Hydro-mechanically induced transient changes in fracture volume elude an analysis of pressure and flow rate transients by conventional diffusion-based models. We used a previously developed fully coupled, inherently non-linear numerical simulation model to demonstrate that harmonic hydraulic excitation of fractures leads to systematic overtones in the response spectrum that can thus be used as a diagnostic criterion for hydro-mechanical interaction. The examination of response spectra, obtained from harmonic testing at four different field sites, for the occurrence of overtones confirmed their potential for the hydro-mechanical characterization of tested reservoirs. A non-dimensional analysis identified relative aperture change as the critical system parameter.

AbstractThere are several finite element-based modeling approaches to deal with fissures, fractures and discontinuities in rocks.

We introduce a partitioned coupling approach for iterative coupling of flow processes in deformable fractures embedded in a poro-elastic medium that is enhanced by interface quasi-Newton (IQN) methods. In this scope, a unique computational decomposition into a fracture flow and a poro-elastic domain is developed, where communication and numerical coupling of the individual solvers are realized by consulting the open-source library preCICE. The underlying physical problem is introduced by a brief derivation of the governing equations and interface conditions of fracture flow and poro-elastic domain followed by a detailed discussion of the partitioned coupling scheme. We evaluate the proposed implementation and undertake a convergence study to compare a classical interface quasi-Newton inverse least-squares (IQN-ILS) with the more advanced interface quasi-Newton inverse multi-vector Jacobian (IQN-IMVJ) method. These coupling approaches are verified for an academic test case before the generality of the proposed strategy is demonstrated by simulations of two complex fracture networks. In contrast to the development of specific solvers, we promote the simplicity and computational efficiency of the proposed partitioned coupling approach using preCICE and FEniCS for parallel computations of hydro-mechanical processes in complex, three-dimensional fracture networks.

In this work, we propose a hydro-mechanical simulation model to study the strong interaction of fluid flow and fracture deformation under in situ stress conditions. The general model is reduced under physics-based assumptions to provide an efficient numerical approach for inverse analysis of experimental studies and is applied to experimental field data obtained from hydraulic tests conducted at the Grimsel Test Site, Switzerland. The present set of hydro-mechanical measurement data provides not only valuable information about the transient pressure and flow evolution but also the transient change of fracture deformation. We aim to introduce a strongly coupled hydro-mechanical model to numerically characterize the fractured reservoir based on experimental data below the limit of hydraulically induced irreversible changes of the reservoir's properties. Insights into the leading mechanisms of flow processes throughout hydraulic testing under in situ conditions are then gained by best numerical fits of the measurement data. Based on the experimental and numerical findings, this study emphasizes the importance of a consistent consideration of local and non-local fracture deformation throughout inverse analysis of hydraulic testing data to (a) better understand hydro-mechanical flow processes in fractured reservoirs and (b) increase the estimation quality of hydraulic properties of tested fractures.

AbstractAn essential scientific goal of the GeomInt project is the analysis of potentials and limitations of different numerical approaches for the modelling of discontinuities in the rocks under consideration in order to improve the understanding of methods and their synergies with regard to theoretical and numerical fundamentals. As numerical methods, the “Lattice Element Method” (LEM), the non-continuous discontinuum methods “Discrete Element Method” (DEM), the “Smoothed Particle Hydrodynamics” (SPH), the “Forces on Fracture Surfaces” (FFS) as well as the continuum approaches “Phase-Field Method” (PFM), “Lower-Interface-Method” (LIE), “Non-Local Deformation” (NLD) and the “Hybrid-Dimensional Finite-Element-Method” (HDF) will be systematically investigated and appropriately extended based on experimental results (Fig. 3.1).

