A Review of Hydraulic Fracturing Simulation

Along with horizontal drilling techniques, multi-stage hydraulic fracturing has improved shale gas production significantly in past decades. In order to understand the mechanism of hydraulic fracturing and improve treatment designs, it is critical to conduct modelling to predict stimulated fractures. In this paper, related physical processes in hydraulic fracturing are firstly discussed and their effects on hydraulic fracturing processes are analysed. Then historical and state of the art numerical models for hydraulic fracturing are reviewed, to highlight the pros and cons of different numerical methods. Next, commercially available software for hydraulic fracturing design are discussed and key features are summarised. Finally, we draw conclusions from the previous discussions in relation to physics, method and applications and provide recommendations for further research

Flow and transport in fractured geothermal reservoirs on different scales: Linking experiments and numerical models

Die Erdwärme stellt eine wichtige erneuerbare Energiequelle der Zukunft dar, um den Grundbedarf der Menschen an Wärme und Strom zu decken und die Abhängigkeit von fossilen Brennstoffen wie Erdöl und Kohle zu verringern. Die Internationale Energiebehörde schätzt, dass bis zum Jahr 2050 3,5% der weltweiten Energieversorgung durch Geothermie erfolgen können. Die Vorteile der Geothermie liegen dabei in der guten bedarfsabhängigen Regulierbarkeit sowie der uneingeschränkten weltweiten Verfügbarkeit bei gleichzeitig geringem Flächenbedarf. Darüber hinaus ist die Geothermie als eine der wenigen erneuerbaren Energien vollständig grundlastfähig und damit unabhängig von stark wechselnden Umwelteinflüssen, wie Windstärke oder Sonneneinstrahlung. Die größte Herausforderung bei der Geothermie liegt in der Erschließung von Niederenthalpie-Lagerstätten, die in Tiefen von einigen Kilometern liegen. Eine Möglichkeit hierzu stellt die Technologie des Enhanced Geothermal Systems (EGS) dar, die geringdurchlässige Gesteinsschichten eines Reservoirs wirtschaftlich nutzbar macht. Bei EGS werden durch hydraulische Stimulation bestehende natürliche Kluftsysteme erweitert und neue Klüfte geschaffen und so ein effektiver Wärmeaustausch zwischen dem geklüfteten Reservoirgestein und zirkulierenden Fluiden ermöglicht. Bisher gibt es allerdings nur wenige Pilotanlagen, wie z.B. in Soultz-sous-Forêts, Frankreich. Der Nachteil dieser Technologie ist, dass die so entstandenen Klüfte nur einen sehr kleinen Teil des Reservoirvolumens darstellen und sich alle an der Fluidzirkulation beteiligten natürlichen und induzierten Prozesse auf engstem Raum abspielen. Das grundlegende Verständnis der hochlokalisierten physikalischen Prozesse und Wechselwirkungen stellt somit den Schlüsselfaktor für einen erfolgreichen, umweltverträglichen und sicheren Betrieb von EGS dar. Ein besonderes Augenmerk muss auf die gegenseitigen Wechselwirkungen zwischen der Kluft und dem zirkulierenden Fluid sowie dem damit verbundenen Transport von Wärme und gelösten Stoffen gelegt werden. Die Kluftöffnung wird oft vereinfacht als der Abstand zwischen zwei parallelen Platten dargestellt. In Wirklichkeit bestehen die Verbindungen zwischen zwei Bohrungen jedoch aus einem kleinräumigen Netzwerk einzelner Klüfte, die wiederum ein stark veränderliches inneres Porenvolumen aufweisen. Die vorliegende Arbeit trägt zu einem besseren Verständnis der Entstehung und geometrischen Beschaffenheit von bevorzugten Fluidwegsamkeiten in geklüfteten Reservoiren sowie der damit verbundenen Transportprozesse bei. Das übergeordnete Ziel der einzelnen Studien ist eine Verknüpfung experimenteller Untersuchungen mit numerischen Modellen, um die relevanten, teilweise skalenabhängigen physikalischen Prozesse in Klüften zu identifizieren und quantifizieren. In den ersten beiden Studien (Kapitel 4 und 5) werden eine Vielzahl von stochastisch einzigartigen