Fig 2 - uploaded by Daniel Vogler
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Schematic of experimental setup. The flow cell was 100 cm long (in the direction of flow), 50 cm tall, and 20 cm thick. Tracer solutions were pumped through the two-region medium which consisted of 203 embedded inclusions. The inclusions are colored by their respective layer in the shortest system dimension (20 cm, 4 layers of inclusions).
Source publication
In this work we examine the dispersion of conservative tracers (bromide and fluorescein) in an experimentally-constructed three-dimensional dual-porosity porous medium. The medium is highly heterogeneous ($\sigma_Y^2=5.7$), and consists of spherical, low-hydraulic-conductivity inclusions embedded in a high-hydraulic-conductivity matrix. The bi-moda...
Contexts in source publication
Context 1
... experimental system, illustrated in Fig. 2 , consisted of a flow cell (100 cm long, 50 cm tall, 20 cm thick), constructed of an- odized aluminum, packed with a dual-porosity medium. The inlet and outlet end plates of the flow cell were engineered structures (nominally 50 cm by 20 cm anodized aluminum, with ancillary material to allow the end plates to be bolted to the flow ...
Context 2
... finite elements package COMSOL Multiphysics 5.3 was used to numerically solve Eqs. (7) -(16) on this geometry. An illustration of the geometry is given in Fig. 2 . Direct numerical simulations of the system were conducted by meshing volumes (the coarse ma- trix and inclusions) using a tetrahedral mesh; the matrix and in- clusions were separated by a boundary-fitted mesh. The interfacial boundary condition indicated by Eq. (14) was applied at this inter- facial ...
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... transport and diffusive transport were both important in the inclu- sions. Although the intrinsic velocity in the inclusions (|| v ω ω ||) is two orders of magnitude smaller than the intrinsic velocity in the matrix (|| v η η ||), the ω-region is characterized as mobile (values reported in Table 3 ). However, as mentioned previously, on Fig. 2 , this experiment plots near the boundary between the mobile-mobile and mobile-immobile regimes. Thus, for this case, either model is likely to give acceptable results for simulating the breakthrough curve behavior; however, one might expect a mobile- mobile model to be somewhat more accurate (although at a higher computational ...
Citations
... In addition to testing mechanical strength, both porous and jointed 3D-printed specimens can also be used to conduct fluid flow experiments, which strongly depend on a well-defined system geometry and can be challenging to monitor in natural specimens (Zinn et al. 2004;Blunt et al. 2013;Vogler et al. 2018a). To this end, Roy et al. (2016) 3D-printed the topology of a natural shale fracture in clear plastic resin to construct a particle flow cell that allows imaging of proppant movement in the fracture with optical methods. ...
The presented work compares the mechanical behavior from standard unconfined compressive strength and indirect tensile strength tests of natural sandstone and artificial sand-based specimens created by 3D additive manufacturing. Three natural sandstones of varying strength and stiffness were tested to capture a wide range of behavior for comparison with the 3D-printed specimens. Sand grains with furan and silicate binders, as well as, ceramic beads with silicate binder were 3D-printed by commercial suppliers. The tensile and compressive strength, the stiffness, the crack initiation and the crack damage thresholds and the strain behavior were examined to determine if the mechanical behavior of the 3D-printed specimens is similar to natural sandstones. The Sand-Furan 3D-prints behaved the closest to the weak natural sandstone. The compressive strength-to-stiffness ratio, also known as the modulus ratio, and the compressive-to-tensile strength ratio of the 3D-printed Sand-Furan specimens were found to be similar to the natural sandstones tested in this study and literature values. The failed specimens composed of ceramic beads with silicate binder, both in compression and tension, showed fracture growth not commonly observed in natural specimens. The other 3D-printed specimens generally fractured in a similar manner to natural specimens, although several of the quartz sand with furan binder specimens showed fracturing behavior similar to high porosity natural specimens. Over all, using the commercially available quartz sand with furan binder 3D-print materials showed promise to be able to replicate natural rock specimen behavior.
... Such time series are common data types in hydrogeology [see, e.g. Neuman et al. (2007), Riva et al. (2009b), Copty et al. (2011) andZech et al. (2016) for drawdown series and Tsang et al. (1996), Cirpka and Kitanidis (2000), Jose and Cirpka (2004) and Vogler et al. (2018) for breakthrough curves] and are therefore good candidates for our study. To measure success, we will quantify the impact dimensionreduction has on the inference, i.e. the reduction of uncertainty, with Kullback-Leibler divergence. ...
