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Upscaling and Simulation of Two-Phase Flow in Porous Media

Khoozan, Davood | 2015

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 48131 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Firoozabadi, Bahar
  7. Abstract:
  8. Advanced reservoir characterization methods can yield geological models at a very fine resolution, containing 1011-1018 cells while the common reservoir simulators can handle much fewer numbers of cells due to computer hardware limitations. The process of coarsening the fine-scale model to simulation models is known as upscaling. There are three fundamental steps in the procedure of upscaling, i.e. defining the coarse grid geometry, calculating the average properties for the generated coarse grid and simulation of the two-phase flow equations on the generated coarse-scale model. In this thesis, the focus will be on investigating the applicability of optimization in the context of coarse grid geometry definition and introducing a multi-scale simulation method to solve the flow equations on the coarse-scale grid. To do so, a permeability-based and a velocity-based a-priori error estimation techniques based on image processing methods are proposed. The performance of the introduced error estimation methods is investigated thoroughly over highly heterogeneous cases under various coarsening levels, permeability upscaling methods, boundary conditions and mobility ratios and the proper objective function is defined. This objective function is employed to generate the optimum Cartesian structured coarse grid geometry using multi-start global optimization algorithm with generating set search method as its local optimizer. An analytical multi-scale simulation method is also introduced to solve the two-phase flow equations on the optimum coarse-scale model with high accuracy and speed. The performance of the proposed upscaling technique is investigated through various highly heterogeneous test cases under different upscaling levels, coarse grid dimensions, permeability upscaling methods, mobility ratios and boundary conditions. The results show that the proposed upscaling method can yield the optimum coase grid while the introduced analytical multi-scale method yields accurate results with high speed. The results also show that the proposed upscaling method outperforms existing methods noticeably in terms of yielding the most accurate coarse-scale model. To extend the proposed method to unstructured grids, a mixed hybrid finite element method employing the idea of hypothetical triangulation is proposed that can be used to solve the single-phase velocity field over highly heterogeneous porous media. Although the number of equations in the introduced technique is equal to the standard mixed hybrid finite element method, the results show that it can result into highly accurate results in terms of yielding the single-phase velocity field. The results also showed that since the upscaled permeability field can be calculated in each hypothetical triangle, the resulted homogenized permeability field will be inevetibly more accuate than other techniques. Based on the yielded results, one may claim that the proposed mixed hybrid finite element method is a solid step in extending the optimization-based upscaling to unstructured grids
  9. Keywords:
  10. Porous Media ; Global Optimization ; Image Processing ; Upscaling ; Mixed Finite Element Method ; Analytical Solution ; Multi-Scale Simulation

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