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Special Topics & Reviews in Porous Media: An International Journal

ISSN Print: 2151-4798
ISSN Online: 2151-562X

Special Topics & Reviews in Porous Media: An International Journal

DOI: 10.1615/SpecialTopicsRevPorousMedia.2016017276
pages 99-106

A FAST CALCULATION METHOD FOR ESTIMATING THE REPRESENTATIVE ELEMENTARY VOLUME OF A THREE-DIMENSIONAL FRACTURE NETWORK

Na Huang
School of Engineering, Nagasaki University, 1-14 Bunkyo-machi, 8528521 Nagasaki, Japan; State Key Laboratory of Mining Disaster Prevention and Control, Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, P.R. China
Yujing Jiang
School of Engineering, Nagasaki University, 1-14 Bunkyo-machi, 8528521 Nagasaki, Japan; State Key Laboratory of Mining Disaster Prevention and Control, Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, P.R. China
Richeng Liu
School of Engineering, Nagasaki University, 1-14 Bunkyo-machi, 8528521 Nagasaki, Japan; State Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, P.R. China
Bo Li
Rock Mechanics and Geo-Hazards Center, Shaoxing University, Shaoxing 312000, P.R. China

ABSTRACT

A new approach to estimate the representative elementary volume (REV) of the 3-D DFN (discrete fracture network) (DFN) model is proposed. In this method fractures are modeled as circular discks of arbitrary size, orientation, and location. A total of 400 3-D fracture networks with different densities were established, with fractures following well-known statistical distributions. For each fracture density, ten 3-D DFN models with different random numbers are generated, from which smeller square models with side lengths varying from 2 m to 20 m are extracted. The fractal dimensions of these models were calculated using a box-counting method. The parameter RMSNorm was used to quantify the variance of fractal dimensions for DFN models with different random numbers and estimate the size of REV. Results show that the variance of the calculated fractal dimensions decreases significantly with the increasing model size, which justifies the existence of a REV. When taking RMSNorm < 0.05 as a good approximation of the stochastic DFN model to be an equivalent continuum, the calculated REV size would decrease with the increasing fracture network density. A linear expression between fractal dimension and REV size is proposed. This equation can be used to approximate the REV size of the 3-D DFN model in the case where only fracture geometric properties are available.