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Experimental studies suggest that the fracture toughness of rocks increases with the confining pressure. Among many methods to quantify this dependency, a so-called burst experiment (Abou-Sayed, 1978) may be the most widely applied in practice. Its thick wall cylinder geometry leads to a stress state resembling the subsurface condition of a pressurized wellbore with bi-wing fractures. The fracture toughness of a sample, under a given confinement pressure, can be recovered from the critical pressure upon which the bi-wing cracks propagate. Traditionally, this critical pressure is thought to correspond to a sudden drop in injection pressure. However, as the standard configuration was deliberately designed to obtain stable fracture growth at the onset, propagation can take place well before this drop in pressure, and one may overestimate the fracture toughness from measured pressures. Here, we study crack stability in the burst experiment and propose modifications to the experimental design which promotes unstable fracture growth and makes the critical pressure less ambiguous to interpret. We found that experiments with the original, stable design can lead to inconsistent measurement of fracture toughness under confining pressure, while results from unstable configurations are more consistent. Our claim on the stability was also supported by the recorded acoustic emissions from both stable and unstable experiments.

In this chapter we briefly describe information methods and technologies supporting geotechnical systems analyses of to large extend, i.e. using virtual reality methods for data and model integration (Sect. 5.1) and improving computational efficiency by using high-performance-computing techniques (Sect. 5.2).

The principal interest of the GeomInt project consists of the investigation of effects on barrier integrity of three host rock formations: clay, salt and crystalline. The project focuses on distinct physical processes that can influence barrier integrity in these rocks, particularly those related to swelling and shrinkage, pressure-driven percolation and stress redistribution.

GeomInt2 is the follow-up project to the joint project “Geomechanical Integrity of Host and Barrier Rocks—Experiment, Modelling and Analysis of Discontinuities (GeomInt)”. The results of GeomInt made essential contributions to the analysis of the origin and development of discontinuities in clay, salt and crystalline rocks. Discontinuities are considered in many forms, be it as volumetrically distributed damage macroscopically representing fissures in the rock microstructure, discontinuities that can form anew at phase interfaces as well as discrete cracks or fracture networks. The pathways created or extended by these discontinuities entail the risk of migration of fluid phases from deep to near-surface geological layers and must therefore be taken into account in geotechnical safety analyses.

Superhot geothermal environments with temperatures of approximately 400–500 °C at depths of approximately 2–4 km are attracting attention as new kind of geothermal resource. In order to effectively exploit the superhot geothermal resource through the creation of enhanced geothermal systems (superhot EGSs), hydraulic fracturing is a promising technique. Laboratory-scale hydraulic fracturing experiments of granite have recently demonstrated the formation of a dense network of permeable fractures throughout the entire rock body, referred to as a cloud-fracture network, at or near the supercritical temperature for water. Although the process has been presumed to involve continuous infiltration of low-viscosity water into preexisting microfractures followed by creation and merger of the subsequent fractures, a plausible criterion for cloud-fracture network formation is yet to be clarified. The applicability of the Griffith failure criterion is supported by hydraulic fracturing experiments with acoustic emission measurements of granite at 400 °C under true triaxial stress and at 450 °C under conventional triaxial stress. The present study provides, for the first time, a theoretical basis required to establish the procedure for hydraulic fracturing in the superhot EGS.

Wormholes are an effective fluid conduit that dominate the flow path in karst aquifers and are artificially induced in geo-energy applications through acid injection. As acidic fluids infiltrate geologic formations, they react with the minerals in the formation. The reaction localizes and forms a dendritic dissolution pattern under certain conditions, known as the reaction infiltration instability. This instability is instigated by material heterogeneities in most computational models. However, studies have demonstrated that injection of water into a homogeneous plaster can initiate and grow wormholes. In this study, we show that material heterogeneities suppress the wormhole growth in carbonate rocks compared with a homogeneous counterpart. Wormholes were numerically simulated through injection of a strong acid (hydrochloric acid) under both homogeneous and heterogeneous permeability fields using a phase-field approach. The phase-field variable represents calcite dissolution in a diffused manner and is coupled with a reactive flow model assuming convective and diffusive acid transport in the liquid phase and significantly high surface reaction rate, which emulate typical high-rate matrix acidizing treatments in carbonate reservoirs. Heterogeneous permeability fields localize the flow in high-permeability domains and enhance the splitting and branching of wormholes. The length of the dominant wormholes can be suppressed as an increasing amount of acid infiltrates into the branched wormholes. Our findings indicate that material heterogeneities should not be treated as a trigger for wormholes in the numerical simulation but as one of the parameters to control their nucleation and growth.

