Erro variável para modelos especiais que descrevem a transição frágil-dúctil Variável de erro para modelos especiais

  • Orlando Zambrano Mendoza Escuela de Ingeniería de Petróleo. Facultad de Ingeniería, Universidad del Zulia, Apartado postal 4011-A-526. Maracaibo, Zulia, Venezuela.
  • Peter P. Valko Harold Vance Department of Petroleum Engineering Texas A&M University 3116 TAMU College Station, TX 77843-3116
  • James E. Russell Harold Vance Department of Petroleum Engineering Texas A&M University 3116 TAMU College Station, TX 77843-3116

Resumo

Este artigo mostra a aplicação da metodologia baseada no método error in variables (EIV) para ajustar o envelope no plano das principais tensões efetivas, considerando o envelope e descrevendo a transição frágil-dúctil e o colapso dos poros (modelo cap). As equações paramétricas do envelope de rutura foram obtidas através da introdução do conceito de elasticidade dos poros de Biot, representando o estado de tensões pela tensão efetiva média e pela tensão equivalente. Uma forma algébrica não linear representa as equações do envelope, delimitando a região de transição frágil a dúctil do envelope de quebra ou rendimento. Para ilustrar a aplicação desta metodologia, foram utilizadas as informações de resistência frágil e tensão de rendimento à compactação para o arenito de Bentheim e as tensões principais normalizadas para dez arenitos diferentes, nas quais o comportamento de transição frágil para dúctil é descrito. Os resultados mostram que o método EIV fornece uma maneira simples de obter a representação paramétrica do envelope no plano de tensão efetivo principal, descrevendo o mecanismo de deformação da rocha testada que envolve o efeito de colapso dos poros.

Downloads

Não há dados estatísticos.

Referências

Addis, M. (1987). Material metastability in weakly cemented sedimentary rocks. Memoir of the Geological Society of China, 9, 495.

Anand, A., Kumar, S. (2015). Application of multi-objective optimization techniques to geotechnical engineering problems. M. Tech. Thesis. Rourkela: National Institute of Technology.
Biot, M. (1941). General theory of three-dimensional consolidation. Journal of Apply Physics, 12, 182.

Britt, H., Luecke, R. (1973). The estimation of parameters in nonlinear, implicit models. Technometrics, 15, 233.

Chen, W., Mizumo, E. (1990). Nonlinear analysis in soil mechanics: theory and implementation. New York: Elsevier Science.
Deming, W. (1943). Statistical adjustment of data. New York: Willey.

Edgar, T., Liebman, M., Kim, I. (1990). Robust error-in-variables estimation using nonlinear programming techniques. AIChE Journal, 36(7), 985-993.

Esposito, W., Floudas, C. (1998). Parameter estimation in nonlinear algebraic models via global optimization. Computers and Chemical Engineering, 22, 213-220.

Keles, T. (2018). Comparison of classical least squares and orthogonal regression in measurement error models. International Online Journal of Educational Sciences, 10(3), 200-221.

Keles, T., Altun, M. (2016). Comparison of classical least squares and orthogonal regression in measurement error models. Journal of Measurement and Evaluation in Education and Psychology, 7(2), 296-308.

Klein, E., Baud, P., Reuschle, T., Wong, T. (2001). Mechanical behaviour and faliure mode of bentheim sandstone under triaxial compression. Physical Chemical Earth (A), 26(1-2), 21-25.

Kumar, S., Kumar, P. (2011). Parameter optimization of rock failure criterion using error-in-variables approach. International Journal of Geomechanics, 11(1), 36-43.

Liebman, M., Edgar, T. (1988). Data reconciliation for nonlinear processes. Proceedings of the AIChE Annual Meeting. Washington, DC: American Institute of Chemical Engineers (AIChE), 137.

Nur, A., Byerlee, J. (1971). An exact effective stress law for elastic deformation of rock with fluids. Journal of Geophysical Research, 76, 6414.

O’Neil, M., Sinclair, I., Smith, F. (1969). Polynomial curve fitting when abscissas and ordinates are both subject to error. Computer Journal, 12, 52-56.

Peneloux, A., Deyrieux, E., Neau, E. (1976). The maximum likelihood test and the estimation of experimental inaccuracies: application to data reduction for vapor-liquid equilibrium. Journal of Computers, 73, 706-716.

Recio-López, J. (2021). Regresión lineal ortogonal. Pensamiento Matemático, XI (1), 005015.

Reilly, P., Patino-Leal, H. (1981). Bayesian study of the error-in-variables model. Technometrics, 23(3), 221.

Schwetlick, H., Tiller, V. (1985). Numerical methods for estimating parameters in nonlinear models with error in the variables. Technometrics, 27(1), 17-24.

Smits, R., de Wall, J., van Kooten, J. (1988). prediction of abrupt reservoir compaction and surface subsidence caused by pore collapse in carbonates. SPEFE (March), 340-346.

Southwell, W. (1969). Fitting experimental data. Journal of Computational Physics, 4, 465-474.

Terzagui, K. (1943). Theoretical soil mechanics. New York: Wiley.
Valkó, P., Vajda, S. (1987). An extended Marquardt-type procedure for fitting error-in-variables models. Computational Chemical Engineering, 11(1), 37-43.

Von Mises, R. (1913). Mechanik der festen Körper im plastisch deformablen Zustand, Nachrichten von der Königlichen Gesellschaft der Wissenschaften zu Göettingen. Mathematisch-physikalische Klasse, 1, 582592.

Willianson, J. (1968). Least squares fitting of a straight line. Canadian Journal of Physics, 46, 1845-1847.

Wong, T. E., David, C., Zhu, W. (1997). The transition from brittle faulting to cataclastic flow in porous sandstones: mechanical deformation. Journal of Geophysical Research, 102, 3009-3025.

York, P. (1966). Least squares fitting of a straight line. Canadian Journal of Physics, 44(5), 1079-1086.

Zambrano-Mendoza, O., Valkó, P., Russell, J. (2023). Determination of the shear failure envelope by adjusting with the statistical method of error in variables through the relationship between the principal stresses. Revista Técnica de la Facultad de Ingeniería de la Universidad del Zulia, 46, e234613.

Zambrano-Mendoza, O. (2004). Error-in-variables for failure criteria applied to the near-wellbore region. PhD. Dissertation. College Station: Texas A&M University, 134.

Zambrano-Mendoza, O., Valkó, P., Russell, J. (2003). Error-in-variables for rock failure envelope. International Journal of Rock Mechanics and Mining Sciences, 40(1), 137-143.

Zhang, J., Rai, C., Sondergeld, C. (2000). Mechanical strength of reservoir materials: key information for sand prediction. SPE Reservoir Evaluation & Engineering, 3(2), 127-131.
Publicado
2024-12-10
Como Citar
Zambrano Mendoza , O., P. Valko , P. e E. Russell , J. (2024) «Erro variável para modelos especiais que descrevem a transição frágil-dúctil Variável de erro para modelos especiais», Revista Técnica da Faculdade de Engenharia da de Zulia, 47(1), p. e244705. doi: 10.22209/rt.uv4705.
Secção
Artículos de Investigación