2021, Haruzi, Peleg, Katsman, Regina, Halisch, Matthias, Waldmann, Nicolas, Spiro, Baruch

This paper presents a detailed description and evaluation of a multi-methodological petrophysical approach for the comprehensive multi-scale characterization of reservoir sandstones. The suggested methodology enables the identification of links between Darcy-scale permeability and an extensive set of geometrical, textural and topological rock descriptors quantified at the pore scale. This approach is applied to the study of samples from three consecutive sandstone layers of Lower Cretaceous age in northern Israel. These layers differ in features observed at the outcrop, hand specimen, petrographic microscope and micro-CT scales. Specifically, laboratory porosity and permeability measurements of several centimetre-sized samples show low variability in the quartz arenite (top and bottom) layers but high variability in the quartz wacke (middle) layer. The magnitudes of this variability are also confirmed by representative volume sizes and by anisotropy evaluations conducted on micro-CT-imaged 3-D pore geometries. Two scales of directional porosity variability are revealed in quartz arenite sandstone of the top layer: the pore size scale of ∼0.1 mm in all directions and ∼3.5 mm scale related to the occurrence of high- and low-porosity horizontal bands occluded by Fe oxide cementation. This millimetre-scale variability controls the laboratory-measured macroscopic rock permeability. More heterogeneous pore structures were revealed in the quartz wacke sandstone of the intermediate layer, which shows high inverse correlation between porosity and clay matrix in the vertical direction attributed to depositional processes and comprises an internal spatial irregularity. Quartz arenite sandstone of the bottom layer is homogenous and isotropic in the investigated domain, revealing porosity variability at a ∼0.1 mm scale, which is associated with the average pore size. Good agreement between the permeability upscaled from the pore-scale modelling and the estimates based on laboratory measurements is shown for the quartz arenite layers. The proposed multi-methodological approach leads to an accurate petrophysical characterization of reservoir sandstones with broad ranges of textural, topological and mineralogical characteristics and is particularly applicable for describing anisotropy and heterogeneity of sandstones on various rock scales. The results of this study also contribute to the geological interpretation of the studied stratigraphic units.

2018, Zhang, Zeyu, Kruschwitz, Sabine, Weller, Andreas, Halisch, Matthias

We investigate the pore space of rock samples with respect to different petrophysical parameters using various methods, which provide data on pore size distributions, including micro computed tomography (μ-CT), mercury intrusion porosimetry (MIP), nuclear magnetic resonance (NMR), and spectral-induced polarization (SIP). The resulting cumulative distributions of pore volume as a function of pore size are compared. Considering that the methods differ with regard to their limits of resolution, a multiple-length-scale characterization of the pore space is proposed, that is based on a combination of the results from all of these methods. The approach is demonstrated using samples of Bentheimer and Röttbacher sandstone. Additionally, we compare the potential of SIP to provide a pore size distribution with other commonly used methods (MIP, NMR). The limits of resolution of SIP depend on the usable frequency range (between 0.002 and 100 Hz). The methods with similar resolution show a similar behavior of the cumulative pore volume distribution in the overlapping pore size range. We assume that μ-CT and NMR provide the pore body size while MIP and SIP characterize the pore throat size. Our study shows that a good agreement between the pore radius distributions can only be achieved if the curves are adjusted considering the resolution and pore volume in the relevant range of pore radii. The MIP curve with the widest range in resolution should be used as reference.

