Coupled Thermo-hydro-mechanical Processes Research Articles

Coupled Thermo-Hydro-Mechanical Processes in Fractured Rocks: Some Past Scientific Highlights and Future Research Directions

AbstractCoupled thermo-hydro-mechanical (THM) processes in fractured rocks have been a topic of intense scientific research for more than 30 years. The present paper takes a look into the past and highlights some scientific advances which are of an unusual “out-of-the-box” nature, and then looks forward and discusses possible directions of future research in this interesting field of study. Concerning future research directions, we see a trend from a focus on coupled THM processes in single fractures or a few interacting fractures, to the study of coupled THM behavior in complex fracture network systems where the fractures act collectively giving rise to local stress concentration points and points of large pressure gradients. Three examples of future research directions are presented. First is an effort towards identifying characterizing parameters of a fracture network that play a direct controlling role in major coupled THM phenomena (such as induced seismicity and flow channeling), rather than parameters of stochastic distributions of fractures in the network. The second example of research direction is accounting for the heterogeneity and hierarchy of fractures in a fault or fracture zone which has been associated with major THM events in a number of geo-energy projects. The third example is at the opposite end of the first; here it is recognized that in some cases, the coupled THM processes in fractured rocks may be controlled dominantly by only a few key bridges. Identification, characterization, and evaluation of these key bridges should be one of the important research directions in the coming days.

Comparison of two approaches for modelling fracture opening due to cold water injection in geothermal reservoir

Heat and electricity production from deep hot reservoirs through hydrothermal or petrothermal system requires to inject cold fluid in a naturally or artificially fractured medium. Cold water injection in a hot reservoirs causes thermo-hydro-mechanical (THM) coupled processes that may have several influences on operations and long term production [1]. Cold water has a higher viscosity, which means injection can become difficult due to higher flow impedance, while thermal diffusion in the rock matrix causes shrinkage and thus an increasing fracture aperture over time that can lead to flow channeling and a reduction of operation time. A deep understanding of the contribution of coupled THM processes to injection into fractured media is thus important to predict the long-term performance of a geothermal power plant. In this study, coupled THM processes in a single fracture are numerically investigated with two different approaches to model the discontinuity.
 The first numerical approach proposes modelling an implicit fracture in a fracture zone using solid elements (Fig.1 (a)). The impact of the fracture is introduced by means of a stress dependent fracture aperture, which in turn determines the fracture transmissivity. This function allows recovery of the opening, and thus the model replicates opening and closure of the fracture. Then, an equivalent continuum permeability [m2] is obtained as follows:
 where [m] is the elastic opening, br and bmax [m] are the residual and maximum apertures, respectively, a is the stress dependency coefficient; [Pa] is effective normal stress, and [m]the fracture spacing. The combination of the continuum elements to model an implicit fracture embedded in a fracture zone and the evolving permeability has been used successfully used to model elastic opening in volcanic rock [2] and granodiorite rock [3, 4].
 In the second approach, zero-thickness interface elements are used to explicitly model the opening of an existing fracture (Fig.1 (b)), following the work by Liaudat et al. [5]. A constitutive law that is capable of describing the fracture initiation, propagation, closing and opening is implemented in this approach, considering heat transfer in the discontinuity. In this approach, the cubic law is used to estimate the longitudinal transmissivity [m3] as a function of the normal fracture aperture:
 where [m] is the normal separation and [m3] is a constant value which makes it possible to assign an initial longitudinal transmissivity even if the fracture is mechanically closed.
 In both approaches, the simulation of cold water injection requires to consider the heat and hydraulic flows in the fracture alongside mechanical behaviour, since changes in pore water pressure and temperature influence the fracture aperture, thus modifying the fracture transmissivity.
 In order to compare both approaches, a simple synthetic model is studied. The model with its boundary and initial conditions are shown in Fig.2. Water with a temperature of 20 °C and pressure varying from 4 MPa – 10 MPa is injected at the centering point of the fracture. Figure 3 shows the injection pressure profile. Fracture permeability evolution is compared in Fig.4, which shows the two different methods capture different characteristics of the natural fracture behaviour. In the continuum method, the fracture is modelled as a continuum element, thus any pressure or stress change will result in corresponding changes in the fracture permeability, which is reflected in Fig.4 showing that the permeability changes with the injection pressure changing, In contrast, in the interface element, Fig.4 shows only when the injection pressure reaches 10 MPa, the permeability increases sharply from the initial value to the peak value. This is because penalty method is used to allow the small overlapping of the two faces of the discontinuity, thus keeping negligible permeability variation, before it opens. The result in Fig.4 also illustrates the effect of thermal stress on the fracture opening, considering the total vertical stress is 10 MPa while injection pressure is below or equal to 10 MPa.
 In conclusion, though the peak permeability predicted from two methods are consistent, both around 1.5 x 10 -12 D, the behaviour before fracture opens in these two approaches are quite different. For the interface method, permeability variations keep negligible before fracture opens, while for the continuum method, permeability changes with corresponding pressure or stress changes without dependence on the opening of the fracture.

