Speaker
Description
Efficient and accurate simulation of flow and transport in fractured porous media is vital in a variety of applications including carbon sequestration, geothermal energy, and hydrocarbon production. Usually, the uncertainties in these applications are high, which necessitates the use of fast numerical methods to efficiently sample a large number of probable scenarios.
One category of numerical methods employed is the streamline method. This method solves the flow and reconstructs streamlines, which allows for efficient transport simulations as under certain conditions transport can be solved directly along individual streamlines. For the streamline reconstruction, often particle tracking methods (like Pollock's method operating on Cartesian grids) are used.
In this work, however, we propose a mesh-less flow solver that focuses on computing the stream function. Hence, the streamlines can be computed directly from the stream function via contour lines. Furthermore, solving the flow (and stream function) without a mesh allows for greater flexibility. In particular, complex fracture geometries need costly and time-consuming meshing algorithms, whereas mesh-less methods completely circumvent such issues.
The method employs basis functions that numerically approximate the solution near fractures and capture the far-field behavior analytically. This allows to accurately simulate near-field effects once and reuse such high-resolution results in subsequent simulations. Each fracture is then represented by one single basis function, which for a domain containing numerous fractures are superimposed to efficiently compute the entire fractured domain. For a domain with N fractures, this results in solving a linear system of size NxN, which is much smaller than traditional mesh-based methods.
Finally, we show how our basis function method (BFM) can be used to compute the flow, stream function, and transport in fractured porous media. The results are validated, and the accuracy and efficiency of the method is demonstrated in a series of numerical experiments.
| Country | Switzerland |
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