A new approach for solving nonlinear algebraic systems with complementarity conditions. Application to compositional multiphase equilibrium problems

We present a new method to solve general systems of equations containing complementarity conditions, with special focus on those arising in the thermodynamics multicomponent multiphase mixtures at equilibrium. Indeed, unified formulation introduced by Lauser et al. (2011) has recently emerged as promising way automatically handle appearance and disappearance phases porous media compositional flows. From mathematical viewpoint after discretization space time, this leads system consisting algebraic nonlinear equations. Due nonsmoothness latter, semismooth smoothing methods commonly used for solving such are often slow or may not converge all. This observation led us design strategy called NPIPM (NonParametric Interior-Point Method). Inspired from interior-point optimization, technique we propose advantage avoiding any parameter management while enjoying theoretical global convergence. is validated extensive numerical tests, which compare Newton-min method, standard reference almost all reservoir engineers thermodynamicists.