Literatura académica sobre el tema "Compositional hydraulic fracturing model"

La fracturation hydraulique est au cœur d'un certain nombre de phénomènes naturels et induits et est cruciale pour un développement durable de la production de ressources énergétiques. Compte tenu de son rôle crucial, ce phénomène a été pris en compte au cours des trois dernières décennies par le monde académique. Néanmoins, un certain nombre d'aspects très importants de ce processus ont été systématiquement négligés par la communauté. Deux des plus remarquables sont l'incapacité de la grande majorité des modèles existants à aborder la propagation des fractures hydrauliques dans les massifs rocheux fracturés où l'injection de fluide peut à la fois conduire à la fracturation de la roche intacte et à la réactivation de fractures préexistantes. Un autre aspect essentiel de ce processus est qu'il est intrinsèquement tridimensionnel, ce qui est souvent négligé par les modèles actuellement disponibles. Pour aborder ce problème essentiel, un modèle hydro-mécanique couplé basé sur la méthode des éléments discrets a été développé. La masse rocheuse est ici représentée par un ensemble d'éléments discrets interagissant à travers des lois de contact cohésifs qui peuvent se casser pour former des fissures à l'intérieur du milieu simulé. Ces fissures peuvent se coalescer pour former des fractures. Une méthode de volume fini est utilisée pour simuler l'écoulement de fluide entre les éléments discrets. L'écoulement est calculé en fonction de la déformation de l'espace poreux dans le milieu intact et de l'ouverture des fissures dans les fractures. De plus, les fractures naturelles sont modélisées explicitement de sorte qu'elles peuvent présentées des comportements mécanique et hydraulique différents de ceux de la matrice rocheuse intacte. La simulation des processus de fracturation hydraulique dans un milieu initialement intact en considérant plusieurs points d'injection plus ou moins espacés a permis de mettre en évidence l'évolution spatio-temporelle des fractures hydrauliques et de quantifier l'impact des différentes stratégies d'injection sur des indices représentatifs du volume fracturé, de l'intensité et de la densité des fractures ou encore sur la pression de fluide au niveau du puits. De plus, l'injection dans une fente de perforation non alignée sur le plan de contrainte minimum a génère des fractures hydrauliques non planaires percolantes si la connectivité est faible, ce qui peut être gênant pour la mise en place du proppant. En outre, des interactions fortes prennent place entre des fractures hydrauliques étroitement espacées ont été mises en évidence grâce au le suivi de la orientation de contrainte principale locale et ont révélé l'importance des effets d'ombre de contrainte. Des solutions sont proposées pour optimiser les traitements multiples à partir d'un puits de forage non parfaitement aligné. Enfin, l'interaction entre une seule fracture hydraulique et une seule fracture naturelle de propriétés et d'orientations variables a été étudiée à l'aide du modèle proposé. L'évolution de la fracture hydraulique et la réponse globale de l'échantillon ont été enregistrées d'une manière comparable aux données expérimentales existantes pour établir un pont entre les résultats expérimentaux et numériques. Les fractures naturelles persistantes semblent être des barrières pour la fracture hydraulique si leur conductance est élevée par apport a celle de la matrice ou si leur raideur est faible par rapport a la rigidité du milieu environnant. D'autre part, une faible rigidité dans les discontinuités non persistantes pourrait provoquer une bifurcation de la fracture hydraulique principale. De plus, des angles d'approche élevés et des contraintes différentielles fortes semblent favoriser le croisement de la fracture naturelle alors que des angles faibles engendrent plutôt un glissement ou une dilatation par cisaillement de la partie du plan qui n'est pas affectée par la perturbation de la contrainte<br>Hydraulic fracturing is at the core of a number of naturally occurring and induced phenomena and crucial for a sustainable development of energy resource production. Given its crucial role this process has been given increasing attention in the last three decades from the academic world. Nonetheless a number of very significant aspects of this process have been systematically overlooked by the community. Two of the most notable ones are the inability of the vast majority of existing models to tackle at once the propagation of hydraulic fractures in realistic, fractured rocks-masses where hydraulic fracturing is a competing dipole mechanism between fracturing of the intact rock and re-activation of exiting fracture networks. Another essential aspect of this process is that it is intrinsically three-dimensional which is neglected by most models. To tackle this vital problem taking into account these pivotal aspects, a fully coupled hydro-mechanical model based on the discrete element method has been developed. The rock mass is here represented by a set of discrete elements interacting through elastic-brittle bonds that can break to form cracks inside the simulated medium. Theses cracks can coalesce to form fractures. A finite volume scheme is used to simulate the fluid flow in between these discrete elements. The flow is computed as a function of the pore space deformation in the intact medium and of the cracks' aperture in the fractures. Furthermore, the natural fractures are modelled explicitly and present mechanical and hydraulic properties