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Abstract: Seismic studies are essential for accurate characterisation of planetary interior structures, but are dependent on modelling for interpretation, requiring data on the elastic properties of likely constituent minerals. With the potential deployment of seismic stations on icy worlds such as Europa and Titan envisioned for the near future, a campaign of study into the elasticity of potential icy ocean world minerals is of paramount importance. In the paper we assess the role of first-principles computer simulations to this problem, in particular focussing on the application of recent advances in simulating dispersion forces in loosely-bonded molecular solids, likely to be the main constituents of icy ocean worlds. This is of particular interest for these kinds of materials, since the complex sample handling, phase transitions and the difficulty of obtaining single crystals often greatly complicates the experimental determination of the full elastic tensor. We focus on CO2, C6H6, MgSO4·7H2O and CaSO4·2H2O as they allow us to benchmark the performance over a wide range of chemical space, structural topologies, crystal symmetries and bonding types, and moreover have accurate experimentally determined unit-cell dimensions, bulk moduli and full elastic tensors for benchmarking purposes. We demonstrate that the dispersion corrected approaches indeed perform superior in modelling the experimental density profiles (mean unsigned differences of merely 0.04 g/cm3 (CO2), 0.02 g/cm3 (C6H6), 0.003 g/cm3 (MgSO4·7H2O) and 0.013 g/cm3 (CaSO4·2H2O)) and may find application in exploring the compressive parameters of candidate materials, which could then be used in rheological models of icy ocean worlds. Moreover, we have assessed if the elastic constants computed by dispersion corrected density functional theory are accurate enough to be used in a reference data base for the seismic exploration of icy ocean worlds. Despite one approach having demonstrated good accuracy compared with the experimental values in modelling the elasticity of CO2, we instead find average differences from expected P and S wave velocities of around 10 to 25% for the elastically more complex title compounds. In part these differences are due to the large temperature difference between the experimental elasticity data (typically near 300 K) and our calculations, which were performed in the athermal limit.

Open Access

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Abstract: The development of pore and fracture networks at the nano-scale as a response to heating can reveal coupled physical relationships relevant to several energy applications. A combination of time-lapse 3D imaging and finite-element modelling (FEM) was performed on two typical thermally immature shale samples, Kimmeridge Clay and Akrabou shale, to investigate thermal response at the nm-scale for the first time. Samples were imaged using Transmission X-ray Microscopy (TXM) with a voxel resolution of 34 nm at the I13–2 beamline at Diamond Light source, UK. Images were taken after heating to temperatures of 20 °C, 300 °C, 350 °C and 400 °C. The initiation of nano-pores within individual minerals and organic matter particles were observed and quantified alongside the evolution from nano-pores to micro-fractures. The major expansion of pore-volume occurred between 300 and 350 °C in both samples, with the pores elongating rapidly along the organic-rich bedding. The internal pressures induced by organic matter transformation influenced the development of microfractures. Mechanical properties and strain distributions within these two samples were modelled under a range of axial stresses using FEM. The results show that the overall stiffness of the shale reduced during heating, despite organic matter becoming stiffer. The varied roles of ductile (e.g., clay minerals, organic matter) and brittle materials (e.g., calcite, pyrite) within the rock matrix are also modelled and discussed. The configurations of organic matter, mineral components, porosity and connectivity impact elastic deformation during shale pyrolysis. This work extends our understanding of dynamic coupled processes of microstructure and elastic deformation in shales to the nm-scale, which also has applications to other subsurface energy systems such as carbon sequestration, geothermal and nuclear waste disposal.

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Abstract: Fast synchrotron tomography is used to study the impact of capillary number, Ca , on fluid configurations in steady-state two-phase flow in porous media. Brine and n -decane were co-injected at fixed fractional flow, f w = 0.5 , in a cylindrical Bentheimer sandstone sample for a range of capillary numbers 2.1 × 10 − 7 ≤ Ca ≤ 4.2 × 10 − 5 , while monitoring the pressure differential. As we have demonstrated in Gao et al. [Phys. Rev. Fluids 5, 013801 (2020)], dependent on Ca , different flow regimes have been identified: at low Ca only fixed flow pathways exist, while after a certain threshold dynamic effects are observed resulting in intermittent fluctuations in fluid distribution which alter fluid connectivity. Additionally, the flow paths, for each capillary number, were imaged multiple times to quantify the less frequent changes in fluid occupancy, happening over timescales longer than the duration of our scans (40 s). In this paper we demonstrate how dynamic connectivity results from the interaction between oil ganglia populations. At low Ca connected pathways of ganglia are fixed with time-independent small, medium, and large ganglia populations. However, with an increase in Ca we see fluctuations in the size and numbers of the larger ganglia. With the onset of intermittency, fluctuations occur mainly in pores and throats of intermediate size. When Ca is further increased, we see rapid changes in occupancy in pores of all size. By combining observations on pressure fluctuations and flow regimes at various capillary numbers, we summarize a phase diagram over a range of capillary numbers for the wetting and nonwetting phases, Ca w and Ca n w , respectively, to quantify the degree of intermittent flow. These different regimes are controlled by a competition between viscous forces on the flowing fluids and the capillary forces acting in the complex pore space. Furthermore, we plot the phase diagrams of the transition from Darcy flow to intermittent flow over a range of Reynolds and Weber numbers for the wetting and nonwetting phases to evaluate the balance among capillary, viscous, and inertial forces, incorporating data from the literature. We demonstrate that pore geometry has a significant control on flow regime.

Open Access

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Abstract: 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.

Open Access

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Abstract: Penetration of open- and closed-ended model piles into intact chalk, a soft calcareous rock, was investigated using microfocus X-ray computed tomography (XCT). 3D images of the specimens showed that the piles crushed and densified the chalk in their path, creating a crushed chalk annulus around the shaft, a region of compressed destructured chalk below the tip, and fractures across cemented regions of the specimen. Laser-diffraction particle size analyses of the crushed chalk annulus after exhumation showed limited difference with laboratory-remoulded chalk, which suggested thorough de-cementation. Installation stresses and XCT-derived densities were paired using a simplified cylindrical cavity expansion solution to estimate effective radial stress-void ratio states at the pile tip during penetration. More complex numerical solutions could not be applied using the available data. This approach posed significant problems, as it could not suitably incorporate hardening and non-linear stiffness behaviours of Chalk during pile penetration, nor account for the creation of discontinuities. However, effective radial stress-void ratio estimates were found to converge with the reconstituted critical state line of the material at high stresses and low void ratios. This partially supported the use of a critical state framework to characterise pile penetration in Chalk, as proposed in recent literature.