Estudio y evaluación de los modelos matemáticos para la estimación de la dilatancia
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Universidad Industrial de Santander
Abstract
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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.
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.
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.
Keywords
Sanding, Dilatancy, Critical condition, Granular soil, Arenamiento, Dilatancia, Estado crítico, Suelos granulares