A main aspect of wellbore stability analysis is the selection of an appropriate rock failure criterion. The most commonly used criterion for brittle failure of rocks is the Mohr-Coulomb criterion. This criterion involves only the maximum and minimum principal stresses, s1 and s3, and therefore assumes that the intermediate stress s2 has no influence on rock strength. When the Mohr-Coulomb criterion had been developed, it was justified by experimental evidence from conventional triaxial tests (s1>s2=s3). Based on triaxial failure mechanics, the Mohr-Coulomb criterion has been extensively used to represent rock failure under the polyaxial stress state (s1>s2>s3). In contrast to the predictions of Mohr-Coulomb criterion, much evidence has been accumulating to suggest that s2 does indeed have a strengthening effect. In this research, I have shown that Mohr-Coulomb failure criterion only represents the triaxial stress state (s2=s3 or s2=s1), which is a special case that will only occasionally be encountered in situ. Accordingly, I then developed a new true-triaxial failure criterion called the Mogi-Coulomb criterion. This failure criterion is a linear failure envelope in the Mogi domain (toct-sm,2 space) which can be directly related to the Coulomb strength parameters, cohesion and friction angle. This linear failure criterion has been justified by experimental evidence from triaxial tests as well as polyaxial tests. It is a natural extension of the classical Coulomb criterion into three dimensions. As the Mohr-Coulomb criterion only represents rock failure under triaxial stress states, it is expected to be too conservative in predicting wellbore instability. To overcome this problem, I have developed a new 3D analytical model to estimate the mud pressure required to avoid shear failure at the wall of vertical, horizontal and deviated boreholes. This has been achieved by using linear elasticity theory to calculate the stresses, and the fully-polyaxial Mogi-Coulomb criterion to predict failure. The solution is achieved in closed-form for vertical wellbores, for all stress regimes. For deviated or horizontal wellbores, Mathcad programs have been written to evaluate the solution. These solutions have been applied to several field cases available in the literature, and the new model in each case seems to be consistent with the field experience. / QC 20100629

Drilling operation expanded through deep water environments starting from mid-1980. As water depth increased, hydrate bearing formation in the shallow ocean floor is observed and that started to cause problems during drilling and production operations. Problems due to hydrate dissociation and forming during operations are also reported by the companies working in those environments many times. Although there are several factors affect the dissociation of shallow hydrate bearing sediments, heat flux from deeper sections of the well through shallower section during the operation is the major one. In order to mitigate that risk in this study, Black Sea is taken as a reference drilling environment. Hydrate phase boundary of the region is calculated via using actual temperature and pressure data gathered during drilling operations. Generic wellbore is defined and common drilling operation sequence is simulated in this defined wellbore. Heat transfer from section target depths to the shallow wellbore section is observed during simulations. Reducing effect of low inlet temperatures and a low circulation rate on wellbore temperatures are determined. In addition positive effect of riser boosting on depressing wellbore temperature in the well head is determined. Black Sea deep water hydrate stability zone is determined between 2210-2275m. Target depth limitation for generic well designed in drilling operations is determined as 4600m.

Increasing surface pressure buildup levels and surface venting flow rates on intermediate wellbore casing strings provided an opportunity to analyze wellbore field data to determine a distribution of leakage path permeability values. The gas leakage source in the leaky wellbore originated at depth, and formation gas/fluid traveled along defects in the cement to accumulate at the surface wellhead. The most likely pathway is the cement interface with casing or formation. Due to uncertainty about the location of the leak, and the different methods that were used for calculating leakage parameter values, a range of leakage path permeability values was produced. Most leakage pathway permeability values were greater than intact cement permeability (few microdarcies). This finding supports the practice of using cement filled annuli to provide a safe protective barrier against leakage and to prevent gas flow to surface. Proper cementing techniques are presented in order to identify possible reasons for cracks to form. It is hypothesized that the higher permeability values are a result of cracks in the cement interface with the casing or formation. These types of defects could also be found in wellbores that are in communication with CO2 sequestration reservoirs. The risk of leakage along such existing wellbores associated with CO2 sequestration projects is quantified by the distribution of leakage path permeability. The gas migration path through existing leaky wellbores is an analog for wellbores that are in contact with migrating CO2 plumes. Cracks in the leaky wellbores provide a highly permeable conduit for CO2 to migrate out of the injection zone to the surface. By quantifying leakage path permeability, proper leakage risk assessment can be further developed. / text