Numerical modeling on nuclide transport around a nuclear waste repository under coupled thermo-hydro-mechanical condition

Coupled thermo-hydro-mechanical (THM) processes may raise the uncertainty of nuclide transport behavior in long-term operation of nuclear waste repository. A far-field modeling framework on nuclide transport around a nuclear waste repository under coupled THM conditions was developed and verified. Base on conceptual models of high-level waste repository in fractured rocks, a three-dimensional repository model including a vertical fault and a horizontal fracture was built, and influence of coupled THM processes on nuclide transport is numerically investigated. Effects of repository depth, fracture inclination, and internal aperture heterogeneity were investigated using the developed model. The results show that the coupled THM processes significantly affect nuclide transport behavior, especially in the early stages of nuclide leaching. The thermal stress induced by heat release of nuclear waste causes the reduction in fracture aperture around the repository. The nuclide transport under THM conditions is retarded before 103 years than that under hydraulic condition. The deeper locations of the candidate repository exhibit the lower rate of nuclide transport. The inclined fracture induces opposite flow directions between two fractures, which causes the delaying of nuclide transport. Fractures with heterogeneous apertures have preferential flow paths, which results in early arrivals of nuclide transport than fractures with homogenous apertures.

Open-source Python library for modeling coupled thermo-hydro-mechanical (THM) processes

Abstract. The interactions between temperature, fluids, and mechanical properties in a repository system are essentially described scientifically by coupled thermo-hydro-mechanical (THM) processes. THM modeling, i.e., the prediction of the behavior of materials under different conditions, is the fundamental numerical tool here. The confident handling and deep understanding of numerical computation methods is thus the prerequisite for performing and evaluating preliminary safety analyses in the site selection process. At the Federal Office for the Safety of Nuclear Waste Management (BASE), a software library for the simulation of coupled THM processes is currently being developed. The main goal of the in-house development is an open-source toolbox in the scripting language Python and is motivated by several long-term sub-goals: targeted development of expertise within BASE regarding numerical modeling of safety-relevant aspects in the long-term safety analyses; diversification of the testing capabilities regarding the preliminary safety investigations by means of an in-house, independent modeling software; foundation of a library of known benchmarks and evaluation examples for the comparison of different software tools; documentation and processing of basic THM scenarios for internal or, if necessary, public technical training. The focus of this development is on creating a toolbox that is easy to use and at the same time highly flexible. The main methodical aspects are as follows: building a new library based on the pyGIMLi pre- and postprocessing framework (Rücker et al., 2017); creating a finite-element reference implementation in the Python scripting language for maximal transparency; creating an easy-to-use interface to the solution of the weak formulation for the finite-element theory with expressions of a symbolic manner allowing maximal flexibility; defining an interface to allow for the integration of alternative, third-party high-performance libraries; creating a collection of Jupyter notebooks of well-documented test cases and benchmarks. Choosing the open-source approach ensures the best possible transparency and, in the long term, also allows the provision of appropriately quality-assured and documented simulation tools to the public. The presented poster shows the current development status of the software library and the currently implemented quality assurance concepts and gives an outline of the potential applications of the library.