This study explores methods with which multidimensional data, e.g. time series, can be effectively incorporated into a Bayesian framework for inferring geostatistical parameters. Such series are difficult to use directly in the likelihood estimation procedure due to their high dimensionality; thus, a dimension reduction approach is taken to utilize these measurements in the inference. Two synthetic scenarios from hydrology are explored in which pumping drawdown and concentration breakthrough curves are used to infer the global mean of a log-normally distributed hydraulic conductivity field. Both cases pursue the use of a parametric model to represent the shape of the observed time series with physically-interpretable parameters (e.g. the time and magnitude of a concentration peak), which is compared to subsets of the observations with similar dimensionality. The results from both scenarios highlight the effectiveness for the shape-matching models to reduce dimensionality from 100+ dimensions down to less than five. The models outperform the alternative subset method, especially when the observations are noisy. This approach to incorporating time series observations in the Bayesian framework for inferring geostatistical parameters allows for high-dimensional observations to be faithfully represented in lower-dimensional space for the non-parametric likelihood estimation procedure, which increases the applicability of the framework to more observation types. Although the scenarios are both from hydrogeology, the methodology is general in that no assumptions are made about the subject domain. Any application that requires the inference of geostatistical parameters using series in either time of space can use the approach described in this paper.
... However, flow through fractured rock formations is largely governed by 3D effects, as strong heterogeneities at the fracture networkscale affect flow properties in the fracture and porous-medium domains (Tsang and Neretnieks, 1998;de Dreuzy et al., 2012;Vogler et al., 2018a). In 3D, fracture intersections might act as flow conduits within the fracture planes and could become important. ...
This work presents a modeling approach for single-phase flow in 3D fractured porous media with non-conforming meshes. To this end, a Lagrange multiplier method is combined with a parallel variational transfer approach. This Lagrange multiplier method enables the use of non-conforming meshes and depicts the variable coupling between fracture and matrix domain. The variational transfer allows general, accurate, and parallel projection of variables between non-conforming meshes (i.e. between fracture and matrix domain). Comparisons of simulations with 2D benchmarks show good agreement, and the applied finite element Lagrange multiplier spaces show good performance. The method is further evaluated on 3D fracture networks by comparing it to results from conforming mesh simulations which were used as a reference. Application to realistic fracture networks with hundreds of fractures is demonstrated. Mesh size and mesh convergence are investigated for benchmark cases and 3D fracture network applications. Results demonstrate that the Lagrange multiplier method, in combination with the variational transfer approach, is capable of modeling single-phase flow through realistic 3D fracture networks.
... However, flow through fractured rock formations is governed by 3D effects, as strong heterogeneities affect flow properties in the fracture and porousmedium domains [52,16,54,53]. To apply the Lagrange multiplier method to 3D fracture networks, the variational transfer between fractures and matrix for non-conforming methods needs to be implemented both accurately and with parallel processing capabilities. ...
This work presents a modeling approach for single-phase flow in 3D fractured porous media with non-conforming meshes. To this end, a Lagrange multiplier method is combined with a parallel $L^2$-projection variational transfer approach. This Lagrange multiplier method enables the use of non-conforming meshes and depicts the variable coupling between fracture and matrix domain. The $L^2$-projection variational transfer allows general, accurate, and parallel projection of variables between non-conforming meshes (i.e. between fracture and matrix domain). Comparisons of simulations with 2D benchmarks show good agreement, and the method is further validated on 3D fracture networks by comparing it to results from conforming mesh simulations which were used as a reference. Application to realistic fracture networks with hundreds of fractures is demonstrated. Mesh size and mesh convergence are investigated for benchmark cases and 3D fracture network applications. Results demonstrate that the Lagrange multiplier method, in combination with the $L^2$-projection method, is capable of modeling single-phase flow through realistic 3D fracture networks.
... The scale transfer procedure or upscaling has been classified by Bierkens et al. (2000) depending on the involvement or non-involvement of a model in the research cycle, the possible linear relationship between the model and input variables and parameters, the applicability of the model to different locations/time steps, the form of the model at different scales or the possibility of deriving analytically a different scale model. The major classes of upscaling methods consist of averaging the observations or output variables (Brus and de Gruijter, 1997;Viscarra Rossel et al., 2016), finding representative parameters or input variables (Dagan, 1981;Wu et al., 2006), averaging the model equations (Bedrikovetsky, 2008;Whitaker, 1986) and performing a model simplification (de Vries et al., 1998;Vogler et al., 2018). The upscaling procedure applied in this paper corresponds to the methods finding representative parameters since the input variables of the model involved are non-linear, so it cannot be applied at many time steps and the model has the same form at the two scales involved (Bierkens et al., 2000). ...
