Low-frequency distributed acoustic sensing (LF-DAS) has been used for hydraulic fracture monitoring and characterization. Large amounts of DAS data have been acquired across different formations. The low-frequency components of DAS data are highly sensitive to mechanical strain changes. Forward geomechanical modeling has been the focus of current research efforts to better understand LF-DAS signals. Moreover, LF-DAS provides the opportunity to quantify fracture geometry. Recently, Liu et al. (2021a, 2021b) proposed an inversion algorithm to estimate hydraulic-fracture width using LF-DAS data measured during multifracture propagation. The LF-DAS strain data are linked to the fracture widths through a forward model developed based on the displacement discontinuity method. In this study, we first investigated the impacts of fracture height on the inversion results through a numerical case with a four-cluster completion design. Then we discussed how to estimate the fracture height based on the inversion results. Finally, we applied the inversion algorithm to two field examples.
The inverted widths are not sensitive to the fracture height. In the synthetic case, the maximum relative error is less than 10% even when the fracture height is two times the true value. After obtaining the fracture width, the fracture height can be estimated by matching the true strain data under various heights with a strong smooth weight. The error between the calculated strain and true strain decreases as the height approaches the true value. In the two field examples, the temporal evolutions of the width summation of all fractures and the width of each fracture show consistent behaviors with the field LF-DAS measurements. The calculated strain data from the forward model match well with the field LF-DAS strain data. The results demonstrate the robustness and accuracy of the proposed inversion algorithm.