Synthetic fracture network characterization with transdimensional inversion

Abstract

Fracture network geometry is crucial for transport in hard rock aquifers, but it can only be approximated in models. While fracture orientation, spacing, and intensity can be obtained from borehole logs, core images, and outcrops, the characterization of in situ fracture network geometry requires the interpretation of spatially distributed hydraulic and transport experiments. In this study, we present a novel concept using a transdimensional inversion method (reversible jump Markov Chain Monte Carlo, rjMCMC) to invert a two-dimensional cross-well discrete fracture network (DFN) geometry from tracer tomography experiments. The conservative tracer transport is modeled via a fast finite difference model neglecting matrix diffusion. The proposed DFN inversion method iteratively evolves DFN variants by geometry updates to fit the observed tomographic data evaluated by the Metropolis-Hastings-Green acceptance criteria. A main feature is the varying dimensions of the inverse problem, which allows for the calibration of fracture geometries and numbers. This delivers an ensemble of thousands of DFN realizations that can be utilized for probabilistic identification of fractures in the aquifer. In the presented hypothetical and outcrop-based case studies, cross sections between boreholes are investigated. The procedure successfully identifies major transport pathways in the investigated domain and explores equally probable DFN realizations, which are analyzed in fracture probability maps and by multidimensional scaling.

Hydraulic Tomography: 3D Hydraulic Conductivity, Fracture Network, and Connectivity in Mudstone

“…Recently, Hochstetler et al (2016) used HT to investigate a highly heterogeneous (K range of 10 −7 to 10 −1 m/s) unconsolidated sedimentary aquifer at HRFS with highquality results. For HT in fractured aquifers, synthetic and field studies using drawdown, tracer, and temperature data have been conducted in 2D (e.g., Hao et al 2008;Klepikova et al 2014;Trottier et al 2014;Wang et al 2016;Somogyvári et al 2017;Fischer et al 2018), and 3D (e.g., Klepikova et al 2013) but we are only aware of distributed-parameter 3D HT field studies at the Mizunami research site in Japan (Illman et al 2009;Zha et al 2015). The Mizunami studies were at the scale of >0.5 km lateral and vertical extent, or considerably larger than the HRFS focus of this paper and in situ remediation.…”

Convergence Tests for Transdimensional Markov Chains in Geoscience Imaging

“…In practice usually the evolution of the misfits is inspected to decide if the chain is converging. Somogyvári et al (2017) proposed to monitor the changes in the mean of the Markov chain, and terminate the simulation when this mean does not change any more. Still, these solutions do not use any further statistical information about the transdimensional Markov chain.…”

“…The main advantage of this solution is that the results are suitable for visualization directly. Bodin and Sambridge (2009) used this transformation to visualize the mean of an ensemble of seismic velocity distributions, while Somogyvári et al (2017) and Jiménez et al (2016) used similar projections to generate probability maps of the investigated geological features. Note that this approach is more straightforward when dealing with models of continuous features (like velocity distributions in seismic tomography), but we will show in the following that it is well applicable for discrete models as well.…”

“…In the case of fracture modelling, this approach is similar to converting discrete fracture models to equivalent continuum models (Illman and Neuman, 2003;Sahimi, 2011). While the DFN models are better for simulations during the inversion, as DFNbased forward models are very fast and efficient (by reducing the physical modeling to one or two dimensions (Somogyvári et al, 2017)), continuum models are better for analysis and ensemble visualization purposes. Hence, this methodology benefits from the advantages of both approaches.…”

“…DFNs are complex multidimensional models of fractured rocks that contain all relevant information of the fractured media in a simple data structure. The dataset contains the coordinates of the individual fractures, their length and orientation and the relevant physical properties such as fracture transmissivity, aperture or thermal and mechanical properties (Somogyvári et al, 2017). Two separate datasets were used: a simplified, reduced DFN model for early tests, and a field-based realistic one.…”