Fractal analysis of single-phase water and polymer solution flow at high rates in open and horizontally displaced rough fractures

A study on the percolation characteristics of single-phase flow in rough fractures at high rates representing hydraulic fracturing conditions is presented. Two-dimensional transparent models of fractures obtained from different rock types (granite, marble and limestone) were reproduced by molding. To represent typical hydraulic fracturing fluids, water and polymeric solutions were injected at a constant flow rate. The inlet pressure was continuously monitored to correlate the permeability changes due to surface roughness of fractures. The fluid distributions were also mapped using the images acquired through the experiments. The surface roughness was quantified using three fractal methods (variogram, power spectral density, and triangular prism) and the ratio of total and planar areas, and these parameters were correlated to the percent wetted areas and pressure drop (i.e., permeability). This exercise was performed on joint type and horizontally displaced (sheared) model fractures. The percentage of planar flow wetted area representing invasion percolation and pressure drop changed remarkably with rock types. Both parameters were controlled by grain size and the surface roughness of fractures. Increasing degree of the roughness caused a decrease in permeability and area wetted by fluid. Models generated from bigger grain size rocks showed more channeling and a lower percentage of fluid wetted areas as well as lower pressure drop (higher permeability). The variogram fractal dimension showed better agreements among other methods for both fluid (water and polymeric solution) and fracture types (joint and horizontally displaced).