Cross-property correlations and permeability estimation in sandstone

3D structural analysis of the biodegradability of banana pseudostem nanocellulose bioplastics

X-Ray micro-computed tomography (XCT) is used to reveal the micro-structural changes of banana pseudostem nanocellulose bioplastic due to a biodegradation process initiated in a formulated composting media that allowed the growth of aerobic microflora. The bioplastic itself was made of nanocellulose, which was isolated from banana pseudostem using the 2,2,6,6-Tetramethyl-1-piperidinyloxy (TEMPO) mediated oxidation method, and polyethylene glycol (PEG) as plasticiser. XCT provided insights into the 3D structural change of the bioplastic identifying the degradation process at two scales. The results showed that the local thickness and roughness of the bioplastic increased after degradation, while the density of the material decreased. Enlarged voids and tunnels were observed in the material after degradation. The formation of these tunnels is attributed to the popping of internal PEG-containing voids because of the generation of gases, which after forming may further accelerate biodegradation by microbial activity.

New Model for Absolute Permeability Prediction in Coal Samples: Application of Modified Purcell Model to Mercury Injection Pressure and Nuclear Magnetic Resonance Data

The permeability of rocks is a critical parameter in many subsurface geological applications, and pore properties measured on rock samples (including rock fragments) can be used to estimate rock permeability. A major use of MIP and NMR data is to assess the pore properties of a rock in order to estimate the permeability based on empirical equations. Although sandstones have been extensively studied, permeability in coals has received less attention. Consequently, in order to obtain reliable predictions for coal permeability, a comprehensive study of different permeability models was performed on coal samples having a range of permeabilities from 0.003 to 1.26 mD. The model results showed that the seepage pores in coals account for the bulk of the permeability, while the contribution of adsorption pores to permeability is negligible. The models that only consider a single pore size point on the mercury curve, such as the Pittman and Swanson model, or those that use the entire pore size distribution, like the Purcell and SDR model, are inadequate for predicting permeability in coals. This study modifies the Purcell model to determine permeability from the seepage pores of coal, resulting in the enhancement of the predictive capability, with an increased R² and reduction in the average absolute error by approximately 50% compared to the Purcell model. To apply the modified Purcell model to NMR data, a new model was developed that provides a high degree of predictive capability (∼0.1 mD). This new model can be used for cuttings, which could lead to a new method for field permeability estimation.

Developing synthetic sandstones using geopolymer binder for constraining coupled processes in porous rocks

There is a current need for developing improved synthetic porous materials for better constraining the dynamic and coupled processes relevant to the geotechnical use of underground reservoirs. In this study, a low temperature preparation method for making synthetic rocks is presented that uses a geopolymer binder cured at 80 °C based on alkali-activated metakaolin. For the synthesised sandstone, the key rock properties permeability, porosity, compressive strength, and mineralogical composition, are determined and compared against two natural reservoir rocks. In addition, the homogeneity of the material is analysed structurally by micro-computed tomography and high-resolution scanning electron microscopy, and chemically by energy dispersive X-ray spectroscopy. It is shown that simple, homogenous sandstone analogues can be prepared that show permeability-porosity values in the range of porous reservoir rocks. The advance in using geopolymer binders to prepare synthetic sandstones containing thermally sensitive minerals provides materials that can be easily adapted to specific experimental needs. The use of such material in flow-through experiments is expected to help bridge the gap between experimental observations and numerical simulations, leading to a more systematic understanding of the physio-chemical behaviour of porous reservoir rocks.

