On the residual opening of hydraulic fractures

Hydraulic stimulation technologies are widely applied across resource and power generation industries to increase the productivity of oil/gas or hot water reservoirs. These technologies utilise pressurised water, which is applied inside the well to initiate and drive fractures as well as to open a network of existing natural fractures. To prevent the opened fractures from complete closure during production stage, small particles (proppants) are normally injected with the pressurised fluid. These particles are subjected to confining stresses when the fluid pressure is removed, which leads to a partial closure of the stimulated fractures. The residual fracture openings are the main outcome of such hydraulic stimulations as these openings significantly affect the permeability of the reservoirs and, subsequently, the well productivity. Past research was largely focused on the assessment of conditions and characteristics of fluid driven fractures as well as proppant placement techniques. Surprisingly, not much work was devoted to the assessment of the residual fracture profiles. In this work we develop a simplified non-linear mathematical model of residual closure of a plane crack filled with deformable particles and subjected to a remote compressive stress. It is demonstrated that the closure profile is significantly influenced by the distribution and compressibility of the particles, which are often ignored in the current evaluations of well productivity.