| Abstract |
Tiltmeters are widely used in the monitoring of hydraulic fractures, a procedure wherein reservoir rock formations are fractured by the injection of pressurized fluid to enhance well productivity. Tiltmeters measure the fracture induced deformations which can then be inverted to obtain useful fracture parameters. Hydraulic fracturing is now being proposed for stimulation of enhanced geothermal systems in low permeability rock for increased energy extraction. Small scale field sites are proposed as a method to obtain data on the effect of placing multiple hydraulic fractures in an injection well and connecting them to a production well. Fracture growth parameters obtained from tiltmeter mappings at such experiment sites can be used to study the effectiveness of such stimulations. In this work, we propose an approach for the inversion of tilt data using the displacement discontinuity method and the extended Kalman filter [1]. The salient feature of the proposed method is its ability to predict fracture asymmetry with respect to the injection borehole, which is important in knowing if each stimulation in an array has progressed as expected. This approach uses a forward model based on the analytical solution for computing the displacements and tilts due to a point source displacement discontinuity in an elastic half-space developed by Okada [2]. The displacement and tilts for any given fracture geometry are then obtained by numerical integration of this solution, by considering multiple point sources to be located at the quadrature points. The proposed method is validated using synthetic data sets generated from polygon and elliptical shaped fracture geometries. Finally, real data obtained from a field site (but not a geothermal site) has also been analysed. Preliminary results show that the procedure is able to satisfactorily predict fracture geometrical parameters when the fracture is relatively close to the tiltmeter array. References [1]F. A. Rochinha and A. Peirce, Monitoring hydraulic fractures: state estimation using an extended Kalman filter, Inverse Probl., vol. 26, no. 2, p. 025009, Feb. 2010. [2]Y. Okada, Internal deformation due to shear and tensile faults in a half-space,Bull. Seismol. Soc. Am., vol. 82, no. 2, pp. 1018–1040, Apr. 1992. |