Kalman filtering is often used to provide state estimates and corresponding estimation errors. Usually, the process noise and measurement noise information is assumed to be known and independent of inputs. However, for hydraulic fracturing processes that use microseismic monitoring technology, the covariance of measurement noise depends on the input signals, which provides a new method to reduce uncertainty of the system (i.e., estimation errors). The current work proposes two novel control methods for uncertainty reduction during hydraulic fracturing. One method is designed for cases where measurement data are available in real-time. The other method works under relatively long and time-varying feedback delays, whose sufficient condition for convergence is provided as well. Both newly proposed approaches are demonstrated on a simulated model of the hydraulic fracturing process with improved performance compared to industrial standard methods.
['Zhijie Sun', 'Qiuying Gu', 'Jason D. Dykstra']
Uncertainty reduction of hydraulic fracturing process