Constant displacement discontinuity method (DDM) loses accuracy in predicting the opening and shearing displacement discontinuities of multiple fractures when fractures are closely spaced. We introduced an efficient higher order DDM (HDDM) that extensively improves the accuracy of conventional constant DDM but does not increase the computational time. This was accomplished through a patched-elements pattern which does not increase the degrees of freedom on each element but improves the accuracy of the discontinuities via quadratic approximation. The HDDM gives the same results with DDM when the fracturing spacing is large. For close spacing of multiple fractures, constant DDM requires more finer grids to give accurate results, and may fail to capture the fracture behavior using extremely fine, while HDDM does not require finer grid size to give accurate result and precisely predicts the fracture opening shearing using a much larger element size than constant DDM does, which saves a huge amount of computational time in multi-stage fracture modeling.
Multi-stage hydraulic fracturing has been intensively employed to economically produce hydrocarbons from underground reservoirs for many decades. The propagation characteristics and dimension (opening width, lateral length, and height) of the hydraulic fractures are important information in design of fracturing operations. Over the decades, the hydraulic fracture modeling has progressed into a high impact decision making tool for unconventional reservoir development.
