Acta mathematica scientia, Series B >
ANALYSIS OF A COMPRESSIBLE GAS-LIQUID MODEL MOTIVATED BY OIL WELL CONTROL OPERATIONS
Received date: 2011-11-12
Online published: 2012-01-20
Supported by
The research of Steinar Evje has been supported by A/S Norske Shell.
We are interested in a viscous two-phase gas-liquid mixture model relevant for modeling of well control operations within the petroleum industry. We focus on a simplified mixture model and provide an existence result within an appropriate class of weak solutions. We demonstrate that upper and lower limits can be obtained for the gas and liquid masses which ensure that transition to single-phase regions do not occur. This is used together with appropriate a prior estimates to obtain convergence to a weak solution for a sequence of approximate solutions corresponding to mollified initial data. Moreover, by imposing an additional regularity condition on the initial masses, a uniqueness result is obtained. The framework herein seems useful for further investigations of more realistic versions of the gas-liquid model that take into account di?erent flow regimes.
Key words： gas-liquid two-phase model; weak solution; existence; uniqueness
Steinar Evje , K.H. Karlsen . ANALYSIS OF A COMPRESSIBLE GAS-LIQUID MODEL MOTIVATED BY OIL WELL CONTROL OPERATIONS[J]. Acta mathematica scientia, Series B, 2012 , 32(1) : 295 -314 . DOI: 10.1016/S0252-9602(12)60018-6
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