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# CVEEN 7920: Carbon Capture and Storage Wednesday, 20 October 2010 - PowerPoint PPT Presentation

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.

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## PowerPoint Slideshow about ' CVEEN 7920: Carbon Capture and Storage Wednesday, 20 October 2010' - xannon

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Wednesday, 20 October 2010

Topic: Solving PDE’s (solutions to mathematical models)

• 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

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

Possible combinations of (in)homogeneity and (an)isotropicity

(Freeze and Cherry, 1979)

heterogeneous, anisotropic medium

heterogeneous, anisotropic media

heterogeneous, anisotropic media

heterogeneous, anisotropic media

All transient conditions:

heterogeneous, anisotropic medium

heterogeneous, isotropic media

homogeneous, anisotropic media

homogeneous, isotropic media

• 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

Three primary approaches:

(1) Analytical (applied more often than you might think)

(2) Graphical (flow nets)

(3) Numerical (most common)

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

• 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

• 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