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.
Abstract. Active thermal tracer testing is a technique to get information about the flow and transport properties of an aquifer. In this paper we propose an innovative methodology using active thermal tracers in a tomographic setup to reconstruct cross-well hydraulic conductivity profiles. This is facilitated by assuming that the propagation of the injected thermal tracer is mainly controlled by advection. To reduce the effects of density and viscosity changes and thermal diffusion, early-time diagnostics are used and specific travel times of the tracer breakthrough curves are extracted. These travel times are inverted with an eikonal solver using the staggered grid method to reduce constraints from the predefined grid geometry and to improve the resolution. Finally, non-reliable pixels are removed from the derived hydraulic conductivity tomograms. The method is applied to successfully reconstruct cross-well profiles as well as a 3-D block of a high-resolution fluvio-aeolian aquifer analog data set. Sensitivity analysis reveals a negligible role of the injection temperature, but more attention has to be drawn to other technical parameters such as the injection rate. This is investigated in more detail through model-based testing using diverse hydraulic and thermal conditions in order to delineate the feasible range of applications for the new tomographic approach.
In the summer of 2015, a series of thermal tracer tests were conducted at the Widen field site in northeast Switzerland to validate travel time-based thermal tracer tomography for reconstruction of aquifer heterogeneity. Repeated thermal tracer tests and distributed temperature observations were used to obtain a multisource/multireceiver tomographic experimental setup. After creating forced hydraulic gradient conditions, heated water was injected as a pulse temperature signal via a double-packer system. With this solution, long temperature recovery periods were not required between the repeated injections at the expense of smaller observed temperatures. The recorded temperature breakthrough curves delivered a tomographic travel time data set that was inverted assuming advection-dominated condition. The obtained hydraulic conductivity tomogram for a small aquifer profile is validated with the results of the findings from previous field investigations at the same site. The reconstructed profile confirms the presence of a thin sand layer with low permeability and reveals a previously unknown low-permeable zone close to the bottom of the aquifer. The inverted hydraulic conductivity values also correspond with those from previous tracer tests. Thus, the results of this study demonstrate the potential of thermal tracer tomography for resolving structures and transport characteristics of heterogeneous aquifers.
This study presents the first field validation of using DNA-labeled silica nanoparticles as tracers to image subsurface reservoirs by travel time based tomography. During a field campaign in Switzerland, we performed short-pulse tracer tests under a forced hydraulic head gradient to conduct a multisource−multireceiver tracer test and tomographic inversion, determining the two-dimensional hydraulic conductivity field between two vertical wells. Together with three traditional solute dye tracers, we injected spherical silica nanotracers, encoded with synthetic DNA molecules, which are protected by a silica layer against damage due to chemicals, microorganisms, and enzymes. Temporal moment analyses of the recorded tracer concentration breakthrough curves (BTCs) indicate higher mass recovery, less mean residence time, and smaller dispersion of the DNA-labeled nanotracers, compared to solute dye tracers. Importantly, travel time based tomography, using nanotracer BTCs, yields a satisfactory hydraulic conductivity tomogram, validated by the dye tracer results and previous field investigations. These advantages of DNA-labeled nanotracers, in comparison to traditional solute dye tracers, make them well-suited for tomographic reservoir characterizations in fields such as hydrogeology, petroleum engineering, and geothermal energy, particularly with respect to resolving preferential flow paths or the heterogeneity of contact surfaces or by enabling source zone characterizations of dense nonaqueous phase liquids.
Classic inversion methods adjust a model with a predefined number of parameters to the observed data. With transdimensional inversion algorithms such as the reversible-jump Markov Chain Monte Carlo (rjMCMC), it is possible to vary this number during the inversion and to interpret the observations in a more flexible way. Geoscience imaging applications use this behaviour to automatically adjust model resolution to the inhomogeneities of the investigated system, while keeping the model parameters on an optimal level. The rjMCMC algorithm produces an ensemble as result, a set of model realizations which together represent the posterior probability distribution of the investigated problem. The realizations are evolved via sequential updates from a randomly chosen initial solution, and converge toward the target posterior distribution of the inverse problem. Up to a point in the chain, the realizations may be strongly biased by the initial model, and have to be discarded from the final ensemble. With convergence assessment techniques, this point in the chain can be identified. Transdimensional MCMC methods produce ensembles which are not suitable for classic convergence assessment techniques because of the changes in parameter numbers. To overcome this hurdle, three solutions are introduced to convert model realizations to a common dimensionality while maintaining the statistical characteristics of the ensemble. A scalar, a vector and a matrix representation for models is presented, inferred from tomographic subsurface investigations, and three classic convergence assessment techniques are applied on them. It is shown that appropriately chosen scalar conversions of the models could retain similar statistical ensemble properties as geologic projections created by rasterization.
Information on structural features of a fracture network at early stages of Enhanced Geothermal System development is mostly restricted to borehole images and, if available, outcrop data. However, using this information to image discontinuities in deep reservoirs is difficult. Wellbore failure data provides only some information on components of the in situ stress state and its heterogeneity. Our working hypothesis is that slip on natural fractures primarily controls these stress heterogeneities. Based on this, we introduce stress‐based tomography in a Bayesian framework to characterize the fracture network and its heterogeneity in potential Enhanced Geothermal System reservoirs. In this procedure, first a random initial discrete fracture network (DFN) realization is generated based on prior information about the network. The observations needed to calibrate the DFN are based on local variations of the orientation and magnitude of at least one principal stress component along boreholes. A Markov Chain Monte Carlo sequence is employed to update the DFN iteratively by a fracture translation within the domain. The Markov sequence compares the simulated stress profile with the observed stress profiles in the borehole, evaluates each iteration with Metropolis‐Hastings acceptance criteria, and stores acceptable DFN realizations in an ensemble. Finally, this obtained ensemble is used to visualize the potential occurrence of fractures in a probability map, indicating possible fracture locations and lengths. We test this methodology to reconstruct simple synthetic and more complex outcrop‐based fracture networks and successfully image the significant fractures in the domain.
Abstract. The Waiwera aquifer hosts a structurally complex geothermal groundwater system, where a localized thermal anomaly feeds the thermal reservoir. The temperature anomaly is formed by the mixing of waters from three different sources: fresh cold groundwater, cold seawater and warm geothermal water. The stratified reservoir rock has been tilted, folded, faulted, and fractured by tectonic movement, providing the pathways for the groundwater. Characterization of such systems is challenging, due to the resulting complex hydraulic and thermal conditions which cannot be represented by a continuous porous matrix. By using discrete fracture network models (DFNs) the discrete aquifer features can be modelled, and the main geological structures can be identified. A major limitation of this modelling approach is that the results are strongly dependent on the parametrization of the chosen initial solution. Classic inversion techniques require to define the number of fractures before any interpretation is done. In this research we apply the transdimensional DFN inversion methodology that overcome this limitation by keeping fracture numbers flexible and gives a good estimation on fracture locations. This stochastic inversion method uses the reversible-jump Markov chain Monte Carlo algorithm and was originally developed for tomographic experiments. In contrast to such applications, this study is limited to the use of steady-state borehole temperature profiles – with significantly less data. This is mitigated by using a strongly simplified DFN model of the reservoir, constructed according to available geological information. We present a synthetic example to prove the viability of the concept, then use the algorithm on field observations for the first time. The fit of the reconstructed temperature fields cannot compete yet with complex three-dimensional continuum models, but indicate areas of the aquifer where fracturing plays a big role. This could not be resolved before with continuum modelling. It is for the first time that the transdimensional DFN inversion was used on field data and on borehole temperature logs as input.
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