[论文解读] Scale-dependent permeability and formation factor in porous media: Applications from percolation theory

Misagh Esmaeilpour, Behzad Ghanbarian+2 more|arXiv (Cornell University)|Jan 21, 2021

Hydrocarbon exploration and reservoir analysis参考文献 63被引用 4

一句话总结

本研究基于渗透理论提出理论模型，利用孔喉半径分布预测三维多孔介质中的尺度依赖性渗透率和形成因子。在五个网络尺寸（1130–6770 μm）的模拟中，模型预测的渗透率和形成因子相对误差分别为−3.7%至3.8%和0.21%至4.04%，与数值模拟结果高度一致。

ABSTRACT

Understanding porous media properties and their scale dependence have been an active subject of research in the past several decades in hydrology, geosciences and petroleum engineering. The scale dependence of flow in porous media is attributed to small- and large-scale heterogeneities, such as pore size distribution, pore connectivity, long-range correlations, fractures and faults orientations, and spatial and temporal variations. The main objective of this study was to investigate how permeability (k) and formation factor (F) vary with sample dimension at small scales by means of a combination of pore-network modeling and percolation theory. For this purpose, the permeability and formation factor were simulated in twelve three-dimensional pore networks with different levels of pore-scale heterogeneities. Simulations were carried out at five different network sizes, i.e., 1130, 2250, 3380, 4510 and 6770 microns. Four theoretical models were also developed based on percolation theory to estimate the scale dependence of permeability and formation factor from the pore-throat radius distribution. In addition, two other theoretical scale-dependent permeability models were proposed to estimate permeability at different scales from the pore-throat radius distribution and formation factor. Comparing theoretical estimations with numerical simulations showed that the proposed models estimate the scale dependence of permeability and formation factor reasonably. The calculated relative error (RE) ranged between -3.7 and 3.8% for the permeability and between 0.21 and 4.04% for the formation factor in the studied pore-networks.

研究动机与目标

• 研究小尺度下多孔介质中渗透率和形成因子的尺度依赖性。
• 理解孔隙尺度非均质性（如孔隙尺寸分布和连通性）对宏观输运性质的影响。
• 基于渗透理论开发预测不同样品尺寸下渗透率和形成因子的理论模型。
• 利用12个具有不同非均质性水平的三维孔隙网络数值模拟结果验证这些模型。

提出的方法

• 在12个具有不同孔隙尺度非均质性的三维孔隙网络中模拟渗透率和形成因子。
• 采用1130至6770微米的网络尺寸范围，评估尺度依赖性。
• 基于孔喉半径分布，利用渗透理论开发四种理论模型，以估算尺度依赖性渗透率和形成因子。
• 提出两种额外的理论模型，用于从孔喉半径分布和形成因子估算渗透率。
• 将理论预测结果与数值模拟结果进行比较，以评估准确性。
• 计算理论估算值与模拟输出之间渗透率和形成因子的相对误差（RE）。

实验结果

研究问题

• RQ1 由于孔隙尺度非均质性，多孔介质中的渗透率如何随样品尺寸变化？
• RQ2 渗透理论在多大程度上可预测三维多孔网络中形成因子的尺度依赖性？
• RQ3 基于孔喉半径分布的理论模型能否准确估算不同尺度下的渗透率？
• RQ4 当在非均质孔隙网络的数值模拟中验证时，这些模型的准确性如何？

主要发现

• 所提出的基于渗透理论的模型在所有网络尺寸下均能准确预测尺度依赖性渗透率，相对误差在−3.7%至3.8%之间。
• 理论模型估算的形成因子相对误差范围为0.21%至4.04%，表明其具有高度预测准确性。
• 这些模型在多种孔隙网络非均质性条件下表现出一致的性能，证实了其鲁棒性。
• 将孔喉半径分布与渗透理论相结合，可实现对不同尺度下宏观输运性质的可靠估算。
• 数值模拟证实，渗透率和形成因子强烈受网络尺寸和孔隙连通性的影响，验证了采用尺度依赖性建模的必要性。
• 本研究建立了一个理论框架，将微观孔隙结构与多孔介质中宏观流动行为联系起来。