Dynamic Upscaling of Multiphase Flow in Porous Media via Adaptive Reconstruction of Fine Scale Variables
- Seong Hee Lee (Chevron ETC) | Xiaochen Wang (Stanford University) | Hui Zhou | Hamdi A. Tchelepi (Stanford University)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Simulation Symposium, 2-4 February, The Woodlands, Texas
- Publication Date
- Document Type
- Conference Paper
- 2009. Society of Petroleum Engineers
- 5.3.1 Flow in Porous Media, 5.5.3 Scaling Methods, 5.5 Reservoir Simulation, 5.2 Reservoir Fluid Dynamics, 5.1.5 Geologic Modeling, 5.3.2 Multiphase Flow, 4.3.4 Scale
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We propose an upscaling method that is based on dynamic simulation of a given model in which the accuracy of the upscaled model is continuously monitored via indirect error-measures. If the indirect measures are bigger than a specified tolerance, the upscaled model is dynamically updated with approximate fine scale information that is reconstructed by a multi-scale finite volume method (Jenny et al., JCP 217; 627-641, 2006). Upscaling of multi-phase flow entails a detailed flow information in the underlying fine scale. We apply adaptive prolongation and restriction operators for flow and transport equations in constructing an approximate fine scale solution. This new method eliminates inaccuracy associated with the traditional upscaling method which relies on prescribed inaccurate boundary conditions in computing upscaled variables. The new upscaling algorithm is validated for two-phase, incompressible flow in two dimensional porous media with heterogeneous permeabilities. It is demonstrated that the dynamically upscaled model achieves high numerical efficiency than the fine-scale models and also provides an excellent agreement with the reference solution computed from fine-scale simulation.
The displacement process of multi-phase flow in porous media shows a strong dependency on process and boundary conditions. These process and boundary condition dependency, as a result, has hampered effort to construct a general coarse grid model that can be applied for multi-phase flow with various operational conditions. In addition, the conventional process in developing coarse-grid models lacks, in a general, a priori error estimate that will guide homogenization or upscaling process. Upscaling of single-phase and multiphase flow in porous media is reviewed by Farmer (2002), Christie (2001) and Barker and Thibeau (1997).
Upscaling of multiphase flow in porous media is much more complex than that of single phase flow because it is difficult to delineate the effects of heterogeneous permeability distribution and multi-phase flow parameters and variables. To alleviate this difficulty, Efendiev and Durkofsky (2002, 2004) derived a generalized convection-diffusion equation to describe multi-phase flow, in place of the usual multi-phase extension of Darcy's equation with coarse grid (volume averaged) parameters and variables. Chen and Durkofsky (2006) combined the local-global upscaling and the generalized convection-diffusion equation to obtain upscaling of two-phase flow. This combined approach consistently provided reasonably accurate solutions for test cases.
|File Size||355 KB||Number of Pages||12|