Numerical simulation of long-term performance of deep geological repository placement rooms in crystalline and sedimentary rocks

Evaluation of the stability of placement rooms and damages in the geosphere surrounding a deep geological repository (DGR) for high-level nuclear waste are essential components for assessing the overall repository performance. Assessments of the performance of placement rooms for the duration of the regulatory period (typically 1 million years) usually involves simulations using numerical codes capable of modeling coupled thermo-hydro-mechanical (THM) processes induced by different natural and repository-induced perturbations over different time and length scales. The numerical constitutive model used to represent the host medium should be capable of capturing highly nonlinear responses to stress changes, including development of damage and fracturing. In this study, a novel approach for simulation of damage evolution and fracturing around the repository rooms, based on the bonded block model (BBM) devised for analyzing coupled THM processes, is used to perform a study of the long-term geomechanical performance of the Nuclear Waste Management Organization hypothetical DGR configurations in sedimentary and crystalline geological settings. The perturbation effects of different loading conditions, including in-situ stress changes by room excavation, heat generated from the used fuel canisters, and glaciation were analyzed. Each THM analysis was conducted using a 3D continuum numerical code to generate evolving temperature and pore pressure fields in the rock mass. The temperature and pore pressure data were then imported in the 2D BBM model for simulating evolution of damage around the placement rooms. Sensitivity analysis was conducted to investigate the effect of different poro-mechanical parameters, rock mass permeabilities, and different approaches for calibrating the BBM, on predictions of room stability and extent of the excavation damage zone around the placement room. The modeling results indicate that the confinement provided by the bentonite backfill inside the room clearly prevents any unravelling but also limits the extent of the damage to less than 1.6 m into the room walls in any of the analyzed cases considering different loading conditions and uncertainty of the material properties.

An evaluation framework for production performance of high-temperature fractured and karstified geothermal reservoirs: Production mechanism, sensitivity study, and key parameters ranking

High-temperature (>150 °C) geothermal resources have great potential for sustainable power generation. These geothermal resources can be exploited efficiently through highly permeable geological structures, i.e. tectonic fractures and dissolution caves, which thus are categorized as fractured and karstified geothermal reservoirs. However, the study of long-term cold fluids injection into these high-temperature geothermal systems is faced with significant unsolved challenges, i.e. the simulation of coupled porous media flow and free flow in multiscale and heterogeneous fracture-cave networks with distinct thermo-hydro-mechanical (THM) coupling effects. To address these challenges, we develop a novel coupled THM model based on the discrete fracture-cave network approach. We then apply this model to perform the analysis of THM coupling mechanism, sensitivity study, and key parameters ranking to identify the development characteristics of high-temperature geothermal reservoirs. Results show that with respect to coupled THM processes, the fluid flow and heat transfer are dominated by connected fracture clusters and are strongly influenced by the inclusion of caves. However, the behavior of solid deformation is governed by the distribution of caves. As to the reservoir thermal performance under different working fluids, i.e. water and CO2, the water-based geothermal reservoir exhibits longer service life, greater global thermal power, and higher heat extraction rate than the CO2-based one. Regarding sensitivity analysis and key factors ranking, fracture attributes (fracture length and density) are the two most important parameters in regulating the geothermal extraction performance. Caves fall out as the third most significant parameter. However, the operating parameters (i.e. injection temperature, injection pressure, production pressure, well length, and well distance) play a limited role in influencing thermal performance compared with geometrical parameters of fractures and caves. The developed model and insights obtained from our research have crucial implications for understanding and optimizing the thermal production of high-temperature fractured and karstified geothermal reservoirs.

Numerical Prediction of the Large-Scale in Situ PRACLAY Heater Test in the Boom Clay

