# SPE Journal Volume 12, Number 2, June 2007, pp. 188-195

SPE-93395-PA

### Adaptive Multiscale Finite-Volume Framework for Reservoir Simulation

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DOI  10.2118/93395-PA http://dx.doi.org/10.2118/93395-PA

### Citation

• Tchelepi, H.A., Jenny, P., Lee, S.H. and Wolfsteiner, C. 2007. Adaptive Multiscale Finite-Volume Framework for Reservoir Simulation. SPE J.  12 (2): 188-195. SPE-93395-PA.

### Discipline Categories

• 6.5 Reservoir Simulation

### Summary

A multiscale finite-volume (MSFV) framework for reservoir simulation is described. This adaptive MSFV formulation is locally conservative and yields accurate results of both flow and transport in large-scale highly heterogeneous reservoir models. IMPES and sequential implicit formulations are described. The algorithms are sensitive to the specific characteristics of flow (i.e., pressure and total velocity) and transport (i.e., saturation). To compute the fine-scale flow field, two sets of basis functions - dual and primal - are constructed. The dual basis functions, which are associated with the dual coarse grid, are used to calculate the coarse scale transmissibilities. The fine-scale pressure field is computed from the coarse grid pressure via superposition of the dual basis functions. Having a locally conservative fine scale velocity field is essential for accurate solution of the saturation equations (i.e., transport). The primal basis functions, which are associated with the primal coarse grid, are constructed for that purpose. The dual basis functions serve as boundary conditions to the primal basis functions. To resolve the fine-scale flow field in and around wells, a special well basis function is devised. As with the other basis functions, we ensure that the support for the well basis is local.

Our MSFV framework is designed for adaptive computation of both flow and transport in the course of a simulation run. Adaptive computation of the flow field is based on the time change of the total mobility field, which triggers the selective updating of basis functions. The key to achieving scalable (efficient for large problems) adaptive computation of flow and transport is the use of high fidelity basis functions with local support. We demonstrate the robustness and computational efficiency of the MSFV simulator using a variety of large heterogeneous reservoir models, including the SPE 10 comparative solution problem.

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### History

• Original manuscript received: 14 December 2004
• Revised manuscript received: 28 December 2006
• Manuscript approved: 1 January 2007
• Version of record: 20 June 2007