  Compositional simulation is challenging, because of highly nonlinear
couplings between multi-component flow in porous media with thermodynamic phase
behavior. The coupled nonlinear system is commonly solved by the fully-implicit
scheme. Various compositional formulations have been proposed. However, severe
convergence issues of Newton solvers can arise under the conventional
formulations. Crossing phase boundaries produces kinks in discretized
equations, and subsequently causing oscillations or even divergence of Newton
iterations. The objective of this work is to develop a smooth formulation that
removes all the property switches and discontinuities associated with phase
changes. We show that it can be very difficult and costly to smooth the
conservation equations directly. Therefore, we first reformulate the coupled
system, so that the discontinuities are transferred to the phase equilibrium
model. In this way a single and concise non-smooth equation is achieved and
then a smoothing approximation can be made. The new formulation with a
smoothing parameter provides smooth transitions of variables across all the
phase regimes. In addition, we employ a continuation method where the solution
progressively evolves toward the target system. We evaluate the efficiency of
the new smooth formulation and the continuation method using several complex
problems. Compared to the standard natural formulation, the developed
formulation and method exhibit superior nonlinear convergence behaviors. The
continuation method leads to smooth and stable iterative performance, with a
negligible impact on solution accuracy. Moreover, it works robustly for a wide
range of flow conditions without parameter tuning.
