Determination of the Effective Viscosity of Non-newtonian Fluids Flowing Through Porous Media
Determination of the Effective Viscosity of Non-newtonian Fluids Flowing Through Porous Media
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DOI：
10.3389/fphy.2019.00071
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发表时间：
2019-05-30
影响因子：
3.1
通讯作者：
Holzner, Markus
中科院分区：
文献类型：
--
作者：
Eberhard, Ursin;Seybold, Hansjoerg J.;Holzner, Markus
当非牛顿流体流过多孔介质时，孔隙空间的拓扑结构会产生较宽范围的流速和剪切速率。因此，流体的局部粘度也在空间中变化，与达西速度呈非线性相关。因此，通常用有效粘度mu(eff)来描述达西标度下的流动。对于大多数非牛顿流体，流体的流变性可以通过剪切速率的（非线性）函数来描述。目前的方法通过首先主要通过采用流变学幂律模型并包括经验校正因子来计算有效剪切速率来估计有效粘度。在第二步中，将平均剪切速率与流体的实际流变性一起使用来计算 mu(eff)。在这项工作中，我们使用 Carreau 型流体推导了局部粘度曲线的半解析表达式，这是比幂律模型更广泛适用的模型。通过求解毛细管圆形横截面中的流动方程，我们能够直接计算平均粘性阻力作为局部粘性的空间平均值。这种方法避开了经典毛细管束模型的使用，并允许将平均孔径达到达西尺度的孔隙中的粘度分布放大。与常用的毛细管束模型不同，所提出的方法既不需要弯曲度也不需要渗透率作为输入参数。因此，我们的模型仅使用多孔介质的特征长度尺度，不需要经验系数。将所提出的模型与在单分散球形珠填充床上进行的流动池实验进行比较表明，我们的方法仅使用流体的物理流变学、孔隙率和估计的平均孔径即可表现良好，而无需确定有效剪切率。我们的模型与流动实验和现有模型的良好一致性表明，平均粘度是有效达西粘度 mu(eff) 的良好估计，为多孔介质中非牛顿流动的放大提供了物理见解。
When non-Newtonian fluids flow through porous media, the topology of the pore space leads to a broad range of flow velocities and shear rates. Consequently, the local viscosity of the fluid also varies in space with a non-linear dependence on the Darcy velocity. Therefore, an effective viscosity mu(eff) is usually used to describe the flow at the Darcy scale. For most non-Newtonian flows the rheology of the fluid can be described by a (non linear) function of the shear rate. Current approaches estimate the effective viscosity by first calculating an effective shear rate mainly by adopting a power-law model for the rheology and including an empirical correction factor. In a second step this averaged shear rate is used together with the real rheology of the fluid to calculate mu(eff). In this work, we derive a semi-analytical expression for the local viscosity profile using a Carreau type fluid, which is a more broadly applicable model than the power-law model. By solving the flow equations in a circular cross section of a capillary we are able to calculate the average viscous resistance directly as a spatial average of the local viscosity. This approach circumvents the use of classical capillary bundle models and allows to upscale the viscosity distribution in a pore with a mean pore size to the Darcy scale. Different from commonly used capillary bundle models, the presented approach does neither require tortuosity nor permeability as input parameters. Consequently, our model only uses the characteristic length scale of the porous media and does not require empirical coefficients. The comparison of the proposed model with flow cell experiments conducted in a packed bed of monodisperse spherical beads shows, that our approach performs well by only using the physical rheology of the fluid, the porosity and the estimated mean pore size, without the need to determine an effective shear rate. The good agreement of our model with flow experiments and existing models suggests that the mean viscosity is a good estimate for the effective Darcy viscosity mu(eff) providing physical insight into upscaling of non-Newtonian flows in porous media.