SPE Journal
Volume 16, Number 1, March 2011, pp. 162-171

Summary

We develop an adjoint model for a simulator consisting of a multiscale pressure solver and a saturation solver that works on flow-adapted grids. The multiscale method solves the pressure on a coarse grid that is close to uniform in index space and incorporates fine-grid effects through numerically computed basis functions. The transport solver works on a coarse grid adapted by a fine-grid velocity field obtained by the multiscale solver. Both the multiscale solver for pressure and the flow-based coarsening approach for transport have shown earlier the ability to produce accurate results for a high degree of coarsening. We present results for a complex realistic model to demonstrate that control settings based on optimization of our multiscale flow-based model closely match or even outperform those found by using a fine-grid model. For additional speed-up, we develop mappings used for rapid system updates during the timestepping procedure. As a result, no fine-grid quantities are required during simulations and all fine-grid computations (multiscale basis functions, generation of coarse transport grid, and coarse mappings) become a preprocessing step. The combined methodology enables optimization of waterflooding on a complex model with 45,000 grid cells in a few minutes.

© 2010. Society of Petroleum Engineers

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History

• Original manuscript received: 4 November 2008
• Meeting paper published: 3 February 2009
• Revised manuscript received: 1 January 2010
• Manuscript approved: 1 April 2010
• Published online: 23 August 2010
• Version of record: 15 March 2011