Summary

The production of hydrocarbon mixtures from wet gas reservoirs can be at times extremely sensitive to variations in pressure and other flow parameters. In such cases, changes in the operating conditions of the wellbore may lead to the formation of a significant amount of condensate which is above the maximum limit that the gas flow is capable of carrying upwards by interfacial drag along the channel. This accumulation of fluid in the wellbore, the so-called liquid loading, generates a backpressure that reduces or even interrupts the production of gas from the reservoir. In this context, the present work is the first of a research line aimed at developing phenomenological models for transient two-phase gas-liquid flows in wellbores. The mass, momentum and energy conservation equations for the phases involved are solved by the Split Coefficient Matrix Method (SCMM) proposed by Chakravarthy et al. (1980) for systems of hyperbolic Partial Differential Equations systems. The numerical discretization is performed using the Finite Differences Method. The model advanced in the present work is concerned with the annular gas-liquid flow pattern in a vertical channel and takes into account the presence of three separate fields: the liquid film, the gaseous core and the liquid entrained as droplets in the gas stream. Mass transport between the two liquid fields is modeled based on correlations available in the literature for the rates of droplet entrainment and deposition. The calculation procedure proposed here for annular flow is verified against the solution of ancillary problems in order of increasing complexity. To solve the simpler problems, one resorts to single phase, two-phase homogeneous and two fluid models (Städtke, 2006), and the results from this simpler models are compared to analytical (in the case of the flow in a shock tube, for example) and known numerical solutions. The annular flow model is verified through comparisons with the GRAMP2 program, developed by Barbosa and Hewitt (2006), for steady-state annular flows.

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