1 / 22

CVEEN 7920: Carbon Capture and Storage Wednesday, 20 October 2010

CVEEN 7920: Carbon Capture and Storage Wednesday, 20 October 2010 Topic: Solving PDE’s (solutions to mathematical models). Models of CCS = Models of Fluid Flow & Other Processes. Reprise: the continuity equation and groundwater (fluid) flow equation.

xannon
Download Presentation

CVEEN 7920: Carbon Capture and Storage Wednesday, 20 October 2010

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CVEEN 7920: Carbon Capture and Storage Wednesday, 20 October 2010 Topic: Solving PDE’s (solutions to mathematical models)

  2. Models of CCS = Models of Fluid Flow & Other Processes • Reprise: the continuity equation and groundwater (fluid) flow equation. • What do you need to solve the groundwater flow equation? • Taylor Series - the backbone of the FDM • Building an FDM Approximation

  3. Groundwater Flow Equation Left side of continuity equation has q, this is driven by Let’s try to relate the left side to h Assume the axes of are parallel to x,y,z Then If K axes not aligned with x, y, z, then we must use

  4. Groundwater Flow Equation Possible combinations of (in)homogeneity and (an)isotropicity (Freeze and Cherry, 1979)

  5. Groundwater Flow Equation heterogeneous, anisotropic medium heterogeneous, anisotropic media heterogeneous, anisotropic media heterogeneous, anisotropic media

  6. Groundwater Flow Equation All transient conditions: heterogeneous, anisotropic medium heterogeneous, isotropic media homogeneous, anisotropic media homogeneous, isotropic media

  7. Groundwater Flow Equation homogeneous, isotropic, steady-state

  8. Models of CCS = Models of Fluid Flow & Other Processes • Reprise: the continuity equation and groundwater (fluid) flow equation. • What do you need to solve the groundwater flow equation? • Taylor Series - the backbone of the FDM • Building an FDM Approximation

  9. Solving the Groundwater Flow Equation Three primary approaches: (1) Analytical (applied more often than you might think) (2) Graphical (flow nets) (3) Numerical (most common)

  10. Solving the Groundwater Flow Equation The ‘Boundary Value Problem’ (BVP): Governing equation 2) Region of flow (e.g., geometry, dimensions, etc.) Material properties, or parameterization Boundary conditions Initial conditions (transient problems) Method of solution

  11. Models of CCS = Models of Fluid Flow & Other Processes • Reprise: the continuity equation and groundwater (fluid) flow equation. • What do you need to solve the groundwater flow equation? • Taylor Series - the backbone of the FDM • Building an FDM Approximation

  12. Backbone of FDM: Taylor Series Expansion

  13. Backbone of FDM: Taylor Series Expansion

  14. Backbone of FDM: Taylor Series Expansion

  15. Backbone of FDM: Taylor Series Expansion

  16. Backbone of FDM: Taylor Series Expansion

  17. Models of CCS = Models of Fluid Flow & Other Processes • Reprise: the continuity equation and groundwater (fluid) flow equation. • What do you need to solve the groundwater flow equation? • Taylor Series - the backbone of the FDM • Building an FDM Approximation

  18. The FDM

  19. The FDM

  20. Construction of an FDM Approximation

  21. Construction of an FDM Approximation

More Related