2021, Costabel, Stephan, Hiller, Thomas

Geophysical nuclear magnetic resonance (NMR) applications are used to estimate pore size distributions (PSDs) of rocks and sediments. This is commonly realized by empirical calibration using information about the surface-to-volume ratio of the material. Recent research has developed joint inversion concepts for NMR relaxation data that provides the PSD with a minimum of information. The application requires the NMR signal of a sample at saturation and at least one at partial saturation and at known suction. The new inversion concept physically simulates the desaturation process as part of the forward operator. The cross-section of the model capillaries in the underlying bundle can be either circular or triangular. Our study investigates the performance of the NMR joint inversion to predict water retention function (WRF) and capillary-based hydraulic conductivity (Kcap) as functions of saturation for different sands. The angularity of the pores has no significant impact on the estimated WRF but affects the Kcap estimation significantly. Our study shows that the WRF is predicted reliably for sand samples under fast diffusion conditions. The Kcap estimations are also plausible but tend to systematic overestimation, for which we identified the tortuosity being the main reason. Because NMR relaxation data generally do not provide tortuosity information, a plausible tortuosity model remains an issue of classical calibration. Further development of the approach will thus consider tortuosity measurements (e.g., by electrical resistivity measurements and/or gradient NMR) and will consider the relaxation mechanisms outside fast diffusion conditions to enhance its applicability for coarse soils.

2018, Costabel, Stephan, Weidner, Christoph, Müller-Petke, Mike, Houben, Georg

The capability of nuclear magnetic resonance (NMR) relaxometry to characterise hydraulic properties of iron-oxide-coated sand and gravel was evaluated in a laboratory study. Past studies have shown that the presence of paramagnetic iron oxides and large pores in coarse sand and gravel disturbs the otherwise linear relationship between relaxation time and pore size. Consequently, the commonly applied empirical approaches fail when deriving hydraulic quantities from NMR parameters. Recent research demonstrates that higher relaxation modes must be taken into account to relate the size of a large pore to its NMR relaxation behaviour in the presence of significant paramagnetic impurities at its pore wall. We performed NMR relaxation experiments with water-saturated natural and reworked sands and gravels, coated with natural and synthetic ferric oxides (goethite, ferrihydrite), and show that the impact of the higher relaxation modes increases significantly with increasing iron content. Since the investigated materials exhibit narrow pore size distributions, and can thus be described by a virtual bundle of capillaries with identical apparent pore radius, recently presented inversion approaches allow for estimation of a unique solution yielding the apparent capillary radius from the NMR data. We found the NMR-based apparent radii to correspond well to the effective hydraulic radii estimated from the grain size distributions of the samples for the entire range of observed iron contents. Consequently, they can be used to estimate the hydraulic conductivity using the well-known Kozeny–Carman equation without any calibration that is otherwise necessary when predicting hydraulic conductivities from NMR data. Our future research will focus on the development of relaxation time models that consider pore size distributions. Furthermore, we plan to establish a measurement system based on borehole NMR for localising iron clogging and controlling its remediation in the gravel pack of groundwater wells.

2016, Peche, Aaron, Halisch, Matthias, Bogdan Tatomir, Alexandru, Sauter, Martin

In this case study, we present the implementation of a finite element method (FEM)-based numerical pore-scale model that is able to track and quantify the propagating fluid–fluid interfacial area on highly complex micro-computed tomography (μ-CT)-obtained geometries. Special focus is drawn to the relationship between reservoir-specific capillary pressure (pc), wetting phase saturation (Sw) and interfacial area (awn). The basis of this approach is high-resolution μ-CT images representing the geometrical characteristics of a georeservoir sample. The successfully validated 2-phase flow model is based on the Navier–Stokes equations, including the surface tension force, in order to consider capillary effects for the computation of flow and the phase-field method for the emulation of a sharp fluid–fluid interface. In combination with specialized software packages, a complex high-resolution modelling domain can be obtained. A numerical workflow based on representative elementary volume (REV)-scale pore-size distributions is introduced. This workflow aims at the successive modification of model and model set-up for simulating, such as a type of 2-phase problem on asymmetric μ-CT-based model domains. The geometrical complexity is gradually increased, starting from idealized pore geometries until complex μ-CT-based pore network domains, whereas all domains represent geostatistics of the REV-scale core sample pore-size distribution. Finally, the model can be applied to a complex μ-CT-based model domain and the pc–Sw–awn relationship can be computed.