The knowledge of Inflow Performance Relationship is an essential piece of information for well performance evaluation and optimization. For single phase oil flow, production rate is proportional to pressure drawdown and therefore the IPR curve is a straight line. Several empirical relations have been proposed in the literature to predict the performance of oil wells producing with two phase flow conditions. However, these relationships are empirical and limited in application.
This paper presents a general approach for determination of IPR curves of oil wells below the bubble point pressure. This approach uses the results of well test analysis along with relative permeability and PVT data in the proper fluid flow equations for generation of IPR curves. The proposed method is also capable of predicting future IPR curves.
To show that the presented approach is applicable to a wide variety of cases, it is applied to an example oil well in a naturally fractured reservoir. The new method proposed for fractured reservoirs is then compared with some of the empirical methods. It is shown that the new method can predict well deliverability more accurately than other methods. Among different methods evaluated in this work, although underestimating flow rates, Vogel's relation best matched our work.
The approach presented in this paper eliminates the need for multipoint tests, and the required data can be obtained from a buildup test. This approach can be applied to both initial well tests (transient flow) and tests done later during production (pseudo steady state flow). The new analytical method proposed for determination of IPR curve is considered a reliable method since it can closely match the flow tests data.
Inflow Performance Relationship (IPR) of a well is the relation between the production rate and flowing bottom hole pressure. For oil wells, it is frequently assumed that fluid inflow rate is proportional to the difference between reservoir pressure and wellbore pressure. This assumption leads to a straight line relationship that can be derived from Darcy's law for steady state flow of an incompressible, single phase fluid and is called the Productivity Index (PI). However, this assumption is valid only above the bubble point pressure.
Evinger and Muskat , based on multi-phase flow equations showed that a curved relationship existed between flow rate and pressure, when two phase flow occurs in the reservoir (i.e. saturated oil).
In 1968, Vogel  presented an empirical inflow performance relationship for solution-gas drive reservoirs, based on computer simulation results and a wide range of rock and fluid properties. His famous dimensionless IPR was developed for flow of saturated oil from a solution-gas drive reservoir into well ignoring skin effects.
After Vogel, several empirical relationships have been developed to predict the performance of oil wells in saturated reservoirs [3–12]. However, these IPRs are empirical and have been developed for homogeneous, solution-gas drive reservoirs and may not be applicable to other cases.