...
LaTeX Math Block |
---|
|
q(t)=q_0 \cdot \left( 1+b \cdot D_0 \cdot t \right)^{-1/b} |
where
| Initial production rate of a well (or groups of wells) |
LaTeX Math Inline |
---|
body | D=-\frac{1}{q}\frac{dq}{dt}_0 |
---|
|
| model parameter characterizing the decline rate decline decrement (the higher the the stronger is decline) |
| defines the type of decline (see below) |
...
LaTeX Math Block |
---|
|
Q_{\rm max}=Q(t=\infty)=\int_0^\infty q(t) \, dt =\frac{q_0}{D_0 \cdot (1-b)} |
Arp's model splits into three types based on the value of
coefficient:
Exponential Production Decline | Hyperbolic Production Decline | Harmonic Production Decline |
---|
| | |
LaTeX Math Block |
---|
| q(t)=q_0 \exp \left( -D_0 \, t \right) |
|
LaTeX Math Block |
---|
| q(t)=q_0 \cdot \left( 1+b \cdot D_0 \cdot t \right)^{-1/b} |
|
LaTeX Math Block |
---|
| q(t)=\frac{q_0}{1+D_0 \, t} |
|
LaTeX Math Block |
---|
| Q(t)=\frac{q_0-q(t)}{D_0} |
|
LaTeX Math Block |
---|
| Q(t)=\frac{q_0}{D_0 \, (1-b)} \, \left[ 1- \left( \frac{q(t)}{q_0} \right)^{1-b} \right]
|
|
LaTeX Math Block |
---|
| Q(t)=\frac{q_0}{D_0} \, \ln \left[ \frac{q_0}{q(t)} \right] |
|
LaTeX Math Block |
---|
| Q_{\rm max}=\frac{q_0}{D_0} |
|
LaTeX Math Block |
---|
| Q_{\rm max}=\frac{q_0}{D_0 \cdot (1-b)} |
|
LaTeX Math Block |
---|
| Q_{\rm max}=\infty |
|
...