[pt] Este trabalho faz uma análise da variação dos parâmetros que têm importância na propagação de fraturas hidráulicas e da influência desses parâmetros na conten-ção do fraturamento. Os experimentos numéricos foram feitos em um modelo 2D utilizando um simulador de elementos finitos com acoplamento sequencial hidro-dinâmico, tendo como premissa o comportamento dos processos envolvidos em es-tado estacionário. Inicialmente foram feitos testes de validação das soluções numé-ricas empregadas neste trabalho a partir de casos cujas soluções são bem conheci-das. Então, efeitos de variações de poropressão, de estado de tensões, propriedades das rochas, intervalos de início da fratura hidráulica, efeitos térmicos e o dano à permeabilidade da formação permoporosa foram utilizados para avaliar a contenção da fratura hidráulica. Primeiramente os efeitos foram avaliados separadamente e, em seguida, foram combinados aos pares, por meio de sorteio, e então avaliados. Os estudos levaram à conclusão de que o fator de maior influência para o início da propagação da fratura hidráulica na rocha capeadora (primeiros metros) é o valor da tensão mínima de confinamento do reservatório e a continuidade da propagação vertical na rocha selante é dominada pelo contraste de tensões entre rochas reserva-tório e capeadora. Entretanto, os demais parâmetros exercem influência na conten-ção do fraturamento hidráulico e devem ser levados em consideração neste tipo de estudo, principalmente os que servirão de insumo para a tomada de decisões. / [en] This master thesis analyzes the parameter s variation on the hydraulic frac-ture s propagation importance and the influence of these parameters on fracture containment. The numerical experiments were performed in a 2D model using a finite element simulator with sequential hydrodynamic coupling, having the sta-tionary behavior of the processes involved as premise. Validation tests were ini-tially performed for the numerical solutions used in this thesis from cases which solutions are well known. Then, effects of pore pressure variations, stress state, rock properties, hydraulic fracture opening intervals, thermal effects, and damage to the permoporous formation were used to evaluate the hydraulic fracture containment. At first, the effects were evaluated separately, then sorted for pair combinations, so they could be analyzed. These analyzes led to the conclusion that the most influen-tial factor for the hydraulic fracture initial propagation in the cap rock (first meters) is the reservoir’s minimum confinement stress value, and the vertical propagation continuity in the sealing rock is dominated by the stress contrast between reservoir and cap rocks. However, other parameters influence the hydraulic fracturing con-tainment and should be considered for this type of study, especially those that will serve as input for decision-making.

The negative impact of gas turbine emissions on the environment and human health is a growing concern. Recent studies suggest injecting water into the combustion process effectively reduces emissions and increases power output. However, this approach presents new challenges that need to be thoroughly investigated. Siemens Energy (SE) has recently conducted a study on water injection and its effects on gaseous combustion mixtures but encountere challenges the simulation results when adding water. Therefore, the primary objective of this thesis is to evaluate the methodologies available in Star CCM+ for modeling water injection in a simplified combustor model (SCM) using both liquid (diesel) and gas (methane) fuels. In addition, the behavior of the flame, temperature field inside the combustor, and burner outlet temperature, are investigated.The study has compared physical phenomena such as, the flame shape, velocity, and vorticity field of SCMs with the complete combustor model of the SGT-800 gas turbine for gas fuel. Additionally, the thesis has examined the capability of STAR CCM+ for predicting flame temperature at the outlet against in-house calculation data and Cantera software for parametric cases. The methodology involves a parametric study using the Realizable k-ε TwoLayer turbulence model for steady-state RANS simulations. Combustion is modeled using the FGM method, while Lagrangian multiphase approach is used for liquid injection.The employed FGM combustion model, Lagrangian multiphase model, and RANS simulations yielded realistic results. In addition, the convergence of gas fuel cases was smoother compared to liquid fuel cases, which involved multiphase modelling and evaporation, makes it more complex. The physical phenomena were captured by CFD simulations for the SCM. Flame shape, velocity and vorticity field have good agreement with the theory in the field of gas turbine combustion and other literature sources. Disagreements between CFD and in-house calculations were observed, with the greatest differences being 24 ℃ for premixed methane (at WFR (Water Fuel Ratio) of 0) and 28 ℃ for non-premixed diesel (at WFR of 1). On the other hand, Cantera results for Vapor and for methane cases with water addition were in limit of 10 ℃ with CFD results for WFR between 0-0.5. Nevertheless, achieving a simulation accuracy within a 10 ℃ limit proved challenging due to limitations and potential sources of error in the in-house calculation sheet, combustion modelling, RANS simulations, and reaction mechanism.

