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

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

Sample fracture geometry

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

Interaction scheme 2

Java or Matlab program Comsol server connection

Matlab function External

computational code