.2118/945228-G

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