effective properties of fractured media
TRANSCRIPT
Effective Properties of Fractured Media
Using Java, Matlab and Comsol
Pål Næverlid Sævik, UiB
Presented at Bergen User Group Workshop, October 31st 2012
Upscaling of fractures
• Impossible to resolve all fractures • Only statistical fracture information available • Therefore: Replace heterogeneous medium
with equivalent homogeneous medium • How to find the equivalent property? • Solution: Numerical or analytical
homogenization
Homogenizable properties
• Laplace equation-type properties
• Electrical conductivity • Thermal conductivity • Diffusion coefficient • Hydraulic permeability • Mechanical stress tensor
Numerical vs. analytical
Numerical • Generate sample geometry
and simulate physics • Potentially accurate • Needs very fine mesh, and
many realizations • In practice: Coarse mesh
and few realizations used • …and it’s still slow
Analytical • Predictions based on
analytical approximations • Very fast • Tight analytical error
estimates are lacking • Extensive comparisons with
numerical upscaling are lacking
Effective medium methods
• Represents fractures as thin ellipsoids
• Self-consistent methods • Differential method • Input parameters:
– Fracture density – Shape – Orientation – Aperture and
conductivity contrast
Challenges
• Mesh generation – Periodic meshing – Generate less
demanding geometry • Parametric sweep
– Flux direction – Mesh size – Geometry parameters
• Numerical convergence – Extremely large number
of elements required
• Large number of realizations – Parallelization – Handle failed
computations – Memory leakage
• Setting material properties – Individual fractures
needs tailored material properties
Solutions
• Schedule computational tasks using Java • Generate realizations in Matlab • Solve the equations using Comsol batch job • Handling specialized parameter sweep in Java • Monitoring the solution process using Java • Post-process and store results using Java
Ways of combining Comsol with Java and Matlab
• Integrate Matlab function with Comsol • Call Java class from Comsol • Connect to Comsol server from Java or Matlab • Initiate Comsol instance within Java or Matlab • Call Comsol batch job from Java or Matlab
Interaction scheme 1
External job scheduler Comsol batch job
Java class Matlab function External
computational code