Tortuosity estimate through paramagnetic gas diffusion in rock saturated with two fluids using T2 (z, t) low-field NMR

Petrophysical interpretation of 1H NMR relaxation responses from saturated rocks is complicated by paramagnetic species present in fluids. Oxygen dissolved in liquids is one common example. Dipolar interactions of oxygen’s unpaired electron spins with the magnetic moment of fluid nuclei provide a strong relaxation mechanism known as paramagnetic relaxation enhancement (PRE). As a result even low concentrations of dioxygen in its common triplet ground state significantly shorten longitudinal and transverse relaxation times of host fluids. This effect may be employed similarly to any standard tracer technique to study pore connectivity in porous media by detecting a change of oxygen concentration due to diffusion resolved in time and space. Since relaxation enhancement effect is likely stronger in non-wetting phase than in wetting one (where surface relaxation process dominates) this difference can be utilized to study wettability in immiscible multiphase systems. We use a relaxation time contrast between air-saturated and oxygen-free fluids to evaluate oxygen concentration change within two fluid phases saturating rock, to estimate time required to establish equilibrium concentration and to calculate a mutual diffusion coefficient of oxygen. A spatially- and time-resolved T2(z,t) experiment provides the time-dependent oxygen concentration change along the fully- and partially-saturated carbonate core plug exposed to air saturated oil at its inlet. We derive an effective mutual diffusion coefficient of oxygen and accordingly a tortuosity estimate as a function of position along the core and rock saturation. The spatially resolved oxygen diffusion-based tortuosity is compared to simulated conductivitybased tortuosity. The latter is calculated on a high-resolution micro-tomographic image of Mount Gambier limestone by solving the Laplace equation for conductivity

A digital rock physics approach to effective and total porosity for complex carbonates: pore-typing and applications to electrical conductivity

Recent advances in micro-CT techniques allow imaging heterogeneous carbonates at multiple scales and including voxel-wise registration of images at different resolution or in different saturation states. This enables characterising such carbonates at the pore-scale targeting the optimizing of hydrocarbon recovery in the face of structural heterogeneity, resulting in complex spatial fluid distributions. Here we determine effective and total porosity for different pore-types in a complex carbonate and apply this knowledge to improve our understanding of electrical properties by integrating experiment and simulation in a consistent manner via integrated core analysis. We consider Indiana Limestone as a surrogate for complex carbonate rock and type porosity in terms of macro- and micro-porosity using micro-CT images recorded at different resolution. Effective and total porosity fields are derived and partitioned into regions of macro-porosity, micro-porosity belonging to oolithes, and micro-porosity excluding oolithes’ rims. In a second step we use the partitioning of the micro-porosity to model the electrical conductivity of the limestone, matching experimental measurements by finding appropriate cementation exponents for the two different micro-porosity regions. We compare these calculations with calculations using a single cementation exponent for the full micro-porosity range. The comparison is extended to resistivity index at partial saturation, further testing the assignment of Archie parameters, providing insights into the regional connectivity of the different pore types

A numerical analysis of NMR pore-pore exchange measurements using micro X-ray computed tomography

Pore-pore relaxation exchange experiments are a recent development and hold great promise to spectrally derive length scales and connectivity information relevant for transport in porous media. However, for large pores, NMR diffusion-relaxation techniques reach a limit because bulk relaxation becomes dominant. A combination of NMR and Xray-CT techniques could be beneficial and lead to better models for regions of unresolved porosity in CT images, increasing the accuracy of image based calculations of transport properties. In this study we carry out numerical NMR pore-pore exchange experiments on selected Xray-CT images of sandstones and carbonate rock, while at the same time tracking information about the geometry and topology of the pore space. We use pore partitioning techniques and geometric distance fields to relate T2-T2 relaxation exchange spectra to underlying structural quantities. It is shown that T2-T2 pore-pore exchange measurements at room temperatures for the samples considered likely reflect exchange between pores and throats or pores and roughness

Quantitative properties of complex porous materials calculated from X-ray μCT images

