HR: 1330h
AN: H42F-1135    [PDF]
TI: Discrete-Fracture Implicit-Pressure Implicit-Saturation Control-Volume Finite-Element Simulation of Multiphase Flow in Complexly Fractured Rock
AU: * Matthai, S K
EM: s.matthai@imperial.ac.uk
AF: Imperial College London, Department of Earth Science and Engineering, London, SW7 2AZ United Kingdom
AU: Mezentsev, A
EM: a.mezentsev@imperial.ac.uk
AF: Imperial College London, Department of Earth Science and Engineering, London, SW7 2AZ United Kingdom
AU: Eaton, M
EM: m.eaton@imperial.ac.uk
AF: Imperial College London, Department of Earth Science and Engineering, London, SW7 2AZ United Kingdom
AU: Pain, C
EM: c.pain@imperial.ac.uk
AF: Imperial College London, Department of Earth Science and Engineering, London, SW7 2AZ United Kingdom
AB: Meter- to kilometer-scale multiphase fluid flow in complexly fractured rock is difficult to investigate in experiments, but is of wide scientific and economic interest. Numerical simulation is an attractive alternative to experiments but physical realism requires an adequate discretization of the flow equations in space and in time (1), the exact representation of material interfaces and a separate interior of the fractures (2), and a treatment of the non-linearities in the equations arising from the dependence of phase mobility on saturation and history-dependent capillary pressure - saturation relationships (3). The simultaneous spatial discretization of the rock matrix and fractures with large aspect ratios can be achieved with unstructured grids. However, even if large-aspect ratio hybride prism-tetrahedron-pyramid-hexahedron FE meshes (LARHM) are used, the smallest cells will occur inside fractures or at their intersections where the fastest flow will take place. This disqualifies transport schemes that are constrained by the grid Courant number, because a prohibitively large number of very small time steps would be necessary to model the fluid displacement of interest. Here we present our first CVFE-LARHM-based computations of the Buckley-Leverett equation in porous media with discrete three-dimensional fracture representations. Our original implicit pressure - implicit saturation scheme is second-order accurate in space and in time. This is demonstrated for the linear and the Brooks-Corey relative-permeability and capillary-pressure relationships in the fractures and the matrix, respectively, evaluating the schemes accuracy and performance through a comparison with an established CFL-dependent IMPES FEM-CV higher-order accurate schemes. We show that our new scheme largely overcomes the CFL limitation. It still weakly relates to CFL as it becomes increasingly diffusive when CFLmax=1 is exceeded. In unstructured fracture-matrix models, flow velocity in the fractures is typically 2-3 orders of magnitude higher than in the matrix where suitable elements can be up to 1,000 times larger. Thus, for a reasonable global choice of $CFL_{max}$ (100-10,000), the scheme is sub-CFL and second-order accurate in the coarse matrix. Its more diffusive super-CFL behavior in fast-flowing fracture segments is offset by their orders-of-magnitude higher refinement. A limit on time step size is imposed by the progressive invalidation of the velocity field by the changing saturation. Ways to relax this limit by predicting saturation changes using the shock velocity are shown.
DE: 1857 Reservoirs (surface)
DE: 3210 Modeling
DE: 3220 Nonlinear dynamics
DE: 3230 Numerical solutions
DE: 8045 Role of fluids
SC: Hydrology [H]
MN: 2003 Fall Meeting