Hydraulic fracturing is widely applied in unconventional reservoirs to generate fracture networks for productivity enhancement. Interactions between hydraulic fractures and natural fractures have a great impact on fracture propagation. In this study, we use a two-dimensional phase field model to investigate interactions between hydraulic fractures and different frictional or cemented fractures under different in-situ stress, injection rate, natural fracture orientation and strength. We find that with the increasing stress anisotropy, hydraulic fracture is more likely to cross natural fracture and leads to a lower fracture complexity. A moderate injection rate is conducive for complex fractures. The approaching angle between the hydraulic fracture and natural fracture impact fracture topology. Complex fractures are formed when the angles are not so steep. With the increasing strength contrast between natural fractures and the rock matrix, the material heterogeneity increases for hydraulic fractures to generate complex fractures. Compared with frictional NFs, opening stronger cemented NFs requires more pressure than hydraulic fracture propagating outside the interface. The numerical investigations in this study can provide theoretical support and design guidance for fracturing operations in complex geological conditions.

Hydraulic fractures often turn or branch, interacting with pre-existing discontinuities (e.g. natural fracture, grain boundary). Such fracture complexities, especially in the proximity of borehole, impact the subsequent well conductivity. When a fracture finds a discontinuity, it either penetrates or deflects depending supposedly on the in-situ stress and the discontinuity geometry. However, our hydraulic fracture experiments on carbonates show that the fractures deflected more frequently at a grain boundary as they propagated farther away from the borehole. In other words, the fracture complexity consistently increases with the propagation distance. In this study, using energy release rate analyses, we show that the energy dissipation of a penetrating fracture increases with the distance away from the borehole. This means, the farther away the hydraulic fracture propagates, the more easily it deflects at a grain boundary from the energetic point of view. This tendency was also confirmed by numerical hydraulic fracture simulations based on a successive energy minimization approach. Our findings challenge the conventional hydraulic fracture penetration/deflection criteria based only on the in-situ stress and the discontinuity geometry.

At the interface between the steel canister and the bentonite in a nuclear waste repository, we expect generation of hydrogen gas because of corrosion processes. The pressurized gas might fracture the engineered or natural clay barrier system, enhancing radionuclide transport into the geosphere. To assess the long-term integrity of the clay host rock under various conditions and scenarios, we need a large number of numerical simulations. However, a simulation tool for complex fracture propagation is often prohibitively expensive to run many realizations. Here, we developed a risk analysis tool based on the Design of Experiments to overcome the computational challenges by generating a computationally inexpensive proxy fracture model using a set of critical factors known as heavy hitters. We provided parameters and their probability distributions that are subject to uncertainty, as well as an objective function that assesses the risk of fracturing due to high gas pressures. Through various scenarios, we found that the fracture toughness dominates the impact on the risk.

Developing high-enthalpy geothermal systems requires a sufficiently permeable formation to extract energy through fluid circulation. Injection experiments above water’s critical point have shown that fluid flow can generate a network of highly conductive tensile cracks. However, what remains unclear is the role played by fluid and solid rheology on the formation of a dense crack network. The decrease of fluid viscosity with temperature and the thermally activated visco-plasticity in rock are expected to change the deformation mechanisms and could prevent the formation of fractures. To isolate the solid rheological effects from the fluid ones and the associated poromechanics, we devise a hydro-fracture experimental program in a non-porous material, polymethyl methacrylate (PMMA). In the brittle regime, we observe rotating cracks and complex fracture patterns if a non-uniform stress distribution is introduced in the samples. We observe an increase of ductility with temperature, hampering the propagation of hydraulic fractures close to the glass transition temperature of PMMA, which acts as a limit for brittle fracture propagation. Above the glass transition temperature, acoustic emission energy drops of several orders of magnitude. Our findings provide a helpful guidance for future studies of hydro-fracturing of supercritical geothermal systems.

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).

Awi 18-1 is an injection well drilled in the Cianten Caldera, near the western margin of the Salak (Awibengkok) reservoir in west Java, Indonesia. As the initial well injectivity was low, a long-term hydraulic stimulation was conducted to improve the permeability and establish a better connection to existing natural fractures. A geologic model of the area was built by integration of surface mapping, log and core data, and well performance information. The well penetrated pre- and post-caldera volcanics, the caldera ring fault intrusion and contact metamorphic zone, and marine sedimentary rocks. Permeability was found primarily near the caldera margin in pre-caldera lavas and ring fault intrusion along steeply dipping N to NW and NE trending fractures that were partially sealed by mineral precipitation. A geomechanical simulation model was developed from the geologic model to understand the injectivity evolution mechanisms and behaviours under different injection conditions, and also predict long term future injectivity performance. The model domain contains the completed interval of a deviated injection well (Awi 18-1) and covers the majority of microseismic events observed during the course of the stimulation. It simulates injectivity evolution using fully coupled processes of heat and mass transfers in poro-elastic media. The model was history-matched against the injection data (i.e. pressure) by calibrating rock mechanical and fracture properties. A few what-if scenarios under different operation conditions were simulated to evaluate the effects of injection pressure and temperature on the injectivity. These what-if scenario simulations indicate that both colder injection temperature and higher wellhead pressure lead to better injection efficiency. Also, the higher pressure had prolonged impacts while the colder temperature impacts are limited at the early time.

