| THEORY & FORMULAE |
The relationship between well flow rate and the pressure drawdown (or flowing bottomhole pressure FBHP) is defined as the Inflow performance relationship (IPR). If the FBHP is below the bubblepoint pressure or if inertial effects become significant at high rates, IPR becomes curvilinear rather than linear.
A number of empirical methods have been proposed to generate IPRs, beginning with the seminal work of Vogel on the subject. These methods usually require a least one stabilized flow test (so-called single-point test) in which flow rate, FBHP and average reservoir pressure are measured. These 3 attributes uniquely define the IPRs coresponding to that reservoir pressure.
In Vogel's method, the IPR curve for a well producing saturated oil from a solution gas drive reservoirs can be approximated by the dimensionless quadratic equation:
    
The standard Vogel's method was modified by Klins et al to explicitly account for the effects of bubblepoint presure and skin, as follows:
    
where
     qo = oil flow rate, bbl/day
     (qo)max = oil flow rate at FBHP = 0, bbl/day
     (qo)maxs=0 = oil flow rate at FBHP = 0 & skin = 0, bbl/day
     pwf = FBHP = flowing bottom hole pressure, psia
     pr = reservoir pressure, psia
     pb = bubblepoint pressure, psia
     s = skin factor, dimensionless, psia
     M = skin-dependent multiplier
     n = bubblepoint-dependent exponent
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