The large-scale PRACLAY heater test has been running since November 2014 in the HADES URF (Belgium) to examine the combined impact on the host Boom Clay of the thermo-hydro-mechanical (THM) perturbations due to gallery construction and a large-scale thermal load which simulates the heat dissipation of radioactive waste. To get an insight into the expected evolution of the test, which will be helpful to guide the test, numerical prediction of the PRACLAY heater test had been performed before the heater was switched on. The numerical prediction, based on the existing related knowledge before the switch-on of the heater test, took into account the complex coupled THM processes and interactions in all the involved materials of the experimental set-up (Boom Clay, bentonite, concrete lining, backfill sand, etc.) and the test phases from the gallery excavation till the end of heating which is planned in 2025. A large number of constitutive models and associated parameters required to define the numerical problem had been identified and calibrated on the basis of literature review, results of extensive laboratory tests and back analysis of many relevant in situ measurements from the HADES URF. The results of the numerical prediction are constantly and extensively compared with the in situ measured data obtained since the switch-on of the heater till 4-year stationary heating. Overall, it can be stated that the general Boom Clay THM responses in the PRACLAY heater test are in good agreement with the numerical prediction, which gives good indications on the model capacity and confirms the existing knowledge of the Boom Clay THM behaviour.

Combined Effects of Thermal Perturbation and In-situ Stress on Heat Transfer in Fractured Geothermal Reservoirs

We develop a new fully coupled thermo-hydro-mechanical (THM) model to investigate the combined effects of thermal perturbation and in-situ stress on heat transfer in two-dimensional fractured rocks. We quantitatively analyze the influence of geomechanical boundary constraints and initial reservoir temperature on the evolutionary behavior of fracture aperture, fluid flow and heat transfer, and further identify the underlying mechanisms dominating the coupled THM processes. The results reveal that, apart from enhancing normal opening of fractures, the transient cooling effect of thermal front may trigger shear dilations under the anisotropic in-situ stress condition. It is found that the applied in-situ stress tends to impose a strong impact on the spatial and temporal variations of fracture apertures and flow rates, and eventually affect heat transfer. The enhancement of reservoir transmissivity during transient cooling tends to be significantly overestimated if the in-situ stress effect is not incorporated, which may lead to unrealistic predictions of heat extraction performance. Our study also provides physical insights into a fundamental thermo-poroelastic behavior of fractured rocks, where fracture aperture evolution during heat extraction tends to be simultaneously governed by two mechanisms: (1) thermal expansion-induced local aperture enlargement and (2) thermal propagation-induced remote aperture variation (can either increase or decrease). The results from our study have important implications for optimizing heat extraction efficiency and managing seismic hazards during fluid injections in geothermal reservoirs.

Fully coupled thermo-hydro-mechanical model with oversaturation and its validation to experimental data from FEBEX experiment

The paper is devoted to the formulation of a mathematical model which enables analysis of coupled thermo-hydro-mechanical (THM) processes with a special focus on processes in bentonite and bentonite-based sealing barriers which are component of designs of deep geological repositories for a high-level radioactive waste including the spent nuclear fuel. Such modelling is important as the analysis of coupled THM processes in the near field is crucial for the understanding of the long-term behaviour of the barriers. The developed model uses generally available data from standard tests but attempts to incorporate special characteristics of the bentonite behaviour, let us mention the oversaturation, swelling and strong couplings of the processes. The model is implemented via COMSOL Multiphysics and validated by the simulation of THM processes which were monitored during operation of the FEBEX experiment and analysed during two dismantling phases of the experiment.

A study of thermal pressurization and potential for hydro-fracturing associated with nuclear waste disposal in argillaceous claystone

We present coupled Thermo–Hydro–Mechanical (THM) modeling of geologic nuclear waste disposal in argillaceous claystone, focusing on thermally-induced pressure changes and the potential for such pressure changes to induce hydro-fracturing. To investigate this possibility, we first conduct a three-dimensional repository scale model, with host rock properties, repository design, and nuclear waste decay heat functions derived from the French concept of geologic disposal in argillaceous claystone. The model simulations show that the highest potential for hydro-fracturing occurs between emplacement micro-tunnels (cells) at the center rather than at the edge of the repository. We further investigate the use of a two-dimensional single cell model as a simpler surrogate for a full three-dimensional model. Our results reveal that such geometric simplification is reasonably accurate for modeling coupled THM processes at the center of the repository, though it overestimates the likelihood for hydro-fracturing and substantially overpredicts ground surface uplift. A parameter study shows the importance of adjacent higher permeability geological layers that play a significant role in dissipating overpressure in the host rock layer. Finally, the study shows the importance of the spacing between emplacement tunnels, which if too short results in a higher fluid pressure and a strongly increased potential for hydro-fracturing. Overall, the study suggests, the limiting factor in the thermal management and design of a repository is not necessarily the maximum temperature in the engineered barrier system near the waste packages, but rather the more modest host rock temperature between emplacement tunnels, due to the potential for thermal damage.