Rigorous coupling of fracture–porous medium fluid flow and topologically complex fracture propagation is of great scientific interest in geotechnical and biomechanical applications. In this paper, we derive a unified fracture–porous medium hydraulic fracturing model, leveraging the inherent ability of the variational phase-field approach to fracture to handle multiple cracks interacting and evolving along complex yet, critically, unspecified paths. The fundamental principle driving the crack evolution is an energetic criterion derived from Griffith’s theory. The originality of this approach is that the crack path itself is derived from energy minimization instead of additional branching criterion. The numerical implementation is based on a regularization approach similar to a phase-field model, where the cracks location is represented by a smooth function defined on a fixed mesh. The derived model shows how the smooth fracture field can be used to model fluid flow in a fractured porous medium. We verify the proposed approach in a simple idealized scenario where closed form solutions exist in the literature. We then demonstrate the new method’s capabilities in more realistic situations where multiple fractures turn, interact, and in some cases, merge with other fractures.

Fractures control fluid flow and the coupled geomechanical response of geological media in many geo-engineering applications. For instance, fractures dominate fluid flow and deformation in enhanced geothermal systems, underground radioactive waste repositories, and CO2 storage. Coupled thermo-hydro-mechanical processes in rock masses are a result of perturbations in the pore pressure, as in fluid injection and/or production, and/or temperature, as in cold fluid injection and disposal of radioactive waste. For example, fractures open as a result of pore pressure increase, which simultaneously increases permeability and reduces overpressure. Geo-engineering and geo-energy applications involve a large portion of rock masses that include several fractures. Numerical computations of coupled processes occurring in rock masses while considering a large number of fractures pose several challenges. In this study, we firstly focus on a simple problem to fully understand the hydro-mechanical behavior of a single fracture subjected to a constant injection flow rate. We use the FEM software CODE_BRIGHT, which solves the thermohydro- mechanical governing equations in a fully coupled way. Since standard FEM can solve equations in continuum media, we investigate the behavior of a single fracture by analyzing the hydro-mechanical parameters that control the fracture response in a continuum fashion. However, simulating fractures with the real aperture is not simply feasible, hence, we search the equivalent properties of thicker fractures that are more feasible to be discretized in large-scale models with several fractures.

Superhot geothermal environments with temperatures of approximately 400-500︒C at depth of approximately 2-4 km are expected as a new geothermal energy frontier. In order to efficiently exploit the superhot geothermal resources, fracture systems are necessary as flow path of working fluid. Hydraulic fracturing is a promising technique because it is able to create a new fracture system or enhance the permeability of preexisting fracture system. Laboratory-scale hydraulic fracturing experiments of granite have demonstrated the formation of densely distributed network of permeable fractures throughout the entire rock body at or near the supercritical temperature for water. Though the process has been presumed to involve continuous infiltration of low-viscosity water into preexisting microfractures followed by creation and merger of the subsequent fractures, plausible criterion for the fracturing is yet to be clarified. The possibility that the Griffith failure criterion is available to predict the occurrence of fracturing was shown by hydraulic fracturing experiments with acoustic emission measurements of granite at 400︒C under true triaxial stress. The present study provides a theoretical basis required to establish the procedure for hydraulic fracturing in superhot geothermal environment.

This paper proposes a diffused approach to approximate failure at interfaces that physically occupy negligible space compared to the bulk material. For an interface diffused over a certain length, we derive an effective interface fracture toughness based on the diffused length and the fracture toughness of the bulk and the interface. Our derivation ensures the energetic equivalence between the sharp and the diffused representations of interface. We verified the critical energy release rates in a steadily propagating tensile fracture example as well as the critical fracture pressure and the crack length evolution in toughness dominated hydraulic fracturing . The proposed model does not require any changes in existing implementation of phase-field models. The only requirement is to assign the analytically calculated effective interface fracture toughness over a diffused sub-domain.

Data 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.

The 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.

The 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.

