Finite element method for coupled thermo-hydro-mechanical processes in discretely fractured and non-fractured porous media

Numerical analysis of multi-field problems in porous and fractured media is an important subject for various geotechnical engineering tasks such as the management of geo-resources (e.g. engineering of geothermal, oil and gas reservoirs) as well as waste management. For practical usage, e.g. for geothermal, simulation tools are required which take into account both coupled thermo-hydro-mechanical (THM) processes and the uncertainty of geological data, i.e. the model parametrization. For modeling fractured rocks, equivalent porous medium or multiple continuum model approaches are often only the way currently due to difficulty to handle geomechanical discontinuities. However, they are not applicable for prediction of flow and transport in subsurface systems where a few fractures dominates the system behavior. Thus modeling coupled problems in discretely fractured porous media is desirable for more precise analysis. The subject of this work is developing a framework of the finite element method (FEM) for modeling coupled THM problems in discretely fractured and non-fractured porous media including thermal water flow, advective-diffusive heat transport, and thermoporoelasticity. Pre-existing fractures are considered. Systems of discretely fractured porous media can be considered as a problem of interacted multiple domains, i.e. porous medium domain and discrete fracture domain, for hydraulic and transport processes, and a discontinuous problem for mechanical processes. The FEM is required to take into account both kinds of the problems. In addition, this work includes developing a methodology for the data uncertainty using the FEM model and investigating the uncertainty impacts on evaluating coupled THM processes. All the necessary code developments in this work has been carried out with a scientific open source project OpenGeoSys (OGS). In this work, fluid flow and heat transport problems in interactive multiple domains are solved assuming continuity of filed variables (pressure and temperature) over the two domains. The assumption is reasonable if there are no infill materials in fractures. The method has been successfully applied for several numerical examples, e.g. modeling three-dimensional coupled flow and heat transport processes in discretely fractured porous media at the Gross Schoenebck geothermal site (Germany), and three-dimensional coupled THM processes in porous media at the Urach Spa geothermal site (Germany). To solve the mechanically discontinuous problems, lower-dimensional interface elements (LIEs) with local enrichments have been developed for coupled problems in a domain including pre-existing fractures. The method permits the possibility of using existing flow simulators and having an identical mesh for both processes. It enables us to formulate the coupled problems in monolithic scheme for robust computation. Moreover, it gives an advantage in practice that one can use existing standard FEM codes for groundwater flow and easily make a coupling computation between mechanical and hydraulic processes. Example of a 2D fluid injection problem into a single fracture demonstrated that the proposed method can produce results in strong agreement with semi-analytical solutions. An uncertainty analysis of THM coupled processes has been studied for a typical geothermal reservoir in crystalline rock based on the Monte-Carlo method. Fracture and matrix are treated conceptually as an equivalent porous medium, and the model is applied to available data from the Urach Spa and Falkenberg sites (Germany). Reservoir parameters are considered as spatially random variables and their realizations are generated using conditional Gaussian simulation. Two reservoir modes (undisturbed and stimulated) are considered to construct a stochastic model for permeability distribution. We found that the most significant factors in the analysis are permeability and heat capacity. The study demonstrates the importance of taking parameter uncertainties into account for geothermal reservoir evaluation in order to assess the viability of numerical modeling

Numerical simulation of fracture pattern development and implications for fuid flow

Simulations are instrumental to understanding flow through discrete fracture geometric representations that capture the large-scale permeability structure of fractured porous media. The contribution of this thesis is threefold: an efficient finite-element finite-volume discretisation of the advection/diffusion flow equations, a geomechanical fracture propagation algorithm to create fractured rock analogues, and a study of the effect of growth on hydraulic conductivity. We describe an iterative geomechanics-based finite-element model to simulate quasi-static crack propagation in a linear elastic matrix from an initial set of random flaws. The cornerstones are a failure and propagation criterion as well as a geometric kernel for dynamic shape housekeeping and automatic remeshing. Two-dimensional patterns exhibit connectivity, spacing, and density distributions reproducing en echelon crack linkage, tip hooking, and polygonal shrinkage forms. Differential stresses at the boundaries yield fracture curving. A stress field study shows that curvature can be suppressed by layer interaction effects. Our method is appropriate to model layered media where interaction with neighbouring layers does not dominate deformation. Geomechanically generated fracture patterns are the input to single-phase flow simulations through fractures and matrix. Thus, results are applicable to fractured porous media in addition to crystalline rocks. Stress state and deformation history control emergent local fracture apertures. Results depend on the number of initial flaws, their initial random distribution, and the permeability of the matrix. Straightpath fracture pattern simplifications yield a lower effective permeability in comparison to their curved counterparts. Fixed apertures overestimate the conductivity of the rock by up to six orders of magnitude. Local sample percolation effects are representative of the entire model flow behaviour for geomechanical apertures. Effective permeability in fracture dataset subregions are higher than the overall conductivity of the system. The presented methodology captures emerging patterns due to evolving geometric and flow properties essential to the realistic simulation of subsurface processes