[pt] Esta dissertação apresenta um estudo numérico, utilizando o método dos elementos finitos, para simular o entupimento de rochas provocado pela injeção de água contendo partículas sólidas. Dentre os diferentes parâmetros que afetam o declínio de injetividade, quatro foram analisados, considerando-se a situação de fluxo unidimensional: fator de dano, concentração de partículas sólidas presentes no fluido de injeção, coeficiente de filtragem e taxa de injeção. Um estudo paramétrico ressaltando a influência destes fatores na perda de injetividade é também apresentado neste trabalho, concluindo-se que os resultados numéricos obtidos concordam satisfatoriamente com as observações experimentais disponíveis e soluções analíticas publicadas na literatura. O trabalho estuda também numericamente a simulação do entupimento dos poros da rocha considerando dois modelos de redução de permeabilidade e recupera valores do coeficiente de filtragem (Lambda ) e do fator de dano ( Beta ) através de análises inversa pelo método dos elementos finitos. / [en] This dissertation presents a numerical study, based on the finite element method, to simulate rock pore plugging caused by the injection of water containing solid particles in suspension. Amongst the parameters that affect rock injectivity decline, the following four were analyzed, considering undimensional flow: damage coefficient, solid particle concentration present in the injection fluid, filtration coefficient and injection rate. A parametric study standing out the influence of the these factors in the loss of injectivity is also presented in this work, concluding that the numerical results agree satisfactorily with the available experimental data and analytical solutions published in the literature. This work also numerically investigates the process of rock pore plugging considering two different permeability reduction models and recovers values of the filtration coefficient (Lambda ) and the damage factor ( Beta ) through inverse analyses carried outn by the finite element method.

Geothermal energy is the energy naturally present inside the earth crust. When a large volume of hot water and steam is trapped in subsurface porous and permeable rock structure and a convective circulating current is set up, it forms a geothermal reservoir. A geothermal system can be defined as - convective water in the upper crust of earth, which transfers heat from a heat source (in the reservoir) to a heat sink, usually the free surface. A geothermal system is made up of three main elements: a heat source, a reservoir and a fluid, which is the carrier that transfers the heat. As an alternative source of energy geothermal energy has been under attention of the researchers for quite some time. The reason behind this is the existence of several benefits like clean and renewable source of energy which has considerable environmental advantage, with no chemical pollutants or wastes are generated due to geothermal emissions, and the reliability of the power resource. Hence research has been directed in several directions like exploration of geothermal resources, modeling the characteristics of different types of geothermal reservoirs and technologies to extract energy from them. The target of these models has been the prediction of the production of the hot water and steam and thus the estimation of the electricity generating potential of a geothermal reservoir in future years. In a geothermal power plant reinjection of the heat depleted water extracted from the geothermal reservoir has been a common practice for quite some time. This started for safe wastewater disposal and later on the technology was employed to obtain higher efficiency of heat and energy extraction. In most of the cases a very small fraction of the thermal energy present in the reservoir can be recovered without the reinjection of geothermal fluid. Also maintaining the reservoir pressure is essential which gradually reduces due to continuous extraction of reservoir fluid without reinjection, especially for reservoirs with low permeabilities. Although reinjection of cold-water has several benefits, the possibility of premature breakthrough of the cold-water front, from injection well zone to production well zone, reduces the efficiency of the reservoir operation drastically. Hence for maintaining the reservoir efficiency and longer life of the reservoir, the injectionproduction well scheme is to be properly designed and injection and extraction rates are to be properly fixed. Modeling of flow and heat transport in a geothermal reservoir due to reinjection of coldwater has been attempted by several researchers analytically, numerically and experimentally. The analytical models which exist in this field deal mostly with a single injection well model injecting cold-water into a confined homogeneous porous-fractured geothermal reservoir. Often the thermal conductivity is neglected in the analytical study considering it to be negligible which is not always so, as proved in this study. Moreover heterogeneity in the reservoir is also a major factor which has not been considered in any such analytical study. In the field of numerical modeling there also exists a need of a general coupled three-dimensional thermo-hydrogeological model including all the modes of heat transport (advection and conduction), the heat loss to the confining rocks, the regional groundwater flow and the geothermal gradient. No study existing so far reported such a numerical model including those mentioned above. The present study is concerned about modeling the non-isothermal flow and heat transport in a geothermal reservoir due to reinjection of heat depleted water into a geothermal reservoir. Analytical and numerical models are developed here for the transient temperature distributions and advancement of the thermal front in a geothermal reservoir which is generated due to the cold-water injection. First homogeneous geothermal aquifers are considered and later heterogeneities of different kinds are brought into picture. Threedimensional numerical models are developed using a software code DuMux which solves flow and heat transport problems in porous media and can handle both single and multiphase flows. The results derived by the numerical models have been validated using the results from the analytical models derived in this study. Chapter 1 of the thesis gives a brief introduction about different types of geothermal reservoirs, followed by discussion on the governing differential equations, the conceptual model of a