用随机梯度下降优化法估算断裂网络中的幂律分形指数

IF 4.2 2区 地球科学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS
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引用次数: 0

摘要

裂缝对油气勘探有很大影响,因为它们改变了储层岩石中的流体流动特性,形成了一个相互连接的网络。油气储层通常难以评估,而从这些地点获取信息的方法提供的数据过于稀少或空间分辨率较低。而露头岩层则可以直接在现场或利用露头岩层的二维和三维数字图像进行断裂特征描述。这些断裂网络通常与分形传播和幂律分布参数有关,可用作数据源,在根据储层模拟规模进行适当调整后提供有用信息。从这个意义上说,最大似然估计器(MLE)等属性估计器和使用 MLE 的算法,因其与线性回归估计器相比的鲁棒性而被广泛使用。然而,由于幂律特征描述中的挑战,如分布尾部出现的巨大波动,尽管 MLE 很有效,但仍可能获得非最佳值。我们的工作提出使用基于随机梯度下降(SGD)的动量优化算法来获取幂律分布的最佳拟合参数。首先利用合成数据和几个拟合度量对所提出的方法进行了评估,随后利用从储层模拟露头的数字露头模型(DOM)裂缝特征描述中获得的经验数据对该方法进行了评估。基于经验数据的随机 DFN 采样也用于模拟删减效应。结果表明,在使用经验数据时,SGD 方法比其他基于 MLE 的方法提供了更好的分布拟合,而在使用合成数据时,则减少了偏差。在随机 DFN 数据中估计幂律参数时,应用所提出的方法也得到了最佳拟合结果。总之,建议的优化方法被证明是估计幂律分布的一种有价值的替代方法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Stochastic Gradient Descent optimization to estimate the power-law fractal index in fracture networks

Fractures greatly impact hydrocarbon exploration as they modify fluid flow properties within reservoir rocks, creating an interconnected network. The hydrocarbon reservoirs are often difficult to assess, and the methods employed in acquiring information from these locations offer too sparse data or have a low spatial resolution. Otherwise, outcrops allow fracture characterization directly in the field or using 2D and 3D digital representations of outcrops. These fracture networks, usually related to fractal propagation and power-law distribution parameters, can be used as data sources providing useful information when properly adjusted to the reservoir simulation scale. In this sense, attribute estimators, like the Maximum Likelihood Estimator (MLE) and algorithms using MLE, have been widely used for their robustness when compared to linear regression estimators. However, due to the challenges in the power-law characterization, such as the large fluctuations that occur in the tail of the distribution, non-optimum values can be obtained despite the effectiveness of the MLE. Our work proposes the use of an optimization algorithm based on Stochastic Gradient Descent (SGD) with momentum to obtain best-fitting parameters for power-law distributions. The proposed method was first evaluated with synthetic data and several goodness-of-fitness metrics and later using empirical data obtained from fracture characterization in the Digital Outcrop Model (DOM) of a reservoir analogue outcrop. Stochastic DFN sampling based on empirical data was also used to simulate censoring effects. The results showed that the SGD method provided better distribution fitting than other methods based on the MLE when using empirical data while presenting reduced bias when using synthetic data. The estimation of power-law parameters in stochastic DFN data also presented the best-fitting results when applying the proposed method. In conclusion, the proposed optimization method proved a valuable alternative to estimate power-law distributions.

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来源期刊
Computers & Geosciences
Computers & Geosciences 地学-地球科学综合
CiteScore
9.30
自引率
6.80%
发文量
164
审稿时长
3.4 months
期刊介绍: Computers & Geosciences publishes high impact, original research at the interface between Computer Sciences and Geosciences. Publications should apply modern computer science paradigms, whether computational or informatics-based, to address problems in the geosciences.
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