Real-time estimation of fracture volume and hydraulic fracturing treatment efficiency

In this paper, we describe a method to estimate, in real-time, the volume of a hydraulic fracture from tiltmeter measurements recorded during the treatment. The resolution of fracture dimensions and orientation is discussed at first. 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 established. The proposed method of analysis takes advantage of this, often neglected, fundamental properties of the elastic kernels (St. Venant principle). We recognize that, in most cases without additional information, only the fracture volume and orientation can be accurately estimated from tiltmeter measurements. The knowledge of the fracture volume estimated from tilt data together with the injected volume at time t furnish the efficiency of the treatment at this time. Furthermore, because the method employed to analyse the tilt data is computationally efficient, the volume and efficiency can be obtained in real time (i.e. as the data arrive) throughout a hydraulic fracturing treatment.