不同胶结度的多孔介质中溶质横向弥散的孔隙尺度模拟研究

doi:10.13745/j.esf.sf.2023.9.32

摘要/Abstract

摘要：

深入理解、精确刻画溶质孔隙尺度横向弥散行为是揭示溶质运移现象内在机制、提高溶质运移模拟精度的关键。基于孔隙尺度模拟方法研究了不同胶结度的多孔介质中溶质横向弥散特征。结果表明:当胶结度增大时,溶质横向弥散程度有所增强,但与纵向弥散相比增强幅度较小,且在模拟的胶结度范围内横向弥散未展现显著的尺度效应。研究还发现多孔介质中横向弥散系数D_T与纵向弥散系数D_L间的差异程度不是固定不变的,而是随着溶质运移距离逐渐增大最终达到稳态的过程,并且D_L/D_T的渐进值及达到渐进值所需时间均受胶结度的影响。因此,将D_T视为比D_L小一个数量级的值与溶质实际弥散行为存在较大偏差。同时,通过对比不同介质中流体流速横向、纵向分量概率密度及溶质对流速率概率密度的差异,揭示了以上溶质横向弥散特征变化及其与纵向弥散特征变化不同的内在机制。

关键词: 横向弥散, 多孔介质, 胶结度, 孔隙尺度, 数值模拟

Abstract:

Deeply understanding and accurately characterizing the transverse dispersion behavior of solutes at the pore scale is crucial for unveiling the internal mechanisms of solute transport phenomena and enhancing the precision of solute transport simulations. In this study, utilizing a pore-scale simulation method, we have investigated the transverse dispersion behavior of solutes in porous media with varying degrees of cementation. The findings of this research are as follows: The transverse dispersion of solutes increases with the cementation degree, although the degree of enhancement is lower compared to longitudinal dispersion. The transverse dispersion does not exhibit a significant scale effect within the range of simulated cementation degrees. The study revealed that the difference between the transverse diffusion coefficient (D_T) and the longitudinal diffusion coefficient (D_L) in all media is not constant but gradually increases, eventually reaching a steady state with solute transport. Both the asymptotic value of D_L/D_T and the time required to reach this value are influenced by the cementation degree. There is a notable discrepancy between assuming D_T to be one order of magnitude smaller than D_L and the actual solute dispersion behavior. By comparing the probability density of the lateral and longitudinal components of flow velocity and the probability density of the advective rate of solutes in different media, this paper elucidates the internal mechanisms underlying the variations in solute transverse dispersion characteristics and highlights the differences between transverse and longitudinal dispersion behaviors.

Key words: transverse dispersion, porous media, cementation degree, pore scale, numerical simulation

中图分类号:

P641.2
X523

侯玉松, 胡晓农, 吴吉春. 不同胶结度的多孔介质中溶质横向弥散的孔隙尺度模拟研究[J]. 地学前缘, 2024, 31(3): 59-67.

HOU Yusong, HU Xiaonong, WU Jichun. Pore scale simulation study of transverse dispersion of solute in porous media with different cementation degrees[J]. Earth Science Frontiers, 2024, 31(3): 59-67.

图/表 8

图1 多孔介质结构及胶结过程(a)和不同时刻溶质粒子空间分布图(b)

Fig.1 Schematic diagram of porous medium structure and bonding process (a), and spatial distribution of solute particles at different times (b)

表1 介质属性

Table 1 Properties of porous media

多孔介质	孔隙率n	平均粒径r_avg/mm	胶结体积比例P_c/%
PM43	0.43	2.00	0.0
PM35	0.35	2.12	2.26
PM30	0.30	2.20	4.67
PM25	0.25	2.28	8.13

图2 横向上溶质羽空间二阶中心矩M2,T(a)和纵向上溶质羽空间二阶中心矩M2,L(b)的模拟结果及幂律拟合曲线

Fig.2 Second spatial central moment along the transverse direction M2,T(a) and the second spatial central moment along the longitudinal direction M2,L(b)

表2 溶质弥散特征

Table 2 Solute dispersion characteristics

多孔介质	m_T	m_L	D_T,asym/(m²·s^-1)	(D_L/D_T)_asym	t_asym/s
PM43	1.029	1.037	1.50×10^-8	14.40	1 080
PM35	0.988	1.016	1.76×10^-8	25.71	1 080
PM30	1.007	1.073	2.23×10^-8	31.04	1 896
PM25	1.003	1.295	2.48×10^-8	77.59	7 500

图3 不同介质中溶质横向弥散系数DT(a)和纵向弥散系数DL(b)

Fig.3 Solute transverse dispersion coefficient DT (a) and longitudinal dispersion coefficient DL (b) in different media

图4 不同介质中溶质纵向弥散系数与横向弥散系数的比值DL/DT

Fig.4 The ratio of longitudinal dispersion coefficient of solute to transverse dispersion coefficient in different media DL /DT

图5 不同介质中流体横向流速分量及纵向流速分量的概率密度分布(PDF)

Fig.5 Probability density distributions (PDF) of transverse |vx|/|vx|avg and longitudinal |vz|/|vz|avg flow velocity components in different media

图6 不同介质中溶质横向对流速率及纵向对流速率的概率密度分布(PDF)

Fig.6 Probability density distributions (PDF) of solute transverse and longitudinal advective rates in different media

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