Weak solutions of a gas-liquid drift-flux model with general slip law for wellbore operations

Steinar Evje; Huanyao Wen

doi:10.3934/dcds.2013.33.4497

Article Contents

2013, Volume 33, Issue 10: 4497-4530. Doi: 10.3934/dcds.2013.33.4497

This issue Previous Article Dispersive estimates for matrix Schrödinger operators in dimension two Next Article Polynomial and rational first integrals for planar quasi--homogeneous polynomial differential systems

Weak solutions of a gas-liquid drift-flux model with general slip law for wellbore operations

Steinar Evje^1, and
Huanyao Wen^2,

1.
University of Stavanger (UiS), 4036 Stavanger
2.
University of Stavanger, NO-4036 Stavanger

Received: November 2012

Revised: January 2013

Published: October 2013

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Abstract

In this work we study a compressible gas-liquid models highly relevant for wellbore operations like drilling. The model is a drift-flux model and is composed of two continuity equations together with a mixture momentum equation. The model allows unequal gas and liquid velocities, dictated by a so-called slip law, which is important for modeling of flow scenarios involving for example counter-current flow. The model is considered in Lagrangian coordinates. The difference in fluid velocities gives rise to new terms in the mixture momentum equation that are challenging to deal with. First, a local (in time) existence result is obtained under suitable assumptions on initial data for a general slip relation. Second, a global in time existence result is proved for small initial data subject to a more specialized slip relation.

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Mathematics Subject Classification: Primary: 76T10, 76N10; Secondary: 65M12, 35L60.

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References

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