granitähnlichen Kluftgeometrien erstellt. Anschließend werden numerische Modelle entwickelt, um die präferentiellen Fluidpfade und deren Eigenschaften im Klufhohlraum unter geothermie-typischen Strömungsbedingungen und unter Verwendung der komplexen Navier-Stokes-Gleichungen zu quantifizieren. Das Ziel der ersten Studie ist die Quantifizierung von räumlichen Unterschieden zwischen den dreidimensionalen und den vereinfachten zweidimensionalen Kluftmodellen. Ein Vergleich zwischen äquivalenten Modellierungen mittels der Navier-Stokes-Gleichungen und dem lokalen kubischen Gesetz erlaubt eine Vorhersage über die Gültigkeit dieser Vereinfachungen. In Abhängigkeit von Fließund Scherrichtung sowie dem angelegten Druckgradienten bilden sich in allen Klüften Kanäle aus, die einen großen Teil des Volumenstroms umfassen, während im Rest der Kluft nur geringe Anteile an Fluidbewegung zu beobachten sind. Innerhalb dieser Kanäle zeigen beide Fließgesetze eine gute Übereinstimmung sowohl für rein laminare als auch turbulente Strömungen (mit Reynolds-Zahlen deutlich über 1). Außerhalb von Kanälen ergibt sich unabhängig vom Fließregime für die zweidimensionale Vereinfachung eine deutliche Überschätzung des zu erwartenden Volumenstroms. In der zweiten Studie werden die einzelnen Kanäle innerhalb der dreidimensionalen Kluft hinsichtlich ihrer Geometrie sowie Transporteigenschaften quantifiziert. Die Ergebnisse zeigen eine starke Anisotropie hinsichtlich der Fließ- und Scherrichtung. Obwohl eine senkrechte Ausrichtung von Strömung und Scherung zu einem deutlich verbesserten Durchfluss führt, haben die gut ausgebildeten und geraden Kanäle nur eine begrenzte Kontaktfläche mit dem umgebenden Gestein und behindern somit einen effizienten Wärmeaustausch. Anders ist dies bei einer parallelen Ausrichtung von Scherung und Strömung. In diesem Fall sind die Kanäle deutlich weniger ausgeprägt und haben zudem einen stark verlängerten absoluten Fließweg und damit verbundene höhere Kontaktfläche. Die dritte Studie (Kapitel 6) umfasst die Verknüpfung von Triaxialexperimenten, durchgeführt an zwei Sandsteinenderivaten mit steigenden Temperaturund Druckbedingungen, mit numerischen Modellen. Ziel ist eine Vorhersage der hydraulischen und mechanischen Gesteinseigenschaften eines potentiellen Reservoirgesteins. Die Ergebnisse zeigen eine poroelastische Kompaktion des Gesteins sowie anschließende nichtlineare Deformation, welche beide mit numerischen Modellen vorhergesagt werden können. Das Drucker-Prager-Kriterium ermöglicht die Bewertung der kritischen Scherspannung unter Berücksichtigung der drei Hauptspannungen. Die Studie zeigt, dass kleinstskalige Veränderungen, wie die mineralogische Zusammensetzung, zwar die Materialeigenschaften des Gesteins beeinflussen, numerische und analytische Modelle dessen Verhalten dennoch beschreiben können. In der vierten und fünften Studie (Kapitel 7 und 8) werden die kleinskalig gewonnen Erkenntnisse sowie weiterführende Felduntersuchungen dazu genutzt, um ein Modell des großräumigen Strömungsregimes im geklüfteten Reservoir von Soultz-sous-Forêts zu entwickeln. In der vierten Studie wird ein Strukturmodell des Soultz-Reservoirs entwickelt und das Strömungsregime entlang von Klüften zwischen den einzelnen Bohrungen mittels numerischer Modelle bestimmt. Durch die Verknüpfung mit den experimentellen Daten mehrerer Zirkulations- sowie Tracerversuche kann das Strömungsregime in bohrlochfernen Bereichen des Reservoirs quantifiziert werden. Darüber hinaus kann eine geologische Struktur identifiziert werden, die die Bohrungen GPK3 und GPK4 zwar hydraulisch separiert, allerdings störungsparallel eine Anbindung an das Fließregime des Oberrheingrabens herstellt. In der fünften Studie wird auf Grundlage des zuvor entwickelten hydraulischen Modells die Sensitivität der Produktionstemperatur hinsichtlich verschiedener operativer Rahmenbedingungen (Injektionstemperatur und Fließraten) untersucht

