An integrated extended Kalman filter–implicit level set algorithm for monitoring planar hydraulic fractures

Abstract

We describe a novel approach to the inversion of elasto-static tiltmeter measurements to monitor planar hydraulic fractures propagating within three-dimensional elastic media. The technique combines the extended Kalman filter (EKF), which predicts and updates state estimates using tiltmeter measurement time-series, with a novel implicit level set algorithm (ILSA), which solves the coupled elasto-hydrodynamic equations. The EKF and ILSA are integrated to produce an algorithm to locate the unknown fracture-free boundary. A scaling argument is used to derive a strategy to tune the algorithm parameters to enable measurement information to compensate for unmodeled dynamics. Synthetic tiltmeter data for three numerical experiments are generated by introducing significant changes to the fracture geometry by altering the confining geological stress field. Even though there is no confining stress field in the dynamic model used by the new EKF-ILSA scheme, it is able to use synthetic data to arrive at remarkably accurate predictions of the fracture widths and footprints. These experiments also explore the robustness of the algorithm to noise and to placement of tiltmeter arrays operating in the near-field and far-field regimes. In these experiments, the appropriate parameter choices and strategies to improve the robustness of the algorithm to significant measurement noise are explored.