Thermo-hydro-mechanical simulation of a generic geological disposal facility for radioactive waste

Geological disposal is required for the safe and long-term disposal of legacy radioactive waste. High level waste and spent fuel generate significant heat that will cause thermo-hydro-mechanical coupled processes in the rock mass. The thermal expansion of the fluid will be greater than the grains causing a decrease in mean effective stress with the low permeability restricting Darcy flow and excess pore pressure equilibration. A decrease in mean effective stress can reduce material strength in granular materials, which may be significant near excavations where differential stress is increased. Microseismic monitoring provides cost effective, non-intrusive and three-dimensional data that can be calibrated with the stress and strain behaviour of a rock mass. However, there is no precedent for the microseismic monitoring of heat-producing radioactive waste. Generic concepts, analogue materials and data from in situ experiments are used to demonstrate the potential for the microseismic monitoring of heat-producing radioactive waste in lower strength sedimentary rocks. A mechanism for early post-closure microseismicity is demonstrated, whereby excess pore pressure decreases the mean effective stress towards yielding in shear. The rock and fluid property uncertainties are ranked according to their contribution to the excess pore pressure. Permeability is found to be important as expected, however, Biot's coefficient is demonstrably more important and yet often overlooked. Furthermore, the microseismic event locations, timings and pseudo scalar seismic moments are shown to have statistically significant relationships with the engineered backfill swelling pressure. Therefore, early post-emplacement microseismic monitoring could provide constraints for the engineered backfill swelling pressure and rock property uncertainties whilst the facility is still operational. Insights could prove timely for adapting the engineering designs, if they are not behaving as expected, in further high level waste and spent fuel tunnels

Analysing stress field conditions of the Colima Volcanic Complex (Mexico) by integrating finite-element modelling (FEM) simulations and geological data

In recent decades, finite-element modelling (FEM) has become a very popular tool in volcanological studies and has even been used to describe complex system geometries by accounting for multiple reservoirs, topography, and het- erogeneous distribution of host rock mechanical properties. In spite of this, the influence of geological information on numerical simulations is still poorly considered. In this work, 2D FEM of the Colima Volcanic Complex (Mexico) is pro- vided by using the Linear Static Analysis (LISA) software in order to investigate the stress field conditions with increas- ingly detailed geological data. By integrating the published geophysical, volcanological, and petrological data, we mod- elled the stress field considering either one or two magma chambers connected to the surface via dykes or isolated (not connected) in the elastic host rocks (considered homoge- neous and non-homogeneous). We also introduced tectonic disturbance, considering the effects of direct faults bordering the Colima Rift and imposing an extensional far-field stress of 5 MPa. We ran the model using the gravity in calculations. Our results suggest that an appropriate set of geological data is of pivotal importance for obtaining reliable numerical out- puts, which can be considered a proxy for natural systems. Beside and beyond the importance of geological data in FEM simulations, the model runs using the complex feeding system geometry and tectonics show how the present-day Col- ima volcanic system can be considered in equilibrium from a stress state point of view, in agreement with the long-lasting open conduit dynamics that have lasted since 1913

Seismic Waves

The importance of seismic wave research lies not only in our ability to understand and predict earthquakes and tsunamis, it also reveals information on the Earth's composition and features in much the same way as it led to the discovery of Mohorovicic's discontinuity. As our theoretical understanding of the physics behind seismic waves has grown, physical and numerical modeling have greatly advanced and now augment applied seismology for better prediction and engineering practices. This has led to some novel applications such as using artificially-induced shocks for exploration of the Earth's subsurface and seismic stimulation for increasing the productivity of oil wells. This book demonstrates the latest techniques and advances in seismic wave analysis from theoretical approach, data acquisition and interpretation, to analyses and numerical simulations, as well as research applications. A review process was conducted in cooperation with sincere support by Drs. Hiroshi Takenaka, Yoshio Murai, Jun Matsushima, and Genti Toyokuni