During the production and transportation of oil and gas, flow assurance issues may occur due to the solid deposits that are formed and carried by the flowing fluid. Solid deposition may cause serious damage and possible failure to production equipment in the flow lines. The major flow assurance problems that are faced in the fields are concerned with asphaltene, wax and scale deposition, as well as hydrate formations. Hydrates, wax and asphaltene deposition are mostly addressed in deep-water environments, where fluid flows through a long path with a wide range of pressure and temperature variations (Hydrates are generated at high pressure and low temperature conditions). In fact, a large change in the thermodynamic condition of the fluid yields phase instability and triggers solid deposit formations. In contrast, scales are formed in aqueous phase when some incompatible ions are mixed. Among the different flow assurance issues in hydrocarbon reservoirs, asphaltenes are the most complicated one. In fact, the difference in the nature of these molecules with respect to other hydrocarbon components makes this distinction. Asphaltene molecules are the heaviest and the most polar compounds in the crude oils, being insoluble in light n-alkenes and readily soluble in aromatic solvents. Asphaltene is attached to similarly structured molecules, resins, to become stable in the crude oils. Changing the crude oil composition and increasing the light component fractions destabilize asphaltene molecules. For instance, in some field situations, CO₂ flooding for the purpose of enhanced oil recovery destabilizes asphaltene. Other potential parameters that promote asphaltene precipitation in the crude oil streams are significant pressure and temperature variation. In fact, in such situations the entrainment of solid particulates in the flowing fluid and deposition on different zones of the flow line yields serious operational challenges and an overall decrease in production efficiency. The loss of productivity leads to a large number of costly remediation work during a well life cycle. In some cases up to $5 Million per year is the estimated cost of removing the blockage plus the production losses during downtimes. Furthermore, some of the oil and gas fields may be left abandoned prematurely, because of the significance of the damage which may cause loss about $100 Million. In this dissertation, we developed a robust wellbore model which is coupled to our in-house developed compositional reservoir model (UTCOMP). The coupled wellbore/reservoir simulator can address flow restrictions in the wellbore as well as the near-wellbore area. This simulator can be a tool not only to diagnose the potential flow assurance problems in the developments of new fields, but also as a tool to study and design an optimum solution for the reservoir development with different types of flow assurance problems. In addition, the predictive capability of this simulator can prescribe a production schedule for the wells that can never survive from flow assurance problems. In our wellbore simulator, different numerical methods such as, semi-implicit, nearly implicit, and fully implicit schemes along with blackoil and Equation-of-State compositional models are considered. The Equation-of-State is used as state relations for updating the properties and the equilibrium calculation among all the phases (oil, gas, wax, asphaltene). To handle the aqueous phase reaction for possible scales formation in the wellbore a geochemical software package (PHREEQC) is coupled to our simulator as well. The governing equations for the wellbore/reservoir model comprise mass conservation of each phase and each component, momentum conservation of liquid, and gas phase, energy conservation of mixture of fluids and fugacity equations between three phases and wax or asphaltene. The governing equations are solved using finite difference discretization methods. Our simulation results show that scale deposition is mostly initiated from the bottom of the wellbore and near-wellbore where it can extend to the upper part of the well, asphaltene deposition can start in the middle of the well and the wax deposition begins in the colder part of the well near the wellhead. In addition, our simulation studies show that asphaltene deposition is significantly affected by CO₂ and the location of deposition is changed to the lower part of the well in the presence of CO₂. Finally, we applied the developed model for the mechanical remediation and prevention procedures and our simulation results reveal that there is a possibility to reduce the asphaltene deposition in the wellbore by adjusting the well operation condition. / text

[pt] O conhecimento do comportamento mecânico das rochas é fundamental para o desenvolvimento dos estudos de estabilidade voltados à construção de poços de petróleo. Neste sentido, a estimativa de suas propriedades mecânicas e a determinação do campo de tensões atuante são necessários para compreender as deformações às quais estão sujeitas. De modo a avaliar os efeitos da perfuração no comportamento mecânico das rochas, foram construídos modelos numéricos das litologias comumente descritas no pré-sal de um campo da bacia de Santos em duas etapas. Em um primeiro momento, foi idealizado um estudo de retroanálise de poço a fim de estabelecer a metodologia a ser aplicada neste trabalho. Os resultados numéricos obtidos nesta etapa reproduziram de maneira satisfatória os dados constatados em campo e, desta forma, foi possível validar a técnica utilizada. Em um segundo momento, foram construídos os modelos numéricos de litologias previstas em um poço sintético para um teste cego, tomando por base tanto as propriedades mecânicas estimadas das rochas quanto o estado de tensões in situ determinado em poços de correlação. Por último, os resultados obtidos neste teste foram comparados aos dados reais de um poço da área, de modo que foi possível corroborar a metodologia aplicada neste estudo pela coerência entre os dados numéricos e os constatados em campo. Desta forma, foi possível avaliar o comportamento mecânico das rochas no intervalo do pré-sal de poços correlacionáveis e estimar possíveis problemas geomecânicos a serem encontrados durante a etapa de perfuração. / [en] The modeling of rock mechanical behavior is essential to develop wellbore stability studies. In that sense, estimating rock mechanical properties and the in situ stress field are required tasks to understand the resulting deformations. In order to evaluate drilling effects on rock mechanical behavior, numerical models were constructed to represent the most commonly described rocks in the pre-salt session of an oil field located in Santos basin. Firstly, the author introduced the wellbore retro-analysis methodology proposed for this study. The technique was validated against real wellbore data with a fairly good match. Thereafter, a test model was conducted on a synthetic stratigraphy considering the typical occurrence of pre-salt rocks and the expected in situ stress field, as determined by correlated wellbores data. The numerical results of this test were compared to the data acquired in a local oil well and seemed to provide a reasonable fit, corroborating the applied technique. It was possible to evaluate typical pre-salt rock mechanical behavior by using correlation wellbores and still predict possible wellbore geomechanical problems during the drilling phase.