A microcomputed tomography (μCT) facility and computational infrastructure developed at the Department of Applied Mathematics at the Australian National University is described. The current experimental facility is capable of acquiring 3D images made up of 20003 voxels on porous specimens up to 60 mm diameter with resolutions down to 2 μm. This allows the three-dimensional (3D) pore-space of porous specimens to be imaged over several orders of magnitude. The computational infrastructure includes the establishment of optimised and distributed memory parallel algorithms for image reconstruction, novel phase identification, 3D visualisation, structural characterisation and prediction of mechanical and transport properties directly from digitised tomographic images. To date over 300 porous specimens exhibiting a wide variety of microstructure have been imaged and analysed. In this paper, analysis of a small set of porous rock specimens with structure ranging from unconsolidated sands to complex carbonates are illustrated. Computations made directly on the digitised tomographic images have been compared to laboratory measurements. The results are in excellent agreement. Additionally, local flow, diffusive and mechanical properties can be numerically derived from solutions of the relevant physical equations on the complex geometries; an experimentally intractable problem. Structural analysis of data sets includes grain and pore partitioning of the images. Local granular partitioning yields over 70,000 grains from a single image. Conventional grain size, shape and connectivity parameters are derived. The 3D organisation of grains can help in correlating grain size, shape and orientation to resultant physical properties. Pore network models generated from 3D images yield over 100000 pores and 200000 throats; comparing the pore structure for the different specimens illustrates the varied topology and geometry observed in porous rocks. This development foreshadows a new numerical laboratory approach to the study of complex porous materials

The influence of syndepositional macropores on the hydraulic integrity of thick alluvial clay aquitards

Clay-rich deposits are commonly assumed to be aquitards which act as natural hydraulic barriers due to their low hydraulic connectivity. Postdepositional weathering processes are known to increase the permeability of aquitards in the near surface but not impact on deeper parts of relatively thick formations. However, syndepositional processes affecting the hydraulic properties of aquitards have previously received little attention in the literature. Here, we analyze a 31 m deep sediment core recovered from an inland clay-rich sedimentary sequence using a combination of techniques including particle size distribution and microscopy, centrifuge dye tracer testing and micro X-ray CT imaging. Subaerial deposition of soils within these fine grained alluvial deposits has led to the preservation of considerable macropores (root channels or animal burrows). Connected pores and macropores thus account for vertical hydraulic conductivity (K) of 4.2×10-1m/s (geometric mean of 13 samples) throughout the thick aquitard, compared to a matrix K that is likely < 10-10m/s, the minimum K value that was measured. Our testing demonstrates that such syndepositional features may compromise the hydraulic integrity of what otherwise appears to have the characteristics of a much lower permeability aquitard. Heterogeneity within a clay-rich matrix could also enhance vertical connectivity, as indicated by digital analysis of pore morphology in CT images. We highlight that the paleo-environment under which the sediment was deposited must be considered when aquitards are investigated as potential natural hydraulic barriers and illustrate the value of combining multiple investigation techniques for characterizing clay-rich deposits

A fast FFT method for 3D pore-scale rock-typing of heterogeneous rock samples via Minkowski functionals and hydraulic attributes

The integration of numerical simulation and physical measurements, e.g. digital and conventional core analysis, requires the consideration of significant sample sizes when heterogeneous core samples are considered. In such case a hierarchical upscaling of properties may be achieved through a workflow of partitioning the sample into homogeneous regions followed by characterization of these homogeneous regions and upscaling of properties. Examples of such heterogeneities are e.g. fine laminations in core samples or different micro-porosity types as consequence of source rock components and diagenesis. In this work we utilize regional measures based on the Minkowski functionals as well as local saturation information derived through a morphological capillary drainage transform as a basis for such a classification/partitioning. An important consideration is the size of the measurement elements utilized, which could be considerable in the case of larger heterogeneities; in such case the calculation of the regional measures can be computationally very expensive. Here we introduce an FFT approach to calculate these measures locally, utilizing their additivity. The algorithms are compared against direct summation techniques and shift-overlap approaches for a selection of different averaging supports to illustrate their speed and practical applicability. We consider a range of artificial Boolean models to illustrate the effect of including hydraulic information on the resulting classifications scheme. This allows the determination of bias, since for these model systems local classes are known ab-initio. The classification framework is tested by comparing to the known initial micro-structure distribution and relative bias quantified in terms of choice of averaging elements (size and shape). Importantly, depending on the actual morphological transition between micro-type partitions, partitions including hydraulic attributes differ from pure morphological partitions with applications to electrofacies and hydraulic unit definitions

Tortuosity estimate through paramagnetic gas diffusion in rock saturated with two fluids using T2 (z, t) low-field NMR