Characterisation and modelling of natural fracture networks: geometry, geomechanics and fluid flow

Natural fractures are ubiquitous in crustal rocks and often dominate the bulk properties of geological formations. The development of numerical tools to model the geometry, geomechanics and fluid flow behaviour of natural fracture networks is a challenging issue which is relevant to many rock engineering applications. The thesis first presents a study of the statistics and tectonism of a multiscale fracture system in limestone, from which the complexity of natural fractures is illustrated with respect to hierarchical topologies and underlying mechanisms. To simulate the geomechanical behaviour of rock masses embedded with natural fractures, the finite-discrete element method (FEMDEM) is integrated with a joint constitutive model (JCM) to solve the solid mechanics problems of such intricate discontinuity systems explicitly represented by discrete fracture network (DFN) models. This computational formulation can calculate the stress/strain fields of the rock matrix, capture the mechanical interactions of discrete rock blocks, characterise the non-linear deformation of rough fractures and mimic the propagation of new cracks driven by stress concentrations. The developed simulation tool is used to derive the aperture distribution of various fracture networks under different geomechanical conditions, based on which the stress-dependent fluid flow is further analysed. A novel upscaling approach to fracture network models is developed to evaluate the scaling of the equivalent permeability of fractured rocks under in-situ stresses. The combined JCM-FEMDEM model is further applied to simulate the progressive rock mass failure around an underground excavation in a crystalline rock with pre-existing discontinuities. The scope of this thesis covers the scenarios of both two-dimensional (2D) and three-dimensional (3D) fracture networks with pre-existing natural fractures and stress-induced new cracks. The research findings demonstrate the importance of integrating explicit DFN representations and conducting geomechanical computations for more meaningful assessments of the hydromechanical behaviour of naturally fractured rocks.Open Acces

Image-Based Modeling of Porous Media Using FEM and Lagrangian Particle Tracking

The study of fundamental flow and transport processes at the pore scale is essential to understanding how the mechanisms affect larger, field-scale, processes that occur in oil and gas recovery, groundwater flow, contaminant transport, and CO2 sequestration. Pore-scale imaging and modeling is one of the techniques used to investigate these fundamental mechanisms. Although extensive development of pore-scale imaging and modeling has occurred recently, some areas still need further advances. In this work, we address two areas: (1) imaging of bulk proppants and proppant-filled fractures under varying loading stress and flow simulation in these systems and (2) nanoparticle (NP) transport modeling in porous media. These are briefly explained below. Rock fracturing, followed by proppant injection, has been used for years to improve oil and gas production rates in low permeability reservoirs and is now routinely used in low-permeability resources such as a shales and tight sands. While field data makes clear the effectiveness of this technique, there is still much room to improve on the science, including how the proppant-filled fracture system responds to changes in loading stress which affect permeability and conductivity. Here, we use high-resolution x-ray computed tomography (XCT) to image two unsaturated rock/fracture/proppant systems under a series of stress levels typical of producing reservoirs: one with shale, one with Berea sandstone. The resulting XCT images were segmented, analyzed for structural and porosity changes, and then used for image-based flow modeling of Stokes flow using both finite element (FEM) and Lattice Boltzmann methods. NPs have been widely used commercially and have the potential to be extensively used in petroleum engineering as stabilizers in enhanced oil recovery operations or as tracers or sensors to detect rock and fluid properties. %In spite of a wide range of applications, many NP transport details are still unknown. In this work, we describe a Lagrangian particle tracking algorithm to model NP transport that can be used to better understand the impact of pore-scale hydrodynamics and surface forces on NP transport. Two XCT images, a Berea sandstone and a 2.5D micromodel, were meshed and used for image-based flow modeling of FEM Stokes flow. The effects of particle size, surface forces, flow rate, particle density, surface capacity, and surface forces mapped to XCT-image based mineralogy were studied

Numerical computations of rock dissolution and geomechanical effects for CO 2 geological storage

