Multiscale Simulation of Highly Heterogeneous and Fractured Reservoirs

We seek to demonstrate that multiscale methods can be used to simulate fluid flow with acceptable accuracy directly on industry-standard geomodels (corner-point and S-faulted grids) of highly heterogeneous and fractured reservoirs. In particular, we focus on:

• Combining a multiscale mixed finite-element formulation with mimetic discretisation principles in the underlying fine-grid solver to develop (compressible) pressure solvers that are robust with respect to grid geometries and the choice of coarse grids
• Developing efficient methods for communicating between various coarse grids and a general methodology and an application for choosing coarse grids semi-automatically in the multiscale pressure solver to meet requirements with respect to accuracy and computational efficency.
• Developing a new multiphysics multiscale solver for flow in carbonate reservoirs modelled using the Stokes-Brinkmann equations on the fine scale and the standard Darcy flow equations on the coarse scale. 
• Developing efficient transport solvers using flow-based griding (nonuniform coarsening) and reordering principles.
• Combining the items above to develop prototype reservoir simulators and apply them to industry-standard geomodels consisting of multimillion cells or multiple geostatistical realisations to demonstrate proof-of-concept.
• Developing a Matlab toolbox for reservoir simulation to be released under the GNU public license (GPL).

Key Publications

1. S. Krogstad, V. L. Hauge, and A. F. Gulbransen. Adjoint multiscale mixed finite elements. Paper 119112 presented at 2009 SPE Reservoir Simulation Symposium, The Woodlands, Texas, USA, 2-4 February.
2. A. F. Gulbransen, V. L. Hauge, and K.-A. Lie. A multiscale mixed finite-element method for vuggy and naturally-fractured reservoirs. Paper SPE 119104 presented at 2009 SPE Reservoir Simulation Symposium, The Woodlands, Texas, USA, 2-4 February.
3. V. L. Hauge and J. E. Aarnes. Modeling of fractured two-phase flow in fractured porous media on unstructured non-uniform coarse grids. Transport in Porous Media. DOI: 10.1007/s11242-008-9284-y.
4. J. E. Aarnes, V. L. Hauge, and Y. Efendiev. Coarsening of three-dimensional structured and unstructured grids for subsurface flow. Advances in Water Resources, Vol. 30, Issue 11, November 2007, pp. 2177-2193. DOI: 10.1016/j.advwatres.2007.04.007.
5. J. E. Aarnes, S. Krogstad, and K.-A. Lie. Multiscale mixed/mimetic methods on corner-point grids. Computational Geosciences, Special issue on multiscale methods, Vol. 12, No. 3, pp. 297-315, 2008. DOI: 10.1007/s10596-007-9072-8