Model Synthetic Samples for Validation of NMR Signal Simulations

Simulations of nuclear magnetic resonance (NMR) signal from fluids contained in porous media (such as rock cores) need to account for both enhanced surface relaxation and the presence of internal magnetic field gradients due to magnetic susceptibility contrast between the rock matrix and the contained fluid phase. Such simulations are typically focussed on the extraction of the NMR T2 relaxation distribution which can be related to pore size and indirectly to system permeability. Discrepancies between such NMR signal simulations on digital rock cores and associated experimental measurements are however frequently reported; these are generally attributed to spatial variations in rock matric composition resulting in heterogeneously distributed NMR surface relaxivities (ρ) and internal magnetic field gradients. To this end, a range of synthetic sediments composed of variable mixtures of quartz and garnet sands were studied. These two constituents were selected for the following reasons: they have different densities allowing for ready phase differentiation in 3D μCT images of samples to use as simulation lattices and they have distinctly different ρ and magnetic susceptibility values which allow for a rigorous test of NMR simulations. Here these 3D simulations were used to calculate the distribution of internal magnetic field gradients in the range of samples, these data were then compared against corresponding NMR experimental measurements. Agreement was reasonably good with the largest discrepancy being the simulation predicting weak internal gradients (in the vicinity of the quartz sand for mixed samples) which were not detected experimentally. The suite of 3D μCT images and associated experimental NMR measurements are all publicly available for the development and validation of NMR simulation efforts.

Three-phase flow displacement dynamics and Haines jumps in a hydrophobic porous medium

We use synchrotron X-ray micro-tomography to investigate the displacement dynamics during three-phase—oil, water and gas—flow in a hydrophobic porous medium. We observe a distinct gas invasion pattern, where gas progresses through the pore space in the form of disconnected clusters mediated by double and multiple displacement events. Gas advances in a process we name three-phase Haines jumps, during which gas re-arranges its configuration in the pore space, retracting from some regions to enable the rapid filling of multiple pores. The gas retraction leads to a permanent disconnection of gas ganglia, which do not reconnect as gas injection proceeds. We observe, in situ, the direct displacement of oil and water by gas as well as gas–oil–water double displacement. The use of local in situ measurements and an energy balance approach to determine fluid–fluid contact angles alongside the quantification of capillary pressures and pore occupancy indicate that the wettability order is oil–gas–water from most to least wetting. Furthermore, quantifying the evolution of Minkowski functionals implied well-connected oil and water, while the gas connectivity decreased as gas was broken up into discrete clusters during injection. This work can be used to design CO₂ storage, improved oil recovery and microfluidic devices.

Dynamics of water injection in an oil-wet reservoir rock at subsurface conditions: Invasion patterns and pore-filling events

We use fast synchrotron x-ray microtomography to investigate the pore-scale dynamics of water injection in an oil-wet carbonate reservoir rock at subsurface conditions. We measure, in situ, the geometric contact angles to confirm the oil-wet nature of the rock and define the displacement contact angles using an energy-balance-based approach. We observe that the displacement of oil by water is a drainagelike process, where water advances as a connected front displacing oil in the center of the pores, confining the oil to wetting layers. The displacement is an invasion percolation process, where throats, the restrictions between pores, fill in order of size, with the largest available throats filled first. In our heterogeneous carbonate rock, the displacement is predominantly size controlled; wettability has a smaller effect, due to the wide range of pore and throat sizes, as well as largely oil-wet surfaces. Wettability only has an impact early in the displacement, where the less oil-wet pores fill by water first. We observe drainage associated pore-filling dynamics including Haines jumps and snap-off events. Haines jumps occur on single- and/or multiple-pore levels accompanied by the rearrangement of water in the pore space to allow the rapid filling. Snap-off events are observed both locally and distally and the capillary pressure of the trapped water ganglia is shown to reach a new capillary equilibrium state. We measure the curvature of the oil-water interface. We find that the total curvature, the sum of the curvatures in orthogonal directions, is negative, giving a negative capillary pressure, consistent with oil-wet conditions, where displacement occurs as the water pressure exceeds that of the oil. However, the product of the principal curvatures, the Gaussian curvature, is generally negative, meaning that water bulges into oil in one direction, while oil bulges into water in the other. A negative Gaussian curvature provides a topological quantification of the good connectivity of the phases throughout the displacement.

