Comparison of nonlinear formulations for two-phase multi-component EoS based simulation

We analyze several widely used nonlinear formulations for general-purpose compositional reservoir simulation. All the formulations are implemented using a unified computational framework based on automatic differentiation. The numerical behaviors using different variable sets, including the so-called natural and mass variables, are investigated. The fully implicit method (FIM) is used throughout this work. In the FIM framework, the full Jacobian matrix with all the equations and constraint relations as a function of the primary and secondary variables is computed. For a given formulation, rigorous construction of the Schur-complement, in which the full Jacobian is reduced to a system for the primary equations in terms of the primary unknowns, is performed purely algebraically. We study multi-component multiphase displacements with significant pressure variation in both space and time, and we focus on challenges posed by nonlinear phenomena, including the appearance and disappearance of phases, and crossing into and out of the critical region. We analyze the behavior of the Newton-based nonlinear solver as a function of timestep size for different variable sets and for different nonlinear updating strategies.