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Combination of a Multi-scale Finite Volume and Streamline Methods for Reservoir Simulation

Faroughi, Salahaddin | 2011

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 42168 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Taghizadeh Manzari, Mehrdad
  7. Abstract:
  8. In this work, the combination of a multi-scale finite volume and streamline methods is presented for subsurface flow modeling. The used multi-scale method in this work is the same with the traditional type of it in algorithm and formulation. However, because of using a new mesh structure for implementation of multi-scale finite volume method, the new method named by Staggered Mesh Multi-scale Finite Volume (SMMsFV) method. Using the staggered mesh has some advantages such as reducing the computational cost and increasing the accuracy of the multi-scale method. In the SMMsFV method, first the coarse grid and dual coarse grid are constructed on the underlying fine grid. Then, the basis and correction functions are calculated to determine the coarse scale transmissibilities. The basis and correction functions are determined by solving the homogeneous and non-homogeneous local problems using the Dirichlet boundary condition in each dual coarse cell, respectively. After calculating the coarse scale transmissibilities, the coarse scale pressure equation is generated that must be solved to find the pressure field in the domain. The required computational cost for solving this equation is the same with that in the traditional upscaling method roughly. In the next step in the SMMsFV method, the fine-scale pressure field is approximated by a linear interpolation of the coarse scale pressure, basis and correction functions. The final step, reconstruction the pressure field, is needed due to that the obtained fine-scale pressure in previous step does not create a mass conservative velocity field. In the proposed multi-scale method, SMMsFV method, a physical improvement on the localization assumption step is also considered. This improvement will extremely be enhanced the accuracy of the approximated pressure by multi-scale method. When the mass conservative velocity field was obtained, the transport equation will be solved by utilizing the streamline method. In the streamline method, first, the streamlines are traced based on the velocity field from the injector cell’s boundary to the product cell’s boundary to obtain the new local coordinate so-called time-of-flight. Then, the two-dimension transport equation is decoupled into multiple one-dimension in terms of time-of-flight. Finally, by solving the multiple 1-D transport equation along each streamlines (in time-of-flight coordinate), the results are interpolated to reach the 2-D transport equation’s result with a less computational time than solving 2-D equation by the conventional methods. Thus in this work, a combination of the SMMsFV method as a pressure solver and the standard streamline (SL) method to solve the transport equation is presented for subsurface flow modeling that named by SMMsFVSL method. Combinations the two rapid methods will assign a minimize computational cost requirements for the simulator. The performance of the SMMsFVSL method is compared with the fine-scale simulation method (traditional simulation) using numerous 2-D examples. The outcomes of these comparisons show that the SMMsFVSL method has good accuracy with low computational cost. For example, it is shown that the speed-up factor of using this method for a problem with 900 to 100000 cells varies between 20 to 200. Therefore, the SMMsFVSL method is more robust than conventional simulation to simulate flow in a reservoir with high resolution geological models.
  9. Keywords:
  10. Time of Flight ; Multiscale Finite Volume Method ; Reservior Simulation ; Hydrocarbon Reservoirs ; Streamline Method ; Pollock Algorithm

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