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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 |
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| body | \frac{q}{q_{max}} = f (p_{wf}) |
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as alternative to | LaTeX Math Block Reference |
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.They are very helpful in practise to design a proper well flow optimization procedure.
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where
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| body | \sigma = \Big \langle \frac{k} {\mu} \Big \rangle \, h = k \, h\, \Big[ \frac{k_{rw}}{\mu_w} + \frac{k_{ro}}{\mu_o} \Big] |
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– water-based or water-oil-based transmissbility above bubble point
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| anchor | Perrine2phase_alpha |
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| page | Linear Perrine multi-phase diffusion model |
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,
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:
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\frac{q}{q_{max}} = 1 -\frac{p_{wf}}{p_R} |
Dry Gas IPR
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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).
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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 |
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is laminar flow coefficient and
It needs two well tests at two different rates to assess
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| body | \{ q_{max} \, , \, n \} |
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or is turbulent flow coefficient. But obviously more tests will make assessment more accruate.
Saturated Oil IPR
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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).
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