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Thursday, March 5 • 12:05 - 12:25
Reservoir/Production: “Rapid Simulation of Hydraulic Fracturing Using a Planar 3D Model,” Bjoern Nordmoen, Aron Anderson, Sergey Nenakhov and Olga Kresse, Schlumberger

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Hydraulic fracturing simulators are widely used in the petroleum industry to design pumping schedules, monitor hydraulic fracturing treatments in real time, and to evaluate pumped treatments. To accurately quantify uncertainties and be able to efficiently optimize fracture treatments, the simulators have to be run multiple times—preferably, “as many times as possible”. Naturally, many independent runs can simply be executed in parallel, but in practice, it is also necessary to have a reasonably short execution time for each individual run.
The fracturing design simulator based on a planar 3D model is designed to produce highly accurate results for planar fractures in layered reservoirs. Unlike many other simulators, this simulator takes into account the properties of each individual reservoir layer. The elastic properties and widths of these layers can vary by orders of magnitude without compromising the integrity of the planar 3D model. Not surprisingly, this simulator feature greatly increases the computational demands compared with other less complex models, especially when there are numerous thin layers in the reservoir. In particular, the nonlinear equations governing the coupling between the fracture width and the pressure have a fully dense Jacobian matrix. To be able to rapidly solve the resulting linear systems, a Fourier transform (FFT)-based method was developed to quickly perform matrix-vector multiplications with the Jacobian matrix, allowing for rapid solutions using iterative methods. This multiplication kernel was heavily tuned (using single-instruction-multiple-data (SIMD) vectorization) and parallelized. Furthermore, the Jacobian matrix can be rather accurately approximated by a sparse matrix, which can be factorized and used as a preconditioner. By carefully assembling this sparse Jacobian matrix and using highly optimized routines for performing the (approximate) factorization, it is possible to achieve a near-constant iteration count with respect to the mesh size, and simultaneously limit the cost of factorizing the preconditioner.
As a result of these efforts, typical problems can be simulated in minutes and even the most challenging simulations can now be completed in a few hours on consumer-grade hardware. These results greatly improve the general usability of the fracturing design simulator based on a planar 3D model and will enable it to be used much more easily for optimization and uncertainty analysis

Thursday March 5, 2015 12:05 - 12:25 CST
BioScience Research Collaborative 6500 Main Street, Houston, Tx 77005

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