Building a certified reduced basis for coupled thermo-hydro-mechanical systems with goal-oriented error estimation

A goal-oriented a-posteriori error estimator is developed for transient coupled thermo-hydro-mechanical (THM) parametric problems solved with a reduced basis approximation. The estimator assesses the error in some specific Quantity of Interest (QoI). The goal-oriented error estimate is derived based on explicitly-computed weak residual of the primal problem and implicitly-computed adjoint solution associated with the QoI. The time-dependence of the coupled THM system poses an additional complexity as the auxiliary adjoint problem evolves backwards in time. The error estimator guides a greedy adaptive procedure that constructs progressively an optimal reduced basis by smartly selecting snapshot points over a given parametric training sample. The reduced basis obtained is used to drastically reduce the coupled system spatial degrees of freedom by several orders of magnitude. The computational gain obtained from the developed methodology is demonstrated through applications in 2D and 3D parametrized problems simulating the evolution of coupled THM processes in rock masses.

Comparison of numerical codes for coupled thermo-hydro-mechanical simulations of fractured media

Geo-energy and geo-engineering applications, such as improved oil recovery (IOR), geologic carbon storage, and enhanced geothermal systems (EGSs), involve coupled thermo-hydro-mechanical (THM) processes that result from fluid injection and production. In some cases, reservoirs are highly fractured and the geomechanical response is controlled by fractures. Therefore, fractures should explicitly be included into numerical models to realistically simulate the THM responses of the subsurface. In this study, we perform coupled THM numerical simulations of water injection into naturally fractured reservoirs (NFRs) using CODE_BRIGHT and TOUGH-UDEC codes. CODE_BRIGHT is a finite element method (FEM) code that performs fully coupled THM analysis in geological media and TOUGH-UDEC sequentially solves coupled THM processes by combining a finite volume method (FVM) code that solves non-isothermal multiphase flow (TOUGH2) with a distinct element method (DEM) code that solves the mechanical problem (UDEC). First, we validate the two codes against a semi-analytical solution for water injection into a single deformable fracture considering variable permeability based on the cubic law. Then, we compare simulation results of the two codes in an idealized conceptual model that includes one horizontal fracture and in a more realistic model with multiple fractures. Each code models fractures differently. UDEC calculates fracture deformation from the fracture normal and shear stiffnesses, while CODE_BRIGHT treats fractures as equivalent porous media and uses the equivalent Young's modulus and Poisson's ratio of the fracture. Finally, we obtain comparable results of pressure, temperature, stress and displacement distributions and evolutions for the single horizontal fracture model. Despite some similarities, the two codes provide increasingly different results as model complexity increases. These differences highlight the challenging task of accurately modeling coupled THM processes in fractured media given their high nonlinearity.

Experimental Investigation on Permeability Evolution of Limestone Caprock under Coupled THM Processes

To investigate the gas sealing capacity of limestone as cap rock for gas reservoir at different burial depths, triaxial compression coupled with permeability tests of limestone subjected to different confining pressures and temperatures were carried out using the improved MTS 815 test machine. During the tests, acoustic emission (AE) monitoring system was also employed to estimate the rock damage. Test results demonstrated a degradation of triaxial compression strength with the increase in temperature and decrease of confining pressure. An empirical equation for the peak stress was established considering confining pressure and temperature. Three different permeability evolution patterns of limestone samples can be proposed based on the experimental results under different coupled thermo-hydro-mechanical (THM) conditions. According to the spatial-temporal characteristics of AE signals, permeability evolution was highly related to the fracture growth and connection in limestone. Ultimately, the experimental results revealed that the permeability of limestone gradually decreased with the increasing confining pressure and temperature. In addition, an exponential relationship between initial permeability and confining pressure was established.