We applied a hybrid-dimensional flow model to pressure transients recorded during pumping experiments conducted at the Reiche Zeche underground research laboratory to study the opening behavior of fractures due to fluid injection. Two distinct types of pressure responses to flow-rate steps were identified that represent radial-symmetric and plane-axisymmetric flow regimes from a conventional pressure-diffusion perspective. We numerically modeled both using a radial-symmetric flow formulation for a fracture that comprises a non-linear constitutive relation for the contact mechanics governing reversible fracture surface interaction. The two types of pressure response can be modeled equally well. A sensitivity study revealed a positive correlation between fracture length and normal fracture stiffness that yield a match between field observations and numerical results. Decomposition of the acting normal stresses into stresses associated with the deformation state of the global fracture geometry and with the local contacts indicates that geometrically induced stresses contribute the more the lower the total effective normal stress and the shorter the fracture. Separating the contributions of the local contact mechanics and the overall fracture geometry to fracture normal stiffness indicates that the geometrical stiffness constitutes a lower bound for total stiffness; its relevance increases with decreasing fracture length. Our study demonstrates that non-linear hydro-mechanical coupling can lead to vastly different hydraulic responses and thus provides an alternative to conventional pressure-diffusion analysis that requires changes in flow regime to cover the full range of observations.

The present paper gives an overview of the GeomInt project “Geomechanical integrity of host and barrier rocks—experiment, modelling and analysis of discontinuities” which has been conducted from 2017–2020 within the framework of the “Geo:N Geosciences for Sustainability” program. The research concept of the collaborative project is briefly introduced followed by a summary of the most important outcomes. The research concept puts geological discontinuities into the centre of investigations—as these belong to the most interesting and critical elements for any subsurface utilisation. Thus, while research questions are specific, they bear relevance to a wide range of applications. The specific research is thus integrated into a generic concept in order to make the results more generally applicable and transferable. The generic part includes a variety of conceptual approaches and their numerical realisations for describing the evolution of discontinuities in the most important types of barrier rocks. An explicit validation concept for the generic framework was developed and realised by specific “model-experiment-exercises” (MEX) which combined experiments and models in a systematic way from the very beginning. 16 MEX have been developed which cover a wide range of fundamental fracturing mechanisms, i.e. swelling/shrinkage, fluid percolation, and stress redistribution processes. The progress in model development is also demonstrated by field-scale applications, e.g. in the analysis and design of experiments in underground research laboratories in Opalinus Clay (URL Mont Terri, Switzerland) and salt rock (research mine Springen, Germany).

AbstractThe FFS method (see Sect. 10.1007/978-3-030-61909-1_3) was developed to simulate direct shear tests. To provide a tool for the project work and get things easier done a graphical user interface (GUI) was also created. The GUI simply calls all necessary functions by letting the user either fill form fields or choose input files from the working folder. The rock parameters and the conditions of the direct shear test with the normal stress levels and shear displacements have to be selected. If an experiment is simulated the lab results can be selected as a text file so a visual comparison is possible. The geometry has to be loaded as a point cloud or an artificial surface can be generated. With small modifications the code can do multiple executions using artificial surfaces.

AbstractThe basic idea of Model-Experiment-Exercises (MEX) is to link modelling and experimental works from the very beginning i.e. in the conceptual phase. Due to the complexity of each part in the systems analysis, this combination is sometimes lost. Moreover, both models and experiments require highly sophisticated tools and equipment as well as highly specialized professionals, which also necessitate adequate measures and incentives for collaboration. GeomInt is introducing the MEX concept exactly for this purpose. Therefore, the following MEX studies occupy the largest part of the GeomInt book and feed most of the publications with research material.

AbstractData management includes the development and use of architectures, guidelines, practices and procedures for accurate managing of data during the entire data lifecycle of an institutional unit or a research project. Data are defined as different information units such as numbers, alphabetic characters, and symbols that are particularly formatted and can be processed by computer. The data in the project is provided by various actors which can be GeomInt partners, their legal representatives, employees, and external partners.

In the community of porous and fractured geomaterials properties regarding underground fluid storage and matter are of high interest. Investigations on fluid‐filled fractures require strong hydro mechanical coupling of fracture and porous domain to reproduce deformation triggered, non‐local phenomena such as the Noordbergum effect. Special numerical treatment is necessary to solve the tightly coupled system consisting of high aspect ratio fractures and a surrounding porous matrix, since other approaches such as Direct Numerical Simulations fail due to technical issues (number of Degrees of Freedom (DoF)). Once heterogeneous initial aperture distributions are of interest coarse grained continuum approaches (Biot's poroelasticity theory) facing technical limitations since explicit meshing of the fracture geometry is required. This work uses hybrid‐dimensional interface elements in a fully coupled implicit formulation to investigate its capacities regarding heterogeneous fracture surfaces in three dimensions.

