Premium
Analytical 2D model to invert hydraulic pumping tests in fractured rocks with fractal behavior
Author(s) -
Delay Frederick,
Porel Gilles,
Bernard Stephane
Publication year - 2004
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/2004gl020500
Subject(s) - scaling , fractal , fractal dimension , geology , box counting , statistical physics , geotechnical engineering , mechanics , mathematical analysis , fractal analysis , mathematics , geometry , physics
A solution to interference pumping tests in fractal fractured media of Euclidean dimension two has been developed. It is proposed in dimensioned variables with a pre‐conditioning of its most sensitive parameter and a Gauss‐Newton inversion. The method allows for a rapid identification of hydrodynamic parameters by fitting experimental data. The fractal dimension and the scale exponent of the hydraulic diffusion are also determined without any other calculation or reference to a theoretical medium. Thus, the results provide a reliable appraisal of how the hydrodynamic parameters evolve with the size of the system. This feature has important applications in hydrology and petroleum engineering especially when up‐scaling approaches are needed.