Experiment-Based Validation and Uncertainty Quantification of Partitioned Models: Improving Predictive Capability of Multi-Scale Plasticity Models

Partitioned analysis involves coupling of constituent models that resolve their own scales or physics by exchanging inputs and outputs in an iterative manner. Through partitioning, simulations of complex physical systems are becoming evermore present in scientific modeling, making Verification and Validation of partitioned models for the purpose of quantifying the predictive capability of their simulations increasingly important. Parameterization of the constituent models as well as the coupling interface requires a significant amount of information about the system, which is often imprecisely known. Consequently, uncertainties as well as biases in constituent models and their interface lead to concerns about the accumulation and compensation of these uncertainties and errors during the iterative procedures of partitioned analysis. Furthermore, partitioned analysis relies on the availability of reliable constituent models for each component of a system. When a constituent is unavailable, assumptions must be made to represent the coupling relationship, often through uncertain parameters that are then calibrated. This dissertation contributes to the field of computational modeling by presenting novel methods that take advantage of the transparency of partitioned analysis to compare constituent models with separate-effect experiments (measurements contained to the constituent domain) and coupled models with integral-effect experiments (measurements capturing behavior of the full system). The methods developed herein focus on these two types of experiments seeking to maximize the information that can be gained from each, thus progressing our capability to assess and improve the predictive capability of partitioned models through inverse analysis. The importance of this study stems from the need to make coupled models available for widespread use for predicting the behavior of complex systems with confidence to support decision-making in high-risk scenarios. Methods proposed herein address the challenges currently limiting the predictive capability of coupled models through a focused analysis with available experiments. Bias-corrected partitioned analysis takes advantage of separate-effect experiments to reduce parametric uncertainty and quantify systematic bias at the constituent level followed by an integration of bias-correction to the coupling framework, thus ‘correcting’ the constituent model during coupling iterations and preventing the accumulation of errors due to the final predictions. Model bias is the result of assumptions made in the modeling process, often due to lack of understanding of the underlying physics. Such is the case when a constituent model of a system component is entirely unavailable and cannot be developed due to lack of knowledge. However, if this constituent model were to be available and coupled to existing models of the other system components, bias in the coupled system would be reduced. This dissertation proposes a novel statistical inference method for developing empirical constituent models where integral-effect experiments are used to infer relationships missing from system models. Thus, the proposed inverse analysis may be implemented to infer underlying coupled relationships, not only improving the predictive capability of models by producing empirical constituents to allow for coupling, but also advancing our fundamental understanding of dependencies in the coupled system. Throughout this dissertation, the applicability and feasibility of the proposed methods are demonstrated with advanced multi-scale and multi-physics material models simulating complex material behaviors under extreme loading conditions, thus specifically contributing advancements to the material modeling community

Fluid driven transition from damage to fracture in anisotropic porous media - a multiscale XFEM approach

Copyright © 2019 SpringerIn this paper, a numerical method is proposed to simulate multiscale fracture propagation driven by fluid injection in transversely isotropic porous media. Intrinsic anisotropy is accounted for at the continuum scale, by using a damage model in which two equivalent strains are defined to distinguish mechanical behavior in the direction parallel and perpendicular to the layer. Nonlocal equivalent strains are calculated by integration, and are directly introduced in the damage evolution law. When the weighted damage exceeds a certain threshold, the transition from continuum damage to cohesive fracture is performed by dynamically inserting cohesive segments. Diffusion equations are used to model fluid flow inside the porous matrix and within the macro fracture, in which conductivity is obtained by Darcy's law and the cubic law, respectively. In the fractured elements, the displacement and pore pressure fields are discretized by using the XFEM technique. Interpolation on fracture elements is enriched with jump functions for displacements, and with level-set-based distance functions for fluid pressure, which ensures that displacements are discontinuous across the fracture, but that the pressure field remains continuous. After spatial and temporal discretization, the model is implemented in a Matlab code. Simulations are carried out in plane strain. The results validate the formulation and implementation of the proposed model, and further demonstrate that it can account for material and stress anisotropy

