Fluids exhibiting non-Newtonian rheologies are used in a range of applications, including hydraulic fracturing, enhanced oil recovery, remediation, and industrial processes. Hydraulic fracturing in particular has received attention from environmental scientists, policy-makers, and the general public due in part to concerns about the possibility of contamination of groundwater resources by the complex and potentially harmful fluids used in the process. The non-Newtonian nature of many hydraulic fracturing fluids complicates the prediction of their movement, and precludes use of most traditional flow and transport models. To improve understanding of the flow of such fluids in porous media, a series of column experiments was conducted and a pore-scale lattice Boltzmann model (LBM) was developed, verified, and used to simulate analogous systems. Flow experiments were conducted with guar gum solutions of varying concentration and three porous media systems. The LBM was developed for transient, three-dimensional porous medium systems and included a shear rate-dependent dynamic viscosity based on the Cross rheological model. The LBM was verified using a semi-analytical solution for Cross model fluid flow, OpenFOAM simulations, and grid resolution inter-comparisons between two different solution approaches. Simulations were performed on synthetic porous medium systems produced with a sphere packing algorithm to approximate the properties of the experimental systems. The simulations were in good agreement with the experimental results, particularly for systems that exhibited the greatest non-Newtonian character. The modeling approach developed in this work provides a valuable tool for investigating relationships between pore-scale fluid flow and macroscale variables of interest for simulating movement of non-Newtonian fluids at larger scales.

表现出非牛顿流变性的流体可用于多种应用，包括水力压裂，提高采油率，修复和工业过程。特别是水力压裂受到了环境科学家，政策制定者和公众的关注，部分原因是担心该过程中使用的复杂且潜在有害的流体可能污染地下水资源。许多水力压裂液的非牛顿性质使它们运动的预测变得复杂，并且排除了使用大多数传统流动和运输模型的可能性。为了更好地理解这种流体在多孔介质中的流动，进行了一系列的柱实验，并开发，验证了孔尺度晶格玻尔兹曼模型（LBM），并用于模拟类似系统。用不同浓度的瓜尔胶溶液和三种多孔介质系统进行流动实验。LBM是为瞬态三维多孔介质系统开发的，包括基于交叉流变模型的剪切速率相关的动态粘度。通过使用用于交叉模型流体流动的半分析解决方案，OpenFOAM模拟以及两种不同解决方案方法之间的网格分辨率互比较来验证LBM。对用球形填充算法生产的合成多孔介质系统进行了模拟，以近似实验系统的性能。仿真与实验结果非常吻合，特别是对于那些表现出最大非牛顿特性的系统。