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.
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.