The present work discusses some improvements that have been introduced in a dynamic model, which was developed for simulating the two-phase flow transient phenomena associated with underbalanced drilling operations. The model enhancements are basically obtained by implementing mechanistic closure relationships and more accurate numerical schemes. This process of improvement is validated through comparison to full-scale experimental data in transient scenarios, showing that the gains in terms of increasing the model accuracy are significant.


Flow modelling has become more and more important in the whole planning process of an UBD operation. Steady-state models have been used for years for designing the operational window. The only drawback here is that steady-state models are not able to reproduce accurately the transient behaviour that occurs during e.g. unloading, connections, and other inevitable transient situations that occur while performing the operation. On the other hand, dynamic models have this capability.

Proper modelling can ensure that the operation can be designed in an optimum manner, and predict the drawdown for various conditions. It is of direct importance to maintain the underbalanced conditions throughout the whole operation to avoid formation damage. Previous experiences indicate that even temporarily overbalanced conditions can reduce the formation productivity. In that sense, both steady-state and dynamic modelling can be of great importance and, in this respect; reliable models are necessary.

The present work is concerned with improvements in transient modelling of underbalanced operations. The accuracy of the model, which is an approximation of the reality, depends heavily on using proper closure laws (mechanistic model) for flow pattern description, pressure losses and gas slippage. Another source of error is the basic numerical scheme that solves the fundamental flow equations.

The process of improvement involves a new mechanistic approach that has been implemented in a transient model. The simulation results are compared with full-scale data in both steady-state and transient conditions, with the main focus on performing connections. The enhanced model not only matchs up very well with the experimental data but also shows a significant improvement compared to older models, particularly, with regards to describing gas dominated systems properly.

The paper also focuses on how numerical schemes can be improved with regards to numerical diffusion. Schemes of high accuracy are required for giving a correct description of the maximum flowrates occurring at the separator (e.g. during the liquid unloading). This is of great importance for sizing properly the surface equipment, particularly the separator. Results are presented showing how a numerical scheme with reduced false diffusion differs from a conventional one that greatly underestimates the maximum flowrates.

Constructing a Flow Model

In general, multi-phase flow can be described by the fundamental two-fluid model1. It consists of separate conservation equations for each of the phases with respect to mass, momentum and energy. A simpler model can be obtained by adding the momentum conservations equations into a mixture momentum equation. This model is named drift flux. In addition, if the temperature modeling is not of large importance, it is also possible to neglect the energy equations and assume a fixed temperature gradient. Based on this assumption, a simplified version of the drift flux model is presented below.

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