Isogeometric analysis through Bézier extraction for thermo-hydro-mechanical modeling of saturated porous media

We present a modeling framework developed based upon Isogeometric analysis (IGA) for fully coupled numerical simulation of thermo-hydro-mechanical (THM) problems in saturated porous media. The framework employs Bézier extraction to connect IGA with the conventional finite element method and to take advantage of the features offered by both methods. The mathematical model of non-isothermal multiphase geomaterials is based on the hybrid mixture theory. Using the standard Galerkin method, the weak formulations of linear momentum, mass, and energy balance equations of the overall continuum are developed. The Bézier extraction operator is used to derive Non-Uniform Rational B-Splines (NURBS) basis functions to discretize the governing equations in space. The generalized backward Euler scheme is implemented for time discretization. The final nonlinear system of equations is linearized using the Newton-Raphson scheme with a monolithic approach. The results from the proposed method are verified against an analytical solution. Several important considerations in modeling coupled THM processes in saturated porous media are presented and discussed. The application of the method is illustrated for two example problems. The results show that the proposed method offers a robust alternative for modeling THM problems especially where cubic approximation functions are used.

Thermo-poroelastic numerical modelling for enhanced geothermal system performance: Case study of the Groß Schönebeck reservoir

Significant pressure and temperature changes can occur within geothermal reservoirs caused by injection and production of fluid which can affect transport properties of the rocks and therefore alter reservoir performance and sustainability. To understand the coupling between transport properties evolution and state variable changes, a complete description of the mechanical behavior of the reservoir is required which should consider thermo- and poroelastic effects. This study aims to integrate transport properties evolution for coupled thermo-hydro-mechanical (THM) process modelling of fluid-bearing reservoirs. This approach is here applied to the geothermal research site of Groß Schönebeck (40km north of Berlin, Germany) which consists of a doublet system at a target depth of about −4100m in which both injection and production wells have been hydraulically stimulated. A 3D reservoir model including the main geological units, major natural fault zones and hydraulic fractures is integrated in the finite-element method-based simulator OpenGeoSys for modelling coupled THM processes during geothermal activity. One challenge of this study is to integrate both hydro-geological and physical complexity to better describe the dynamic behavior of the geothermal reservoir. From the results of the simulation, thermal breakthrough is observed after 18years of injection and life time of the system has been evaluated as 50years. Furthermore, a 5.5% increase of porosity around the injection well is observed as well as an increase of the anisotropy ratio for permeability (kz/kxy) of about 2%. These transport properties enhancements lead to a decrease of the thermal breakthrough time (around −8%) and life time of the system (−14%) compared to classic thermo-hydro simulations with constant transport properties. The results presented here provide therefore valuable insights for understanding porosity and permeability distributions and evolutions during injection and production of geothermal fluids and related impacts on reservoir performance.

불포화지반에 대한 열-수리-역학 거동의 수식화

일반적인 불포화지반의 거동뿐만 아니라, 열과 관련된 분야, 지반환경 분야 등 다양한 분야에서 불포화 다공질 재료의 열적-수리적-역학적으로 결합된 문제들이 대두되면서 이러한 문제들을 해석하기 위한 수치도구 개발의 필요성이 대두되고 있다. 본 논문에서는 거시적 접근법(macroscopic approach)에 근거하여 불포화지반에 대한 열-수리-역학거동의 수식화를 하였다. 흙, 물, 공기에 대한 질량보존의 법칙, 에너지 보존법칙, 그리고 하중평형 조건식으로부터 결합된(coupled) 4개의 지배방정식을 유도하였다. Galerkin 간략화와 시간적분으로부터 주 변수인 변위(u), 가스압(<TEX>$P_g$</TEX>), 유체압(<TEX>$P_1$</TEX>), 온도(T)를 Newton의 반복과정을 이용하여 구하는 유한요소 프로그램(FEM)을 작성하였다. 개발된 프로그램을 이용하여 다공질재료에서 2상 흐름 문제 중 일차원 배수실험(u-<TEX>$P_g-P_1$</TEX>), 온도 압밀(u-<TEX>$P_1$</TEX>-T), 그리고 지표면 온도변화에 의한 말뚝의 주변지반에 대한 영향(u-<TEX>$P_1$</TEX>-T)에 대하여 수치해석을 수행하고 논의하였다. Emerging issues related with fully coupled Thermo-Hydro-Mechanical (THM) behavior of unsaturated soil demand the development of a numerical tool in diverse geo-mechanical and geo-environmental areas. This paper presents general governing equations for coupled THM processes in unsaturated porous media. Coupled partial differential equations are derived from three mass balances equations (solid, water, and air), energy balance equation, and force equilibrium equation. With Galerkin formulation and time integration of these governing equations, finite element code is developed to find nonlinear solution of four main variables (displacement-u, gas pressure-<TEX>$P_g$</TEX>), liquid pressure-<TEX>$P_1$</TEX>), and temperature-T) using Newton's iterative scheme. Three cases of numerical simulations are conducted and discussed: one-dimensional drainage experiments (u-<TEX>$P_g-P_1$</TEX>), thermal consolidation (u-<TEX>$P_1$</TEX>-T), and effect of pile on surrounding soil due to surface temperature variation (u-<TEX>$P_1$</TEX>-T).

