MODELAGEM DE FRATURAMENTO HIDRÁULICO UTILIZANDO O MÉTODO ESTENDIDO DOS ELEMENTOS FINITOS (XFEM)
DOI:
https://doi.org/10.26512/ripe.v2i8.21747Keywords:
Geomecânica. Fraturamento Hidráulico. Método Estendido dos Elementos Finitos. Modelo de Zona Coesiva. Método dos Nós Fantasmas.Abstract
Um dos principais objetivos da engenharia de petróleo é desenvolver e aplicar técnicas capazes de aumentar a produtividade de poços de petróleo, incluindo a estimulação do maciço rochoso através de operações de fraturamento hidráulico. Estudos sobre a propagação de fraturas podem ser feitos analiticamente para situações simplificadas envolvendo homogeneidade, isotropia e condições de contorno simples, ou por meio de métodos numéricos, como o método dos elementos finitos para casos mais complexos. A aplicação da formulação convencional do método dos elementos finitos tem a desvantagem de necessitar a atualização da malha de elementos à medida que a fratura se propaga, o que implica em maior esforço computacional e perda de precisão numérica na transferência de resultados da antiga para a nova malha. A aplicação do método estendido dos elementos finitos, em conjunto com o modelo de zona coesiva, apresenta a vantagem da fratura não ser fisicamente modelada, dispensando sucessivas gerações de malha. Neste artigo é apresentada uma simulação de fraturamento hidráulico comparando resultados analíticos com soluções numéricas obtidas pelo método estendido dos elementos finitos em modelagens bidimensionais (estado plano de deformação) e tridimensionais.
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References
ABAQUS, 2014. ABAQUS Documentation. Version 6.14. Adachi, J. I., 2001.Fluid-driven fracture in permeable rock. PhD. Thesis, Univ. of Minnesota, Minneapolis.
Adachi, J., Siebrits, E., Peirce, A. & Desroches, J. (2007). Computer simulation of hydraulic fractures. Int. J. Rock Mech. Min. Sci. 44: 19.
Barenblatt, G.I., 1959. The formation of equilibrium cracks during brittle fracture: general ideas and hypotheses. Journal of Applied Mathematics and Mechanics 23:22”“36.
Barenblatt, G.I., 1962. The mathematical theory of equilibrium cracks in brittle fracture. Advances in Applied Mechanics 7:55”“129.
Béchet E., Minnebo H., Moës N. e Burgardt B., 2005. Improved implementation and robustness study of the X-FEM for stress analysis around cracks. International Journal for Numerical Methods in Engineering 64:1033”“1056.
Bunger, A. P., Detournay, E., Garagash, D. I., 2005. Toughness-Dominated Hydraulic Fracture with Leak-Off, International Journal of Fracture, vol. 134, pp.175-190
Carrier B., Granet S., 2012.Numerical Modeling Of Hydraulic Fracture Problem In Permeable Medium Using Cohesive Zone Model, Engineering Fracture Mechanics, vol. 79, pp. 312”“328
Detournay, E., Adachi, J., Garagash, D. I., Savitski, A., 2006. Interpretation and Design of Hydraulic Fracturing Treatments, United States Patent No. US 7111681B2
Dugdale, D.S., 1960. Yielding of steel sheets containing slits. Journal of the Mechanics and Physics of Solids 8:100”“104.
Garagash, D. I., Detournay, E., Adashi, J., 2011. Multiscale Tip Asymptotics in Hydraulic Fracture with Leak-Off, J. Fluid Mech., vol. 669, pp. 260”“297.
Geertsma, J. & Klerk, F. (1969). A Rapid Method of Predicting Width and Extent of Hydraulically Induced Fractures. J. Pet. Technol. 21: 1571-1581.
Guangming, Z., Chunming, X., Jiandong, L., Juan, J. & Luhe, S. (2011). Finite element analysis method for horizontal well hydraulic fracturing. SREE Conference on Engineering Modeling and Simulation 12: 8.
Hansbo A e Hansbo P., 2004. A finite element method for the simulation of strong and weak discontinuities in solid mechanics. Computer Methods in Applied Mechanics and Engineering 193:3523 ”“ 3540.
Laborde P., Pommier J., Renard Y. e Salaün M., 2005. High-order extended finite element method for cracked domains. International Journal for Numerical Methods in Engineering 64:354”“381.
Li, L. C., Tang, C.A, Li, G., Wang, S.G., Liang, Z.Z. & Zhang, Y.B. (2012). Numerical simulation of 3D hydraulic fracturing based on an improved flow-stress-damage model and a parallel FEM technique. Rock Mech. Rock Eng. 45: 18.
Moes N., Dolbow J. e Belytschko T., 1999. A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering 46: 131”“150.
Papanastasiou, P., 1999. The effective fracture toughness in hydraulic fracturing, International Journal of Fracture 96, pp. 127-147.
Perkins, T. K. & Kern, L.R. (1961). Widths of Hydraulic Fracture. J. Pet. Sci. Technol. 89: 937-949.
Rabczuk T., Zi G., Gerstenberger A. e Wall W.A., 2008. A new crack tip element for the phantom node method with arbitrary cohesive cracks. International Journal of Numerical Methods in Engineering 75(5): 577-599.
Sarris, E. & Papanastasiou, P. (2012). Modeling of hydraulic fracturing in a poroelastic cohesive formation. Int. J. Geomech. 12: 8.
Song, J. H., Areias, P. M. A. e Belytschko, T. , 2006. A method for dynamic crack and shear band propagation with phantom nodes. International Journal for Numerical Methods in Engineering 67: 868”“893.
Yew, C. H., Mechanics of Hydraulic Fracturing, Gulf Publishing Company, Houston, TX, 1997.
Zhang, G. M., Liu, H., Zhang, J., Wu, H.A. & Wang, X.X. (2010). Three-dimensional finite element simulation and parametric study for horizontal well hydraulic fracture. J. Pet. Sci. Eng.: 8.
Zielonka, M. G., Searles K. H., 2014. Development and validation of fully-coupled hydraulic fracturing simulation capabilities, Simulia Community Conference.
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