Dual evolution mixed variational analysis of multiphase flow in the subsurface

Abstract

Dual evolution mixed variational formulations of multiphase flow models in the subsurface are established and analyzed. Specifically, compositional multiphase flow of a triphasic water–oil–gas multicomponent flow is treated, with a dual Gibbs oil–gas mass transfer model. Qualitative analysis of the mixed variational models is performed applying composition duality principles and methods. For multiphysics as well as parallel computing, macro-hybrid variational reformulations are considered. Dual semi-implicit time-marching schemes are presented as semi-discrete approximations for the flow-transport variational models, as well as for a precondition augmented exactly penalized dual Gibbs optimality variational formulation, which are all implementable as parallel proximal penalty–duality algorithms. In this manner, bases for fully discrete non-conforming macro-hybrid mixed finite element numerical realizations are rendered.