Analytical 2D model to invert hydraulic pumping tests in fractured rocks with fractal behavior

Abstract

[1] 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.

Understanding diagnostic plots for well-test interpretation

“…Using the diagnostic plot allows for the replacement of all these specialized tools with a simple and unique approach that can be applied to any new solutions, as it has been done for example by Hamm and Bideaux (1996), Delay et al (2004), or Beauheim et al (2004). Today most of the theoretical works related to well testing include diagnostic plots both in hydrogeology and the petroleum industry.…”

A new method of data inversion for the identification of fractal characteristics and homogenization scale from hydraulic pumping tests in fractured aquifers

“…Thus, D cannot be determined without a prior guess on h, and vice versa. Recently, Delay et al (2004) have proposed an approximate solution for cylindrical radial flow (Euclidean dimension d = 2) in a fractal fractured medium, but handling dimensional variables. This solution can be inverted directly on observation data and does not require any additional modeling exercise or prior information to get all the parameters, including D and h.…”

“…Then the method by Delay et al (2004) for obtaining the dimensional solution is shown. This solution is compared to the Chang and Yortsos model under various conditions to address its relevance and accuracy.…”

Analysis of slug-tests with high-frequency oscillations

“…One of the specific research topics explored in the HES is the investigation of spatial variability of hydrodynamic parameters by multiple hydraulic-tests in the geometric well array (Delay et al, 2004). As a part of this study, a large number of slug tests (about 100) were performed in order to estimate the hydraulic conductivity of the aquifer in the vicinity of boreholes.…”