Discrete fracture modelling in DuMuX

What are fractures?

Joints

Faults

Why are fractures important?

Example applications


hydraulic fracturing
geothermal energy production

Hydraulic effects

(results from the DuMuX fracture exercise)


Capillary effects

(results from the DuMuX two-phase discrete fracture model)


Model concept

Discretization


equi-dimensional
lower-dimensional
non-matching

Problem abstraction


Problem abstraction


Problem formulation

Consider the model equation $\nabla \cdot \left( - \mathbf{K} \nabla p \right) = q$



\begin{equation} \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) \\ \mathbf{u}_i \cdot \mathbf{n}_i &= - \frac{2 k_\eta}{a} ( P_f - p_i ) &&\mathrm{in} \, \gamma. \end{aligned} \end{equation}

Problem formulation

Consider the model equation $\nabla \cdot \left( - \boldsymbol{\Lambda} \nabla u \right) = q$



\begin{equation} \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) \\ P_f &= p_i &&\mathrm{in} \, \gamma. \end{aligned} \end{equation}

Fracture exercise

Buoyancy-driven gas migration


Tasks



  • change boundary conditions

  • change fracture properties

  • use different coupling conditions

  • make use of domain markers