Summary
Fracture-network mapping and estimation of its permeability constitute two
major steps in static-model preparation of naturally fractured reservoirs.
Although several different analytical methods were proposed in the past for
calculating fracture-network permeability (FNP), different approaches are still
needed for practical use. We propose a new and practical approach to estimate
FNP using statistical and fractal characteristics of fracture networks. We also
provide a detailed sensitivity analysis to determine the relative importance of
fracture-network parameters on the FNP in comparison to single-fracture
conductivity using an experimental-design approach.
The FNP is controlled by many different fracture-network parameters such as
fracture length, density, orientation, aperture, and single-fracture
connectivity. Five different 2D fracture data sets were generated for random
and systematic orientations. In each data set, 20 different combinations of
fracture density and length for different orientations were tested. For each
combination, 10 different realizations were generated. The length was
considered as constant and variable. This yielded a total of 1,000 trials. The
FNPs were computed through a commercial discrete-fracture-network (DFN)
modeling simulator for all cases. Then, we correlated different statistical and
fractal characteristics of the networks to the measured FNPs using
multivariable-regression analysis. Twelve fractal (sandbox, box counting, and
scanline fractal dimensions) and statistical (average length, density,
orientation, and connectivity index) parameters were tested against the
measured FNP for synthetically generated fracture networks for a wide range of
fracture properties. All cases were above the percolation threshold to obtain a
percolating network, and the matrix effect was neglected.
The correlation obtained through this analysis using four data sets was
tested on the fifth one with known permeability for verification. High-quality
match was obtained.
Finally, we adopted an experimental-design approach to identify the
most-critical parameters on the FNP for different fracture-network types. The
results are presented as Pareto charts.
It is believed that the new method and results presented in this paper will
be useful for practitioners in static-model development of naturally fractured
reservoirs and will shed light on further studies on modeling and understanding
the transmissibility characteristics of fracture networks. It should be
emphasized that this study was conducted on 2D fracture networks and could be
extended to 3D models. This, however, requires further algorithm development to
use 2D fractal characteristics for 3D systems and/or development of fractal
measurement techniques for a 3D system. This study will provide a guideline for
this type of research.
© 2009. Society of Petroleum Engineers
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History
- Original manuscript received:
27 January 2008
- Meeting paper published:
29 March 2008
- Revised manuscript received:
9 September 2008
- Manuscript approved:
22 September 2008
- Published online:
1 June 2009
- Version of record:
1 June 2009
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