A new comprehensive, mechanistic model that allows more precise predictions of wellbore pressure and two-phase flow parameters for underbalanced drilling (UBD) is proposed. The model incorporates the effects of fluid properties and pipe sizes and, thus, is largely free of the limitations of empirically based correlations.

The model is validated against actual UBD field data and full-scale experiments in which the gas and liquid injection flow rates as well as drilling fluid properties were similar to those used in common UBD operations. Additionally, a comparison against two different commercial, empirically based UBD simulators shows better performance with the mechanistic model.


It is generally accepted that the success of UBD operations is dependent on maintaining the wellbore pressure between the boundaries determined by formation pressure, wellbore stability, and the surface equipment's flow capacity. Therefore, the ability to accurately predict wellbore pressure is critically important for both designing the UBD operation and predicting the effect of changes in the actual operation.

Because of the complex nature of the hydraulic system of UBD operations in which two or more phases (liquid, gas, and solids) commonly flow, the prediction of pressure drop and flow parameters, such as liquid holdup and in-situ liquid and gas velocities, are performed mainly with empirical, two-phase flow methods. The Beggs and Brill1 correlation is the most popular among the current, commercial UBD simulators. However, it is recognized by the petroleum industry that most of these empirical correlations were developed from experimental databases, thereby making extrapolation hazardous.2 Moreover, the Beggs and Brill1 correlation has been shown to overpredict or fail to predict bottomhole pressures for both vertical and horizontal UBD operations.3,4

Since the mid-1970s, significant progress has been made in understanding the physics of two-phase flow in pipes and production systems. This progress has resulted in several two-phase flow mechanistic models to simulate pipelines and wells under steady-state as well as transient conditions. Consequently, mechanistic models, rather than empirical correlations, are being used with increasing frequency for designing multiphase production systems. Based on this trend of improvement, the application of mechanistic models to predict wellbore pressure and two-phase flow parameters seems to be the solution to increasing the success of UBD operations by improving such predictions.

Literature Review.

Bijleveld et al.5 developed a steady-state UBD program to assist well engineers in planning and executing underbalanced operations. This in-house computer program uses the mechanistic two-phase flow approach. However, there is almost no technical information in the literature about implementing the mechanistic models in UBD operations.

Hasan and Kabir6 developed a mechanistic model to estimate the void fraction during upward concurrent two-phase flow in annuli, and Hasan7 developed a mechanistic model to estimate the void fraction during downward, concurrent two-phase flow in pipes. These models used the drift-flux approach to predict the gas void fraction in bubble and slug flow. However, for slug flow this represents a simplification that does not rigorously consider the difference in the drift-flux between the liquid slug and the Taylor bubble, so inaccurate predictions may be expected from a model that strictly follows this approach.

Recently, Lage et al. 8,8 and Lage 10 developed a mechanistic model based on a comprehensive experimental and theoretical investigation of upward two-phase flow in a concentric annulus. Although the model was extensively validated against small and full-scale experimental data gathered from annular geometries. they recommended evaluating it in other annular configurations. Moreover, they did not consider downward two-phase flow through the drillstring and bit nozzles in their mechanistic model.

Even though other mechanistic approaches, such as OLGA11 and Ansari,12 have been used to predict pressure-drop calculations for flow in annuli during UBD pilot tests,3 they have not bee. specially developed or modified for UBD operations. Consequently, they are not typically used for designing UBD operations.10

Given the necessity for accurately predicting wellbore pressures during UBD operations and the fact that mechanistic models perform better than empirical correlations, the previous literature review reveals that further work is needed to implement the phenomenological approach into the current UBD models. Therefore, the main purpose of this study was to develop a new, comprehensive, mechanistic model capable of predicting pressures and two-phase flow parameters throughout a vertical well during UBD operations. This will provide more accurate wellbore pressure predictions because the model incorporates fluid properties and pipe sizes and, thus, is largely free of the limitations of empirically based correlations.

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