In this study, we infer the structural and hydraulic properties of the highly fractured zone at the Grimsel Test Site in Switzerland using a stochastic inversion method. The fractured rock is modeled directly as a discrete fracture network (DFN) within an impermeable rock matrix. Cross-hole transient pressure signals recorded from constant-rate injection tests at different intervals provide the basis for the (herein presented) first field application of the inversion. The experimental setup is realized by a multi-packer system. The geological mapping of the structures intercepted by boreholes as well as data from previous studies that were undertaken as part of the In Situ Stimulation and Circulation (ISC) experiments facilitate the setup of the site-dependent conceptual and forward model. The inversion results show that two preferential flow paths between the two boreholes can be distinguished: one is dominated by fractures with large hydraulic apertures, whereas the other path consists mainly of fractures with a smaller aperture. The probability of fractures linking both flow paths increases the closer we get to the second injection borehole. These results are in accordance with the findings of other studies conducted at the site during the ISC measurement campaign and add new insights into the highly fractured zone at this prominent study site.

Solid rocks, such as in crystalline and bedrock formations, typically have a compact matrix of low permeability. Water pathways are focused on mechanical discontinuities that separate individual rock blocks over multiple scales. Such fractures are commonly described as planar structures and form a network that is hard to resolve at field sites. This is due to the high diversity and complexity of natural fracture networks, the difficulty involved with identifying fracture connectivities, and thus the difficulty involved with interpreting the hydraulic regime of an entire formation based on local fracture detection. Accordingly, fractured-aquifer characterization represents a challenge, with a relatively high cost related to the application of specialized field investigation techniques and to gathering a sufficient data set for reliable hydraulic description. The general poor understanding of how groundwater flows in fractured field sites is in contrast to the relevance of fractured environments that host elementary freshwater reservoirs worldwide

Depending on the chosen experimental setting and the available data, different interpretations of the hydraulic and structural properties of a fracture network are possible. A fractured site can be inspected locally by borehole data (e.g., core mapping and geophysical image logs such as optical or acoustic televiewer). The depth and orientation of structures intercepted by boreholes characterize fracture intensity and prevalent fracture orientations

Detailed insight into the properties of flow paths between adjacent boreholes can be gained by tomographic methods. The principle of all tomographic methods is perturbing the investigated system (e.g., by an injection of fluid, a tracer, a thermal anomaly, or an electric current) and recording the response at nearby receivers. In particular, geophysical tomographic methods are applied for the characterization of the rock properties, the identification of fractured (in particular highly fractured) zones, and the monitoring of flow pathways

In contrast to geophysical exploration techniques, hydraulic, pneumatic, or tracer tomography is based on a fluid or tracer injection at a source well. The response is recorded at different adjacent boreholes at different depth intervals. In most cases, the pressure signals or tracer arrival curves are evaluated by a continuous hydraulic conductivity distribution based on an equivalent porous media (EPM) concept

Our inversion approach differs from previous studies insofar as the fractured rock is represented explicitly as a discrete fracture network (DFN) and the hydraulic and structural parameters of the fractures are inferred directly. The great number of unknown parameters prevents the minimization of an objective function between simulated and observed data, resulting in a single deterministic DFN. Instead, a stochastic approach is applied to consider the nonuniqueness of the results. This is accomplished by generating several realizations of the fracture network that are equally likely to be evaluated as a fracture probability map. The validity of the approach has been demonstrated for synthetic test cases in two dimensions (2D)

The paper is structured as follows: in Sect. 2, we describe the site and the hydraulic tomography experiments to be used for the inversion; the implementation of the inversion is elaborated upon in Sect. 3; we then review the forward modeling procedure (Sect. 3.1) and the general inversion framework (Sect. 3.2) developed in previous works with synthetic test cases; in Sect. 3.3 and 3.4, we explain the site-dependent inversion setting (i.e., the conceptual model and the prior parameter distributions that serve as basis for a stochastic inversion procedure) and discuss and justify the necessary constraints and assumptions; finally, the inversion results are interpreted and compared with findings from related ISC experiments in Sect. 4.

The GTS is an underground rock laboratory located in the Aar Massif in the Swiss Alps. The ISC experiments, which serve as the basis for this study, utilized 15 boreholes of 20–50 m depth, including two injection boreholes (Inj1 and Inj2). The other boreholes are used for stress and strain measurement as well as seismic, pressure, and temperature monitoring during the hydraulic stimulation phases

The crystalline rock in the southern part of the GTS (ISC experiment volume) has been moderately fractured. Ductile (S1) and brittle–ductile (S3) shear zones can be distinguished from the investigated rock volume (Fig.

