Porosity in naturally fractured media: A fractal classification

  • Ma. Eugenia Miranda-Martínez Posgrado en Ciencias de la Tierra, Instituto de Geología, Universidad Nacional Autónoma de México, Circuito de la Investigación Científica s/n, Ciudad Universitaria, Del. Coyoacán, Apartado Postal 70296, 04510 México D.F.
  • Klaudia Oleschko Centro de Geociencias, Universidad Nacional Autónoma de México, Campus Juriquilla, Apdo. Postal 1-742, 76001, Querétaro, Qro., México.
  • Jean-Francois Parrot Instituto de Geografía, Universidad Nacional Autónoma de México, Circuito de la Investigación Científica s/n, Ciudad Universitaria, Del. Coyoacán, 04510 México D.F.
  • Fernando Castrejón-Vacio Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas Norte No. 152, 07730 México D.F.
  • Hind Taud Instituto Mexicano del Petróleo, Eje Central Lázaro Cárdenas Norte No. 152, 07730 México D.F.
  • Fernando Brambila-Paz Departamento de Matemáticas, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Del. Coyoacán, 04510, México D.F.
Keywords: fractal dimension, X-ray tomography, digital images, structure, porosity, fractured media.

Abstract

The flow and distribution of fluids through pores in porous media are governed by their geometry. The self-similar behavior of the structure of these sets has been the subject of numerous studies that have documented the power laws relationship, among the principal measures of pores and solids, and the resolution of the method used for their analysis. A fractal scheme is introduced in order to extract and measure some geometric features of pores, using the mean values of their fractal classifiers, dividing these in global (firmagram) and local (reference line) classifiers. The mass fractal dimension (Dm), the spectral dimension or fracton (⎯d), the Hurst exponent (H) and the lacunarity (L) of naturally fractured reservoirs (YNF) of southeastern Mexico, have shown to be statistically different for the three most representative porosity sets: fractures, cavities and mixed porosity. The fractal classifiers, extracted from digital images obtained using X-ray computerized tomography, were useful for porosity classification in different patterns, starting from the core images. Dm and⎯d must be determined on presegmented images, which distinguish the pore and solid sets, prior to the fractal quantification, while H and L can be extracted from the original image, which drastically diminishes the bias in the porosity estimation. All fractal classifiers, including mass dimensions and lacunarity of the porosity patterns specified above for YNF, showed a statistically significant correlation with the porosity of the geological strata as determined by traditional techniques. All our results offer new perspectives for the modeling and forecasting of porosity in the naturally fractured deposits.

 

Published
2018-04-18
Section
Articles