geothermal reservoir system, the efficiency of geothermal reservoirs, the modeling and simulation concepts (models construction, boundary conditions, model calibration etc.). Some problems related with geothermal reservoirs and geothermal power is also discussed. The scenario of India in the context having a huge geothermal power potential is described and different potential geothermal sites have been pointed out. In Chapter 2, the concept of reinjection of the heat depleted (cold) water into the geothermal reservoir is introduced. Starting with a brief history of the geothermal reinjection, the chapter describes the purpose and the need of reinjection of geothermal fluid giving examples of different geothermal fields over the world where reinjection has been in practice and benefitted by that. The chapter further discusses on the problems and obstacles faced by the geothermal projects resulting from the geothermal reinjection, most important of which is the thermal-breakthrough and cooling of production wells. Lastly the problem of this thesis is discussed which is to model the transient temperature distribution and the movement of the cold-water thermal front generated due to the reinjection. The need of this modeling is elaborated which represents the motivation of taking up the problem of the thesis. Chapter 3 describes an analytical model developed for the transient temperature in a porous geothermal reservoir due to injection of cold-water. The reservoir is composed of a confined aquifer, sandwiched between rocks of different thermo-geological properties. The heat transport processes considered are advection, longitudinal conduction in the geothermal aquifer, and the conductive heat transfer to the underlying and overlying rocks of different geological properties. The one-dimensional heat transfer equation has been solved using the Laplace transform with the assumption of constant density and thermal properties of both rock and fluid. Two simple solutions are derived afterwards, first neglecting the longitudinal conductive heat transport and then heat transport to confining rocks. The analytical solutions represent the transient temperature distribution in the geothermal aquifer and the confining rocks and model the movement of the cold-water thermal front in them. The results show that the heat transport to the confining rocks plays an influential role in the transient heat transport here. The influence of some parameters, e.g. the volumetric injection rate, the longitudinal thermal conductivity and the porosity of the porous media, on the transient heat transport phenomenon is judged by observing the variation of the transient temperature distribution with different values of the parameters. The effects of injection rate and thermal conductivity have been found to be high on the results. Chapter 4 represents another analytical model for transient temperature distribution in a heterogeneous geothermal reservoir underlain and overlain by impermeable rocks due to injection of cold-water. The heterogeneity of the porous medium is expressed by the spatial variation of the flow velocity and the longitudinal effective thermal conductivity of the medium. Simpler solutions are also derived afterwards first neglecting the longitudinal conduction, then the heat loss to the confining rocks depending on the situation where the contribution of them to the transient heat transport phenomenon in the porous media is negligible. Solution for a homogeneous aquifer with constant values of the rock and fluid parameters is also derived with an aim to compare the results with that of the heterogeneous one. The effect of heat loss to the confining rocks in this case is also determined and the influence of some of the parameters involved, on the transient heat transport phenomenon is assessed by observing the variation of the results with different magnitudes of those parameters. Results show that the heterogeneity plays a major role in controlling the cold-water thermal front movement. The transient temperature distribution in the geothermal reservoir depends on the type of heterogeneity. The heat loss to the confining rocks of the geothermal aquifer also has influence on the heat transport phenomenon. In Chapter 5 another analytical model is derived for a heterogeneous reservoir where the heterogeneous geothermal aquifer considered is a confined aquifer consisted of homogeneous layers of finite length and overlain and underlain by impermeable rock media. All the different layers in the aquifer and the overlying and underlying rocks are of different thermo-hydrogeological properties. Results show that the advancement of the cold-water thermal front is highly influenced by the layered heterogeneity of the aquifer. As the cold-water thermal front encounters layers of different thermo-hydrogeological properties the movement of it changes accordingly. The analytical solution derived here has been compared with a numerical model developed by the multiphysics software code COMSOL which shows excellent agreement with each other. Lastly it is shown that approximation of the properties of a geothermal aquifer by taking mean of the properties of all the layers present will lead to erroneous estimation of the temperature distribution. Chapter 6 represents a coupled three-dimensional thermo-hydrogeological numerical model for transient temperature distribution in a confined porous geothermal aquifer due to cold-water injection. This 3D numerical model is developed for solving more practical problems which eliminate the assumptions taken into account in analytical models. The numerical modeling is performed using a software code DuMux as mentioned before. Besides modeling the three-dimensional transient temperature distribution in the model domain, the chapter investigates the regional groundwater flow has been found to be a very important parameter to consider. The movement of the thermal front accelerates or decelerates depending on the direction of the flow. Influence of a few parameters involved in the study on the transient heat transport phenomenon in the geothermal reservoir domain, namely the injection rate, the permeability of the confining rocks and the thermal conductivity of the geothermal aquifer is also evaluated in this chapter. The models have been validated using analytical solutions derived in this thesis. The results are in very good agreement with each other. In Chapter 7 the main conclusions drawn from the study have been enlisted and the scope of further research is also pointed out.

