Sequential fully implicit Newton method for compositional flow and transport

Compositional simulation for flow and transport in porous media is essential for modeling Enhanced Oil Recovery (EOR) processes. The Sequential Fully Implicit (SFI) scheme is considered as a more flexible and potentially more computationally efficient alternative to the commonly used Fully Implicit Method (FIM). SFI was proposed along with the multiscale method where the flow and transport problems are solved in sequence. SFI opens the door for flexible discretizations, specialized linear solvers, and adaptive strategies. In the SFI method, a time step entails several ‘outer’ iterations. Each iteration consists of two steps: (1) a pressure equation is formed and solved implicitly, and then (2) a set of transport equations is solved, also implicitly. The (outer) iterations are conducted in a fixed-point manner until global convergence is reached. SFI can suffer from slow convergence, or even convergence failure, in strongly coupled flow and transport problems. Examples include dominant buoyancy and complex phase behaviors which are typical in compositional processes. Wong et al. [40] proposed the Sequential Fully Implicit Newton (SFIN) method for multi-physics problems in reservoir simulation and achieved superior outer loop convergence. In this work, we develop the SFIN method for compositional flow and transport problems, and in particular, show how the main assumption of fixing the total velocity can be incorporated. The key step of the SFIN method is a global Newton update that is performed at the end of each flow-transport iteration. During this outer Newton step, the pressure and transport variables are updated together to resolve the coupling between them better. The corresponding linear system is solved by a Krylov solver (e.g., GMRES) using a Jacobian-free approach that only entails matrix-vector multiplications. The latter is constructed by reusing previously computed Jacobian matrices and their preconditioners' information in a computationally efficient way. We present several challenging two- and three-dimensional examples and show that the SFIN method can significantly reduce the number of outer and inner loop iterations compared with the original (non-accelerated) SFI method. We analyze both the nonlinear and linear convergence behaviors for the SFIN method's key components and provide potential speedup estimates with respect to the SFI method.