Computational Modelling of Concrete and Concrete Structures

Computational Modelling of Concrete and Concrete Structures contains the contributions to the EURO-C 2022 conference (Vienna, Austria, 23-26 May 2022). The papers review and discuss research advancements and assess the applicability and robustness of methods and models for the analysis and design of concrete, fibre-reinforced and prestressed concrete structures, as well as masonry structures. Recent developments include methods of machine learning, novel discretisation methods, probabilistic models, and consideration of a growing number of micro-structural aspects in multi-scale and multi-physics settings. In addition, trends towards the material scale with new fibres and 3D printable concretes, and life-cycle oriented models for ageing and durability of existing and new concrete infrastructure are clearly visible. Overall computational robustness of numerical predictions and mathematical rigour have further increased, accompanied by careful model validation based on respective experimental programmes. The book will serve as an important reference for both academics and professionals, stimulating new research directions in the field of computational modelling of concrete and its application to the analysis of concrete structures. EURO-C 2022 is the eighth edition of the EURO-C conference series after Innsbruck 1994, Bad Gastein 1998, St. Johann im Pongau 2003, Mayrhofen 2006, Schladming 2010, St. Anton am Arlberg 2014, and Bad Hofgastein 2018. The overarching focus of the conferences is on computational methods and numerical models for the analysis of concrete and concrete structures

New innovations in pavement materials and engineering: A review on pavement engineering research 2021

Sustainable and resilient pavement infrastructure is critical for current economic and environmental challenges. In the past 10 years, the pavement infrastructure strongly supports the rapid development of the global social economy. New theories, new methods, new technologies and new materials related to pavement engineering are emerging. Deterioration of pavement infrastructure is a typical multi-physics problem. Because of actual coupled behaviors of traffic and environmental conditions, predictions of pavement service life become more and more complicated and require a deep knowledge of pavement material analysis. In order to summarize the current and determine the future research of pavement engineering, Journal of Traffic and Transportation Engineering (English Edition) has launched a review paper on the topic of “New innovations in pavement materials and engineering: A review on pavement engineering research 2021”. Based on the joint-effort of 43 scholars from 24 well-known universities in highway engineering, this review paper systematically analyzes the research status and future development direction of 5 major fields of pavement engineering in the world. The content includes asphalt binder performance and modeling, mixture performance and modeling of pavement materials, multi-scale mechanics, green and sustainable pavement, and intelligent pavement. Overall, this review paper is able to provide references and insights for researchers and engineers in the field of pavement engineering

Numerical Study of Concrete

Concrete is one of the most widely used construction material in the word today. The research in concrete follows the environment impact, economy, population and advanced technology. This special issue presents the recent numerical study for research in concrete. The research topic includes the finite element analysis, digital concrete, reinforcement technique without rebars and 3D printing

Computational Modelling of Concrete and Concrete Structures

Computational Modelling of Concrete and Concrete Structures contains the contributions to the EURO-C 2022 conference (Vienna, Austria, 23-26 May 2022). The papers review and discuss research advancements and assess the applicability and robustness of methods and models for the analysis and design of concrete, fibre-reinforced and prestressed concrete structures, as well as masonry structures. Recent developments include methods of machine learning, novel discretisation methods, probabilistic models, and consideration of a growing number of micro-structural aspects in multi-scale and multi-physics settings. In addition, trends towards the material scale with new fibres and 3D printable concretes, and life-cycle oriented models for ageing and durability of existing and new concrete infrastructure are clearly visible. Overall computational robustness of numerical predictions and mathematical rigour have further increased, accompanied by careful model validation based on respective experimental programmes. The book will serve as an important reference for both academics and professionals, stimulating new research directions in the field of computational modelling of concrete and its application to the analysis of concrete structures. EURO-C 2022 is the eighth edition of the EURO-C conference series after Innsbruck 1994, Bad Gastein 1998, St. Johann im Pongau 2003, Mayrhofen 2006, Schladming 2010, St. Anton am Arlberg 2014, and Bad Hofgastein 2018. The overarching focus of the conferences is on computational methods and numerical models for the analysis of concrete and concrete structures

