A new mathematical model of asymmetric hydraulic fracture growth

Hydraulic fractures generated by fluid injection in rock formations are often mapped by seismic monitoring. In many cases, the microseismicity is asymmetric relative to the injection well, which has been interpreted by stress gradient along the direction of the hydraulic fracture. We present a mathematical model of asymmetric hydrofracture growth based on relations between the solid-phase stress and the fracture hydraulics. For single fracture and single injection point, the model has three parameters, hydraulic conductivities of the fracture wings, and normalised stress gradient and predicts the positions of the fracture tips as functions of time. The model is applied to a set of microseismic event locations that occurred during and after an injection process. Two different methods are suggested that make it possible to delineate the fracture tips from the set of microseismic events. This makes it possible to determine the model parameters and to check the agreement between the model prediction and the measured data. The comparison of the measured and modelled growth of fracture wings supports both the assumption of the non-zero stress gradient and the existence of the post-injection unilateral growth.