[pt] Este trabalho desenvolve uma metodologia para obter experimentalmente a pressão capilar de diferentes fluidos em contato com folhelhos, comparando-a com valores obtidos analiticamente a partir da caracterização dos fluidos e dos folhelhos individualmente. Foram realizados ensaios numa célula de difusão a qual permite simular as condições de pressão aplicadas no campo, avaliar a interação físico- química entre fluidos e rochas, além de determinar os parâmetros de transporte de massa devido a gradientes químicos e hidráulicos. Verifica-se que os valores de pressão capilar obtidos diretamente na célula de difusão são inferiores aos obtidos a partir da equação de pressão capilar utilizando a tensão interfacial, o ângulo de contato e o raio de poros do folhelho. Desta forma, conclui-se que caso seja realizada uma análise de estabilidade considerando a pressão capilar do fluido, este parâmetro deve ser determinado experimentalmente na célula de difusão. Caso contrário, valores superestimados poderão ser encontrados. / [en] A methodology was developed to experimentally obtain the capillary pressure of different fluids in contact with shales and compare these values with analytical results from individual characterization of fluids and shales. Tests were carried out in a diffusion cell, which allows the simulation of in-situ pressure conditions, the evaluation of physical-chemical interactions between fluids and rocks and the determination of mass transport parameters due to hydraulic and chemical gradients. It is observed that the values of capillary pressure directly obtained in the diffusion cell are inferior to the ones obtained from the capillary pressure equation using the interfacial tension, the contact angle and the pore radius of shales. Thus, it can be concluded that, if a stability analysis considering the capillary pressure of the fluid is carried out, this parameter should be experimentally determined in the diffusion cell. Otherwise, overestimated values can be found.

[pt] A grande maioria dos problemas de estabilidade de poços de petróleo ocorre em trechos de folhelhos, rochas nas quais, uma especificação eficiente da pressão do fluido de perfuração requer previamente uma especificação correta da concentração salina e da temperatura. Todavia, para um dimensionamento adequado das características do fluido de perfuração necessárias à estabilidade do poço, é necessário o uso de modelos matemáticos que considerem um acoplamento adequado entre efeitos poroelásticos, químicos e térmicos. Entretanto, a complexidade matemática das equações de modelos acoplados normalmente leva à adoção de soluções numéricas, que consomem um tempo computacional muito grande e, por isso, esses modelos não são atrativos à aplicação na análise da estabilidade de poços. Este trabalho apresenta um modelo acoplado termo-químico-poroelástico representado por duas soluções, uma numérica, que utiliza o método dos elementos finitos, e outra analítica, baseada no método das transformadas de Laplace. Ao comparar ambas as soluções é demonstrado que a solução analítica consegue representar tão bem quanto à solução numérica os principais processos acoplados presentes durante a perfuração de folhelhos e que influenciam na sua estabilidade e, por esta razão, pode ser utilizada na análise de estabilidade de poços em folhelhos. Através de um estudo de caso, é verificado que um controle eficiente da estabilidade do poço é obtido especificando a pressão do fluido de perfuração em função da sua temperatura e concentração salina. Estes resultados também indicam as razões de alguns problemas não previstos por modelos desacoplados, e que quase sempre ocorrem durante a perfuração em folhelhos. / [en] Wellbore stability problems are most common when drilling through shales. In order to avoid such problems in this kind of rocks the solute concentration and temperature must be properly defined in the drilling fluid composition, which requires considering poroelastic, thermal and chemical effects in a coupled way. The equations complexity of coupled models usually results in numerical solutions that are very time consuming, thus, unattractive for stability analysis. In an opposite way, it is very difficult to develop closed- form solutions for coupled models. This work presents a thermochemoporoelastic model represented by a numerical solution based upon the finite element method and an analytical solution based upon the Laplace transform method. A comparison between the results of the numerical solution and analytical solution shows that the later can reproduce the coupled processes involved in the wellbore stability problem in shales as well as the former, and for this reason the closed-form solution can be applied as a practical tool in wellbore stability analysis. The analysis of a typical wellbore drilled through shales showed that an efficient control of wellbore stability can be obtained through an adequate specification of the drilling fluid pressure when taking in account its solute concentration and temperature. The model was also able to explain some problems not predicted by uncoupled models, but almost always seen while drilling through shales.

