Stochastic inversion for equivalent hydraulic fracture characterization using low-frequency distributed acoustic sensing data

Abstract

Distributed fiber-optic sensing, a game-changing technology, has been successfully applied in monitoring hydraulic fracturing treatments. The cross-well fiber-optic strain/strain-rate responses are directly related to the fracture-propagation process and dynamic fracture geometry. Extracting the insightful information regarding hydraulic fractures requires robust interpretation workflows. In this paper, we aim to develop a stochastic inversion approach to characterize the dynamic equivalent fracture geometry and quantify the associated uncertainties using cross-well low-frequency distributed acoustic sensing (LF-DAS) measurements. A fast analytical forward solver based on the 3D displacement discontinuity method is developed to model the strain. The objective function is the sum-of-squares error between the modeled strain and the measured strain. We focus on an equivalent fracture geometry with a predefined length centered around the monitoring well, which is a reasonable assumption considering the spatial sensitivity of LF-DAS. Therefore, the model parameters reduce to fracture width and height of the equivalent fracture. We adopted the delayed rejection adaptive metropolis (DRAM) algorithm, an efficient Markov-chain Monte Carlo (MCMC)-based method, to perform the optimization. The efficiency and accuracy of the algorithm are tested using a synthetic case that has three monitoring wells at different locations. The mean values of fracture width and height are both close to the true values with negligible standard deviations for all the three monitoring wells. The algorithm performance is not sensitive to the initial guess and the predefined length needs to be large enough. Then, a field case with a single cluster from the HFTS-2 project is presented. The fracture width increases from about 0.5 mm to about 0.9 mm during the pumping stage and gradually decreases during the shut-in period. The fracture height changes during the pumping stage and stabilizes at about 150 m during the shut-in period, the trend of which is consistent with the LF-DAS signals from the offset vertical monitoring well. To the best of our knowledge, this is the first algorithm that can efficiently quantify the fracture width and height simultaneously. The results could provide novel insights on the characteristics of fracture geometry and significantly improve the understanding of complex fracture propagation processes in subsurface reservoirs.