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

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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.