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One of the most general form of   IPR model below bubble-point pressure:

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a \, q + b \, q^2 = \PsiPsi^n(p_r) - \PsiPsi^n(p_{wf})  \quad , \quad p_b > p_r > p_{wf}

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bodyp_{wf}

bottom-hole pressure (BHP)

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bodyp_r

drainarea formation pressure

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bodyp_b

bubble-point pressure

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bodyn

pseudo-pressure curvature

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bodya

laminar flow coefficient

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bodyb

turbulent flow coefficient

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body\Psi(p)

pseudo-pressure function specific to fluid type

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