Dissipation-Based Nonlinear Solver for Efficient Implicit Simulation of Compositional and Discrete Fracture Models

The solution of nonlinear equation-system resulting from the Fully Implicit Method (FIM) remains a challenge for numerically simulating multi-phase flow in subsurface fracture media. The Courant numbers can vary orders of magnitude across discrete fracture- matrix (DFM) models because of the high contrasts in the permeability and length-scale between matrix and fracture. The standard Newton solver is usually unable to converge for big timestep sizes or poor initial guesses. Limited research has been conducted on nonlinear solver techniques for multi-phase compositional flow-transport in fractured media. We make an extension of a new dissipation-based continuation (DBC) algorithm to compositional and DFM models. Our goal is to prevent time-step cuttings and sustain efficient time-stepping for FIM. The DBC algorithm builds a homotopy of the discretized conservation equations through the addition of numerical dissipation terms. We introduce a continuation parameter for controlling the dissipation and ensuring that accuracy of the computed solution will not be reduced. Under the nonlinear framework of DBC, general dissipation operators and adaptive methods are developed to provide the optimal dissipation matrix for multiphase compositional hyperbolic systems. We assess the new nonlinear solver through multiple numerical examples. Results reveal that the damped-Newton solver suffers from serious restrictions on timestep sizes and wasted iterations. In contrast, the DBC solver provides excellent computational performance. The dissipation operators are able to successfully resolve the main convergence difficulties. We also investigate the impact of star-delta transformation which removes the small cells at fracture intersections. Moreover, we demonstrate that an aggressive time-stepping does not affect the solution accuracy.