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We present a new implicit higher-order finite element (FE) approach toefficiently model compressible multicomponent fluid flow on unstructured gridsand in fractured porous subsurface formations. The scheme is sequentialimplicit: pressures and fluxes are updated with an implicit Mixed Hybrid FiniteElement (MHFE) method, and the transport of each species is approximated withan implicit second-order Discontinuous Galerkin (DG) FE method. Discretefractures are incorporated with a cross-flow equilibrium approach. This is thefirst investigation of all-implicit higher-order MHFE-DG for unstructuredtriangular, quadrilateral (2D), and hexahedral (3D) grids and discretefractures. A lowest-order implicit finite volume (FV) transport update is alsodeveloped for the same grid types. The implicit methods are compared to anImplicit-Pressure-Explicit-Composition (IMPEC) scheme. For fractured domains,the unconditionally stable implicit transport update is shown to increasecomputational efficiency by orders of magnitude as compared to IMPEC, which hasa time-step constraint proportional to the pore volume of discrete fracturegrid cells. However, when lowest-order Euler time-discretizations are used,numerical errors increase linearly with the larger implicit time-steps,resulting in high numerical dispersion. Second-order Crank-Nicolson implicitMHFE-DG and MHFE-FV are therefore presented as well. Convergence analyses showtwice the convergence rate for the DG methods as compared to FV, resulting intwo to three orders of magnitude higher computational efficiency. Numericalexperiments demonstrate the efficiency and robustness in modeling compressiblemulticomponent flow on irregular and fractured 2D and 3D grids, even in thepresence of fingering instabilities.

Implicit Finite Volume and Discontinuous Galerkin Methods for Multicomponent Flow in Unstructured 3D Fractured Porous Media