different from the rock matrix. Employing this model in an intact numerical specimen, single fluid injection and multiple closely spaced sequential injections, enabled the description the full spatio-temporal evolution of HF propagation and its impact on quantitative indexes used in description of hydraulic fracturing treatments, such as fractured volume, fracture intensity and down-the-hole pressure for different control parameters and in-situ stress-fields. Moreover, injections from perforation slots which are not well aligned to the minimum stress plane showed possible creation of percolating non-planar hydraulic fractures of low connectivity, which can be troublesome for proppant placement. Also, strong interactions between closely spaced HF were highlighted by tracking the local principal stress rotation around the injection zones, emphasizing the importance of stress shadow effects. Optimization solutions are proposed for multiple treatments from a non-perfectly aligned wellbore. Finally, interaction between a single hydraulic fracture and a single natural fracture of varying properties and orientations was studied using the proposed model. The evolution of the hydraulic fracture and the global response of the specimen were recorded in a way comparable to existing experimental data to bridge the experimental and numerical findings. Persistent natural fractures appeared to be barriers for the hydraulic fracture if their conductance is high compared to the matrix conductivity or if their stiffness is significantly low compared to the rock matrix rigidity. Low stiffness in non-persistent defects might also cause a bifurcation of the main hydraulic fracture due to the local stress field perturbation around the defect and ahead of the hydraulic fracture tip. Furthermore, high approach angles and differential stresses seemed to favour crossing of the natural fracture while low angles enable shear slippage or dilation on the part of the plane which is not affected by the local stress perturbation

Hydraulic fracturing is a multi-physics multi-scale problem related to natural processes such as the formation of dikes. It also has wide engineering applications such as extraction of unconventional resources, enhanced geothermal energy and carbon capture and storage. Current simulators are highly simplified because of the assumption of homogeneous reservoir. Unconventional reservoirs are heterogeneous owing to the presence of natural fracture network. Because of high computational effort, three-dimensional multi-scale simulations are uncommon, in particular, modelling material as a heterogeneous medium. Lattice Element Method (LEM) is therefore proposed for multi-scale simulation of heterogeneous material. In LEM, material is discretised into cells and their interactions are modelled by lattices, hence a three-dimensional model is simplified to a network of one-dimensional lattice. Normal, shear and rotational springs are used to define the constitutive laws of a lattice. LEM enables desktop computers for simulation of a lattice model that consists of millions of lattices. From simulations, normal springs govern the macroscopic bulk deformation while shear springs govern the macroscopic distortion. There is fluctuation of stresses even under uniform loading which is one of the characteristics of a lattice model. The magnitude increases with the stiffness ratio of shear spring to normal spring. Fracturing process can be modelled by LEM by introducing a microscopic tensile strength and a microscopic shear strength to the lattice properties. The strength parameters can be related to fracture toughness with the length scales of cells. From simulations, the relationships between model parameters and macroscopic parameters that are measurable in experiments are identified. From the simulations of uni-axial tension tests, both the spring stiffness ratio and the applied heterogeneity govern the fracturing process. The heterogeneity increases the ductility at the expense of the reduction on the macroscopic strengths. Different stages of fracturing are identified which are characterised by the model heterogeneity. Heterogeneous models go through the stages of the spatially distributed microscrack formation, the growth of multiple fracture clusters to the dominant fracture propagation. For homogeneous models, one of the microcracks rapidly propagates and becomes a dominant fracture with the absence of intermediate stages. From the uni-axial compression test simulations, the peak compressive stress is reached at the onset of the microscopic shear crack formation. Ductility is governed by the stiffness reduction ratio of a lattice in closed fractured stage to its unfractured stage. A novel Dual Lattice Model (DLM) is proposed for hydraulic fracture simulation by coupling a solid lattice model with a fluid lattice model. From DLM simulations of hydraulic fracturing of the classical penny shape crack problem under hydrostatic condition, the heterogeneities from both the fracture asperity and the applied heterogeneity increase the apparent fracture toughness. A semi-analytical solution is derived to consider the effect of fluid viscosity in the elastic deformation regime. Two asymptotes are identified that gives steep pressure gradients near the injection point and near the fracture tip which are also identified in the DLM simulations. Simulations also show three evolving regimes on energy dissipation/transfer mechanisms: the viscosity dominant, the elastic deformation dominant and the mixture of elastic deformation and toughness.

