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二维和三维裂缝密度通常对矿山安全设计、裂缝性油气藏储量估计、地下流体在裂缝介质中的运移描述等都是一个重要参数。然而在实际中由于受天然露头和测量条件等因素的限制,裂缝测量工作往往只能在一维上进行(如测线和钻井),而二维密度一般难以直接获得。本文提出了一种以ARC/INFO为平台的裂缝网络一维频度(f)和二维密度测量技术,并辅之于数学实验,以确定测量方法的可靠性。通过对36个天然裂缝网络频度和密度的测量以及相关关系分析,发现了两者之间的线性关系,即:在给定裂缝长度分布函数的前提下,推导出了有量纲裂缝密度(D_1)与无量纲裂缝密度(D_2,D_3)的解析关系。利用这些关系式对已知的36个天然裂缝网络的裂缝密度(D_1)和裂缝度(D_2)进行了计算,最后应用交叉实验法对计算结果作了统计检验。检验结果表明,在给定裂缝长度分布函数后,可在实际中较为准确地利用裂缝一维频度去估算天然裂缝网络的二维裂缝密度,在理论上,也可以进行三维裂缝密度的估算。
Two-dimensional and three-dimensional fracture densities are often an important parameter for mine safety design, estimation of fractured reservoir reserves, and the description of the migration of subsurface fluids in fractured media. In practice, however, due to the limitations of natural outcrops and measurement conditions, the work of measuring fractures often can only be carried out in one dimension (such as surveying and drilling), while the two-dimensional density is generally difficult to obtain directly. In this paper, a one-dimensional frequency (f) and two-dimensional density measurement technique of fracture network based on ARC / INFO is proposed, which is complemented by mathematical experiments to determine the reliability of the measurement method. Through the measurement of the frequency and density of 36 natural fractured networks and the correlation analysis, the linear relationship between the two is found, namely, given the crack length distribution function, D_1) and the dimensionless fracture density (D_2, D_3). Based on these relations, the crack density (D_1) and fracture degree (D_2) of 36 known natural fracture networks are calculated. Finally, the cross-test method is used to test the calculated results. The test results show that the given fracture length distribution function can be used to accurately estimate the two-dimensional fracture density of the natural fracture network in practice. In theory, the three-dimensional fracture density can also be estimated.