General Inflow Performance Relationship for Solution-Gas Reservoir Wells

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Summary Two equations are developed to describe the inflow performance relationship (IPR) of wells producing from solution-gas drive reservoirs. These are general equations (extensions of the currently available IPR's) that apply to wells with any drainage-area shape at any state of completion flow efficiency and any stage of reservoir depletion. Introduction The dimensionless IPR presented by Vogel1 was developed for flow of saturated oil from a solution-gas drive reservoir into an "ideal" well (a well without any negative or positive skin effect). For real wells (damaged or stimulated), Standing2 developed a modification to Vogel's IPR and presented a set of dimensionless curves for a range of flow efficiencies different from one. An analytical approach for flow efficiency correction of Vogel's IPR that provides a simple equation to calculate the productivities of real wells at present time was presented by Couto.3 Standing4 suggested a simple procedure to obtain the IPR of an ideal well at any future depletion stage. Applying Couto's approach for flow efficiency correction to Standing's development of future IPR yields a more generalized single IPR equation that accounts for any state of completion flow efficiency and reservoir depletion. A different approach to predict future IPR of a real well has been proposed by Fetkovich.5 His procedure can be rearranged to yield a single IPR equation somewhat similar to the general equation' derived from Vogel's approach. Each of the two equations developed may be used to predict future-time IPR of small- to medium-capacity real wells. Vogel's Present-Time Generalized IPR According to Vogel, the present-time dimensionless IPR for an ideal well (in which flow efficiency E=1) may be expressed asEquation 1 Substituting the dimensionless bottom hole flowing pressure R=pwf/p in Eq. 1 yieldsEquation 2 Couto has shown that for real wells, in which E?1, Vogel's equation can be written for the ideal part of the pressure drawdown asEquation 3 where p'wf=pwf+Dps is the ideal bottom flowing pressure and j=(p-p'wf)/(p-pwf) is the actual flow efficiency of the real well. Eq. 3 applies for any p'wf/p 0. Rewriting Eq. 3 in terms of the dimensionless ideal bottom hole flowing pressure R'=p'wf/p, we obtainEquation 4 which applies for any R' 0.