Thesis (MEng)--Stellenbosch University, 2014.<br>ENGLISH ABSTRACT: Current numerical methods in the eld of hydraulic fracturing are based mainly on continuum methods, such as the Finite Element Method (FEM) and the Boundary Element Method (BEM). These methods are governed by Linear Elastic Fracture Mechanics (LEFM) criteria, which su er from the inherent aw of a non-physical stress representation at the fracture tip. In response to this, a non-local method is proposed, namely the peridynamic theory, to model sleeved hydraulic fracture. A 2D implicit quasi-static ordinary state based peridynamic formulation is implemented on various benchmark problems, to verify the ability to capture constitutive behaviour in a linear elastic solid, as well as, the quanti cation of adverse e ects on the accuracy of the displacement solution, due to the nature of the non-local theory. Benchmark tests consist of a plate in tension, where convergence to the classical displacement solution, non-uniform re nement and varying cell sizes are tested, as well as, a thick walled cylinder with internal pressure, where three di erent loading techniques are tested. The most accurate loading technique is applied to the sleeved fracture model, in order to simulate fracture initiation and propagation. This model is then veri ed and validated by using the Rummel & Winter hydraulic fracturing model and experimental results, respectively. Displacement error minimisation methods are implemented and as a result, the displacement solutions for a plate in tension converges to the analytical solution, while the thick walled cylinder solutions su er from inaccuracies due to an applied load on an irregularly discretized region. The fracture initiation test captures the fracture tip behaviour of the Rummel & Winter model and the fracture propagation test show good correlation with experimental results. This research shows that the peridynamic approach to sleeved hydraulic fracture can yield a realistic representation of fracture initiation and propagation, however, further research is needed in the area of a pressure load application on a solid using the peridynamic approach.<br>AFRIKAANSE OPSOMMING: Huidige numeriese metodes in die veld van hidrouliese breking is hoofsaaklik gebaseer op kontinuum metodes, soos die Eindige Element Metode (EEM) en die Rand Element Metode (REM). Hierdie metodes word beheer deur Linie^ere Elastiese Breukmeganika (LEB) kriteria, wat ly aan die inherente gebrek van 'n nie- siese voorstelling van die spanning by die fraktuur punt. Om hierdie probleme aan te spreek, word 'n nie-lokale metode voorgestel, naamlik die peridinamiese teorie, om gehulsde hidrouliese breking te modelleer. 'n 2D implisiete kwasi-statiese ordin^ere toestand gebaseerde peridinamika formulering word ge mplimenteer op verskeie norm probleme, om te veri eer of dit oor die vermo e beskik om die konstitutiewe gedrag van 'n linie^ere elastiese soliede materiaal te modeleer, asook die kwanti sering van nadelige e ekte op die verplasings oplossing as gevolg van die natuur van die nie-lokale teorie. Normtoetse bestaan uit 'n plaat in trek spanning, waar konvergensie na die klassieke verplasings oplossing, nie-uniforme verfyning en vari^eerende sel groottes getoets word, asook 'n dikwandige silinder onder interne druk, waar drie verskillende belasting aanwendingstegnieke getoets word. Die mees akkurate belasting aanwendingstegniek word dan gebruik in die gehulsde hidrouliese breking model, om fraktuur aanvangs en uitbreiding na te boots. Die model word dan geveri- eer deur die Rummel & Winter hidrouliese breking model en eksperimentele resultate, onderskeidelik. Fout minimering metodes word toegepas en as 'n resultaat, konvergeer die verplasing oplossing vir die plaat na die analitiese oplossing, terwyl die oplossing van die dikwandige silinder onakuraathede toon as gevolg van 'n toegepaste belasting op 'n onre elmatig gediskretiseerde gebied. Die modellering van die fraktuur inisi ering by die fraktuur punt, stem goed ooreen met die Rummel en Winter voorspelling en die fraktuur uitbreiding stem goed ooreen met eksperimentele resultate. Hierdie navorsing toon dat die peridinamiese benadering tot gehulsde hidrouliese breking wel die fraktuur inisi ering en uitbreiding realisties kan modelleer, maar nog navorsing word wel benodig in die area waar 'n druk belasting op 'n peridinamiese soliede model toegepas word.

