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

Pore characterization through propagator-resolved transverse relaxation exchange

We use the propagator-resolved transverse relaxation exchange experiment to characterize the pore space and fluid behavior of water saturated, tight-packed quartz sand. The experiment uses T2 exchange plots to observe the number of molecules that shift their environment for a range of mixing times. The propagator dimension allows us to determine how far the molecules have moved. The peak intensities are integrated and then plotted as a function of displacement and mixing time. We also model our system using both a probabilistic pore-hopping simulation and a spreading Gaussian model. We use the results of these simulations to interpret the peak intensity plots. From this, we can estimate pore features such as characteristic time, pore radii, and interpore spacing. The tortuosity of the different pore sizes can then be calculated from these values

Experiment and simulation on NMR and electrical measurements on Liège Chalk

Liège Chalk is a limestone of considerable commercial interest to the petroleum industry and formation factor a quantity required in this context. In this work we compare the formation factors based on electrical conductivity and diffusional displacement in a long time limit both experimentally and numerically. Measurements are performed on Liège Chalk samples while simulations are performed on two model structures represented by randomly packed ellipsoids and utilizing a Gaussian random field approach. We ensure similarity in petrophysical sense of modelled media to Liège Chalk by matching experimental and simulated NMR relaxation response, Mercury Injection Capillary Pressure curves and electrical resistivity. Following this, the diffusional-based formation factor is estimated from a set of apparent diffusion coefficients in the tortuosity limit obtained with PGSTE NMR. All measurements have been numerically-simulated and are in good agreement with experiment. We have shown that for Liège Chalk, the NMR diffusion and electrical resistivity based formation factors do agree

Measurement of NMR flow propagators and local numerical analysis of dual scale porous media

Flow propagators have been frequently used in characterisation of porous media and the study of fluid transport behaviour. Previous work considered the shape of measured flow propagators using Nuclear Magnetic Resonance (NMR) discussed the influence of pore geometry, dispersion, relaxation and internal gradients. In addition, numerically simulated flow propagators were also reported. However, a uantitative numerical analysis of local contributions to flow propagators has not been considered in the literature, yet may provide significant new insights into the flow behaviour through complex porous media. In this work we use two types of beads to realize a dual-scale bead pack consisting of micro- and macropore regions for the NMR experiments. A low-field NMR system (2 MHz) was used to measure flow propagators for this sample. We further generated a dual-scale Gaussian Random Field (GRF) image based on porosity, beads diameters and volume fraction of each type of bead for numerical simulations. A Lattice Boltzmann Method (LBM) and Random Walk (RW) technique were combined to derive the simulated flow propagators and validated against experiments. We carry out a local analysis of the flow propagators showing a significant difference in bandwidth of displacements in micro- and macro-pore regions. In addition, the local flow propagators indicate a linear relationship between mixing (the fluid exchange on regions' boundaries) and flow velocities as well as a non-linear correlation between mixing and evolution times

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

An x-ray tomography facility for quantitative prediction of mechanical and transport properties in geological, biological and synthetic systems

A fully integrated X-ray tomography facility with the ability to generate tomograms with 20483 voxels at 2 micron spatial resolution was built to satisfy the requirements of a virtual materials testing laboratory. The instrument comprises of a continuously pumped micro-focus X-ray gun, a milli-degree rotation stage and a high resolution and large field X-ray camera, configured in a cone beam geometry with a circular trajectory. The purpose of this facility is to routinely analyse and investigate real world biological, geological and synthetic materials at a scale in which the traditional domains of physics, chemistry, biology and geology merge. During the first 2 years of operation, approximately 4 Terabytes of data have been collected, processed and analysed, both as static and in some cases as composite dynamic data sets. This incorporates over 300 tomograms with 10243 voxels and 50 tomograms with 20483 voxels for a wide range of research fields. Specimens analysed include sedimentary rocks, soils, bone, soft tissue, ceramics, fibre-reinforced composites, foams, wood, paper, fossils, sphere packs, bio-morphs and small animals. In this paper, the flexibility of the facility is highlighted with some prime examples

3D imaging and flow characterization of the pore space of carbonate core samples

Carbonate rocks are inherently heterogeneous having been laid down in a range of depositional environments and having undergone significant diagenesis. They are particularly difficult to characterise as the pore sizes can vary over orders of magnitudes and connectivity of pores of different scales can impact greatly on flow properties. For example, separate vuggy porosity in an underlying matrix pore system can increase the porosity, but not the permeability and lead to large residual oil saturations due to trapping in vugs. A touching vug network can have a dramatic effect on permeability and lead to higher recoveries. In this paper we image a range of carbonate core material; from model carbonate cores to core material from outcrops and reservoirs via 3D via micro-CT. Image-based calculations of porosity, MICP and permeability on 3D images of the carbonate systems are directly compared to experimental data from the same or sister core material and give good agreement. The carbonate systems studied include samples with well connected macroporous systems and other where the macroporosity is poorly connected. Simulation of permeability on these systems and direct analysis of local flow properties within the system allows one to directly illustrate the important role of the connectivity of macropores on flow properties. Pore network models generated from the images illustrate the varied topology obtained in different carbonate samples and show a dramatic difference when compared to clastic samples. Many carbonate samples can include a significant proportion of microporosity (pores of 2 microns or less in extent) which are not directly accessible via current micro-CT capabilities. We discuss how one can map the structure and the topology of microporous regions crucial in studies of flow, production and recovery in carbonates. A hybrid numerical scheme is developed to measure the contribution of microporosity to the overall core permeability. Overall these results show the important role of identifying the connectivity of the pore sizes in dictating the single phase flow properties. Implications to two phase relative permeability and recovery are briefly discussed