fractures.md

title: DuMuX for modelling fractures in porous media

What are fractures?

Joints

Credit: flickr.com/photos/dietmardownunder/44733263071, licensed under CC-BY-2.0.

Faults

Credit: Wikipedia.

Why are fractures important?

Example applications I

Hydraulic fracturing

Credit: Wikipedia.

Example applications II

Geothermal energy production

Credit: Wikipedia.

Hydraulic effects

(Results from the DuMuX fracture exercise)

Capillary effects

(Results from the DuMuX fracture exercise)

Model concept

Discretization

Problem Abstraction

Problem Formulation

:::::: {.columns} ::: {.column width=33%}

::: ::: {.column width=67%} $$ \small \begin{aligned} \mathbf{u}_i &= - \mathbf{K}_i \nabla p_i, \\ \nabla \cdot \mathbf{u}_i &= q_i, &&\mathrm{in} \, \Omega_i, \\ \mathbf{U}_f &=- a \mathbf{K}_{f, \tau} \nabla_\tau P_f, \\ \nabla_\tau \cdot\mathbf{U}_f &= q_f + \left( \mathbf{u}_1 \cdot \mathbf{n}_1 + \mathbf{u}_2 \cdot \mathbf{n}_2 \right), &&\mathrm{in} \, \Omega_f, \\ \mathbf{u}_i \cdot \mathbf{n}_i &= - \frac{2 k_\eta}{a} ( P_f - p_i ), &&\mathrm{in} \, \gamma_N, \\ P_f &= p_i, &&\mathrm{in} \, \gamma_D. \end{aligned} $$ ::: ::::::

Fracture exercise

Buoyancy-driven gas migration

Tasks

• Change boundary conditions
• Change fracture properties
• Use different coupling conditions
• Make use of domain markers