Coupled thermo-hydro-mechanical (THM) models are used for the assessment of nuclear waste disposal, reservoir engineering, and other branches of geo-environmental engineering. Model-based decision-making and design optimization in these domains require sensitivity analyses (SA) and uncertainty quantification (UQ) methods that are suitable for coupled THM problems on an engineering scale. Due to different coupling levels, non-linearities, and large spatial and temporal extents, these analyses can often be challenging both conceptually and computationally.For an initial evaluation in a setting relevant to nuclear waste disposal we start by employing an analytical solution for thermal consolidation around a point heat source which encompasses the most relevant primary couplings and allows us to cover the entire parameter space robustly and efficiently. For uncertainty quantification, we applied an experimental design (DoE-) based history-matching approach. This approach uses DoE methods to construct a proxy model, which is used later for efficient Monte Carlo sampling and subsequent filtering of the uncertainty space of the history-match error. As a result, we obtain a family of curves that is compatible with the prior parameter set and experimental data to match, which then enables further uncertainty quantification. In our work, we demonstrate the applicability of the workflow and discuss its particular suitability to this problem class, including its (in-)sensitivity to prior parameter distribution assumptions.For SA, we contrast the conclusions drawn via two different approaches: local one variable at a time (OVAT) and global sensitivity analysis (GSA) based on Sobol indices for different spatio-temporal settings to observe near and far-field effects as well as early- and late-stage system response. The conducted studies can serve as a benchmark for UQ and SA software designed around numerical THM simulators.

In every tight formation reservoir, natural fractures play an important role for mass and energy transport and stress distribution. Enhanced Geothermal Systems (EGS) make no exception, and stimulation aims at increasing the reservoir permeability to enhance fluid circulation and heat transport. EGS development relies upon the complex task of predicting accurate hydraulic fracture propagation pathway by taking into account reservoir heterogeneities and natural or preexisting fractures. In this contribution, we employ the variational phase-field method, which handles hydraulic fracture initiation, propagation, and interaction with natural fractures and is tested under varying conditions of rock mechanical properties and natural fractures distributions. We run bidimensional finite element simulations employing the open-source software OpenGeoSys and apply the model to simulate realistic stimulation scenarios, each one built from field data and considering complex natural fracture geometries in the order of a thousand of fractures. Key mechanical properties are derived from laboratory measurements on samples obtained in the field. Simulations results confirm the fundamental role played by natural fractures in stimulation's predictions, which is essential for developing successful EGS projects.

Phase-field models for fracture have gained exceptional popularity in the last couple of decades and have been extended into areas well beyond brittle quasi-static fracture propagation to ductile, dynamic, or hydraulic fracturing. Despite the significant theoretical advancements in these more complex physical settings, little attention has been paid to the quantification of crack opening displacement to date as most applications do not explicitly require the crack opening displacement for the morphological evolution of cracks. However, one of the exemptions would be hydraulic fracturing where the crack propagation is driven by the fluid pressure which strongly depends on the crack opening displacement. In this study, we look into two known approaches, a line integral and a level-set method, for crack opening computation mainly from an implementation point of view. Firstly, we derive an approximation of a discontinuous function field in the variational phase-field setting which is then applied to obtain the crack opening (displacement jump) and verify the approximation against a closed solution. We then propose a “certain distance from the crack” required for the level-set function using a one-dimensional analysis. Finally, we compare these approaches under several different conditions such as crack alignment to the mesh or under loading (asymmetric displacement field) and investigate the convergence with respect to the mesh size.

Hydraulic fracture containment in layered reservoirs is simulated using a numerical model that couples fluid flow with a lattice representation of the solid with quasi-random distributed nodes connected by springs. We consider the influence of horizontal stress contrasts between layers, vertical stress, material fracture toughness, and the presence of horizontal weak interfaces. Observed results define distinct regions in a parametric space characterized by height growth, containment, and growth along the horizontal weak interface (T-shape growth). These numerical results match well to laboratory experimental benchmarks, and they extend the parametric study beyond what can be considered in the laboratory.

Decades of research have led to numerous insights in modeling the impact of stresses and rock properties on hydraulic fracture height growth. However, the conditions under which weak horizontal interfaces are expected to impede height growth remain for the most part unknown. We have developed an experimental study of the impact of weak horizontal discontinuities on hydraulic fracture height growth, including the influences of (1) abrupt stress contrasts between layers, (2) material fracture toughness, and (3) contrasts of stiffness between the reservoir and bounding layers. The experiments are carried out with an analog three-layered medium constructed from transparent polyurethane, considering toughnesses resisting vertical fracture growth. There are four observed geometries: containment, height growth, T-shape growth, and the combination of height growth and T-shape. Results are developed in a parametric space embodying the influence of the horizontal stress contrast, vertical stress, and horizontal barrier stress contrast, as well as the fluid pressure. The results indicate that these cases fall within distinct regions when plotted in the parametric space. The locations in the parametric space of these regions are strongly impacted by the vertical fracture toughness: Increasing the value of the vertical interface fracture toughness leads to a suppression of height growth in favor of containment and T-shaped growth. Besides providing detailed experimental data for benchmarking 3D hydraulic fracture simulators, these experiments show that the fracture height is substantially less than would be predicted in the absence of the weak horizontal discontinuities.

