Bayesian full-waveform inversion of tube waves to estimate fracture aperture and compliance

Abstract

Abstract. The hydraulic and mechanical characterization of fractures is crucial for a wide range of pertinent applications, such as, for example, geothermal energy production, hydrocarbon exploration, CO2-sequestration, and nuclear waste disposal. Direct hydraulic and mechanical testing of individual fractures along boreholes does, however, tend to be slow and cumbersome. To alleviate this problem, we propose to estimate the effective hydraulic aperture and the mechanical compliance of isolated fractures intersecting a borehole through a Bayesian Markov chain Monte Carlo (MCMC) inversion of full-waveform tube-wave data recorded in a vertical seismic profiling (VSP) setting. The solution of the corresponding forward problem is based on a recently developed semi-analytical solution. This inversion approach has been tested for and verified on a wide range of synthetic scenarios. Here, we present the results of its application to observed hydrophone VSP data acquired along a borehole in the underground Grimsel Test Site in the Central Swiss Alps. While the results are consistent with the corresponding evidence from televiewer data and exemplarily illustrate the advantages of using a computationally expensive stochastic, instead of a deterministic, inversion approach, they also reveal the inherent limitation of the underlying semi-analytical forward solver.

Estimates of Individual Fracture Compliances Along Boreholes From Full‐Waveform Sonic Log Data

“…Interestingly, the highest compliance values were associated with fractures for which strong tube waves were excited in the VSP experiment reported by Hunziker et al. (2020). This correlation was attributed to the expected scaling between hydraulic and mechanical properties of fractures, according to which hydraulically open fractures tend to be more compliant (Pyrak‐Nolte & Nolte, 2016).…”

“…Also using VSP data, Hunziker et al. (2020) developed a Bayesian Markov chain Monte Carlo (MCMC) full‐waveform inversion algorithm to simultaneously infer hydraulic (i.e., aperture) and mechanical (i.e., compliance) characteristics of individual fractures from tube wave signals. The authors considered a subsection containing three fractures of a VSP data set acquired along a borehole at the Grimsel Test Site (GTS) in Switzerland and estimated fracture compliance and hydraulic aperture as well as the elastic moduli of the background rock.…”

Mechanical Compliance of Individual Fractures in a Heterogeneous Rock Mass From Production‐Type Full‐Waveform Sonic Data

“…From the ATV log, we observe that N1 exhibits clearly a larger aperture than the man‐made fracture, and thus a larger hydraulic conductivity. This is supported by another wave phenomena, so called tube waves, which have been utilized to estimate hydraulic properties from VSP data (e.g., Bakku et al., 2013; Hunziker et al., 2020; Li et al., 1994). The larger the amplitude of the generated tube waves at the fracture opening intersecting the borehole, the larger is the hydraulic conductivity of the fracture.…”

Seismic Applications of Downhole DAS

“…Tube waves have been shown useful to characterize near-borehole conditions, particularly fracture networks [ 129 , 130 ]. As DAS fibers are usually deployed across the entire length of the well, they can follow tube wave behavior in great detail.…”