Deep slurry injection is a process of solid waste disposal that involves grinding the solid waste to a relatively fine-grained consistency, mixing the ground waste with water and/or other liquids to form slurry, and disposing of the slurry by pumping it down a well at a high enough pressure that fractures are created within the target formation. This thesis describes the site assessment criteria involved in selecting a suitable target reservoir for deep slurry injection. The main goals of this study are the follows: <ul> <li>Identify the geological parameters important for a prospective injection site</li> <li>Recognize the role of each parameter</li> <li>Determine the relationships among different parameters</li> <li>Design and develop a model which can assemble all the parameters into a semi-quantitative evaluation process that could allow site ranking and elimination of sites that are not suitable</li> <li>Evaluate the model against several real slurry injection cases and several prospective cases where slurry injection may take place in future</li> </ul> The quantitative and qualitative parameters that are recognized as important for making a decision regarding a target reservoir for deep slurry injection operations are permeability, porosity, depth, areal extent, thickness, mechanical strength, and compressibility of a reservoir; thickness and flow properties of the cap rock; geographical distance between an injection well and a waste source or collection centre; and, regional and detailed structural and tectonic setup of an area. Additional factors affecting the security level of a site include the details of the lithostratigraphic column overlying the target reservoir and the presence of overlying fracture blunting horizons. Each parameter is discussed in detail to determine its role in site assessment and also its relationship with other parameters. A geological assessment model is developed and is divided into two components; a decision tree and a numerical calculation system. The decision tree deals with the most critical parameters, those that render a site unsuitable or suitable, but of unspecified quality. The numerical calculation gives a score to a prospective injection site based on the rank numbers and weighting factors for the various parameters. The score for a particular site shows its favourability for the injection operation, and allows a direct comparison with other available sites. Three categories have been defined for this purpose, i. e. average, below average, and above average. A score range of 85 to 99 of 125 places a site in the ?average? category; a site will be unsuitable for injection if it belongs to the ?below average? category, i. e. if the total score is less than 85, and the best sites will generally have scores that are in the ?above average? category, with a score of 100 or higher. One may assume that for sites that fall in the ?average? category there will have to be more detailed tests and assessments. The geological assessment model is evaluated using original geological data from North America and Indonesia for sites that already have undergone deep slurry injection operations and also for some possible prospective sites. The results obtained from the model are satisfactory as they are in agreement with the empirical observations. Areas for future work consist of the writing of a computer program for the geological model, and further evaluation of the model using original data from more areas representing more diverse geology from around the world.

Les simulations numériques des fissures fragiles par les modèles d’endommagement à gradient deviennent main- tenant très répandues. Les résultats théoriques et numériques montrent que dans le cadre de l’existence d’une pre-fissure la propagation suit le critère de Griffith. Alors que pour le problème à une dimension la nucléation de la fissure se fait à la contrainte critique, cette dernière propriété dimensionne le paramètre de longueur interne.Dans ce travail, on s’attarde sur le phénomène de nucléation de fissures pour les géométries communément rencontrées et qui ne présentent pas de solutions analytiques. On montre que pour une entaille en U- et V- l’initiation de la fissure varie continument entre la solution prédite par la contrainte critique et celle par la ténacité du matériau. Une série de vérifications et de validations sur diffèrent matériaux est réalisée pour les deux géométries considérées. On s’intéresse ensuite à un défaut elliptique dans un domaine infini ou très élancé pour illustrer la capacité du modèle à prendre en compte les effets d’échelles des matériaux et des structures.Dans un deuxième temps, ce modèle est étendu à la fracturation hydraulique. Une première phase de vérification du modèle est effectuée en stimulant une pré-fissure seule par l’injection d’une quantité donnée de fluide. Ensuite on étudie la simulation d’un réseau parallèle de fissures. Les résultats obtenus montrent qu’il a qu’une seule fissure qui se propage et que ce type de configuration minimise mieux l’énergie la propagation d’un réseau de fractures. Le dernier exemple se concentre sur la stabilité des fissures dans le cadre d’une expérience d’éclatement à pression imposée pour l’industrie pétrolière. Cette expérience d’éclatement de la roche est réalisée en laboratoire afin de simuler les conditions de confinement retrouvées lors des forages.La dernière partie de ce travail se concentre sur la rupture ductile en couplant le modèle à champ de phase avec les modèles de plasticité parfaite. Grâce à l’approche variationnelle du problème on décrit l’implantation numérique retenue pour le calcul parallèle. Les simulations réalisées montrent que pour une géométrie légèrement entaillée la phénoménologie des fissures ductiles comme par exemple la nucléation et la propagation sont en concordances avec ceux reportées dans la littérature<br>Phase-field models, sometimes referred to as gradient damage, are widely used methods