The tip behavior of hydraulic fractures is characterized by a rich nesting of asymptotic solutions, comprising a formidable challenge for the development of efficient and accurate numerical simulators. We present experimental validation of several theoretically-predicted asymptotic behaviors, namely for hydraulic fracture growth under conditions of negligible fracture toughness, with growth progressing from early-time radial geometry to large-time blade-like (PKN) geometry. Our experimental results demonstrate: 1) existence of a asymptotic solution of the form w ∼ s 3/2 (LEFM) in the near tip region, where w is the crack opening and s is the distance from the crack tip, 2) transition to an asymptotic solution of the form w ∼ s 2/3 away from the near-tip region, with the transition length scale also consistent with theory, 3) transition to an asymptotic solution of the form w ∼ s 1/3 after the fracture attains blade-like (PKN) geometry, and 4) existence of a region near the tip of a blade-like (PKN) hydraulic fracture in which plane strain conditions persist, with the thickness of this region of the same order as the crack height.

A variational fracture model coupled to an external reservoir simulator through variable exchange is presented. While convergence is not optimal without Jacobian matrices with which fully coupling can provide, the presented coupling scheme is versatile enough that the reservoir simulator could be easily replaced with any other simulator. A variational approach to fracture is introduced first by comparison to the classic Griffith criteria, and is then expanded to include poro-elasticity and in-situ stresses that are required in hydraulic applications. The coupled code has been tested against existing analytical solutions of fluid-driven fracture propagation. Finally, illustrative examples are shown to demonstrate that the methodology's ability to simulate multi fracture interaction with the unified approach for turning and merging fractures.

Due to a stress redistribution after the excavation of an underground tunnel for radioactive waste disposal, an Ed/DZ (excavation disturbed/damaged zone) will be generated in the near field of the opening, resulting in significant changes in the hydraulic and mechanical properties of the rock mass in the zone. Initially more or less randomly distributed hydrocarbons at grain boundaries in rock salt, which sometimes can only be observed with ultraviolet light, can then be mobilised and migrate at a potentially significant rate towards the excavation. Within the international cooperative project DECOVALEX 2019, the migration mechanism of such fluid inclusions in rock salt is being studied intensively. A multi-scale modelling strategy has been developed. A macroscale coupled hydro-mechanical modelling of an underground excavation was performed to determine hydraulic and time-dependent deviatoric stress conditions, by taking into account the rock salt creep behaviour. Under the obtained macro-scale constraints, micro-scale modelling of a pathway dilation along halite grain boundaries was performed using different model strategies: a) coupled hydromechanical modelling with a consideration of hydraulic pressure-induced dilatant deformation, b) nonlinear dynamic model taking account of fluid migration, stress-dependent grain boundary wetting and shear-induced dilatancy of salt, and c) phase-field modelling of flow pathway propagation. The permeability increase resulting from the pathway dilation is estimated to be as high as two orders of magnitude. Based on the permeability determined, a series of pressure build-ups measured from a borehole with a high hydrocarbon release rate, a total of 430 build-ups within a monitoring time of 938 days, can be simulated with a macro-scale compressible flow model accounting for different zones around the opening.

In the context of geotechnical and geological barriers, a thorough analysis of uncertainty and sensitivity is a crucial aspect of any physics-based performance assessment. While experimental data are scarce in actual waste repositories, large-scale experiments in underground research laboratories (URLs) provide such data that can be used to not only qualify THMC process models but also uncertainty assessment methodologies. In this paper, we adopt a Design of Experiments (DoE)-based history matching workflow – an approach popular in the oil and gas industry – and scrutinize its applicability for multiphysical analyses of nuclear waste disposal-related processes using synthetic experimental data. Based on an analytical solution of a coupled thermo-hydro-mechanical (THM) problem of a heat source embedded in a fluid-saturated porous medium mimicking a disposal cell in an argillaceous host formation, we discuss the adaptability of the workflow as a way to address parameter and model uncertainties for barrier integrity assessment. We thereby put particular focus on the relative importance of providing defined input parameter distributions for quantities generally afflicted with epistemic uncertainty and the constraints imposed by experimental (URL) or monitoring (repository) data. We found that once constraining data is available, the particular a priori distribution plays only a minor role for the outcome, such that we can conclude that the often unknown distributions can be substituted by uniform priors under such conditions. However, detailed knowledge of parameter distributions can increase the efficiency of the workflow significantly. We conclude that the presented workflow is particularly suitable for performing uncertainty quantification and sensitivity analysis for geotechnical applications where monitoring or other experimental data are available, as it allows us to deal with models of great complexity, epistemic uncertainty and it incorporates canonically to use of measured data in order to reduce uncertainty.

