Flow in porous media in the weak inertia regime visualized by µ-PIV and MRI velocimetry

我们对裂隙多孔介质中单相流和多相流中发生的物理过程的演变的基本理解对科学界来说具有更高的重要性。就现实生活的影响而言，对这些过程的彻底了解将增加我们在地下水文、地球物理、油藏工程和生物力学领域的应用清单。虽然蠕动流区的低流速可以用达西的S关系式来描述，但对于Forchheimer提出的显著增加的流速，必须考虑更高阶的附加项。对于纯蠕动流态和纯湍动流态，已经有了大量的工作，但没有出现在两者之间，更具体地说，是在弱惯性流区，即两个极端之间的过渡。鉴于这种实验证据的缺乏，我们的目标是以高空间分辨率将日益复杂的系统中的弱惯性区域的流场从2D映射到3D。首先，我们研究了具有单通道、重复通道-孔隙单元的2D微观模型，以及具有粗糙孔隙表面的2D模型裂缝。这些系统可以将2D微粒子成像测速仪(Micro-PIV)与3D血流敏感磁共振成像(MRI)相结合。为了匹配这两种方法的分辨率，还使用MRI来确定空间分辨率传播算子，以允许分辨率体素内的速度场。然后，它们充当速度场的代理，并可应用于3D和不透明系统。在第二步中，我们研究了第一个3D系统，一个均匀的多孔玻璃圆柱体。在低速时，在达西关系的意义上，人们期望通过所有的孔隙产生整体效应。随着雷诺数的增加，尾流区变大，流动路径被拉伸。到目前为止所获得的知识现在将用于项目的第二个主要部分，用于水力压裂天然岩心的调查。为了研究流动，天然岩心将被垂直破裂，这是斯图加特大学目前可用的一项技术。对于磁共振成像，这种天然的多孔介质需要使用多层双极梯度对脉冲序列来最小化内部梯度效应。与目前所研究的模型系统的不同之处在于，流动是由孔隙系统和裂缝之间的水交换控制的。由此可见，随着达西流型向弱惯性流型的转变，优先流型会随着静止区域的发展而发展。这些实验获得的三维流场随后可用于测试和进一步发展理论方法，如福奇海默的S关系式，以验证其有效性和局限性。

Our fundamental understanding of the evolution of the physical processes taking place during single- and multi-phase flow in fractured porous media is of elevated importance for the scientific community. In terms of real-life implications, a thorough understanding of such processes will enhance our applications inventory in the fields of subsurface hydrology, geophysics, reservoir engineering, and biomechanics. While low flow velocities in the creeping flow regime are best described by Darcy´s relation, additional terms of higher order must be considered for significantly increased velocities as proposed by Forchheimer. There has been a waste number of works for the purely creeping flow regime and the purely turbulent one, but not in between, and more specifically in the weak inertia regime, i.e. the transition between the two extremes. Given this lack of experimental evidence, we aim to map flow fields in the weak inertia regime in systems of increasing complexity from 2D to 3D at high spatial resolution. First, we investigate 2D micromodels with a single channel, a repeating channel-pore unit, and a 2D model fracture with rough pore surfaces. These systems allow the combination of 2D micro-particle imaging velocimetry (micro-PIV) with 3D flow-sensitive magnetic resonance imaging (MRI). To match the resolutions of both methods, MRI is also used to determine spatially resolved propagators that allow resolution of velocity fields within a voxel. They then serve as proxies for velocity fields and can be applied to 3D and opaque systems. In the second step, we investigate the first 3D system, a homogenous porous glass cylinder. At low velocities, one expects bulk effects through all pores in the sense of the Darcy relationship. As the Reynolds numbers increase, larger wake areas appear combined with stretched flow paths. The knowledge gained so far will now be used in the 2nd main part of the project for the investigation of fracked natural cores. To study flow, a natural rock core will be fractured vertically, a technique now available at the University of Stuttgart. With respect to MRI, this natural porous medium requires the use of a multi-slice bipolar gradient pair pulse sequence to minimize internal gradient effects. The difference to the model systems investigated so far is that the flow is controlled by water exchange between the pore system and the fracture. It is therefore to be expected that preferential flow patterns develop along with stationary areas with the transition from Darcy to weak inertia flow regime. These experimentally obtained 3D flow fields are then available to test and further develop theoretical approaches such as Forchheimer´s relation for their validity and limitations.