Efficient dissipation-based nonlinear solver for multiphase flow in discrete fractured media

Abstract

Solving nonlinear equation systems resulting from the Fully Implicit Method (FIM) remains a challenge for numerical simulation of multiphase flow in subsurface fractured 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.Limited research has been conducted on nonlinear solver techniques for multiphase flow and transport in fractured media. We make an extension of a new dissipation-based continuation (DBC) method to DFM models. Our goal is to prevent timestep cuts and maintain 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 strategies are developed to provide the optimal dissipation matrix for the multiphase hyperbolic system.We assess the new nonlinear solver using 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 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.