International audienceThe paper is motivated by the long term safety analysis of the CO 2 geological storage. We present a methodology for the assessment of the ge-omechanical impact of progressive rock dissolution. The method is based on the use of X-ray tomography and the numerical dissolution technique. The influence of evolution of the microstructure on the macroscopic properties of the rock is analysed by using periodic homogenization method. The numerical computations show progressive degradation of all components of the stiffness (orthotropic) tensor. Moreover, the evolution of associated mass transfer properties (as tortuosity and conductivity tensors), by using the periodic homogenization method, is also calculated. The correlation between the mechanical parameters and the transfer properties during the dissolution pro-cess is presented. The results show that the highest increase of the hydraulic conductivity (in direction Y) is not associated with the highest decrease of Young modulus in this direction. Moreover, the highest decrease of Young modulus (in the direction X) is not associated with percolation in this direction. Finally, an incremental law to calculate settlement, in case of a rock with evolving microstructure, is proposed. The solution of the macroscopic settlement problem under constant stress and drained conditions showed that the geomechanical effects of the rock dissolution are rather limited

Combined finite-discrete element modelling of key instabilities which characterise deep-seated landslides from massive rock slope failure

The expression “landslide from massive rock slope failure” (MRSF) is used to indicate large-scale landslides characterised by a variety of complex initial failure processes and unpredictable postfailure behaviour. In this context, deep-seated landslides are classified as “landslides from massive rock slope failure”. Typically, deep-seated landslides are slow mountain deformations which may involve movement along discrete shear surfaces and deep seated mass creep. The long-term development of deep-seated slope deformations creates suitable conditions for the subsequent occurrence of other slope deformations. Deep-seated landslides in mountain areas can be spatially interconnected with other types of slope deformations such as debris flows, debris slides, rock avalanches, topple, translational, rotational and compound sliding and complex type of mass movements. It is to be recognized that many aspects of large-scale landslides need be investigated in order to gain the necessary confidence in the understanding and prediction of their behaviour and in the associated risk assessment. The present thesis is to contribute to such understanding with specific reference to a number of mass movements which characterize large-scale landslides. An advanced numerical technique (FDEM) which combines finite elements with discrete elements has been applied in this thesis for improving such understanding. The open source research code, called Y2D, developed at the Queen Mary, University of London by Prof. Munjiza has been used. Considering that this code has not yet been applied to slope stability problems, a series of numerical tests have been carried out to assess its suitability to properly and efficiently simulate geomechanical problems. To this purpose standard rock failure mechanisms as well as laboratory tests have been modelled first and the results obtained have been compared with available analytical and numerical solutions. The advantages of the application of FDEM has been outlined by showing that both the simulation of failure initiation and progressive development to fragmentation of the rock mass is possible as this is deposited at the slope toe. The case study of interest for this thesis is the Beauregard massive landslide located in the Aosta Valley (Northwestern Italy). At this site the presence of an extensive deep-landslide insisting on the left abutment of an arch-gravity dam is well recognised. Based on detailed studies, the investigated area has been subdivided into zones which are characterised by different geomorphologic and geostructural features. Different landslide mechanics as well as different landslide activities upstream of the dam site have been identified and studied in detail. Such an area is thought to be at an intermediate stage of development of the deep seated landslide compared with the sector which insists on the dam. The observed failure mechanism has been ascribed to a large sliding on a compound surface. Some other failure mechanisms have been recognized, such as large flexural toppling and local block toppling instability. The final part of the thesis has been devoted to the FDEM numerical modelling of a large scale failure mechanism based on brittle behaviour of the rock mass. The aim is to apply the “total slope failure” approach through the application of FDEM. Such a technique has demonstrated the significant potential in predicting the development of possible slope instability phenomena

Investigation of strain-sensitive properties of porous media through micro-CT imaging and numerical modelling

Strain-sensitive characteristics of porous media are studied through micro-CT imaging and numerical simulations. First, high-fidelity Discrete Element Method (DEM) models are constructed for practical porous media based on micro-CT images. These DEM models prioritize the overall system morphology over individual grain/particle shapes, ensuring robustness and flexibility controlled by easily adjustable algorithm parameters. Subsequently, we validate the accuracy of our proposed DEM models by comparing them with the Finite Element Method (FEM), achieving consistent agreement across all test cases. Finally, the CT-image based DEM approach is employed to investigate strain-sensitive properties of porous media, such as permeability, porosity, tortuosity, specific surface area, and fractal dimension. With a primary focus on transport and morphology properties, our approach is versatile and applicable to exploring various other properties of porous media. This study introduces a generic methodology for examining practical porous media under in-situ conditions, providing valuable insights into their response to stress and deformation