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Flow (in Porous Media) with Mathematica
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| Organization: | Texas A&M University |
| Department: | Harold Vance Department of Petroleum Engineering |
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College
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The course teaches modeling flow in porous media using analytical, semi-analytical and numerical methods. It relies heavily on the services of Mathematica and therefore it contains an introductory part dealing with the software itself. Fluid flow in porous media concepts are introduced and revisited in the context of problem solving approach.
The primary goal is to equip the students with tools to conduct engineering research.
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A web site is dedicated to the course. The index file contains a "live" calendar with links to Mathematica notebooks.
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Mathematica can support effectively many of the computations in petroleum engineering research by providing an unprecedented insight into the theoretical basis and everyday practice of modeling flow in porous media. In this course analytical, semi-analytical and numerical methods are developed and illustrated. Mathematica is used exclusively as a medium to derive, illustrate, and present the material.
The classes are held in a computerized classroom with enough computers to accommodate every student. A workshop atmosphere is maintained thorough the course.
Topics:
Numbers, symbolics, plots
Palettes, typesetting, styles
Variables and expressions
Lists, tables, matrices
Graphs
Animation
More visualization in 2D
Algebraic solve
More visualization in 3D
Derivatives and integrals
Differential equations
Data handling
Add-ons
Single phase flow in homogenous and isotropic porous media (6 hours)
Reservoir-well systems
Driving mechanisms, under-saturated, gas cap, water drive
Outer boundary conditions
Inner boundary conditions / well models well
Flow regimes and time invariant characteristics
Analytical and semi-analytical methods (6 hours)
Solutions in Laplace space
Numerical inversion of Laplace transform
Modeling numerical methods in Mathematica (4 hours)
Finite difference / finite volume element
Handling boundary conditions and wells
Matrix formalism and linear algebra solution methods
Streamline simulation
Collocation/weighted residuals
Finite element/boundary element
Outlook (4 hours)
Numerical well test analysis
Horizontal, deviated, multi-lateral and fracture treated wells
Heterogeneous and anisotropic media / fractured reservoirs
Layers, flow units, flow compartments
Coupling reservoir simulation with geomechanical modeling
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