Task description

Let’s consider the cylindrical part of reservoir with horizontal well and transverse hydraulic fracture inside. The well is cylindrical pipe with radius \(r_w\) and lenght 2L. The fracture is a circle with radius equals to reservoir radius. Both reservoir and fracture are saturated with fluid.

_images/domain.svg

The geometry of reservoir and fracture as follows:

  • R – reservoir radius, m;

  • L – cylindr half height, m;

  • \(r_w -\) well radius, m;

  • \(\delta -\) fracture half thickness, m.

Reservoir and fluid properties:

  • k – reservoir permeability, m2;

  • \(k_f -\) fracture permeability, m2;

  • \(m_f -\) fracture porosity,

  • \(\mu -\) fluid viscosity, Pa*s.

The domain bounds are follows: \(\Gamma_B -\) side face of cylindrical reservoir, \(\Gamma_T -\) bearing faces of cylindrical reservoir, \(\Gamma_w -\) wellbore, \(\Gamma_f -\) fracture/reservoir bound, \(\Gamma_w^f -\) fracture/well bound.

Note

Fracture permeability and porosity are constant values.

The rate of hydraulically fractured horizontal well need to be defined.