Generalized three-phase inflow performance relationships (IPRS) for the oil and water phases are presented in this paper. These relationships yield adequate estimates of the production-pressure behavior of oil wells producing from homogeneous, bounded reservoirs during boundary-dominated flow. The IPRs are empirical relationships based on linear regression analysis of simulator results and cover a wide range of reservoir fluid and rock properties. Methods to study the effects of changes in flow efficiency and to predict future performance are also presented.


Predicting the performance of individual oil wells is an important responsibility of the petroleum engineer. Reasonable estimates of well performance allow the engineer to determine the optimum production scheme, design production and artificial lift equipment, design stimulation treatments and forecast production for planning purposes. Each of these items is important to the efficient operation of producing wells and successful reservoir management.

When estimating oilwell performance, it is often assumed that fluid inflow is proportional to the difference between reservoir pressure and wellbore pressure. One of the first relationships to be used based on this assumption was the Productivity Index (PI). This straight-line relationship can be derived from Darcy's law for the steady-state flow of a single incompressible fluid and is the ratio of the producing rate to the pressure difference. However, Evingerand Muskat pointed out that a straight-line relationship should not be expected when multiple phases are flowing in the reservoir. They presented theoretical calculations that showed a curved relationship between flow rate and pressure for two- and three-phase flow.

Vogel later developed an empirical inflow performance relationship (IPR) for solution-gas drive reservoirs that accounted for the flow of two phases, oil and gas, in the reservoir based on computer simulation results. The resulting IPR equation is


Fetkovich also presented an empirical inflow performance relationship based on field data that has gained wide acceptance. His relationship, of a form similar to the empirical gas well deliverability equation proposed by Rawlinsand Schellhardt, is


Both Vogel's and Fetkovich's relations were developed for solution-gas drive reservoirs and are widely used due to their simplicity.

In an attempt to extend Vogel's approach to three-phase flow, Brownpresented a method proposed by Petrobras for determining the inflow performance of oil wells producing water.

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