[论文解读] Modélisation à l'échelle des pores de l'écoulement non newtonien dans les milieux poreux

Taha Sochi|SPIRE - Sciences Po Institutional REpository|Oct 1, 2007

Rheology and Fluid Dynamics Studies被引用 24

一句话总结

本研究提出一种孔隙尺度网络模型，利用砂粒堆和Berea砂岩的体素图像生成的三维拓扑无序网络，模拟多孔介质中的非牛顿流体流动。该模型采用迭代数值方法和埃利斯（Ellis）与赫施尔-巴克利（Herschel-Bulkley）模型的解析流动定律，成功预测了埃利斯流体的实验数据，并开发了新型算法以模拟屈服应力流体和黏弹性流体，包括针对博伊斯塔-马纳罗（Bautista-Manero）模型的改进型塔迪（Tardy）算法，在收敛-发散几何结构中展现出有希望的初步结果。

ABSTRACT

The thesis investigates the flow of non-Newtonian fluids in porous media using pore-scale network modeling. Non-Newtonian fluids show very complex time and strain dependent behavior and may have initial yield stress. Their common feature is that they do not obey the simple Newtonian relation of proportionality between stress and rate of deformation. They are generally classified into three main categories: time-independent, time-dependent and viscoelastic. Two three-dimensional networks representing a sand pack and Berea sandstone were used. An iterative numerical technique is used to solve the pressure field and obtain the flow rate and apparent viscosity. The time-independent category is investigated using two fluid models: Ellis and Herschel-Bulkley. The analysis confirmed the reliability of the non-Newtonian network model used in this study. Good results are obtained, especially for the Ellis model, when comparing the network model results to experimental data sets found in the literature. The yield-stress phenomenon is also investigated and several numerical algorithms were developed and implemented to predict threshold yield pressure of the network. An extensive literature survey and investigation were carried out to understand the phenomenon of viscoelasticity with special attention to the flow in porous media. The extensional flow and viscosity and converging-diverging geometry were thoroughly examined as the basis of the peculiar viscoelastic behavior in porous media. The modified Bautista-Manero model was identified as a promising candidate for modeling the flow of viscoelastic materials which also show thixotropic attributes. An algorithm that employs this model was implemented in the non-Newtonian code and the initial results were analyzed. The time-dependent category was examined and several problems in modeling and simulating the flow of these fluids were identified.

研究动机与目标

• 开发一种能够模拟复杂多孔结构中非牛顿流体流动的孔隙尺度网络模型。
• 研究时间无关性、黏弹性和时间依赖性非牛顿流体在真实多孔介质网络中的行为。
• 将模型与埃利斯和赫施尔-巴克利流体的实验数据进行验证，并评估其在屈服应力预测中的局限性。
• 开发并实现数值算法，以预测多孔网络中的临界屈服压力。
• 将模型扩展至模拟黏弹性行为，特别是采用基于塔迪算法的改进型博伊斯塔-马纳罗模型。

提出的方法

• 从砂粒堆和Berea砂岩的三维体素图像构建三维拓扑无序孔隙网络，保留孔隙大小、形状和连通性。
• 为孔隙和喉道分配形状因子（面积与周长平方之比），以反映实际横截面几何形态。
• 采用迭代数值技术求解压力场，并计算网络中的总体积流量和表观黏度。
• 对于时间无关性流体，基于埃利斯和赫施尔-巴克利模型，采用单管流动的解析表达式。
• 对于黏弹性流动，实现了一种改进的塔迪算法，以模拟收敛-发散几何结构中的稳态行为。
• 采用两种算法预测屈服应力临界压力：记忆入侵渗流法（IPM）和新型最小压力路径法（PMP），后者计算效率更高。

实验结果

研究问题

• RQ1 与实验数据相比，孔隙尺度网络模型在预测埃利斯和赫施尔-巴克利流体流动行为方面的准确性如何？
• RQ2 屈服应力流体预测中的差异由何引起？网络结构与流动导率如何影响屈服阈值？
• RQ3 收敛-发散几何结构如何影响多孔介质中黏弹性流体的行为？
• RQ4 改进的塔迪算法能否正确模拟稳态黏弹性效应，包括剪切变稀和弹性行为？
• RQ5 在模拟时间依赖性非牛顿流体时存在哪些局限性和挑战？如何解决？

主要发现

• 该网络模型对埃利斯流体的实验数据预测具有良好一致性，证实了模型在剪切变稀、时间无关性行为中的可靠性。
• 对于赫施尔-巴克利流体，预测精度较低，主要由于屈服应力过程中孔隙几何形状的表征不足，而不仅仅是流动导率问题。
• 最小压力路径（PMP）算法在立方网络中与IPM算法预测结果完全一致，在随机网络中也得到相似结果，且计算效率更高。
• PMP与IPM算法预测的临界屈服压力低于实际网络模拟结果，这是由于对流动回溯假设存在差异。
• 针对博伊斯塔-马纳罗模型的改进型塔迪算法在黏弹性行为中表现出定性正确的趋势，支持其作为未来弹性与触变性研究的基础。
• 实现结果表明，收敛-发散几何结构显著影响黏弹性效应，尤其在剪切变稀和弹性恢复现象中。