Implementing a stochastic approach along with the conventional wellbore stability analysis enables to take into account uncertainty from input data in order to obtain more realistic and reliable predictions which improve decision making process in drilling operations. By means of the methodology proposed, the uncertainty assessment for each parameter can be addressed through distinct methods depending on available information, and a sensitivity analysis is used as complement to the Monte Carlo Simulation to identify those lesser impact variables which can be treated as deterministic values and so that processing time is reduced. As result of this workflow, quantified uncertainties are propagated into model and probability distributions for collapse and fracture mud weights are generated, and a mud weight window as a function of success probability for drilling without instability problems is built. Ultimately, a study case is developed to assess the probabilistic mud weight window for a drilling process in a Cretaceous Colombian formation.

*A quien debe dirigirse la correspondencia RESUMEN el artículo muestra una revisión bibliográfi ca de los principales modelos que existen para el cálculo de la dilatancia en la roca. una vez explicado cada modelo, se procede a realizar el modelamiento matemático de ésta propiedad. Esto se realiza mediante datos suministrados por la literatura, las cuales son: esfuerzos sometidos a la roca σ1,σ2,σ3, ángulo de fricción interna ∅, pendiente de la línea de estado critico M, el parámetro de estado , y otras constantes que se requieren para cada modelo. Una vez hechos los cálculos de la dilatancia en la roca, se procede a validar el modelamiento con datos reales, los cuales también son suministrados por la literatura. En éstas pruebas se midió la dilatancia real en dos tipos de arena, (Banding y Miga) y se realizaron 5 pruebas. Finalmente éstas mediciones se compararon con los cálculos realizados, y así llegar a la conclusión de que el mejor modelo para predecir el fenómeno dilatante de una roca es el de Li & Dafalias.Palabras clave: Arenamiento, dilatancia, estado crítico, suelos granulares. Study and evaluation of mathematical models for estimating dilatancyABSTRACT the article shows a literature review of the main models that exist for the calculation of dilatancy in the rock, which is a property that has an application in the study of the phenomenon of sanding in oil wells. Having explained each model, we proceed to perform mathematical modeling of this property. This is done using data supplied by the literature, which are: strain in the rock σ1, σ2, σ3, internal friction angle ∅, slope of the critical state line M, the state parameter φ, and other constants which are required for each model. Once dilatancy calculations are made in the rock, we proceed to validate the modeling with real data, which are also supplied by the literature. in these tests, the dilatancy was measured in two types of sand, (Banding and crumb) from which 5 tests were done; these measurements were compared with calculations, and fi nally concludes that the best model to predict the dilatant rock phenomenon is Li & Dafalias.

*a quien debe dirigirse la correspondencia RESUMEN el objetivo de este trabajo es analizar el impacto del índice de fragilidad en el fracturamiento hidráulico de formaciones de shale gas a nivel mundial y defi nir parámetros para identifi car zonas de interés o sweet spots fracturables en shale plays prospectos.Se realizó una revisión bibliográfi ca de las propiedades petrofísicas y mecánicas que exhiben diversas formaciones de shale gas en países como estados unidos, China, Holanda, noruega, Dinamarca y suecia. una vez estructurada la base de datos, se calcularon índices de fragilidad utilizando diferentes métodos teniendo en cuenta la composición mineralógica y los módulos elásticos estáticos y dinámicos de cada formación de shale estudiada.El cálculo de índices de fragilidad en profundidad y su relación con el contenido orgánico total permitió identifi car posibles sweet spots para las formaciones de shale gas de mayor prospección. Adicionalmente, el análisis de la relación entre el índice de fragilidad y el comportamiento mecánico de dichas formaciones permitió determinar que fl uido de fractura es el apropiado para utilizar en caso de realizar un fracturamiento hidráulico en la zona de interés.Palabras clave: shale gas, fracturamiento hidráulico, índice de fragilidad, módulos elásticos, mineralogía, sweet spot. Brittleness analysis to identify sweet spots in shale gas formations ABSTRACThe purpose of this paper is to analyze the impact of the Brittleness index in hydraulic fracturing on shale gas formations worldwide, and thereby defi ne parameters to identify fraccable feasibly sweet spots in prospects shale plays.A literature review was made so as to gather the largest amount of petrophysical and mechanical data from shale gas formations from countries all over the world such as United States, China, Holland, Norway, Denmark and Sweden. Once available the data, different methods were used to calculate the brittleness index of each study case considering the effect of the mineralogical composition and elastic moduli (static and dynamic).The relation between the brittleness index at depth and the total organic carbon allowed to identify possible sweet spots within each prospect formation. Additionally, the analysis of brittleness index and mechanical behavior of those formations permitted to stablish which fracture fl uid should be used in case of a hydraulic fracturing stimulation at the sweet spot.

