On the necessity and a generalized conceptual model for the consideration of large strains in rock mechanics

This contribution presents a generalized conceptual model for the finite element solution of quasi-static isothermal hydro-mechanical processes in (fractured) porous media at large strains. A frequently used averaging procedure, known as Theory of Porous Media, serves as background for the complex multifield approach presented here. Within this context, a consistent representation of the weak formulation of the governing equations (i.e., overall balance equations for mass and momentum) in the reference configuration of the solid skeleton is preferred. The time discretization and the linearization are performed for the individual variables and nonlinear functions representing the integrands of the weak formulation instead of applying these conceptual steps to the overall nonlinear system of weighted residuals. Constitutive equations for the solid phase deformation are based on the multiplicative split of the deformation gradient allowing the adaptation of existing approaches for technical materials and biological tissues to rock materials in order to describe various inelastic effects, growth and remodeling in a thermodynamically consistent manner. The presented models will be a feature of the next version of the scientific open-source finite element code OpenGeoSys developed by an international developer and user group, and coordinated by the authors

On the term and concepts of numerical model validation in geoscientific applications

Modeling and numerical simulation of the coupled physical and chemical processes observed in the subsurface are the only options for long-term analyses of complex geological systems. This contribution discusses some more general aspects of the (dynamic) process modeling for geoscientific applications including reflections about the slightly different understanding of the terms model and model validation in different scientific communities, and about the term and methods of model calibration in the geoscientifc context. Starting from the analysis of observations of a certain part of the perceived reality, the process of model development comprises the establishment of the physical model characterizing relevant processes in a problem-oriented manner, and subsequently the mathematical and numerical models. Considering the steps of idealization and approximation in the course of model development, Oreskes et al. [1] state that process and numerical models can neither be verified nor validated in general. Rather the adequacy of models with specific assumptions and parameterizations made during model set-up can be confirmed. If the adequacy of process models with observations can be confirmed using lab as well as field tests and process monitoring, the adequacy of numerical models can be confirmed using numerical benchmarking and code comparison. Model parameters are intrinsic elements of process and numerical models, in particular constitutive parameters. As they are often not directly measurable, they have to be established by solving inverse problems based on an optimal numerical adaptation of observation results. In addition, numerical uncertainty analyses should be an obligatory part of numerical studies for critical real world applications

Simultaneous flow of water and air across the land surface during runoff

This paper presents an inter-compartment boundary condition for the simulation of surface runoff, soil moisture, and soil air as a coupled system of partial differential equations. The boundary condition is based on a classic leakance approach to balance water between differently mobile regions such as the land surface and subsurface. Present work applies leakances to transfer water and air simultaneously through the land surface for soils, which are connected by an air flux with a steady atmosphere. Shallow flow and two phase flow in a porous medium are sequential calculated in an iteration loop. General criteria are stated to guarantee numerical stability in the coupling loop and for leakances to control inter-compartment fluid fluxes. Using the leakance approach, a numerical model captures typical feedbacks between surface runoff and soil air in near-stream areas. Specifically, displacement of water and air in soils is hampered at full-water saturation over the land surface resulting in enhanced surface runoff in the test cases. Leakance parameters permit the simulation of air out-breaks with reference to air pressures, which fluctuate in the shallow subsurface between two thresholds

Simulation of solute transport in 3d porous media using random walk particle tracking method

Random walk particle tracking (RWPT) method provides a computationally effective way to characterize solute transport process in porous media. In this work, an object-oriented scientific software platform OpenGeoSys (OGS) was adopted for the simulation and visualization of the complex behavior of particles. Finite element method is used for the calculation of the velocity field which is necessary for the determination of the displacement of the particles through space. The RWPT method has been used in the simulation of the hydraulic process, diffusion and dispersion as it is proved to be well suitedfor such studies. In this work, efforts were taken to search for the solutionto simulate the retardation and decay processe in order to investigate the effects that appear in the contaminant plume evolution. Expressions for the effective coefficients governing the solute transport are derived for retardation model, based on a two-rate sorption-desorption approach. The RWPT model was first verified by a benchmark test of solute transport in a one-dimensional homogeneous media to analysis the accuracy of the method with comparison to the analytical solution. The analysis was the next ended to applications witht hree-dimensional homogeneous aquifer. This method can be used as a tool to elicit and discern the detailed structure of evolving contaminant plumes

Modelling Coupled Component Based Multiphase and Reactive Transport Processes in Deep Geothermal Reservoirs using OpenGeoSys

ABSTRACT In deep geothermal reservoirs, artificial fracture networks are often stimulated and enhanced during the well construction, in order to facilitate the efficient heat transfer from the host rocks to the heat carrying fluid. However, throughout the life span of a geothermal power plant, the geochemical reactions on the fracture surfaces will gradually confine the hydraulic and mechanical behavior of the fractures, thus further affect the energy output of the reservoir. The numerical simulation of such long term behavior of the reservoir imposes several challenges to modelers. First, it is a coupled non-isothermal system that often contains multiple fluid and solid phases. In addition, depending on the pressure and temperature conditions, phase change process may happen in certain parts of the modeling domain. To further increase the non-linearity of the system, the long term fluid-rock geochemical reactions have to be included in the consideration and the model must be able to account for their feedback to the hydraulic and flow field. Within the framework OpenGeoSys software, we extended the traditional phase volume based multiphase flow module to chemical component based formulations. This allows a further coupling with geochemical processes on the fracture surface. The developed code will be verified against several benchmark cases, which involves non-isothermal multiphase flow involving phase change and mineral-water geochemical reactive transport processes. The simulation of coupled processes in fracture network dominated geothermal reservoirs will also be presented. INTRODUCTION For the performance analysis of deep geothermal reservoirs, numerical modelling tools are widely employed to simulate the flow processes in the subsurface. With high temperature and pressure in the reservoir, coupled multiphase flow processes often interact with chemical reactions and impose challenges on numerical models. In order to reproduce the phase change behavior mentioned above in the numerical simulation, there exist so far several different numerical schemes. The most popular one is the primary variable switching method proposed b

