Numerical simulation method for reactive solute transport based on micro-continuum medium model
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摘要:
地下环境中流固间的反应溶质运移过程控制着地质介质演化规律, 并受岩石固有非均质性的影响, 衍生出非线性行为与多尺度效应。为了面向更为复杂化的应用需求, 解析微观特征与表观行为间的响应-反馈机制成为了重要的科学与工程命题。本研究系统地介绍了微观连续介质概念与模型框架, 以及该模型方法的实现方式, 并归纳了其在不同研究体系中的应用实例, 最后重点分析了该方法在实验-数值联合研究中的发展前景与预期挑战。数值模拟方法已被广泛应用于反应溶质运移过程的定量研究之中, 但单一孔隙或达西尺度数值模型难以应对机理研究与实例应用间的时空尺度跨度。近年来多尺度数值模拟方法体系不断发展, 其中将Darcy-Brinkman-Stokes方程作为多流态数学统一表达, 以微观连续介质模型作为多尺度信息关联方式的数值模拟框架, 在流固界面追踪、高效数值求解等方面展现出一定的方法优势与应用潜力。
Abstract:Significance Fluid-solid interactions in reactive solute transport processes, governed by physical and chemical heterogeneities, dictate the evolution of subsurface geomaterials, resulting in nonlinear behaviours and multiscale features. It has become increasingly evident that examining the feedback between microscopic features and macroscopic behaviours in geomaterials is critical in various academic and industrial applications.
Progress In this study, we introduce the concept and framework, mathematical and numerical models of the micro-continuum medium, as well as multiscale solvers and applications. Challenges in co-designed simulations and experiments are also discussed.
Conclusion and Prospects Despite offering valuable insights into reactive transport processes, continuum-scale modelling or pore-scale modelling suffers from a gap between theoretical understanding and computational prediction. Recently, an alternative conceptualization of the multiscale problem involves the implementation of the Darcy-Brinkman-Stokes (DBS) equation in a single micro-continuum domain to identify reactive transport patterns across spatial scales under changing flow regimes. As fluid-solid interfaces cannot be explicitly resolved as in pore-scale models, the micro-continuum medium approach has the advantage of accommodating complex geometries or evolving interfaces without increasing computational costs.
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图 1 微观层次特征时间影响下的反应溶质运移模式示意图(据文献[6]修改)
a.孔隙结构概念图;b.不同反应模式下流固界面附近的浓度分布;c, d.2类反应模式主控机制示意图。
tadv为对流特征时间;tdiff为扩散特征时间;treac为反应特征时间Figure 1. Schematic diagram of reactive solute transport phenomena from a microscopic characteristic time
图 4 反应速率与扩散系数变化下的碳酸岩溶蚀演化模式(据文献[31]修改)
a.反应溶质运移模式图;b.面状溶蚀模式;c.锥状蚓孔模式;d.单枝蚓孔模式;e.分枝状蚓孔模式;f.均匀溶蚀模式; Pe, DaⅠ.无量纲参数
Figure 4. Calcite dissolution pattern controlled by different reaction rates and diffusion coefficients
图 5 非均质介质中生物膜生长特征模拟(据文献[32]修改)
a.微米CT灰度图像;b.孔隙度空间分布;c.不同模型硝酸盐穿透曲线对比
Figure 5. Numerical investigation of biofilm growth in heterogeneous porous media
图 6 裂隙型介质溶蚀过程中的隙宽及浓度场演化(据文献[51]修改)
a.裂隙隙宽及浓度场演化;b.裂隙-不可渗透基质的演化过程;c.裂隙-可渗透基质的演化过程
Figure 6. Evolution of fracture aperture and concentrations in fracture media during dissolution
图 7 裂隙型白云岩溶蚀演化特征数值模拟结果(据文献[42]修改)
a. 80 h酸蚀后的裂隙面与改造层空间结构; b. 80 h酸蚀后裂隙-孔隙介质中流场分布; c.80 h多矿物反应速率剖面(纵横比2∶1)
Figure 7. Numerical simulation results of fractured dolomite dissolution evolution
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