Hydraulic-Fracture-Width Inversion Using Low-Frequency Distributed-Acoustic-Sensing Strain Data—Part I: Algorithm and Sensitivity Analysis

Abstract

Summary Low-frequency distributed-acoustic-sensing (LF-DAS) data, which can be treated as linear-scaled strain variations, have been used recently to monitor hydraulic-fracturing treatments. Forward geomechanical modeling has been the subject of recent research efforts to better interpret the observed signatures of field LF-DAS data. To the best of our knowledge, there is no study that attempts to quantitatively characterize fracture geometries by directly inverting the LF-DAS strain data. In this study, we propose an inversion algorithm, in which the strains monitored by LF-DAS along an offset well are related to the fracture widths through a Green function. A 3D displacement-discontinuity method is used to construct the Green function. The least-squares method is first used to solve the linear system of equations. Regularization might be needed to stabilize the underdetermined system. Then, Markov-chain Monte Carlo (MCMC) simulations are conducted to generate fracture-width samples from the target distribution of LF-DAS strain data and to quantify uncertainties associated with the inverted widths. The inversion results obtained by the least-squares method are nonunique, heavily depending on the a priori regularization information. Regardless of the additional constraints imposed on the linear system, the inverted fracture width at the monitor-well location is always consistent with the true value because the LF-DAS data show a dominant sensitivity of fracture width near the monitor well. MCMC simulation results confirm that the LF-DAS strain data can only impose constraints on fracture segments near the monitor well. Moreover, the average value of the inverted widths in the vicinity of the monitor well is usually the same as the width right at the monitor well, except for the very early time after fracture hit when there are sharp width variations near the fracture tip. Therefore, it is efficient to use a single width for each fracture during the inversion process. The presented algorithm is successfully applied to invert the width evolution near the monitor well as a function of injection time. The results of this study demonstrate how much information can be obtained with high confidence from the inversion of LF-DAS strain data, which is beneficial for future use of LF-DAS data. The accurate estimation of fracture width at the monitor well can be used to calibrate hydraulic-fracturing models, improve the design of completion parameters such as proppant size, and provide the possibility of characterizing the whole fracture geometry with additional information or assumptions.