Tato práce je zaměřena na systém vodního vstřikování a způsoby zajištění dostatečného množství potřebné kapaliny pro správný chod tohoto systému. Jedním zajímavým a nezávislým řešením je využití odpadních produktů motoru, a to vodní páry produkované spalováním paliva. Pro zajištění kondenzace je nutné zchlazení výfukových plynů pod rosný bod páry, což lze zajistit opatřením výfukového potrubí chladiči. Vzniklý kondenzát je pak potřeba efektivně oddělit od proudu plynů a zachytit. Návrh takovéhoto systému vychází z reálně naměřených dat a jeho následným ověřením pomocí CFD simulace.

[pt] Modelos analíticos que descrevam o comportamento da pressão são de extrema utilidade na área de avaliação de formações e caracterização de reservatório, pois eles fornecem estimativas sobre diversos parâmetros do reservatório. Este trabalho tem dois objetivos principais: primeiro, estender a solução existente para testes de injetividade e falloff em reservatórios com uma camada e poços horizontais de modo que ela possa ser aplicada também em formações multicamadas com poços horizontais multirramificados. Além disso, este trabalho aplica funções impulso para obter uma formulação alternativa para testes de injetividade em reservatórios estratificados com poços verticais e formações com uma camada e poços horizontais. / [en] Analytical models that describe the pressure behavior are extremely useful for pressure transient analysis and reservoir characterization as they provide estimates of reservoir parameters. This work has two main goals: first, to extend the existing solutions for injectivity/falloff tests in single-layer formations with horizontal wells so that they can be applied to multilayer stratified reservoirs with multilateral horizontal wells. Furthermore, this work applies impulse functions to obtain an alternative formulation for injectivity tests in multilayer commingled formations with vertical wells and single-layer reservoirs with horizontal wells.

[pt] Teste de injetividade é uma técnica convencional em engenharia de reservatórios, utilizada para a recuperação de óleo em reservatórios e avaliação de formações. Geralmente utiliza-se água como fluido injetado, que resulta em um deslocamento do óleo presente devido ao aumento da pressão nos poros. Durante o teste, a resposta de pressão medida fornece diversas informações sobre os parâmetros do reservatório, tal como dados de permeabilidade. Desta forma, pesquisadores têm se dedicado em encontrar equações matemáticas que modelam a resposta de pressão desses testes com objetivo de gerenciamento e manutenção preditiva do reservatório. Neste trabalho, apresentamos uma nova solução analítica para a análise de testes de injetividade, que combina a técnica de convolução pressão-pressão com um modelo radial composto de duas zonas. Essa solução permite avaliar o teste de injetividade mesmo na ausência de dados precisos de vazão, uma vez que a convolução pressão-pressão utiliza exclusivamente os dados de pressão adquiridos em diferentes posições do reservatório. O modelo considerado consiste em dois poços, um injetor, localizado na zona interna do reservatório, e um observador, na zona externa. A validação da solução proposta foi realizada por meio da comparação dos resultados analíticos com aqueles obtidos em um simulador comercial baseado em diferenças finitas. / [en] The injectivity test is a conventional technique in reservoir engineering used for oil recovery and formation evaluation. Typically, water is injected to displace the existing oil by increasing the pressure in the pores. In this test, the pressure response measurement provides valuable information about the reservoir parameters, including permeability data. Therefore, researchers aim to develop mathematical equations that could accurately model pressure response during these tests for reservoir management and maintenance prediction purposes. This work introduces a new analytical solution for injectivity test analysis. The solution combines the pressure-pressure convolution technique with a two-zone radial model. It allows the evaluation of the injectivity test without precise flow rate data, as the pressure-pressure convolution exclusively uses the pressure data acquired at different positions in the reservoir. The reservoir model comprises an injector well in the inner zone of the reservoir and an observation well in the outer zone for measuring pressure response. The proposed solution was validated by comparing the analytical results with those obtained from a finite differences-based commercial simulator.

