SPE Journal
Volume 17, Number 2, June 2012, pp. 568-579

Summary

The predominant way of modeling faults in industry-standard flow simulators is to introduce so-called transmissibility multipliers in the underlying two-point discretization. Although this approach provides adequate accuracy in many practical cases, two-point discretizations are only consistent for K-orthogonal grids and may introduce significant discretization errors for grids that severely depart from being K-orthogonal. Such grid-distortion errors can be avoided by lateral or vertical stair-stepping of deviated faults at the expense of errors in the geometrical fault description. In other words, modelers have the choice of either making (geometrical) errors by adapting faults to a grid that is almost K-orthogonal, or introducing discretization errors because of the lack of K-orthogonality if the grid is adapted to deviated faults.

We propose a method for accurate description of faults in solvers based on a hybridized mixed or mimetic discretization, which also includes the MPFA-O method. The key idea is to represent faults as internal boundaries and calculate fault transmissibilities directly instead of using multipliers to modify grid-dependent transmissibilities. The resulting method is geology-driven and consistent for cells with planar surfaces and thereby avoids the grid errors inherent in the two-point method. We also propose a method to translate fault transmissibility multipliers into fault transmissibilities. This makes our method readily applicable to reservoir models that contain fault multipliers.

© 2012. Society of Petroleum Engineers

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History

• Original manuscript received: 22 April 2010
• Revised manuscript received: 27 April 2011
• Manuscript approved: 11 May 2011
• Published online: 7 June 2012
• Version of record: 11 June 2012