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

LaTeX Math Inline
bodyb
 coefficient:

ExponentialHyperbolicHarmonic
Hyperbolic

LaTeX Math Inline
bodyb=

1

0

LaTeX Math Inline
body

b=0

0<b<1

LaTeX Math Inline
body

0<b<1

b=1


LaTeX Math Block
anchor1
alignmentleft
q(t)=q_{i} \exp \left( -D \, t \right)



LaTeX Math Block
anchor
1
003NF
alignmentleft
q(t)=
\frac{
q_{i}
}{
 \cdot \left( 1+b \cdot D \
,
cdot t
} 
 \right)^{-1/b}



LaTeX Math Block
anchor
003NF
1
alignmentleft
q(t)=\frac{q_{i
} \cdot \left( 1+b \cdot 
}}{1+D \
cdot
, t
\right)^{-1/b}
}



LaTeX Math Block
anchor1
alignmentleft
Q(t)=\frac{q_{i}-q(t)}{D}



LaTeX Math Block
anchor1
alignmentleft
Q(t)=\frac{q_{i}}{D
}
 \,
\ln
(1-b)} \, \left[
\frac{
q_{i}^{1-b}
{
-q(t)^{1-b} \right]



LaTeX Math Block
anchor1
alignmentleft
Q(t)=\frac{q_{i}}{D} \,
(1-b)} \,
\ln \left[ \frac{q_{i}}
^
{
1-b}-
q(t)
^{1-b
} \right]

Arps decline only work for Boundary Dominated Flow.
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