for the numerical simulation of crack propagation in brittle materials. Theoretical results and numerical evidences show that they can predict the propagation of a pre-existing crack according to Griffith’s criterion. For a one- dimensional problem, it has been shown that they can predict nucleation upon a critical stress, provided that the regularization parameter is identified with the material’s internal characteristic length.In this work, we draw on numerical simulations to study crack nucleation in commonly encountered geometries for which closed-form solutions are not available. We use U- and V-notches to show that the nucleation load varies smoothly from the one predicted by a strength criterion to the one of a toughness criterion when the strength of the stress concentration or singularity varies. We present validation and verification of numerical simulations for both types of geometries. We consider the problem of an elliptic cavity in an infinite or elongated domain to show that variational phase field models properly account for structural and material size effects.In a second movement, this model is extended to hydraulic fracturing. We present a validation of the model by simulating a single fracture in a large domain subject to a control amount of fluid. Then we study an infinite network of pressurized parallel cracks. Results show that the stimulation of a single fracture is the best energy minimizer compared to multi-fracking case. The last example focuses on fracturing stability regimes using linear elastic fracture mechanics for pressure driven fractures in an experimental geometry used in petroleum industry which replicates a situation encountered downhole with a borehole called burst experiment.The last part of this work focuses on ductile fracture by coupling phase-field models with perfect plasticity. Based on the variational structure of the problem we give a numerical implementation of the coupled model for parallel computing. Simulation results of a mild notch specimens are in agreement with the phenomenology of ductile fracture such that nucleation and propagation commonly reported in the literature

Hydraulic fracturing is essential for producing gas and oil at an economic rate from low permeability sands. Most fracturing treatments use water and polymers with a gelling agent as a fracturing fluid. The water is held in the small pore spaces by capillary pressure and is not recovered when drawdown pressures are low. The un-recovered water leaves a water saturated zone around the fracture face that stops the flow of gas into the fracture. This is a particularly acute problem in low permeability formations where capillary pressures are high. Depletion (lower reservoir pressures) causes a limitation on the drawdown pressure that can be applied. A hydraulic fracturing process can be energized by the addition of a compressible, sometimes soluble, gas phase into the treatment fluid. When the well is produced, the energized fluid expands and gas comes out of solution. Energizing the fluid creates high gas saturation in the invaded zone, thereby facilitating gas flowback. A new compositional hydraulic fracturing model has been created (EFRAC). This is the first model to include changes in composition, temperature, and phase behavior of the fluid inside the fracture. An equation of state is used to evaluate the phase behavior of the fluid. These compositional effects are coupled with the fluid rheology, proppant transport, and mechanics of fracture growth to create a general model for fracture creation when energized fluids are used. In addition to the fracture propagation model, we have also introduced another new model for hydraulically fractured well productivity. This is the first and only model that takes into account both finite fracture conductivity and damage in the invaded zone in a simple analytical way. EFRAC was successfully used to simulate several fracture treatments in a gas field in South Texas. Based on production estimates, energized fluids may be required when drawdown pressures are smaller than the capillary forces in the formation. For this field, the minimum CO2 gas quality (volume % of gas) recommended is 30% for moderate differences between fracture and reservoir pressures (2900 psi reservoir, 5300 psi fracture). The minimum quality is reduced to 20% when the difference between pressures is larger, resulting in additional gas expansion in the invaded zone. Inlet fluid temperature, flowrate, and base viscosity did not have a large impact on fracture production. Finally, every stage of the fracturing treatment should be energized with a gas component to ensure high gas saturation in the invaded zone. A second, more general, sensitivity study was conducted. Simulations show that CO2 outperforms N2 as a fluid component because it has higher solubility in water at fracturing temperatures and pressures. In fact, all gas components with higher solubility in water will increase the fluid’s ability to reduce damage in the invaded zone. Adding methanol to the fracturing solution can increase the solubility of CO2. N2 should only be used if the gas leaks-off either during the creation of the fracture or during closure, resulting in gas going into the invaded zone. Experimental data is needed to determine if the gas phase leaks-off during the creation of the fracture. Simulations show that the bubbles in a fluid traveling across the face of a porous medium are not likely to attach to the surface of the rock, the filter cake, or penetrate far into the porous medium. In summary, this research has created the first compositional fracturing simulator, a useful tool to aid in energized fracture design. We have made several important and original conclusions about the best practices when using energized fluids in tight gas sands. The models and tools presented here may be used in the future to predict behavior of any multi-phase or multi-component fracturing fluid system.<br>text