The Inflow Performance Relationship (IPR) is a key input for integrated studies and optimisation of well/reservoir performance. Constructing the IPR requires reliable flowing bottomhole pressure (FBHP) data. The relatively cheap and evolving option of using flowing tubing head pressure (FTHP) and other surface production data to estimate FBHP depends heavily on a reliable multiphase flow model, as flow in the wellbore is typically multiphasic.

Most of the common multiphase flow correlations relating FBHP and FTHP are empirical, and in spite of their relative complexities, have limited applications. With the conventional modelling approach of assuming an equivalent 'liquid' and gas system, these correlations are inherently limited to two-phase flow conditions. In order to honour field data, they often require some form of tuning algorithms, undermining their reliability under situations where such field data are not available.

In this paper, a strictly analytic (mechanistic) four-phase model is presented. The model, hinged on the basic principles of mass, momentum and energy conservation, accounts for slip between phases, and estimates FBHP from surface measurements, fluid properties, wellbore geometry and completion string data. Its use for IPR construction is also illustrated.

A field example, comparing its performance against an intrinsic two-phase (Beggs and Brill) and an intrinsic four-phase model (Guo), demonstrates its applicability and reliability. Considering its simplicity and robustness, its use can easily be extended to the analysis of drilling hydraulics and other multiphase flow systems that are not explicitly amenable to the so-called generic two-phase approach.


The Inflow Performance Relationship (IPR) describes gross fluid flow rate from a well as a function of the drawdown, which is the difference between reservoir pressure and flowing bottomhole pressure (FBHP). It is a useful tool for sizing production tubing, monitoring well performance, and evaluating intervention activities such as stimulation and artificial lift.

An important data for constructing IPR is the FBHP, obtainable from downhole gauges. Depending on the gauge, the measurements are expensive, time-consuming, or not readily available. In horizontal wells, it is difficult to insert gauges at the ends. Apart from these, it may be necessary to assess accuracy of the gauges.

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