Real-time Bayesian inversion of hydraulic fracturing treatment efficiency from tiltmeter measurements

In this paper, we describe a method to estimate, in real-time, the efficiency of a hydraulic fracture, treatment performed in porous reservoir from tiltmeter measurements. The poroelastic deformation induced by the fracture opening and the fluid leak off is investigated at first. The resolution of fracture dimensions and orientation from tiltmeter measurements is also discussed. A limit, expressed in terms of the distance between the tiltmeters and the fracture, above which only the volume and orientation of the fracture have an effect on the tilt field is recalled. The proposed method of analysis recognizes that, without additional information, only the fracture volume and orientation can be accurately estimated from tiltmeter measurements. The knowledge of the injected volume at time t together with the tilts data allow to estimate the efficiency of the treatment at this time. Furthermore, because the method is computationally efficient, the treatment efficiency and fracture orientation can be obtained in real time (i.e. as the data arrive) throughout a hydraulic fracturing treatment.