Different aspects of management policies for shallow geothermal systems are currently under development. Although this technology has been used for a long time, doubts and concerns have been raised in the last years due to the massive implementation of new systems. To assess possible environmental impacts and manage subsurface energy resources, collecting data from operating shallow geothermal systems is becoming mandatory in Europe. This study presents novel advances in the upscaling of operation datasets obtained from open-loop geothermal energy systems for an optimal integration in hydrogeological models. The proposed procedure allows efficient numerical simulations to be performed at an urban scale. Specifically, this work proposes a novel methodology to optimize the data treatment of highly transient real exploitation regimes by integrating energy transfer in the environment to reduce more than 90% registered raw datasets. The proposed methodology is then applied to and validated on five different real optimization scenarios in which upscaling transformation of the injection temperature series of 15-min sampling frequency has been considered. The error derived from each approach was evaluated and compared for validation purposes. The results obtained from the upscaling procedures have proven the usefulness and transferability of the proposed method for achieving daily time functions to efficiently reproduce the exploitation regimes of these systems with an acceptable error in a sustainable resource management framework.
Development and Improvement Of NUmerical methods and Tools for modelling coupled processes (DONUT)
Workpackage in the European Joint Programme on Radioactive Waste Management (EURAD)
Recent studies have demonstrated that positron emission tomography (PET) is a valuable tool for in-situ characterization of fluid transport in porous and fractured geologic media at the laboratory scale. While PET imaging is routinely used for clinical cancer diagnosis and preclinical medical research—and therefore imaging facilities are available at most research institutes—widespread adoption for applications in water resources and subsurface energy resources engineering have been limited by real and perceived challenges of working with this technique. In this study we discuss and address these challenges, and provide detailed analysis highlighting how positron emission tomography can complement and improve laboratory characterization of different subsurface fluid transport problems. The physics of PET are reviewed to provide a fundamental understanding of the sources of noise, resolution limits, and safety considerations. We then layout the methodology required to perform laboratory experiments imaged with PET, including a new protocol for radioactivity dosing optimization for imaging in geologic materials. Signal-to-noise and sensitivity analysis comparisons between PET and clinical X-ray computed tomography are performed to highlight how PET data can complement more traditional characterization methods, particularly for solute transport problems. Finally, prior work is critically reviewed and discussed to provide a better understanding of the strengths and weakness of PET and how to best utilize PET-derived data for future studies.
The analysis of dispersive flows in heterogeneous porous media is complicated by the appearance of anomalous transport. Novel laboratory protocols are needed to probe the mixing process by measuring the spatial structure of the concentration field in the medium. Here, we report on a systematic investigation of miscible displacements in a microporous limestone over the range of Péclet numbers, 20<Pe<600. Our approach combines pulse-tracer tests with the simultaneous imaging of the flow by Positron Emission Tomography (PET). Validation of the experimental protocol is achieved by means of control experiments on random beadpacks, as well as by comparing observations with both brine- and radio-tracers (labelled with ¹¹C or ¹⁸F). The application of residence time distribution functions reveals mass transport limitations in the porous rock in the form of a characteristic flow-rate effect. Two transport models, namely the Advection Dispersion Equation (ADE) and the Multi-Rate Mass Transfer (MRMT) model, are thoroughly evaluated with both the experimental breakthrough curves and the internal concentration profiles. We observe that the dispersion coefficient scales linearly with the Péclet number for both porous systems. The tracer profiles acquired on the rock sample are successfully described upon application of the MRMT model that uses two representative grain sizes and a fraction of intra-granular pore space that is independent of the fluid velocity. The analysis of the PET images evidences the presence of macrodispersive spreading caused by subcore-scale heterogeneities, which contribute significantly to the value of the estimated core-scale dispersivity. This effect can be significantly reduced upon application of the ‘dispersion-echo’ technique, which enables decoupling the effects of spreading and mixing in heterogeneous porous media. These observations are likely to apply to any laboratory-scale rock sample and the approach presented here provides a practical means to study anomalous transport in these systems.
