  We present a new implicit higher-order finite element (FE) approach to
efficiently model compressible multicomponent fluid flow on unstructured grids
and in fractured porous subsurface formations. The scheme is sequential
implicit: pressures and fluxes are updated with an implicit Mixed Hybrid Finite
Element (MHFE) method, and the transport of each species is approximated with
an implicit second-order Discontinuous Galerkin (DG) FE method. Discrete
fractures are incorporated with a cross-flow equilibrium approach. This is the
first investigation of all-implicit higher-order MHFE-DG for unstructured
triangular, quadrilateral (2D), and hexahedral (3D) grids and discrete
fractures. A lowest-order implicit finite volume (FV) transport update is also
developed for the same grid types. The implicit methods are compared to an
Implicit-Pressure-Explicit-Composition (IMPEC) scheme. For fractured domains,
the unconditionally stable implicit transport update is shown to increase
computational efficiency by orders of magnitude as compared to IMPEC, which has
a time-step constraint proportional to the pore volume of discrete fracture
grid 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 implicit
MHFE-DG and MHFE-FV are therefore presented as well. Convergence analyses show
twice the convergence rate for the DG methods as compared to FV, resulting in
two to three orders of magnitude higher computational efficiency. Numerical
experiments demonstrate the efficiency and robustness in modeling compressible
multicomponent flow on irregular and fractured 2D and 3D grids, even in the
presence of fingering instabilities.