Petrophysical interpretation of 1H NMR relaxation responses from saturated rocks is complicated by paramagnetic species present in fluids. Oxygen dissolved in liquids is one common example. Dipolar interactions of oxygen’s unpaired electron spins with the magnetic moment of fluid nuclei provide a strong relaxation mechanism known as paramagnetic relaxation enhancement (PRE). As a result even low concentrations of dioxygen in its common triplet ground state significantly shorten longitudinal and transverse relaxation times of host fluids. This effect may be employed similarly to any standard tracer technique to study pore connectivity in porous media by detecting a change of oxygen concentration due to diffusion resolved in time and space. Since relaxation enhancement effect is likely stronger in non-wetting phase than in wetting one (where surface relaxation process dominates) this difference can be utilized to study wettability in immiscible multiphase systems. We use a relaxation time contrast between air-saturated and oxygen-free fluids to evaluate oxygen concentration change within two fluid phases saturating rock, to estimate time required to establish equilibrium concentration and to calculate a mutual diffusion coefficient of oxygen. A spatially- and time-resolved T2(z,t) experiment provides the time-dependent oxygen concentration change along the fully- and partially-saturated carbonate core plug exposed to air saturated oil at its inlet. We derive an effective mutual diffusion coefficient of oxygen and accordingly a tortuosity estimate as a function of position along the core and rock saturation. The spatially resolved oxygen diffusion-based tortuosity is compared to simulated conductivitybased tortuosity. The latter is calculated on a high-resolution micro-tomographic image of Mount Gambier limestone by solving the Laplace equation for conductivity

Tortuosity estimate through paramagnetic gas diffusion in rock saturated with two fluids using T2 (z, t) low-field NMR

Petrophysical interpretation of 1H NMR relaxation responses from saturated rocks is complicated by paramagnetic species present in fluids. Oxygen dissolved in liquids is one common example. Dipolar interactions of oxygen’s unpaired electron spins with the magnetic moment of fluid nuclei provide a strong relaxation mechanism known as paramagnetic relaxation enhancement (PRE). As a result even low concentrations of dioxygen in its common triplet ground state significantly shorten longitudinal and transverse relaxation times of host fluids. This effect may be employed similarly to any standard tracer technique to study pore connectivity in porous media by detecting a change of oxygen concentration due to diffusion resolved in time and space. Since relaxation enhancement effect is likely stronger in non-wetting phase than in wetting one (where surface relaxation process dominates) this difference can be utilized to study wettability in immiscible multiphase systems. We use a relaxation time contrast between air-saturated and oxygen-free fluids to evaluate oxygen concentration change within two fluid phases saturating rock, to estimate time required to establish equilibrium concentration and to calculate a mutual diffusion coefficient of oxygen. A spatially- and time-resolved T2(z,t) experiment provides the time-dependent oxygen concentration change along the fully- and partially-saturated carbonate core plug exposed to air saturated oil at its inlet. We derive an effective mutual diffusion coefficient of oxygen and accordingly a tortuosity estimate as a function of position along the core and rock saturation. The spatially resolved oxygen diffusion-based tortuosity is compared to simulated conductivitybased tortuosity. The latter is calculated on a high-resolution micro-tomographic image of Mount Gambier limestone by solving the Laplace equation for conductivity

A Bayesian optimization approach to the extraction of intrinsic physical parameters from T

NMR transverse relaxation responses in porous media provide a sensitive probe of the micro-structure yet are influenced by a set of factors which are not easily detangled. Low-field T2 transverse relaxation measurements can be carried out quickly and are frequently used to derive pore size distributions and determine derivate parameters like movable fluid volumes or permeability. Here we present an inverse solution workflow extracting related intrinsic physical parameters of the system by tightly fitting experiment and numerical simulation(s). We propose a Bayesian optimization approach that determines five T2 related properties associated with two values of temperature simultaneously. This concurrent optimization (CO-OPT) utilizes Gaussian process regression to determine the intrinsic physical parameters leading to a match to experiment with a minimal number of function evaluations. A multi-modal search strategy is employed to identify non-unique solution sets of the problem. The workflow is demonstrated on Bentheimer sandstone, identifying five intrinsic physical parameters simultaneously, namely the surface relaxivity of quartz and the effective diffusion and relaxation times of the clay regions at 20∘ C and 60∘ C, providing the temperature-dependent quartz surface relaxivity and effective clay parameters. Given the generality of the method, it can easily be adapted to transverse relaxation experiments, or dynamic conditions where e.g., a change in wettability is monitored by intrinsic NMR parameters