Abstract

In a pumping-well buildup test, computation of bottomhole pressure (BHP) and flow rate (BHF) requires the use of a pressure (BHP) and flow rate (BHF) requires the use of a two-phase flow correlation for estimating the gas void-fraction or holdup along the pipe length and shut-in time. Various correlations are available to perform this task.

The purpose of this work is to review these two-phase correlations and to provide an objective evaluation. This analysis is necessitated by the fact that considerable differences in BHP and BHF may occur depending upon the correlation used-in wells with long pumping liquid columns or those that have high gas/liquid ratio production. Consequently, and potential exists for obtaining different reservoir parameters from transient interpretation.

Using laboratory data for two-phase flow in annular geometry, relative strengths of these correlations are explored. Our own data and those of others (a total of 114 points) are used in this comparative study. For static liquid columns, the correlations of Hasan-Kabir, Gilbert, and Podio et al. provide acceptable agreement with experimental data, exceptions being the Godbey-Dimon and Schmidt et al. correlations. In contrast, for the moving liquid column scenario, as in a buildup test, the Hasan-Kabir model provides the best agreement with the dataset used in this work. A basis for smoothing the bubbly/slug transition boundary is given for the Hasan-Kabir method, together with a field example.

Introduction

During a pumping-well buildup test, both the liquid depth and casinghead pressure are measured to allow computation of BHP and BHF. Typically, the liquid head is the major contributor to the BHP. Thus, the key to successful calculation of both BHP and BHF lies in estimating the density of the liquid column at each timestep. Density calculations entail determining the gas void-fraction or holdup from two-phase flow considerations. A number of two-phase flow correlations can be used for this purpose.

Calculations indicate that both BHP and BHF can be significantly influenced by the two-phase flow correlation used. Consequently, the computed reservoir parameters may be affected by wellbore modeling. Thus, the question often arises as to which correlation is most reliable under diverse well operating conditions.

Because of the indirect nature of the acoustic well sounding (AWS) method for obtaining BHP and BHF, an analyst needs to rely on robust two-phase flow modeling in an annular geometry such as in a tubing/casing annulus. In this way the uncertainities pertaining to the AWS measurements can be minimized even though its quality has been shown to be comparable to downhole gauge measurements.

Based on the historical origin and use, we can classify three types of correlations that have been used in modeling two phase flow in pumping wells: those involving stationary liquid phase flow in pumping wells: those involving stationary liquid columns, moving liquid columns and a combination of both. What is important to recognize is that during a buildup test the liquid column is not stationary. That is, vLs, is high at early times and diminishes to a small value with increasing shut-in time. The gas velocity, Vgs, behaves in a similar fashion although its magnitude is almost always higher than vLs. Ideally then, a model should be capable of handling the entire gamut of both the phase velocities.

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