The intrinsic permeability is a crucial parameter to characterise and quantify fluid flow through porous media. However, this parameter is typically uncertain, even if the geometry of the pore structure is available. In this paper, we perform a comparative study of experimental, semi-analytical and numerical methods to calculate the permeability of a regular porous structure. In particular, we use the Kozeny–Carman relation, different homogenisation approaches (3D, 2D, very thin porous media and pseudo 2D/3D), pore-scale simulations (lattice Boltzmann method, Smoothed Particle Hydrodynamics and finite-element method) and pore-scale experiments (microfluidics). A conceptual design of a periodic porous structure with regularly positioned solid cylinders is set up as a benchmark problem and treated with all considered methods. The results are discussed with regard to the individual strengths and limitations of the used methods. The applicable homogenisation approaches as well as all considered pore-scale models prove their ability to predict the permeability of the benchmark problem. The underestimation obtained by the microfluidic experiments is analysed in detail using the lattice Boltzmann method, which makes it possible to quantify the influence of experimental setup restrictions.

Solid particles immersed in a fluid can be found in many engineering, environmental or medical fields. Applications are suspensions, sedimentation processes or procedural processes in the production of medication, food or construction materials. While homogenized behavior of these applications is well understood, contributions in the field of pore-scale fully resolved numerical simulations with non-spherical particles are rare. Using Smoothed Particle Hydrodynamics (SPH) as a simulation framework, we therefore present a modeling approach for Direct Numerical Simulations (DNS) of single-phase fluid containing non-spherically formed solid aggregates. Notable and discussed model specifications are the surface-coupled fluid–solid interaction forces as well as the contact forces between solid aggregates. The focus of this contribution is the numerical modeling approach and its implementation in SPH. Since SPH presents a fully resolved approach, the construction of arbitrary shaped particles is conveniently realizable. After validating our model for single non-spherical particles, we therefore investigate the motion of solid bodies in a Newtonian fluid and their interaction with the surrounding fluid and with other solid bodies by analyzing velocity fields of shear flow with respect to hydromechanical and contact forces. Results show a dependency of the motion and interaction of solid particles on their form and orientation. While spherical particles move to the centerline region, ellipsoidal particles move and rotate due to vortex formation in the fluid flow in between.

<p>Over the last two decades, Digital Rock Physics (DRP) has become a complementary part of the characterization of reservoir rocks due to, among other things, the non-destructive testing character of this technique. The use of high-resolution X-ray Computed Tomography (XRCT) has become widely accepted to create a digital twin of the material under investigation. Compared to other imaging techniques, XRCT technology allows a location-dependent resolution of the individual material particles in volume. However, there are still challenges in assigning physical properties to a particular voxel within the digital twin, due to standard histogram analysis or sub-resolution features in the rock. For this reason, high-resolution image-based data from XRCT, transmitted-light microscope, Scanning Electron Microscope (SEM) as well as inherent material properties like porosity are combined to obtain an optimal spatial image of the studied Ruhr sandstone by a geologically driven segmentation workflow. On the basis of a homogeneity test, which corresponds to the evaluation of the grayscale image histogram, the preferred scan sample sizes in terms of transport, thermal, and effective elastic rock properties are determined. In addition, the advanced numerical simulation results are compared with laboratory tests to provide possible upper limits for sample size, segmentation accuracy, and a calibrated digital twin of the Ruhr sandstone. The comparison of representative grayscale image histograms as a function of sample sizes with the corresponding advanced numerical simulations, provides a unique workflow for reservoir characterization of the Ruhr sandstone.</p>

Over the last 3 decades, Digital Rock Physics (DRP) has become a complementary part of the characterization of reservoir rocks due to the non-destructive testing character of this technique. The use of high-resolution X-ray Computed Tomography (XRCT) has become widely accepted to create a digital twin of the material under investigation. Compared to other imaging techniques, XRCT technology allows a location-dependent resolution of the individual material particles in volume. However, there are still challenges in assigning physical properties to a particular voxel within the digital twin, due to standard histogram analysis or sub-resolution features in the rock. For this reason, high-resolution image-based data from XRCT, transmitted-light microscope, Scanning Electron Microscope (SEM) as well as geological input properties like geological diagenesis, mineralogical composition, sample’s microfabrics, and estimated sample’s porosity are combined to obtain an optimal spatial segmented image of the studied Ruhr sandstone. Based on a homogeneity test, which corresponds to the evaluation of the gray-scale image histogram, the preferred scan sample sizes in terms of permeability, thermal, and effective elastic rock properties are determined. In addition, these numerically derived property predictions are compared with laboratory measurements to obtain possible upper limits for sample size, segmentation accuracy, and a geometrically calibrated digital twin of the Ruhr sandstone. The comparison corresponding gray-scale image histograms as a function of sample sizes with the corresponding advanced numerical simulations provides a unique workflow for reservoir characterization of the Ruhr sandstone.

Solid particles immersed in a fluid can be found in many engineering, environmental or medical fields. Applications are suspensions, sedimentation processes or procedural processes in the production of medication, food or construction materials. While homogenized behavior of these applications is well understood, contributions in the field of pore-scale fully resolved numerical simulations with non-spherical particles are rare. Using Smoothed Particle Hydrodynamics (SPH) as a simulation framework, we therefore present a modelling approach for Direct Numerical Simulations (DNS) of single-phase fluid containing non-spherically formed solid aggregates. Notable and discussed model specifications are the surface-coupled fluid-solid interaction forces as well as the contact forces between solid aggregates. The focus of this contribution is the numerical modelling approach and its implementation in SPH. Since SPH presents a fully resolved approach, the construction of arbitrary shaped particles is conveniently realizable. After validating our model for single non-spherical particles, we therefore investigate the motion of solid bodies in a Newtonian fluid and their interaction with the surrounding fluid by analyzing velocity fields of shear flow with respect to hydromechanical and contact forces. Results show a dependency of the motion and interaction of solid particles on their form and orientation. While spherical particles move to the centerline region, ellipsoidal particles move and rotate due to vortexes formation in the fluid flow in between.