Efficiency Study of the Multiscale Finite Volume Formulation for Multiphase Flow and Transport
Abstract/Contents
- Abstract
- Multiscale methods have been developed to solve multiphase flow and transport problems in large-scale heterogeneous porous media accurately and efficiently. In this re- port, the computational efficiency of the multiscale finite-volume method (MSFV) is analyzed. The power of MSFV lies in its ability to combine local basis functions with a global coarse-scale problem to solve highly details heterogeneous models. In the first part of this report, we compare MSFV with conventional sequential strategies for solving coupled multiphase flow and transport that employ state-of-the-art linear solvers. Specifically, conventional sequential implicit methods with algebraic multigrid (AMG) for the pressure equation and incomplete LU factorization (ILU) for the saturation equations are used as the reference. We developed modular object-oriented simulation codes for both the multiscale and fine-scale simulation methods. Our results indicate that the adaptivity in pressure (reuse of the basis functions), velocity, and saturation calculations employed in MSFV leads to more efficient computations compared with the conventional fine-scale sequential implicit method. In the two test cases described here, the MSFV simulations are, respectively, eight and two times faster than the sequential fine-scale simulation using AMG and ILU. The efficiency study in this part serves as a solid basis for further development of MSFV as a general algebraic approach for solving nonlinear flow and transport in highly detailed heterogeneous reservoir models. In the second part, we employ an MSFV-based upscaling strategy for multiphase flow and transport, where the original MSFV algorithm is used to construct accurate coarse-scale solutions. The computational domain is dynamically divided into ahead- of-the-front, front, and behind-the-front regions, according to the time evolution of local coarse-scale flow information. The fine-scale solution is reconstructed locally and adaptively in the front region, where the flow field changes rapidly so that very accurate fine-scale solutions are necessary. For the other two regions, which are also determined dynamically, only coarse-scale velocity and saturation fields are computed. The accuracy and efficiency of this MSFV-based upscaling method are tested using several numerical examples, including 2D and 3D models, for both incompressible and compressible flows. Our results indicate that MSFV-based upscaling provides coarse-scale solutions that are in excellent agreement with volume averaged fine-scale solutions, which we take as reference, at a cost comparable to conventional coarse- scale simulation of relatively small models. As the size of the coarse-scale model itself increases, the MSFV-based upscaling strategy is expected to be more accurate and much more efficient compared with schemes that work exclusively with coarse-scale operators for flow and transport.
Description
| Type of resource | text |
|---|---|
| Date created | June 2009 |
Creators/Contributors
| Author | Wang, Xiaochen |
|---|---|
| Primary advisor | Tchelepi, Hamdi |
| Degree granting institution | Stanford University, Department of Energy Resources Engineering |
Subjects
| Subject | School of Earth Energy & Environmental Sciences |
|---|---|
| Genre | Thesis |
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Preferred citation
- Preferred Citation
- Wang, Xiaochen. (2009). Efficiency Study of the Multiscale Finite Volume Formulation for Multiphase Flow and Transport. Stanford Digital Repository. Available at: https://purl.stanford.edu/hp434qb8807
Collection
Master's Theses, Doerr School of Sustainability
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