The fractures can be distinguished in wall damage zones adjacent to the S3 faults and linking damage zones, i.e., fractures connecting both fault cores

The hydraulic tomography tests that are applied in this study are part of the characterization phase of the ISC experiment. We utilize transient pressure signals from constant-rate injection tests in the intervals 3 and 4 of the injection boreholes Inj1 and Inj2. The different intervals are isolated by a multi-packer system. The properties of the packer intervals and the parameters of the injection are summarized in Table

Parameters of the packer intervals and the hydraulic tomography experiments.

Between each injection experiment, pressure recovery was possible. The pressure response of the fluid is measured using piezoresistive pressure transducers. The resolution of the pressure response data is approximately 0.5 kPa. The minimum principal stress is of the order of 8 MPa. As the injected fluid pressure is much below the minimum principal stress, the coupling between hydraulic and mechanical effects can be neglected in the forward modeling of the experiment. The fluid pressure is measured with

Pressure response in the different intervals provoked by a constant-rate injection applied sequentially to the intervals Inj1–Int3

The pressure signals are shown in Fig.

Fractures are modeled as 2D objects with constant properties normal to the fracture midplane in a 3D rock matrix that is assumed to be impermeable. The pressure diffusion in a single fracture is described by

The implemented boundary conditions are shown in Fig.

Overview of the volume considered in the forward model and the boundary conditions (BCs). The geometry of the S3 faults is simplified to planes, and the fractures intercepted by the injection intervals are illustrated as plane ellipses.

The boundary conditions are chosen considering the fact that only a small volume of the ISC experiment is investigated in this study. Therefore, the following boundary conditions are applied:

The AU (Auflockerungszone, i.e., excavation effects) tunnel is represented by a pressure boundary condition – in this case, ambient pressure.

The way to the VE (ventilation test) tunnel cannot be modeled explicitly. Thus, we apply a Robin boundary condition as a transfer boundary condition to consider the transition of the flow and the extension of the shear zones towards the VE tunnel

A no-flow boundary condition is applied normal to the planes of the fractures and shear zones.

The parameters of the DFN

The variance

In practice, one iteration of the inversion algorithm operates as follows: assuming that the insertion of a fracture is chosen in the MCMC algorithm, the parameters (position; length; fracture set, i.e., orientation; and hydraulic aperture) of the fracture are generated from the prior functions. The chosen parameters are evaluated by simulating the hydraulic tomography experiment with the proposed parameter set

The overall inversion procedure relies on several simplifications concerning parameters with less importance for our research target. For instance, the parameters specifying the properties of the shear zones have to be fixed. In general, our aim is an optimal balance between the accuracy of the generated results and the computational cost of the inversion procedure.

The underlying conceptual model comprises simplifications of the properties of single fractures that serve as inversion constraints. We assume plane ellipses as the fracture shape, and the length of the minor axis equals half of the length of the major axis (i.e., the length ratio is fixed). The assumption of reducing the fracture shape to a 2D plane is a common assumption and is justified by the derivation of the cubic law and the large ratio between the fracture extensions and the fracture aperture

Orientations of the structures between the fault cores of the S3 shear zones in the injection boreholes observed from optical televiewer logs

The investigated volume is limited to the volume between the two S3 shear zones (Fig.

Overall, the application of constraints and assumptions about the fracture shape limit an exact reproduction of the structural properties of the tested rock mass. However, those parameters that have a major influence on the flow in the DFN are adjusted by the inversion algorithm within prescribed bounds. These are, in particular, the position and the hydraulic aperture of fractures. In contrast, parameters with minor effects on the flow behavior are fixed (e.g., the exact fracture orientation or the length ratio).

The parameters to be inferred are the number of fractures, the position of the fractures, the fracture lengths, the respective hydraulic aperture for each fracture, and the specific storage coefficient that applies to the whole DFN. The specific storage

Uniform prior distributions are applied (i.e., a parameter is specified by a constant probability between minimum and maximum possible values that are given in Table

Uniform prior distributions defined by a minimum and maximum possible value.

All spatial values refer to the position of the midpoint of the ellipse.