[pt] O estudo sobre estabilidade de poços tem como uma de suas principais aplicações a determinação da faixa segura de densidades do fluido de perfuração. A análise de estabilidade de um poço, que determina essa faixa segura, envolve uma série de parâmetros que geralmente apresentam incertezas associadas aos seus valores. Em métodos convencionais, essas incertezas não são consideradas. O objetivo deste trabalho é desenvolver metodologias de análise de estabilidade de poços que considerem as incertezas associadas aos parâmetros. Métodos para quantificação de incertezas associadas aos parâmetros são apresentados para o caso de um poço já perfurado e para o caso de um novo poço em uma região em desenvolvimento. Dois métodos de análise de sensitividade também são apresentados e aplicados ao problema de estabilidade de poços. Para avaliação do efeito que as incertezas associadas aos parâmetros geram no sistema de estabilidade, dois métodos probabilísticos (simulação de Monte Carlo e método FOSM) foram aplicados ao problema, e depois intercomparados. Através do método da simulação de Monte Carlo, desenvolveu- se um simulador computacional para análise probabilística de estabilidade de poços, que permite a consideração das incertezas associadas aos parâmetros. Os métodos probabilísticos de análise fornecem como resposta as probabilidades de ruptura associadas às diferentes pressões internas do poço. Como essas pressões são dependentes da densidade do fluido de perfuração, a avaliação do risco associado à essas pressões constitui um novo critério para a determinação da densidade do fluido de perfuração. / [en] The study on wellbore stability has as one of its main application the determination of the safe range of the drilling-fluid density. The wellbore stability analysis is controlled by a number of parameters that generally present uncertainties associated to their values. In conventional methods, these uncertainties are not considered. The purpose of this work is to develop methodologies of analysis of wellbore stability that consider the uncertainties associated to the controlling parameters. Methods for quantifying the uncertainties associated to the parameters are presented for the case of an open well and for the case of new well located on a development region. Two methods of sensitivity analysis are also presented and applied to the well stability problem. To evaluate the effect that the uncertainties associated to the parameters create on the stability analysis, two probabilistic methods were applied to the problem, and compared to each other. Based upon Monte Carlo method, a computational simulator was developed in order to carry out probabilistic analysis of wellbore stability. The simulator takes into account the uncertainties associated to the parameters. The probabilistic methods of analysis, presented in this dissertation, provide the probability of failure associated to the different internal pressure of the well. As these pressures are dependent upon the density of the drilling - fluid, the evaluation of the risk associated to these pressures constitutes a new criterion to establish the density of the drilling -fluid. / [es] EL estudio sobre estabilidad de pozos tiene como una de sus principales aplicaciones la determinación de la banda de seguridad de las densidades del fluido de perforación. El análisis de estabilidad de un pozo, que determina esa banda segura, incluye una série de parámetros que generalmente presentan errores asociados a sus valores. En métodos convencionales, esos errores no son consideradas. EL objetivo de este trabajo es desarrollar metodologías de análisis de estabilidad de pozos que consideren los errores asociados a los parámetros. Métodos para cuantificación de errores asociadas a los parámetros son presentados para el caso de un pozo perforado y para el caso de un nuevo pozo en una región en desarrollo. Se presentan también dos métodos de análisis de sensitividad y se aplican a problemas de estabilidad de pozos. Para la evaluación de lo que los errores asociados a los parámetros generan en el sistema de estabilidad, se aplican dos métodos probabilísticos (simulación de Monte Carlo y método FOSM). A través del método de la simulación de Monte Carlo, se desarrolla un simulador computacional para el análisis probabilístico de estabilidad de pozos, que permite la consideración de los errores asociados a los parámetros. Los métodos probabilísticos de análisis dan como respuesta las probabilidades de ruptura asociadas a las diferentes presiones internas del pozo. Como esas presiones son dependientes de la densidad del fluido de perforación, la evaluación del riesgo asociado a esas presiones constituye un nuevo criterio para la determinación de la densidad del fluido de perforación.

