ANALYSIS OF A COMPRESSIBLE GAS-LIQUID MODEL MOTIVATED BY OIL WELL CONTROL OPERATIONS

作     者：Steinar Evje K.H.Karlsen 

作者机构：Faculty of Science and TechnologyUniversity of Stavanger Centre of Mathematics for ApplicationsUniversity of Oslo 

出 版 物：《Acta Mathematica Scientia》 (数学物理学报（B辑英文版）)

年 卷 期：2012年第32卷第1期

页      面：295-314页

核心收录：

学科分类：080704[工学-流体机械及工程] 07[理学] 08[工学] 0807[工学-动力工程及工程热物理] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：supported by A/S Norske Shell 

主　　题：gas-liquid two-phase model weak solution existence uniqueness 

摘      要：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 different flow regimes.