Fast Fourier transform and support-shift techniques for pore-scale microstructure classification using additive morphological measures

The Minkowski functionals, as the full set of additive morphological measures in three dimensions (3D) consisting of volume, surface area, mean curvature, and total curvature, can be calculated directly by evaluating the local contributions of vertices of a discrete structure. They are sensitive measures of microstructure, and for microstructures generated by a Boolean process, relate to their physical properties. In this work we introduce fast numerical techniques based on the additivity of the Minkowski functionals to derive fields of regional Minkowski measures over large regional support for large 3D data sets as generated, e.g., from x-ray tomography techniques. We demonstrate the application of these 3D feature fields to microstructure classification for a set of heterogeneous microstructures using a multivariate Gaussian mixture model and a thin-bedded sandstone. It is shown that for the case of a spatially heterogeneous Boolean process the internal boundaries of the generating process are recovered with high accuracy, while for the thin-bedded sandstone, compact partitions with clear layering are extracted.

Fluid flow through packings of elastic shells

Fluid transport in porous materials is commonly studied in geological samples (soil, sediments, etc.) or idealized systems, but the fluid flow through compacted granular materials, consisting of substantially strained granules, remains relatively unexplored. As a step toward filling this gap, we study a model of liquid transport in packings of deformable elastic shells using finite-element and lattice-Boltzmann methods. We find that the fluid flow abruptly vanishes as the porosity of the material falls below a critical value, and the flow obstruction exhibits features of a percolation transition. We further show that the fluid flow can be captured by a simplified permeability model in which the complex porous material is replaced by a collection of disordered capillaries, which are distributed and shaped by the percolation transition. To that end, we numerically explore the divergence of hydraulic tortuosity τ_{H} and the decrease of a hydraulic radius R_{h} as the percolation threshold is approached. We interpret our results in terms of scaling predictions derived from the percolation theory applied to random packings of spheres.

Dynamic imaging of multiphase flow through porous media using 4D cumulative reconstruction

This paper introduces an original application on reconstruction strategies for X-ray computed microtomography, enabling the observation of time-dependent changes that occur during multiphase flow. In general, by sparsely collecting radiographs, the reconstruction of the object is compromised. Optimizations can be achieved by combining specific characteristics of the dynamics with the acquisition. Herein, the proposed method relies on short random intervals in which no drastic changes occur in the sample to acquire as many radiographs as possible that constitute a reconstructible data set. As these intervals are unpredictable, the method tries to guarantee that the collected radiograph data during these specific intervals are enough to recover useful information about the dynamics. Simulations of a percolating fluid in a digital rock are used to replicate an X-ray computed microtomography experiment to test the proposed method. The results demonstrate the potential of the proposed strategy for imaging multiphase flow in porous media and how data collected during distinct events can be combined to enhance the reconstruction of frames of the percolation process.

About the connectivity of dual-scale media based on micro-structure based regional analysis of NMR flow propagators

The characterisation of heterogeneous porous media at multiple length scales typically requires the classification of structure at some scale to allow the calculation of effective transport properties at a scale relevant for macroscopic description. While such a classification may be derived from various imaging methods, a shortcoming is often the simultaneous characterisation of the connectivity between regions representing different micro-structure. In this work we combine NMR based flow propagators with the simulations performed on corresponding reconstructed structure, and relate the NMR measurements to their simulated global and local representations to study fluid transport locally and the exchange between micro- and macro-porous regions. This is achieved by carrying out detailed lattice Boltzmann simulations and random walk method to track the displacements of tracers in each kind of region. Using Euclidean distance maps (EDT) we analyse the fluid invasion to regions of different scale and relate it to the connectivity of the system. We demonstrate that numerical simulation has great flexibility in providing additional sensitivity to the inference of region-region connectivity.