En vue de réduire à moyen terme les émissions de gaz à effet de serre d'origine anthropique, le captage-transport-stockage du dioxyde de carbone (CO2) est considéré comme une technologie prometteuse. Plusieurs sites pilotes existent déjà dans le monde. Cependant, avant de développer la technique de façon industrielle, des recherches expérimentales et numériques doivent être menées afin de garantir le succès et la pérennité d'un projet de stockage. Sur un site de stockage, les discontinuités naturelles ainsi que le(s) puits d'injection constituent des chemins préférentiels pour des fuites éventuelles. Ce travail de doctorat s'attache à l'étude des effets de la présence de dioxyde de carbone sur les géomatériaux en présence et, plus particulièrement, sur le ciment du puits d'injection. L'intégrité du puits et donc la garantie de son étanchéité est critique au niveau de la roche de couverture. Après injection et remontée du panache de dioxyde de carbone vers la roche de couverture, le ciment du puits au niveau de la zone triple (puits/réservoir/couverture) est en contact avec un fluide saturé en CO2 dissous. Un tel fluide, au pH acide, est amené à réagir avec les géomatériaux et entraîne diverses réactions de dissolution des minéraux de la matrice cimentaire ainsi que des réactions de précipitation pouvant altérer le matériau. Ce couplage fort existant entre réactions chimiques et comportement poro-mécanique du ciment du puits peut en effet induire un endommagement de la matrice cimentaire, lié aux modifications de la porosité et des caractéristiques de transport, à la dégradation des modules mécaniques, ou encore à la création de surpressions interstitielles localisées. Un modèle constitutif entièrement couplé a été développé pour simuler le comportement chimio-poromécanique du ciment en présence d'un fluide chargé de CO2. Ce modèle a été implémenté dans deux codes numériques, à savoir, un code aux volumes finis d'une part, et un code aux éléments finis, BIL, développé au Laboratoire Navier, d'autre part. La première implémentation se révèle être bien adaptée aux problèmes de transport réactif à front raide, et est utilisée dans ce mémoire pour modéliser une géométrie unidimensionnelle alliant ciment du puits et roche de couverture. La seconde méthode d'implémentation est quant à elle mieux adaptée à la modélisation du comportement poro-mécanique du ciment, mais, comme nous le verrons, nécessite des adaptations numériques a fin d'être convenable pour la modélisation de phénomènes chimiques impliquant des discontinuités. L'endommagement mécanique lié aux phénomènes chimiques est évalué d'une part via une approche micro-mécanique simplifiée, et d'autre part par une théorie de l'endommagement isotrope. En fin, en ce qui concerne la seconde approche, les résultats sont comparés à des tests expérimentaux issus de la littérature scientifique dans le contexte du stockage géologique du CO2 / In order to reduce in medium-term the anthropogenic original greenhouse gas, the processes of capture-transport-storage of carbon dioxide (CO2) is considered as a promising technology. Several pilot sites already exist in the world. However, before developing the technology on an industrial scale, experimental and numerical researches have to be performed in order to ensure the success and the sustainability of a storage project. In a storage site, the natural discontinuities of the rocks and of the injection wells are normally the preferential leak paths of CO2. In this context, the present PhD research focuses particularly on the cement injection wells. The problems of the integrity of the well and thus ensuring its sealing are the critical points of the caprock.After the injection and the ascent of the CO2 plume to the caprock, the cement paste of well at the triple zone (well/ reservoir/caprock) is contacted with a fluid saturated with dissolved CO2. Because of its acidity, such a fluid is reacted with geomaterials and causes diverse reactions of dissolution of the minerals in the cementitious matrix and precipitation reactions that may affect the material. This strong coupling existing between the chemical reactions and poro-mechanical behavior of the cement well can indeed induce damage to the cementitious matrix related to the modifications of the porosity and the transport characteristics, to the degradation of mechanical modulus, or to the development of localized pore pressure.A constitutive model fully coupled has been developed to simulate the chemo-poro-mechanical behaviour of the hard cement paste of the well with the presence of a CO2-rich fluid. This model has been implemented in two numerical codes: on the one hand, a finite volume code, and on the other hand, a finite element code, BIL, developed at the Navier