Analysis of representative bulk permeability. The simulation has been performed using the research and development software package roxolTM (xxx.xxxxx.xx), which is based on the eXtended Finite Element Method (XFEM). Each model has two opposing pore pressure edges with 10 MPa and 0 MPa, respectively. The remaining two edges are no flow boundaries. The fluid flow follows the pressure gradient through the matrix and fractures via Xxxxx flow. The flow along fractures is derived by assigning each mesh element intersected by a fracture, the fracture permeability while for the remaining mesh elements the matrix permeability is prescribed. The bulk permeability of the model kf is then calculated along the 0 MPa pore pressure boundary through Darcy’s law by kf = q·µ/(∆p/l) in m2 with q = 1/h · ∫h q0·n dh, where h is length of the boundary where the pore pressure equals 0 MPa, l is length of the sample, µ is the dynamic fluid viscosity, qo is the fluid flow velocity, and is ∆p the pressure difference (i.e., 10 MPa). Figure 3: Pore pressure distribution (background colour from red (10 MPa left; 6 MPa right) to green (0 MPa left; 5 MPa right)) and fluid flow calculated for a 10 x 10 m area (left) and close-up (right).
Analysis of representative bulk permeability. The simulation has been performed using the research and development software package roxolTM (xxx.xxxxx.xx), which is based on the eXtended Finite Element Method (XFEM). Each model has two opposing pore pressure edges with 10 MPa and 0 MPa, respectively. The remaining two edges are no flow boundaries. The fluid flow follows the pressure gradient through the matrix and fractures via Xxxxx flow. The flow along fractures is derived by assigning each mesh element intersected by a fracture, the fracture permeability while for the remaining mesh elements the matrix permeability is prescribed. The bulk permeability of the model kf is then calculated along the 0 MPa pore pressure boundary through Darcy’s law by kf = q·µ/(∆p/l) in m2 with q = 1/h · ∫h q0·n dh, where h is length of the boundary where the pore pressure equals 0 MPa, l is length of the sample, µ is the dynamic fluid viscosity, qo is the fluid flow velocity, and is ∆p the pressure difference (i.e., 10 MPa). Figure 3: Pore pressure distribution (background colour from red (10 MPa left; 6 MPa right) to green (0 MPa left; 5 MPa right)) and fluid flow calculated for a 10 x 10 m area (left) and close-up (right). Figure 3 shows exemplarily the pore pressure distribution along with an arrow surface of the fluid flow magnitude for a vertical flow through a 10 x 10 m model. At the top boundary, we observe pressures in the range of the assigned 10 MPa boundary conditions, which progressively decrease to ambient pressures at the bottom boundary. The fractures act as a fluid conduct through the low permeable rock matrix and average the pore pressure along their paths, e.g. a high pore pressure in the matrix at one fracture tip will be reduced in the fracture and transported to the end of the fracture surrounded by a low-pressure matrix. Figure 3 (right) is a close-up of the results in the centre of the model. It can be observed that fractures not connected to the remaining DFN or forming a dead-end do not contribute significantly as fluid pathways as indicated by the arrow surface. As more fractures are generated with increasing scale (see Figure 4 left) forming a greater connection in between the DFN, the fluid can be transported faster through the low permeable matrix. Hence, the bulk permeability increases with investigated scale until the permeability does remain constant with increasing area. The increase in permeability is about 3 to 5 times greater for the flow from top to bottom, i.e., along most of fract...
