A detailed understanding of wellbore flow is essential for production engineers in both the design of site equipment and optimisation of operation conditions. With the depletion of conventional resources, the need for unconventional extraction techniques to leverage untapped reserves has seen the generation of new downhole flow conditions. In particular, the extraction of natural gas from coal seams has led to scenarios where liquid removal from the reservoir can cause the development of a counter-current multiphase flow in the well annulus in pumped wells. In this work, high-fidelity computational fluid dynamics is used to capture the momentum interaction between gas and liquid phases in such a flow configuration, allowing for the evaluation and modification of closure relations used in upscaled models.

The computational fluid dynamics model is based on a recently proposed formulation developed using phase-field theory in the lattice Boltzmann (LB) framework. It has been previously applied to the analysis of Taylor bubbles in tubular and annular pipes at a range of inclinations and flow directions. The robustness of the numerical formulation has been proven with a range of benchmark scenarios that extend upon previously reported results in the LB literature. Future investigations will look to apply the developed closure relations into the two-fluid model and compare with in-house experimental and mechanistic results.

Using the multiphase lattice Boltzmann model, the drag force closure relations are investigated for bubbles covering a range of parameters. This assesses the accuracy of existing closures and provides confidence in the developed computational tool. Following on from this, the size of the liquid slug behind a Taylor bubble is analysed. Comparison of the results with pre-existing relations provides a means to modify current large-scale simulators to accurately capture the momentum exchange between gas and liquid phases in a wellbore. With the improved understanding of phase interactions developed in this study, upscaling work is to be conducted through the implementation of closure models within a two-fluid-type model, not unlike OLGA, as well as in a recent mechanistic model.

The novelty of the high-fidelity computational model is in its ability to resolve high density ratio (liquid-gas) flows under complex, dynamic conditions within the lattice Boltzmann framework. Additionally, the development and validation of novel closure relations for mechanistic and two-fluid models improves the accuracy of predictions associated with wellbore operations, ultimately allowing for more optimised production.

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