Summary The increasing deployment of distributed temperature- and pressure-measuring devices in intelligent-well completions is providing the means to monitor the inflow profiles of wells without any well intervention. If the profiles of pressure and/or temperature are affected by the inflow profiles of the various phases being produced, it is possible to estimate these flow profiles by inverting the measured temperature and pressure profiles. This inversion process is particularly challenging for horizontal wells because the pressure drop along the well is usually small, and temperature changes, caused primarily by Joule-Thomson effects, are also small. This paper presents an inversion method that interprets distributed temperature and pressure data to obtain flow-rate profiles along horizontal wells. The inversion method, which is based on the Levenberg-Marquardt algorithm (Marquardt 1963), is applied to minimize the differences between the measured profiles and the profiles calculated from a forward model of the well and reservoir-flow system. We present synthetic and field examples in this paper to illustrate how to use the inversion model to interpret the flow profile of a horizontal well. The synthetic examples show that even with single-phase oil production, the inflow profile can be estimated in many cases with the inversion method developed. The method is even more robust when water or gas is produced along discrete intervals in an oil production well because of the unique temperature signature of water or gas production. We applied the inversion method to temperature and pressure profiles measured with production logs in a North Sea horizontal oil-producing well. The method successfully inverted pressure and temperature profiles, and the profiles of oil- and water-flow rates determined compared well with the flowmeter-derived profiles.

Summary With the recent development of temperature measurement systems such as fiber-optic distributed temperature sensors, continuous temperature profiles in a horizontal well can be obtained with high precision. Small temperature changes with a resolution on the order of 0.1°F can be detected by modern temperature-measuring instruments in intelligent completions, which may aid the diagnosis of downhole flow conditions. Since in a producing horizontal well fluid inflowing temperature is not affected by elevational geothermal temperature changes, the primary temperature differences for each phase (oil, water, and gas) are caused by frictional effects. While gas production usually causes a temperature decrease, water entry results in either warming or cooling of the wellbore. Warmer water entry is a result of water flow from a warmer aquifer below the producing zone (water coning). In contrast, produced water can be cooler than produced oil because of differences in the thermal properties of these fluids. If both oil and water are produced from the same elevation, oil is heated more by friction while flowing in a porous medium than water is resulting in the produced water having a lower inflow temperature than the oil. Water entry by coning is relatively easy to detect from the temperature profile because of its warmer inflow temperature, but water breakthrough from the same elevation as the oil may not be obvious. In this paper, we illustrate the range of inflow conditions for which water-or-gas entry locations can be identified from the temperature profile of a well from measurable temperature changes. Using a numerical wellbore-temperature-prediction model (Yoshioka et al. 2005a), we calculated temperature profiles for a wide range of water-inflow conditions. In these calculations, we assumed that one section of the well produced water or gas, while the rest of the open section of the well produced oil. From sensitivity studies, we showed the predictions of the relative water-andgas production rates that create detectable temperature anomalies in the temperature profile along the well. By using the model to match an actual temperature log from a horizontal well, we demonstrate how this model can be used to identify water-inflow locations.

One of the most critical capabilities of realistic hydraulic fracture simulation is the prediction of complex (turning, bifurcating, or merging) fracture paths. In most classical models, complex fracture simulation is difficult due to the need for a priori knowledge of propagation path and initiation points and the complexity associated with stress singularities at fracture tips. In this study, we follow Francfort and Marigo's variational approach to fracture, which we extend to account for hydraulic stimulation. We recast Griffith's criteria into a global minimization principle, while preserving its essence, the concept of energy restitution between surface and bulk terms. More precisely, to any admissible crack geometry and kinematically admissible displacement field, we associate a total energy given as the sum of the elastic and surface energies. In a quasistatic setting, the reservoir state is then given as the solution of a sequence of unilateral minimizations of this total energy with respect to any admissible crack path and displacement field. The strength of this approach is to provide a rigorous and unified framework accounting for new cracks nucleation, existing cracks activation, and full crack path determination (including complex behavior such as crack branching, kinking, and interaction between multiple cracks) without any a priori knowledge or hypothesis. Of course, the lack of a priori hypothesis on cracks geometry is at the cost of numerical complexity. We present a regularized phase field approach where fractures are represented by a smooth function. This approach makes handling large and complex fracture networks very simple yet discrete fracture properties such as crack aperture can be recovered from the phase field. We compare variational fracture simulation results against several analytical solutions and also demonstrate the approach's ability to predict complex fracture systems with example of multiple interacting fractures.