The spatial priors are derived in general from the position of fractures intersecting the injection boreholes. The maximum value in the

The prior range for the aperture is approximated from the results of single- and cross-borehole tests

Comparison of the observed pressure response with the simulation of the hydraulic tomography experiment for the posterior DFN realizations for injection in the intervals Inj1–Int3

Overall, 27 000 DFN realizations are considered to be posterior DFN realizations because they minimize the error and fulfill the prior conditions. DFN realizations from the initial 500 iterations are discarded as so-called “burn-in” iterations due to a higher error. The computation of the inversion was executed by an Intel Core i9 workstation with 10 cores and 128 GB RAM and took about 1 week. The posterior realizations are approximately equally likely. They reflect the uncertainty of the inversion results in contrast to a unique solution that would be obtained by a deterministic approach. To reduce the autocorrelation of the results, we keep every 100th realization for further processing, which is called “thinning”

In the first step, the measured and simulated pressure signals are compared to assess the quality of the posterior realizations. Figure

Figure

Evaluation of the results from the fracture probability map

The FPM and the mean hydraulic aperture are shown for different cross sections (

Overall, two different connections with different levels of permeability are present. A flow path dominated by fractures with a large hydraulic aperture exists between injection interval 4 of both boreholes (Inj1–Int4 and Inj2–Int4). The fractures providing this connection are visible with a high probability in the cross sections

Although the volume east of injection borehole 2 towards the AU tunnel is part of the inversion (i.e., fractures can be inserted or moved in this volume), the resolution of the results is low because various DFN realizations (i.e., fracture positions) are possible. Only the volume between the two injection boreholes can be evaluated with a sufficient resolution.

The inferred flow paths consist of fractures with a high or rather low permeability, which is in accordance with the results of

In this study, we characterized the highly fractured zone at the GTS based on transient pressure signals from hydraulic tomography experiments using a new stochastic inversion method. A stochastic approach was applied to assess the uncertainty of the measured data and the nonuniqueness of the results. The fractured rock is represented directly as a DFN model in the forward simulations. Several posterior DFN realizations that are approximately equally likely are evaluated, and two preferential flow paths dominated by a large or small hydraulic aperture are successfully identified. The presented method relies on some investigations that must be applied prior to the inversion (such as the mapping of structures intercepted by boreholes) and benefits from single- and cross-hole permeability tests for the definition of the hydraulic aperture range. If it is possible to further narrow down the prior range of the hydraulic parameters, the specific storage can be inferred separately for each fracture, instead of computing only a mean value for the whole DFN. In general, improved results and more insights into the fractured rock can be gained using the same inversion method but with more pressure signals from additional intervals and boreholes.

Future research is necessary on the generally most suitable definition of prior and proposal distributions, which are elementary for robust inversion and for deriving meaningful results. The efficiency of the MCMC sampling can be improved significantly by implementing more elaborate prior or proposal distributions, for example, relying on soft information and site-specific expertise. A further option is utilizing continuous inversion results (such as continuous hydraulic conductivity distributions) or geophysical measurements for highlighting a priori regions with a higher probability of the insertion of fractures or to define zones that are likely connected by fractures to reduce the number of necessary inversion iterations

The introduced inversion framework can be applied in a highly flexible way for the characterization of different fractured sites by adapting the site-dependent parameters to meet the conditions of the tomography experiment at each site. Moreover, different types and sources of measured data can be processed for the inversion (such as tracer or in situ stress data), provided that a forward model is available that allows for the flexible update of DFN parameters. The workflow for the setup of the inversion problem is similar. The basis is the properties of the fractures intercepted by the boreholes, i.e., their position and orientation, obtained from optical or acoustic televiewer logs or outcrops. This knowledge is utilized for the prior distributions on the spatial parameters and for the specification of fracture sets. The prior distributions on the hydraulic parameters are based on cross-hole flow tests in this study. This can also be done by the evaluation of the hydraulic tomography experiments as a continuous hydraulic conductivity and specific storage tomogram. As the definition of priors and constraints delineates the range of feasible DFN realizations, this step has to be done carefully. However, the presented Bayesian framework allows the combination of multiple and diverse hard and soft data, which often exist in addition to hydraulic test data that are used to guide the inversion. As demonstrated here, overly tight constraints may be avoided by uniform prior distributions with large value ranges at the expense of a higher computational cost for the inversion. In practice, the amount of information describing the fractured rock is determined mainly by the hydraulic tomography data (i.e., by the number of intervals and boreholes).

The present study paves the way towards the applicability of the discrete inversion approach on a larger scale. The main issue will be to balance the degree of field testing with the desired fracture resolution and the associated computational cost. One possible direction is explicitly implementing only large conductive fractures. The role of smaller fractures with a lower permeability could be represented by calibrating a background permeability within the discrete fracture matrix approach

The geological data set used for the setup of the conceptual model is available from

PB was responsible for funding acquisition; MJ carried out measurements; LMR and PB developed the methodology; LMR carried out the inversion and wrote the original manuscript; and MJ and PB reviewed and edited the manuscript.

The contact author has declared that none of the authors has any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

We thank Ryan Pearson for language editing the original manuscript and the two anonymous referees for their valuable comments which helped to improve the quality of the manuscript.

This research has been supported by the German Research Foundation (DFG; grant no. BA-2850-5-1).

This paper was edited by Brian Berkowitz and reviewed by two anonymous referees.