Predictive Modelling of Tribological Systems using Movable Cellular Automata

In the science of tribology, where there is an enormous degree of uncertainty, mathematical models that convey state-of-the-art scientific knowledge are invaluable tools for unveiling the underlying phenomena. A well-structured modelling framework that guarantees a connection between mathematical representations and experimental observations, can help in the systematic identification of the most realistic hypotheses among a pool of possibilities. This thesis is concerned with identifying the most appropriate computational model for the prediction of friction and wear in tribological applications, and the development of a predictive model and simulation tool based on the identified method. Accordingly, a thorough review of the literature has been conducted to find the most appropriate approach for predicting friction and wear using computer simulations, with the multi-scale approach in mind. It was concluded that the Movable Cellular Automata (MCA) method is the most suitable method for multi-scale modelling of tribological systems. It has been established from the state-of-the-art review in Chapter 2 of this thesis, that it is essential to be able to model continuous as well as discontinuous behaviour of materials on a range of scales from atomistic to micro scales to be able to simulate the first-bodies and third body simultaneously (also known as a multi-body) in a tribological system. This can only be done using a multi-scale particle-based method because continuum methods such as FEM are none-predictive and are not capable of describing the discontinuous nature of materials on the micro scale. The most important and well-known particle-based methods are molecular dynamics (MD) and the discrete element methods (DEM). Although MD has been widely used to simulate elastic and plastic deformation of materials, it is limited to the atomistic and nanoscales and cannot be used to simulate materials on the macro-scale. On the other hand, DEM is capable of simulating materials on the meso/micro scales and has been expanded since the algorithm was first proposed by Cundall and Strack, in 1979 and adopted by a number of scientific and engineering disciplines. However, it is limited to the simulation of granular materials and elastic brittle solid materials due to its contact configurations and laws. Even with the use of bond models to simulate cohesive and plastic materials, it shows major limitations with parametric estimations and validation against experimental results because its contact laws use parameters that cannot be directly obtained from the material properties or from experiments. The MCA method solves these problems using a hybrid technique, combining advantages of the classical cellular automata method and molecular dynamics and forming a model for simulating elasticity, plasticity and fracture in ductile consolidated materials. It covers both the meso and micro scales, and can even “theoretically” be used on the nano scale if the simulation tool is computationally powerful enough. A distinguishing feature of the MCA method is the description of interaction of forces between automata in terms of stress tensor components. This way a direct relationship between the MCA model parameters of particle interactions and tensor parameters of material constitutive law is established. This makes it possible to directly simulate materials and to implement different models and criteria of elasticity, plasticity and fracture, and describe elastic-plastic deformation using the theory of plastic flow. Hence, in MCA there is no need for parametric fitting because all model parameters can be directly obtained from the material mechanical properties. To model surfaces in contact and friction behaviour using MCA, the particle size can be chosen large enough to consider the contacting surface as a rough plane, which is the approach used in all MCA studies of contacting surfaces so far. The other approach is to specify a very small particle size so that it can directly simulate a real surface, which allows for the direct investigation of material behaviour and processes on all three scale levels (atomic, meso and macro) in an explicit form. This has still been proven difficult to do because it is too computationally extensive and only a small area of the contact can be simulated due to the high numbers of particles required to simulate a real solid. Furthermore, until now, no commercial software is available for MCA simulations, only a 2D MCA demo-version which was developed by the Laboratory of CAD of Materials at the Institute of Strength Physics and Materials Science in Tomsk, Russia, in 2005. The developers of the MCA method use their own in-house codes. This thesis presents the successful development of a 3D MCA open-source software for the scientific and tribology communities to use. This was done by implementing the MCA method within the framework of the open-source code LIGGGHTS. It follows the formulations of the 3D elastic-plastic model developed by the authors including Sergey G. Psakhie, Valentin L. Popov, Evgeny V. Shilko, and the external supervisor on this thesis Alexey Yu. Smolin, which has been successfully implemented in the open-source code LIGGGHTS. Details of the mathematical formulations can be found in [1]–[3], and section 3.5 of this thesis. The MCA model has been successfully implemented to simulate ductile consolidated materials. Specifically, new interaction laws were implemented, as well as features related to particle packing, particle interaction forces, bonding of particles, and others. The model has also been successfully verified, validated, and used in simulating indentation. The validation against experimental results showed that using the developed model, correct material mechanical response can be simulated using direct macroscopic mechanical material properties. The implemented code still shows limitations in terms of computational capacity because the parallelization of the code has not been completely implemented yet. Nevertheless, this thesis extends the capabilities of LIGGGHTS software to provide an open-source tool for using the MCA method to simulate solid material deformation behaviour. It also significantly increases the potential of using MCA in an HPC environment, producing results otherwise difficult to obtain