Fast Laplace solver approach to pore-scale permeability

We introduce a powerful and easily implemented method to calculate the permeability of porous media at the pore scale using an approximation based on the Poiseulle equation to calculate permeability to fluid flow with a Laplace solver. The method consists of calculating the Euclidean distance map of the fluid phase to assign local conductivities and lends itself naturally to the treatment of multiscale problems. We compare with analytical solutions as well as experimental measurements and lattice Boltzmann calculations of permeability for Fontainebleau sandstone. The solver is significantly more stable than the lattice Boltzmann approach, uses less memory, and is significantly faster. Permeabilities are in excellent agreement over a wide range of porosities.

Direct relations between morphology and transport in Boolean models

We study the relation of permeability and morphology for porous structures composed of randomly placed overlapping circular or elliptical grains, so-called Boolean models. Microfluidic experiments and lattice Boltzmann simulations allow us to evaluate a power-law relation between the Euler characteristic of the conducting phase and its permeability. Moreover, this relation is so far only directly applicable to structures composed of overlapping grains where the grain density is known a priori. We develop a generalization to arbitrary structures modeled by Boolean models and characterized by Minkowski functionals. This generalization works well for the permeability of the void phase in systems with overlapping grains, but systematic deviations are found if the grain phase is transporting the fluid. In the latter case our analysis reveals a significant dependence on the spatial discretization of the porous structure, in particular the occurrence of single isolated pixels. To link the results to percolation theory we performed Monte Carlo simulations of the Euler characteristic of the open cluster, which reveals different regimes of applicability for our permeability-morphology relations close to and far away from the percolation threshold.

Permeability of porous materials determined from the Euler characteristic

We study the permeability of quasi-two-dimensional porous structures of randomly placed overlapping monodisperse circular and elliptical grains. Measurements in microfluidic devices and lattice Boltzmann simulations demonstrate that the permeability is determined by the Euler characteristic of the conducting phase. We obtain an expression for the permeability that is independent of the percolation threshold and shows agreement with experimental and simulated data over a wide range of porosities. Our approach suggests that the permeability explicitly depends on the overlapping probability of grains rather than their shape.

Physical Properties of Gas Hydrates: A Review

Methane gas hydrates in sediments have been studied by several investigators as a possible future energy resource. Recent hydrate reserves have been estimated at approximately1016 m3of methane gas worldwide at standard temperature and pressure conditions. In situ dissociation of natural gas hydrate is necessary in order to commercially exploit the resource from the natural-gas-hydrate-bearing sediment. The presence of gas hydrates in sediments dramatically alters some of the normal physical properties of the sediment. These changes can be detected by field measurements and by down-hole logs. An understanding of the physical properties of hydrate-bearing sediments is necessary for interpretation of geophysical data collected in field settings, borehole, and slope stability analyses; reservoir simulation; and production models. This work reviews information available in literature related to the physical properties of sediments containing gas hydrates. A brief review of the physical properties of bulk gas hydrates is included. Detection methods, morphology, and relevant physical properties of gas-hydrate-bearing sediments are also discussed.

Numerical study of the effects of particle shape and polydispersity on permeability

We study through numerical simulations the dependence of the hydraulic permeability of granular materials on the particle shape and the grain size distribution. Several models of sand are constructed by simulating the settling under gravity of the grains; the friction coefficient is varied to construct packs of different porosity. The size distribution and shapes of the grains mimic real sands. Fluid flow is simulated in the resulting packs using a finite element method and the permeability of the packs is successfully compared with available experimental data. Packs of nonspherical particles are less permeable than sphere packs of the same porosity. Our results indicate that the details of grain shape and size distribution have only a small effect on the permeabilty of the systems studied.