Laboratory. The first implementation was found to be well adapted to the problems of reactive transport with sharp front, and is used in this thesis to modeling an one-dimensional geometry by combining the cement well and the caprock. The second implementation method is best suited to modeling the poro-mechanical behavior of cement, but, as we shall see, requires numerical adaptations in order to be suitable for modeling chemical phenomenon involving discontinuities. The mechanical damage related to chemical phenomena is evaluated firstly via a simplified micro-mechanical approach, and secondly a theory of isotropic damage. Finally, the results are compared to experimental tests from the scientific literature in the context of the CO2 geosequestration

[pt] A ocorrência de eventos de perfuração em poços de óleo e gás é frequente, porém indesejada, uma vez que acarreta aumento no tempo e custo das operações. Sua ocorrência pode levar à perda de circulação do fluido, desmoronamento da parede do poço, restrição da sua funcionalidade, danos à plataforma, problemas ambientais e mesmo a perda de vidas humanas. Desta forma, o conhecimento das tensões é essencial para a estimativa da estabilidade do poço e aumento da segurança da perfuração. Existem diversos métodos para prever a tensão horizontal mínima, entretanto, para a máxima, ainda há dificuldades na sua determinação. No caso de poços inclinados, este cálculo se torna ainda mais complexo, uma vez que as tensões regionais não são alinhadas com o eixo do poço. Identificada essa necessidade, e partindo do princípio de que ao menos um poço já tenha sido perfurado em um campo e que este apresentou instabilidades do tipo colapso ou fraturamento induzido, esta dissertação trabalha na implementação de um algoritmo capaz de obter a magnitude da tensão horizontal máxima que levou ao surgimento dos mesmos. As fraturas Induzidas são falhas de tração, enquanto os Breakouts são gerados pelo colapso da parede do poço por falhas de compressão. Ambos devem ser devidamente identificados a partir de perfis de imagem. Os algoritmos implementados envolvem solução analítica, calculada através de métodos implícito e explícito. O procedimento para a rotação das tensões para poços inclinados é baseado em formulação presente na literatura, e os cálculos das tensões ao redor da parede do poço, nas equações de Kirsch. O fraturamento do material é avaliado de acordo com a tensão de cut-off, e o de ruptura, a partir do critério de Mohr-Coulomb ou Lade-Ewy. Os métodos desenvolvidos são comparados entre si, relatando suas vantagens e desvantagens. Aplicando uma vasta variação de inclinação e azimute do poço, os resultados alcançados apresentam uma diferença pequena com relação aos obtidos por meio de pacotes comerciais, sendo considerados satisfatórios. / [en] The occurrence of oil and gas well drilling events is common, but undesirable, once it increases time and cost of operations. Its occurence can lead to loss of fluid circulation, wellbore wall collapse, restriction of its functionality, platform damage, environmental issues and even the lost of human lives. stresses knowledge is essential to wellbore stability estimation and to the improvement of drilling safety. In fact, there are some methods and tests to compute the minimum horizontal stress, but there still exist difficulties on maximum horizontal stress determination. In the case of deviated wells, the calculations are even more complexes due to the lack of alignment between the regional stresses and well axis. Identified that problem, and considering that at least one wellbore has been drilled in a field and presented compressive or tensile instabilities, this dissertation works on the implementation of algorithms capable of obtaining the maximum horizontal stress magnitude that lead the appearance of breakout or induced fracture. The instability problems are identified and previously interpreted through image logs. The implemented algorithms involve an analytical solution, which is calculated by an explicit method and an implicit one, to the stated problem. The procedure to the stresses rotation on deviated wells used at this work is based on the formulation presented on technical literature, and the calculation of the stresses around the wellbore wall, on Kirsch s equation. The failure of the material is evaluated using a tensile cutoff for induced fractures and Mohr-Coulomb or Lade-Ewy criteria for breakouts. The developed methods are compared between each other, presenting the advantages and disadvantages of then. The results, applying a large variation on the wellbore inclination and azimuth, show that the values accomplished a low difference in relation to the obtained by using a commercial software, being considered as satisfactory.