Les techniques informatiques ont gagné un rôle primordial dans le développement et l'exploitation des ressources d'hydrocarbures naturelles ainsi que dans d'autres opérations liées à des réservoirs souterrains. L'un des problèmes cruciaux de la modélisation de réservoir et les prévisions de production réside dans la présélection des modèles de réservoir appropriés à la quantification d'incertitude et au le calage robuste des résultats de simulation d'écoulement aux réelles mesures et observations acquises du gisement. La présente thèse s'adresse à ces problématiques et à certains autres sujets connexes.Nous avons élaboré une stratégie pour faciliter et accélérer l'ajustement de tels modèles numériques aux données de production de champ disponibles. En premier lieu, la recherche s'était concentrée sur la conceptualisation et l'implémentation des modèles de proxy reposant sur l'analyse de la connectivité, comme une propriété physique intégrante et significative du réservoir, et des techniques avancées du partitionnement de données et de l'analyse de clusters. La méthodologie développée comprend aussi plusieurs approches originales de type probabiliste orientées vers les problèmes d'échantillonnage d'incertitude et de détermination du nombre de réalisations et de l'espérance de la valeur d'information d'échantillon. Afin de cibler et donner la priorité aux modèles pertinents, nous avons agrégé les réalisations géostatistiques en formant des classes distinctes avec une mesure de distance généralisée. Ensuite, afin d'améliorer la classification, nous avons élargi la technique graphique de silhouettes, désormais appelée la "séquence entière des silhouettes multiples" dans le partitionnement de données et l'analyse de clusters. Cette approche a permis de recueillir une information claire et compréhensive à propos des dissimilarités intra- et intre-cluster, particulièrement utile dans le cas des structures faibles, voire artificielles. Finalement, la séparation spatiale et la différence de forme ont été visualisées graphiquement et quantifiées grâce à la mesure de distance probabiliste.Il apparaît que les relations obtenues justifient et valident l'applicabilité des approches proposées pour améliorer la caractérisation et la modélisation d'écoulement. Des corrélations fiables ont été obtenues entre les chemins de connectivité les plus courts "injecteur-producteur" et les temps de percée d'eau pour des configurations différentes de placement de puits, niveaux d'hétérogénéité et rapports de mobilité de fluides variés. Les modèles de connectivité proposés ont produit des résultats suffisamment précis et une performance compétitive au méta-niveau. Leur usage comme des précurseurs et prédicateurs ad hoc est bénéfique en étape du traitement préalable de la méthodologie. Avant le calage d'historique, un nombre approprié et gérable des modèles pertinents peut être identifié grâce à la comparaison des données de production disponibles avec les résultats de... / Computer-based workflows have gained a paramount role in development and exploitation of natural hydrocarbon resources and other subsurface operations. One of the crucial problems of reservoir modelling and production forecasting is in pre-selecting appropriate models for quantifying uncertainty and robustly matching results of flow simulation to real field measurements and observations. This thesis addresses these and other related issues. We have explored a strategy to facilitate and speed up the adjustment of such numerical models to available field production data. Originally, the focus of this research was on conceptualising, developing and implementing fast proxy models related to the analysis of connectivity, as a physically meaningful property of the reservoir, with advanced cluster analysis techniques. The developed methodology includes also several original probability-oriented approaches towards the problems of sampling uncertainty and determining the sample size and the expected value of sample information. For targeting and prioritising relevant reservoir models, we aggregated geostatistical realisations into distinct classes with a generalised distance measure. Then, to improve the classification, we extended the silhouette-based graphical technique, called hereafter the "entire sequence of multiple silhouettes" in cluster analysis. This approach provided clear and comprehensive information about the intra- and inter-cluster dissimilarities, especially helpful in the case of weak, or even artificial, structures. Finally, the spatial separation and form-difference of clusters were graphically visualised and quantified with a scale-invariant probabilistic distance measure. The obtained relationships appeared to justify and validate the applicability of the proposed approaches to enhance the characterisation and modelling of flow. Reliable correlations were found between the shortest "injector-producer" pathways and water breakthrough times for different configurations of well placement, various heterogeneity levels and mobility ratios of fluids. The proposed graph-based connectivity proxies provided sufficiently accurate results and competitive performance at the meta-level. The use of them like precursors and ad hoc predictors is beneficial at the pre-processing stage of the workflow. Prior to history matching, a suitable and manageable number of appropriate reservoir models can be identified from the comparison of the available production data with the selected centrotype-models regarded as the class representatives, only for which the full fluid flow simulation is pre-requisite. The findings of this research work can easily be generalised and considered in a wider scope. Possible extensions, further improvements and implementation of them may also be expected in other fields of science and technology.

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