In the field of porous and fractured media, subsurface flow provides insight into the characteristics of fluid storage and properties connected to underground matter and heat transport. Subsurface flow is precisely described by many diffusion based models in the literature. However, diffusion-based models lack to reproduce important hydro-mechanical coupling phenomena like inverse water-level fluctuations (Noordbergum effect). In theory, contemporary modeling approaches, such as direct numerical simulations (DNS) of surface-coupled fluid-solid (fracture) interactions or coarse-grained continuum approaches like Biot’s theory, are capable of capturing such phenomena. Nevertheless, during modeling processes of fractures with high aspect ratios, DNS methods with the explicit discretization of the fluid domain fail, and coarse-grained continuum approaches require a non-linear formulation for the fracture deformation since large deformation can be reached easily within fractures. Hence a hybrid-dimensional approach uses a parabolic velocity profile to avoid an explicit discretization of the fluid domain within the fracture. For fracture flow, the primary variable is the pressure field only, and the fracture domain is reduced by one dimension. The interaction between the fracture and the surrounding matrix domain, respectively, is realized by modified balance equations. The coupled system is numerically stiff when fluids are described with a low compressibility modulus. Two algorithms are proposed within this work, namely the weak coupling scheme, which uses an implicit staggered-iterative algorithm to find the residual state and the strong coupling scheme which directly couples both domains by implementing interface elements. In the course of this work, a consistent implementation scheme for the coupling of hybrid-dimensional elements with a surrounding bulk matrix is proposed and validated and tested throughout different numerical experiments.

AbstractCharacteristics of underground fluid storage and properties related to heat transport and underground matter are of high interest in the community of porous and fractures media. Especially once hydro‐mechanical phenomena in fluid filled fractures are of interest, such as inverse waterlevel fluctuations during well stimulations (Noordbergum effect), the numerical coupling of the fluid and the porous domain is challenging. Existing strategies such as direct numerical simulations or coarse‐grained approaches (Biot's theory) either fail due to technical issues (number of Degrees of Freedom (DoF)) or are not capable of intuitively taking permeability changes based on the deformation state into account. This work proposes a fully coupled scheme using hybrid‐dimensional element formulations and zero‐thickness interface elements that naturally describes flow in deformable fractures surrounded by porous media.

AbstractThe investigation of subsurface fluid flow in porous and fractured media is of interest in particular to determine the properties of matter and heat transport below the earth surface and the characteristics of the underground storage of fluids. Classical approaches such as extended diffusion equations are lacking the possibilities to capture key phenomena such as inverse water‐level fluctuations (Noordbergum effect) obtained during pumping tests performed on aquifers [1, 2, 4]. In order to efficiently model hydro‐mechanical effects, this contribution presents an implementation of the newly introduced hybrid‐dimensional approach [3] in the DUNE‐PDELab environment. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The computational treatment of discontinuities within the framework of the finite element method (FEM) is a requirement for simulations of fracturing of solids and has become a challenging topic in computational mechanics. Particularly popular amongst the advanced schemes is the extended finite element method (XFEM) which is based on enrichment of shape functions and falls within the framework of the partition of unity method. Because there is no simple way to track the interface of discontinuities, the computer implementation of the XFEM is not as straightforward as the FEM. One method to solve the interface tracking problem is the level set method (LSM) which introduces another partial differential equation. The level set equation describes the change of an interface due to a known velocity field. To obtain its solution, the FEM can also be employed. This contribution investigates the XFEM-LSM technique with element enrichment and the integration of discontinuous elements for the modelling of cracks or material interfaces. Numerical experiments illustrate the capabilities and accuracy of the resulting formulation.

The extrapolation of numerical data from integration points to finite element nodes is a crucial step for finite element analyses. The process is also known as recovery technique. A number of strategies have been proposed in the past, including the well-known Super-convergent Patch Recovery (SPR). One of the authors has also proposed a simpler and more general method based on local extrapolation (Durand-Farias). Later on, the authors of this contribution have shown that the Durand-Farias method is much more efficient than the SPR method for some cases and can perfectly be used for recovering nodal data of porous media problems. This paper shows a comparative study on the numerical performance between the aforementioned methods, including a discussion of the best strategies to define a patch for the SPR method.