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

卷 7, 册 2, 2016, pp. 99-106
DOI: 10.1615/SpecialTopicsRevPorousMedia.2016017276
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摘要

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.

对本文的引用
  1. XU PENG, LIU HAICHENG, SASMITO AGUS PULUNG, QIU SHUXIA, LI CUIHONG, EFFECTIVE PERMEABILITY OF FRACTURED POROUS MEDIA WITH FRACTAL DUAL-POROSITY MODEL, Fractals, 25, 04, 2017. Crossref

  2. Wang Wen-Dong, Su Yu-Liang, Zhang Qi, Xiang Gang, Cui Shi-Ming, Performance-based fractal fracture model for complex fracture network simulation, Petroleum Science, 15, 1, 2018. Crossref

  3. WANG ZHIYUAN, YANG ZHENGMING, DING YUNHONG, HE YING, LIN WEI, WANG WENDONG, SHENG GUANGLONG, A MULTI-LINEAR FRACTAL MODEL FOR PRESSURE TRANSIENT ANALYSIS OF MULTIPLE FRACTURED HORIZONTAL WELLS IN TIGHT OIL RESERVOIRS INCLUDING IMBIBITION, Fractals, 27, 01, 2019. Crossref

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