Orthogonal decomposition of anisotropic constitutive models for the phase field approach to fracture

We propose a decomposition of constitutive relations into crack-driving and persistent portions, specifically designed for materials with anisotropic/orthotropic behavior in the phase field approach to fracture to account for the tension-compression asymmetry. This decomposition follows a variational framework, satisfying the orthogonality condition for anisotropic materials. This implies that the present model can be applied to arbitrary anisotropic elastic behavior in a three-dimensional setting. On this basis, we generalize two existing models for tension-compression asymmetry in isotropic materials, namely the volumetric-deviatoric model and the no-tension model, towards materials with anisotropic nature. Two benchmark problems, single notched tensile shear tests, are used to study the performance of the present model. The results can retain the anisotropic constitutive behavior and the tension-compression asymmetry in the crack response, and are qualitatively in accordance with the expected behavior for orthotropic materials. Furthermore, to study the direction of maximum energy dissipation, we modify the surface integral based energy release computation, $G_\theta$, to account only for the crack-driving energy. The computed energies with our proposed modifications predict the fracture propagation direction correctly compared with the standard G-theta method

Towards the generic conceptual and numerical framework for the simulation of CO2 sequestration in different types of georeservoirs

In this paper, conceptual and numerical modeling of coupled thermo-hydromechanical (THM) processes during CO2 injection and storage is presented. The commonly used averaging procedure combining the Theory of Mixtures and the Concept of Volume Fractions serves as background for the complex porous media approach presented here. Numerical models are based on a generalized formulation of the individual and overall balance equations for mass and momentum, as well as, in non-isothermal case, the energy balance equation. Within the framework of a standard Galerkin approach, the method of weighted residuals is applied to derive the weak forms of governing equations. After discretizing spatially these weak forms, a system of nonlinear algebraic equations can be obtained. For the required time discretization a generalized first order difference scheme is applied, linearization is performed using Picard or Newton-Raphson methods. The corresponding models are implemented within the scientific open source finite element code OpenGeoSys (OGS) developed by the authors, which is based on object oriented programming concepts. This assists the efficient treatment of different physical processes, whose mathematical models are of similar structure. Thus, the paper is mainly focused on a generic theoretical framework for the coupled processes under consideration. Within this context, CO2 sequestration in georeservoirs of different type can be simulated (e.g., saline aquifers, (nearly) depleted hydrocarbon reservoirs)

A thermo-hydro-mechanical finite element model of freezing in porous media-thermo-mechanically consistent formulation and application to ground source heat pumps

Freezing phenomena in porous media have attracted great attention in geotechnics, construction engineering and geothermal energy. For shallow geothermal applications where heat pumps are connected to borehole heat exchangers (BHEs), soil freezing around the BHEs is a potential problem due to persistent heat extraction or inappropriate design which can sig- nificantly influence the temperature distribution as well as groundwater flow patterns in the subsurface, and even lead to frost heave. A fully coupled thermo-hydro-mechanical freezing model is required for advanced system design and scenario analyses. In the framework of the Theory of Porous Media, a triphasic freezing model is derived and solved with the finite element method. Ice formation in the porous medium results from a coupled heat and mass transfer problem with phase change and is accompanied by volume expansion. The model is able to capture various coupled physical phenomena during freezing, e.g., the latent heat ef- fect, groundwater flow with porosity change and mechanical deformation. The current paper is focused primarily on the theoretical derivation of the conceptual model. Its numerical implementation is verified against analytical solutions of selected phenomena including pure phase change and thermo-hydro-mechanical process couplings

GeoLaB – Das geowissenschaftliche Zukunftsprojekt für Deutschland

Geothermische Energie kann bei der Dekarbonisierung des deutschen Energiesystems eine wichtige Rolle einnehmen. Um das große Potenzial der Geothermie im kristallinen Grundgebirge wirtschaftlich nutzbar zu machen, werden Ertüchtigungsmaßnahmen im Reservoir eingesetzt. Eine Voraussetzung für die öffentliche Akzeptanz solcher EGS („Enhanced Geothermal Systems“) ist jedoch die Minimierung der möglichen induzierten Seismizität. Ihre Kontrolle kann nur auf Basis des Verständnisses für die Prozesse und Wechselwirkungen des Fluids mit dem Reservoir erfolgen. Mit dem generischen Untertagelabor GeoLaB („Geothermal Laboratory in the Crystalline Basement“) sollen grundlegende Fragen der Reservoirtechnologie und Bohrlochsicherheit von EGS erforscht werden. Die geplanten Experimente werden wesentlich unser Verständnis der maßgeblichen Prozesse im geklüfteten Kristallingestein unter erhöhten Fließraten verbessern. Der Einsatz und die Entwicklung modernster Beobachtungs- und Auswertemethoden führen zu Erkenntnissen, die für eine sichere und ökologisch nachhaltige Nutzung der Geothermie und des unterirdischen Raumes von großer Bedeutung sind. Als interdisziplinäre und internationale Forschungsplattform wird GeoLaB in Kooperation mit der Deutschen Forschungsgemeinschaft, Universitäten sowie industriellen Partnern und Fachbehörden Synergien erzeugen und technisch-wissenschaftliche Innovationen hervorbringen