Uncertainty analysis of thermo-hydro-mechanical coupled processes in heterogeneous porous media

In this paper we present an uncertainty analysis of thermo-hydro-mechanical (THM) coupled processes in a typical geothermal reservoir in crystalline rock. 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). The finite element method (FEM) is used for the numerical analysis of fully coupled THM processes, including thermal water flow, advective–diffusive heat transport, and thermoelasticity. Non-linearity in system behavior is introduced via temperature and pressure dependent fluid properties. Reservoir parameters are considered as spatially random variables and their realizations are generated using conditional Gaussian simulation. The related Monte-Carlo analysis of the coupled THM problem is computationally very expensive. To enhance computational efficiency, the parallel FEM based on domain decomposition technology using message passing interface (MPI) is utilized to conduct the numerous simulations. In the numerical analysis we considered two reservoir modes: undisturbed and stimulated. The uncertainty analysis we apply captures both the effects of heterogeneity and hydraulic stimulation near the injection borehole. The results show the influence of parameter ranges on reservoir evolution during long-term heat extraction, taking into account fully coupled thermo-hydro-mechanical processes. 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.

The DECOVALEX III project: A summary of activities and lessons learned

Initiated in 1992, the DECOVALEX project is an international collaboration for advancing the understanding and modeling of coupled thermo-hydro-mechanical (THM) processes in geologic systems. The project has made important scientific achievements through three stages and is progressing in its fourth stage. It has played a key role in the development of mathematical modeling and in situ testing of coupled THM processes in fractured rock and buffer/backfill materials, a subject of importance for performance assessment of radioactive waste geologic repositories. This paper summarizes studies under the most recent stage of the project, DECOVALEX III (2000-2003). These studies include those of two major field experiments: (a) the FEBEX experiment at Grimsel, Switzerland, investigating coupled THM processes in a crystalline rock-bentonite system, and (b) the Drift Scale Test (DST) experiment at Yucca Mountain, Nevada, investigating coupled THM processes in unsaturated tuff. These are two of the largest multiyear heater tests undertaken to date for the study of coupled THM processes in geological systems. In addition, three so-called benchmark tests are also studied to evaluate the impact of coupled THM processes under different scenarios and geometries. Within the DECOVALEX project, multiple research teams participated in each of the studies, using different approaches and computer codes. Comparisons of results have provided insight into coupled THM processes, which in turn has stimulated further development of our modeling capabilities. Lessons learned from these studies are discussed. The scientific advances and enhanced insight gained through this kind of international cooperation illustrate the effectiveness of the DECOVALEX project.

Thermohydromechanics of partially saturated geological media: governing equations and formulation of four finite element models

This paper presents the general governing equations for coupled thermohydromechanical (THM) processes in saturated and unsaturated geologic formations and reviews four finite element codes for modeling of such system. Three of the codes are developed for the special purpose of analyzing coupled THM processes in unsaturated porous and fractured geological media, and the fourth is a commercial code that has been used in its standard version, with a few adaptations for this specialized problem. The basic assumptions and fundamental equations for coupled THM processes in unsaturated porous fractured rock are presented, and formulations of the four finite element models are compared.