A mechanistic model is formulated to predict the flow behavior of two-phase mixtures in horizontal or slightly inclined fully eccentric annuli. The model is composed of a procedure for flow pattern prediction and a set of independent models for calculating gas fraction and pressure drop in stratified, intermittent, dispersed bubble, and annular flow.

Small-scale experimental data performed in a 50 m long straight 4" (101.6 mm) ID pipe containing a 2" (50.8 mm) OD tube lying at the bottom validate the predictions of the model. Test matrix covered not only the horizontal inclination, but also -4° and +4° relative to the horizontal. A total number of 115 tests were carried out with the following mixtures:

  1. air and water were used in 61, and

  2. diesel oil and N2 in 54 tests.

The mechanistic model presents also better performance when compared to the results of some empirical models, as the Beggs and Brill1 correlation and a modified version of the Aziz, Govier, and Fogarasi2 method.


Underbalanced drilling (UBD) technology is becoming a valuable instrument for minimizing the problems associated with invasive formation damage, which is notably responsible for reducing the productivity of oil and gas reservoirs. An UBD operation, when suitably planned and executed, mitigates or eradicates a multitude of effects caused by the invasion of mud filtrate as well as the migration of particulate matter. Despite the varied sort of stimulation techniques already available for overcoming impairment, they are indeed effective for treating vertical wells or shallow damage in horizontal wells. Deeper matrix damage is frequently difficult to remove in long horizontal wells. In this scenario, the combination of the underbalanced process with horizontal drilling results in a consistent way to prevent formation damage, as successfully experienced and documented3–5. However, effective damage reduction depends on the continuous maintenance of the underbalanced condition during the whole drilling period, which brings particular importance to downhole pressure prediction and control6. A poorly designed and/or executed UBD procedure can provoke deeper formation damage than that which may result from a properly planned and executed conventional overbalanced drilling operation4.

Effective two-phase flow modeling is one of the essential components for the achievement of a successful UBD operation. In the planning stage, downhole pressure estimates and injection rates are required to investigate and optimize distinct design concepts. Later on, onsite support is also necessary to analyze actual operational parameters and make any required adjustments3,6.

Despite this necessity of accurate prediction of pressure distribution along the well, very limited efforts have been applied in modeling the flow of liquid and gas through horizontal or near-horizontal annuli. Most studies focused on adapting empirical methods, which where originally developed for handling flow through pipes, to treat the annular geometry7,8. Even though, the search for better models to simulate two-phase flow in pipes switched long time ago, as pointed out in the literature9,10, towards the use of mechanistic or phenomenological approaches.

This content is only available via PDF.
You can access this article if you purchase or spend a download.