Summary Layer flow contributions are increasingly being quantified through the analysis of measured sandface flowing temperatures. It is commonly known that the maximum temperature change is affected by the magnitude of the drawdown and the Joule-Thomson expansion coefficient of the fluid. Another parameter that strongly impacts layer sandface flowing temperatures is the layer permeability. Aside from determining the drawdown, the layer permeability also affects the ratio of heat transfer by convection to conduction within a reservoir. The impact of permeability can be represented by the Péclet number, which is a dimensionless quantity representing the ratio of heat transfer by convection to conduction. The Péclet number is directly proportional to reservoir permeability. Through dimensionless analysis, it will be shown that for a given drawdown (based on a dimensionless Joule-Thomson expansion coefficient JTD) the temperature change diminishes at low Péclet numbers and increases at high Péclet numbers. This implies that for low-permeability reservoirs such as shale gas or tight oil, the temperature changes will be minimal (less than 0.1ºF) despite the large drawdowns in many instances. Dimensionless analysis is performed for both steady-state and transient thermal models. Results from multilayer transient simulations illustrate the ability to identify contrasting permeability layers on the basis of the Péclet number effect.

The Salak field is the largest developed geothermal resource in Indonesia. Steam production levels have been maintained at or above the rated power plant capacity for 15 years through periodic infill drilling and injection realignment. The reservoir management strategy for Salak involves injecting separated brine into deep wells on the margins of the reservoir where permeability is known to be low. A technique that has been used to enhance permeability in new injection wells combines hydraulic and thermal fracturing. This involves complex rock/fluid interactions and heat transfer relationships that must be considered in order to design appropriate injection rates, pumping times, and injection temperatures. This paper describes the techniques used to characterize candidate wells and interpret surveillance data collected during long-term cold water injection experiments. Analyzing continuous measurements of well injectivity along with pressure transient data taken periodically shows the evolution of enhanced permeability during stimulation. A high degree of success has been achieved using these techniques at Salak, with significant improvements in well injection capacity. These results provide additional alternatives for managing injection to increase the ultimate heat recovery from the reservoir.

The increasing deployment of distributed temperature and pressure measuring devices in intelligent well completions is providing the means to monitor the inflow profiles of wells without any well intervention. If the profiles of pressure and/or temperature are affected by the inflow profiles of the various phases being produced, it is possible to estimate these flow profiles by inverting the measured temperature and pressure profiles. This inversion process is particularly challenging for horizontal wells because the pressure drop along the well is usually small, and temperature changes, caused primarily by Joule-Thomson effects, are also small. This paper presents an inversion method that interprets distributed temperature and pressure data to obtain flow rate profiles along horizontal wells. The inversion method, which is based on the Levenberg-Marquardt algorithm, is applied to minimize the differences between the measured profiles and the profiles calculated from a forward model of the well and reservoir flow system. We present synthetic and field examples in this paper to illustrate how to use the inversion model to interpret the flow profile of a horizontal well. The synthetic examples show that even with single-phase oil production, the inflow profile can be estimated in many cases with the inversion method developed. The method is even more robust when water or gas is produced along discrete intervals in an oil production well because of the unique temperature signature of water or gas production. We applied the inversion method to temperature and pressure profiles measured with production logs in a North Sea horizontal oil producing well. The method successfully inverted pressure and temperature profiles and the profiles of oil and water flow rates determined compared well with the flowmeter derived profiles.

With the recent development of temperature measurement systems such as fiber optic distributed temperature sensors (DTS), continuous temperature profiles in a horizontal well can be obtained with high precision. Small temperature changes with a resolution on the order of 0.1 °F can be detected by modern temperature-measuring instruments in intelligent completions and may aid the diagnosis of downhole flow conditions. Since in a producing horizontal well, fluid inflowing temperature is not affected by elevational geothermal temperature changes, the primary temperature differences for each phase (oil, water, and gas) are caused by frictional effects. While gas production usually causes a temperature decrease, water entry results in either warming or cooling of the wellbore. Warmer water entry is a result of water flow from a warmer aquifer below the producing zone (water coning). In contrast, produced water can be cooler than produced oil because of differences in the thermal properties of these fluids. If both oil and water are produced from the same elevation, oil is heated more by friction while flowing in a porous medium than water, resulting in the produced water having a lower inflow temperature than the oil. Water entry by coning is relatively easy to detect from the temperature profile because of its warmer inflow temperature, but water breakthrough from the same elevation as the oil may not be obvious. In this paper, we illustrate the range of inflow conditions for which water or gas entry locations can be identified from the temperature profile of a well from measurable temperature changes. Using a temperature prediction model1, we calculated temperature profiles for a wide range of water inflow conditions. In these calculations we assumed that one section of the well was producing water or gas, while the rest of the open section of the well produced oil. From sensitivity studies, we identified the relative water and gas production rates that create detectable temperature anomalies in the temperature profile along the well.