Sand production in oil and gas wells is a complex problem that requires a multidisciplinary analysis and the use of new methodologies and technologies to be solved, which often requires a combination of several of them to arrive at an optimal solution of the problem and thus increase the productivity of oil fields.This comprehensive strategy must start from the drilling, continue in the completion and extends to the production stage. To implement this strategy, a methodology that includes the integration of field and laboratory data and is complemented by an assessment Geomechanics was developed.In the industry there is no software that would make a comprehensive evaluation and analysis described in the previous methodology, therefore it is designed a tool for this purpose, which allows to automate and streamline the decision-making process (developing optimal workflows to reduce evaluation times per well to 50%) and create a friendly graphic environment for the user.The tool includes the following modules: Production, completion and perforation. The Production module includes: selection of wells and quantification of costs associated with interventions by sanding problems, diagnostic charts for root cause analysis of the problem of sand production, characterization graphs of intervals with sand production (mineralogy and grain size), selection of alternatives for management and / or exclusion of sand, production modeling, technical and economic evaluation of selected alternatives, etc.. The completion and drilling module includes: Evaluation of tables of well logs and identification of sensitive areas to the sanding beginning from them, predictive modeling of sand production, conventional perforating optimal design, underbalance optimal, oriented perforating, etc.As a case study, the application of software tools to assess the problem of sanding in the Lisama 166 Well in Colombia, is shown, in which the frequency of interventions was reduced in more than 100% and was increased the productivity, with recommendations implemented.Finally, conclusions and recommendations obtained in this study are shown.

Sand production in oil and gas wells is a complex problem that requires an integral analysis of rock mechanics, mineralogy, granulometry, etc. that allows a risk management in order to make the best technical and economic decision. In this study the background, strategy used in the past and in the present to tackle the problem of sanding, and Cases of evaluation of alternatives SEM (sand exclusion and management) in the recent history of the fields Casabe, Lisama, Galán, Llanito and Bonanza, located in the basin of the Middle Magdalena Valley in Colombia, are shown. The effects of water injection and the gravel packing, in the low drainage and repression of the reservoir in the Casabe field are shown. These effects are: injected water distribution, behavior of pressure and sand cleaning jobs in packaged and unpackaged wells, production, effective injectivity and bsw before and after the gravel packings, number of wells packaged, abandoned producer wells, injectors collapsed, etc. Also mentioned are other factors that affected the low drainage and the repression of the reservoir, such as: reservoir heterogeneity, granulometry (% fines), mineralogy (migratory and swelling clays, etc.). After Casabe field experience, the problem was approached very conservatively, limited at the drawdown control and the use of special metallurgy and sand cleaning jobs, etc. Today the problem is focusing differently, considering new technologies and an integral analysis of the reservoir. To carry out the above, the methodology SEM (Sand Exclusion and Management) was developed for the selection and technical-economic evaluation of alternatives of exclusion and/or management of sand during drilling; completion and production, which including probabilistic risk analysis. The following case studies are presented in this article: Application of the methodology SEMEvaluation and implementation of sand exclusion and management technologies Chemical Consolidation (Laboratory)Chemical Treatment (Laboratory – Oil field)Screen Less Frac (Oil field)Artificial Lift Experiences With Sand ProductionAcoustic MonitoringGeomechanics applied to reduce risk of sanding during drilling, completion and productionDesign and Implementation of Software Tool Finally, conclusions and recommendations obtained in this study are shown.