...
Some analytical correlations can be used to approximate the numerical solutions and some of them are brought below.
These correlations are usually expressed in terms of
or LaTeX Math Inline |
---|
body | \frac{q}{q_{max}} = f (p_{wf}) |
---|
|
as alternative to LaTeX Math Block Reference |
---|
|
.They are very helpful in practise to design a proper well flow optimization procedure.
...
where
LaTeX Math Inline |
---|
body | \sigma = \Big \langle \frac{k} {\mu} \Big \rangle \, h = k \, h\, \Big[ \frac{k_{rw}}{\mu_w} + \frac{k_{ro}}{\mu_o} \Big] |
---|
|
– water-based or water-oil-based transmissbility above bubble point
LaTeX Math Block Reference |
---|
anchor | Perrine2phase_alpha |
---|
page | Linear Perrine multi-phase diffusion model |
---|
|
,
for steady-state SS flow and for pseudo-steady state PSS flow. for steady-state SS flow and for pseudo-steady state PSS flow.
The alternative form of the conatsnt PI WFP – Well Flow Performance is:
LaTeX Math Block |
---|
|
\frac{q}{q_{max}} = 1 -\frac{p_{wf}}{p_R} |
Dry Gas IPR
...
For gas producers, the fluid compressibility is high and formation flow is essentially non-linear, inflicting the downward trend on the whole WFP – Well Flow Performance plot (Fig. 2).
...
LaTeX Math Block |
---|
|
qa \, q + b \, q^2 = \Psi(p_R) - \Psi(p_{wf}) |
where
– is pseudo-pressure function,
is laminar flow coefficient and is turbulent flow coefficient. LaTeX Math Inline |
---|
|
is laminar flow coefficient and
It needs two well tests at two different rates to assess
LaTeX Math Inline |
---|
body | \{ q_{max} \, , \, n \} |
---|
|
or is turbulent flow coefficient. But obviously more tests will make assessment more accruate.
Saturated Oil IPR
...
For 2-phase oil-gas formation flow Saturated Oil reservoir with bottom-hole pressure below bubble point
the
near-reservoir zone free gas slippage
effects inflicting also inflicts the downward trend at the right side of
WFP – Well Flow Performance plot (Fig. 3).
...