Use of distributed temperature sensors is becoming increasingly common for monitoring producing sections of horizontal wells through a real-time measurement of a temperature profile. This information can potentially be inverted to infer the types and amounts of fluid entering along the wellbore. This information is essential for reservoir management to identify excessive water or gas influx, to guide the action of sliding sleeves or other downhole flow control devices, and to decide if reservoir stimulation is needed in a particular horizontal section. The inferences described above require a model to translate temperature information into flow information. This paper presents a model for predicting the temperature profile in a nominally horizontal well during normal production (steady-state flow). A forward model of the temperature profile caused by given flow conditions can be the basis of the inverse model needed to determine flow profiles Prediction of the wellbore temperature profile requires models of all of the often-subtle thermal effects occurring in the reservoir and in the wellbore itself. For the reservoir temperature model, we couple mass and energy balances of fluid flow in a permeable media in a box-shaped homogeneous reservoir with a wellbore temperature model using a multisegment technique. Similarly for the wellbore, we couple mass, momentum, and energy balances to model pressure and temperature behavior. The models presented in this paper account for Joule-Thomson effects, and convective and conductive heat transfer. The primary results of the model are estimates of the extent of temperature change from geothermal temperature during flow. Results show that temperature changes of a few degrees are possible; temperature changes of this magnitude are certainly detectable with current technology. A second result is a demonstration of the inference of single phase and multiphase flow profiles from a synthetic case. Sensitivity studies with the model illustrate the flow conditions that cause measurable temperature changes or anomalies that could be recognized in an analysis of distributed temperature measurements.

This project is motivated by the increasing use of distributed temperature sensors for real-time monitoring of complex wells (horizontal, multilateral and multi-branching wells) to infer the profiles of oil, gas, and water entry. Measured information can be used to interpret flow profiles along the wellbore including junction and build section. In this second project year, we have completed a forward model to predict temperature and pressure profiles in complex wells. As a comprehensive temperature model, we have developed an analytical reservoir flow model which takes into account Joule-Thomson effects in the near well vicinity and multiphase non-isothermal producing wellbore model, and couples those models accounting mass and heat transfer between them. For further inferences such as water coning or gas evaporation, we will need a numerical non-isothermal reservoir simulator, and unlike existing (thermal recovery, geothermal) simulators, it should capture subtle temperature change occurring in a normal production. We will show the results from the analytical coupled model (analytical reservoir solution coupled with numerical multi-segment well model) to infer the anomalous temperature or pressure profiles under various conditions, and the preliminary results from the numerical coupled reservoir model which solves full matrix including wellbore grids. We applied Ramey's model to themore » build section and used an enthalpy balance to infer the temperature profile at the junction. The multilateral wellbore temperature model was applied to a wide range of cases varying fluid thermal properties, absolute values of temperature and pressure, geothermal gradients, flow rates from each lateral, and the trajectories of each build section.« less

This paper presents methods to interpret measurements in complex wells (horizontal, multilateral and multi-branching wells) to determine the inflow profiles of oil, gas and water. These methods are needed to take full advantage of intelligent well, a technology that is rapidly evolving to continuously and permanently monitor downhole temperature, pressure, and perhaps volumetric flow. To realize the value of intelligent wells, the efficient and accurate interpretation of the raw data being acquired is needed. The interpretation of flow profiles of horizontal or multilateral wells from temperature and pressure profiles requires consideration of subtle effects that are often neglected. In this paper, we illustrate how some of these effects can be predicted, and how they can be used to evaluate complex well performance. In particular, we will highlight the following characteristics of flow in horizontal wells, each of which can provide information about the inflow profile of the well. Firstly we discuss about Joule-Thomson effects (the heating of oil and the cooling of gas) on the temperature profiles, seeing if they are noticeable changes or not. The discrete production cases are then considered to infer how the pressure or temperature profiles retain marks where the production starts and ends. Also, we examine well trajectories effects. Small inclinations (+2° and -2°) in nominally horizontal laterals affect both pressure and temperature profiles. The differences in potential energy in up-inclined and down-inclined segments may prove to be diagnostic of relative flow rates of the phases. As a last example, water entry effects on the each profiles are shown. When the production becomes oil and water two-phase flow, the fluid properties change and affect the both profiles. In certain cases, the location of the water entry may be noticeable.