A stochastic two-dimensional geomechanical model developed by the authors and presented herein is used to analyze wellbore stability in heterogeneous formations. It consists of a finite element model and assumes linear elastic and isotropic material behavior under the plane strain state. The model simulates the stress state around vertical and inclined wellbore when a formation is submitted to internal drilling fluid pressure. This new state of stress may lead to rock failure, which is analyzed through a failure criteria. Since the exact variation of formation’s mechanical properties is not known, a spatially correlated field is used to evaluate the variability of a rock mechanical material property. The correlation between each pair of finite elements is determined by a covariance function. A two-dimensional spatially correlated field is used to verify the correlation between the elements of a vertical wellbore. A different approach, however, is necessary to model inclined wellbores. Once the direction and inclination of a wellbore are defined, a three-dimensional spatially correlated field becomes necessary to best simulate the formation field. Simulations using the stochastic model proposed herein and considering constant elastic modulus have been compared. It is observed that when considering the same elastic modulus along the field, the area of the plastic zone is symmetric at the borehole wall; when using the stochastic model, however, the plastic zone area surrounding the well is not symmetric; thus, the most vulnerable plastic zone may lead to premature failure. Stochastic simulations have been carried out with different heterogeneous fields for vertical and inclined wells, and distributions of the total plastic zone areas are obtained for each case. Based on the stochastic field probabilistic analysis, a distribution function is presented, which aims to define a stability framework analysis to best assist a decision making process in determining if a mud pressure is operationally acceptable or not.

Salt formations are common trap zones for prolific reservoirs. Recent discoveries in the Brazilian coast include light oil carbonate reservoirs below massive salt zones. Well construction challenges in such environments include salt creeping, leaching and proper zonal isolation. This article presents a comprehensive integrated methodology for cementing design which accounts for the following hydraulic aspects: Adequate fluid substitution design supported by numerical simulation considering two phase flow in eccentric annuli and lubrication theoryDownhole pressures in the operational window considering free fall effects for deepwater environmentsOpen hole volume prediction based on salt leaching phenomena due to the circulation of unsaturated fluids. Flow rate fluctuation as a result of free fall is consideredIncrease in salt concentration due to conduction effects after placement and its impact on slurry properties. The methodology is exemplified by two typical scenarios for offshore salt cementing in the Brazilian pre-salt cluster. Slurry design, slurry placement schedules and borehole stability considerations are addressed.

RESUMO: Historicamente, modelos numéricos e analíticos têm sido usados na análise do estado de tensão em poços de petróleo. Modelos analíticos não necessitam necessariamente de propriedades elásticas em suas formulações, modelos numéricos por outro lado, geralmente demandam pelo menos dois parâmetros elásticos em seus modelos constitutivos. Tais propriedades elásticas são, em geral, assumidas constantes em todo o meio, onde a heterogeneidade do material não é considerada nas análises. O presente trabalho avalia funções que melhor representam o campo de propriedades elásticas de um meio heterogêneo. A estrutura do modelo utilizado envolve: (i) um processo estocástico para gerar meios heterogêneos; (ii) a simulação de amostras sob compressão uniaxial para a coleta de deformações na face do sólido (substituindo um método de medição de campo completo); (iii) um algoritmo para cálculo das propriedades elásticas, como módulo de Young e coeficiente de Poisson, e por fim, (iv) apresentar uma regressão de kernel capaz de determinar a função de correlação que melhor descreve as propriedades mecânicas da rocha. Espera-se que o presente método se torne uma eficiente ferramenta em análise de estabilidade de poços de petróleo em processos de perfuração, considerando assim, as incertezas do meio no que diz respeito às propriedades elásticas da formação. PALAVRAS-CHAVE: estabilidade de poços, heterogeneidade das formações, meta-modelagem, propriedades elásticas, análise probabilística. ABSTRACT: Historically, numerical and analytical models have been able to compute stress state at wellbore walls. Analytical approaches usually do not take into account material properties in its formulation. Numerical models, on the other hand, require the knowledge of elastic parameters on their constitutive equations. Such elastic properties are, in general, assumed constant over the rock domain, considering average values obtained from laboratory tests or on-site procedures. In those cases, material heterogeneity is not taken into account. The present work evaluates functions that best describe the elastic properties fields from heterogeneous medium. The model structure involves: (i) a stochastic process for heterogeneous field generation; (ii) simulation of samples under axial compression for strain data collection (mitigating a full-field measurement technique); (iii) an algorithm to compute material properties, such as Young's modulus and Poisson's ratio; and (iv) a meta-model capable of determining a correlation function that best describes rock's mechanical properties. It is expected that the method becomes an efficient tool in wellbore stability analysis in drilling operations, thus considering the medium uncertainty with respect to its elastic properties.