On the influence of pore structure on the free-imbibition of sessile drops into nanoporous substrates

We report here a model experimental study on the influence of pore structure on the free-imbibition of sessile drops into nanoporous substrates. The work takes advantage of the existence of distinct pore structures on the two sides of a nanoporous alumina membrane: straight parallel channels versus a denser and tortous network. We show first that the spreading which coexists with the free-imbibition predominates in the early stage well follows on both sides the power-law scaling with time predicted by the universal Tanner's law. More interestingly, we found also that the imbibition rate scales in a similar way with the time on both sides of the membrane, showing that the pore structure does not affect qualitatively the free-imbibition kinetics. On the other hand, our results clearly show that the pore structure has a quantitative impact on the imbibition rate, which increases markedly from the A side (dense network of short and tortuous pores) to the side B (straight vertical channels). This latter result shows that, as regards the free-imbibition, the topology of the pores has a preeminent impact on their volume, which is here comparable for both sides of the membrane. More unexpectedly, this quantitative impact of the pore structure on the imbibition rate seems to display a certain sensitivity to the viscosity of the liquid.

Elastic and transport properties of cellular solids derived from three-dimensional tomographic images

We describe a three-dimensional imaging and analysis study of eight industrial cellular foam morphologies. The foam morphologies were generated by differing industrial processing methods. Tomograms are acquired on an X-ray micro-computed tomography facility at scales of approximately equal to at resolutions down to 7 μm. The image quality is sufficient in all cases to measure local structure and connectivity of the foamed material, and the field of view large enough to calculate a range of material properties. Phase separation into solid and porous components is straightforward.

Three-dimensional structural characteristics are measured directly on the porous and solid phases of the images. A number of morphological parameters are obtained, including pore volume-to-surface-area ratio, connectivity, the pore and solid phase size distributions defined by maximal sphere openings and chord length measurements. We further calculate the pore size distribution associated with capillary pressure via simulating of mercury drainage on the digital images.

The binarized microstructures are used as a basis for calculations of transport properties (fluid permeability, diffusivity and thermal conductivity) and elastic moduli. From the data, we generate property–porosity relationships for the range of foam morphologies imaged and quantitatively analyse the effects of porosity and microstructure on the resultant properties of the foams.

We compare our numerical data to commonly used theoretical and empirical property–porosity relationships. For thermal conductivity, we find that the numerical results agree extremely well with an empirical expression based on experimental data of various foams. The upper Hashin–Shtrikman bound also provides an excellent prediction of the data across all densities. From simulation of the diffusivity, we can define the tortuosity of the pore space within the cellular solid. We find that different processing methods lead to strong variations in the tortuosity of the pore space of the foams. For elastic properties, our results show that for the Young modulus, E , both the differential effective medium theory and the classical correlation give a good correlation. Assuming a constant Poisson's ratio leads to reasonable agreement. The best correlation for is given by assuming a slight variation in as a linear function of porosity. The permeability of the foams varies over three orders of magnitude. Correlations for permeability based on the classical Kozeny–Carman equation lead to reasonable agreement, except at the lowest porosities. Permeability estimations based on mercury porosimetry give excellent agreement for all foams.

Use of a void network model to correlate porosity, mercury porosimetry, thin section, absolute permeability, and NMR relaxation time data for sandstone rocks

The Pore-Cor void network model is used to construct stochastic realizations of the void structures of five sandstone samples of varying lithography. A close match was achieved to experimental porosity and mercury intrusion curves. The samples were resin impregnated and the fragments of voids revealed in thin sections photographed by backscatter electron microscopy at two magnifications. The sizes of these pore fragments matched those derived from a simulated microtoming of the network model much more closely than the sizes derived from the traditional capillary bundle approximation. Absolute permeabilities of the network were calculated by finding the flow capacity of the entire flow network, based on parametrized Navier Stokes equations with Klinkenberg correction, applied to each pore-throat-pore arc. A match to the experimental trend was obtained, although the network model considerably underestimated the experimental values. The results were also compared with the semiempirical equations of Thomson et al. and Kozeny and Carmen modified to accept thin section image analysis. Finally, the simulated pore and throat size distributions were compared to proton NMR transverse (T2) spin-echo relaxation times. Although the shapes of the distributions differed markedly, the mean values trended together. The capillary bundle approximation, however, gave a poor match to the NMR data.