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Numerical Simulations in Support of a Long-Term Test of Gas Production from Hydrate Accumulations on the Alaska North Slope: Reservoir Response to Interruptions of Production (Shut-Ins)

In this work, we investigate by means of numerical simulation a planned year-long field test of depressurization-induced production from a permafrost-associated hydrate reservoir on the Alaska North Slope at the site of the recently drilled Hydrate-01 Stratigraphic Test Well. The main objective of this study is to assess quantitatively the impact of temporary interruptions (well shut-ins) on the expected fluid production performance from the B1 Sand of the stratigraphic Unit B during controlled depressurization over different time scales, as well as on other relevant aspects of the system response that have the potential to significantly affect the design of the field test. We consider eight different cases of depressurization, including (a) rapid depressurization over a 60-day period to a terminal bottomhole pressure P W of 2.8 MPa and (b) a slower depressurization rate to a final P W of 0.6 MPa at the end of the year-long production test, in addition to (c) a multi-step depressurization regime and (d) a quasi-linear continuous depressurization strategy. The results of the study indicate that shut-ins obviously reduce gas release and production during and immediately after their occurrence, but their longer-term effects are strongly dependent on the depressurization regime and on the time of observation, covering the entire range of potential outcomes. Shut-ins (a) have a universally strong negative effect when quasi-linear depressurization is involved regardless of the length of the production period, and (b) have a strong positive effect in multi-step depressurization schemes that becomes apparent earlier for large initial pressure drops, but (c) can also appear to have practically no effect for slow stepwise depressurization at the end of the year-long production test. Shut-ins lead to a rapid reformation of hydrates, even to the point of disappearance of a free gas phase in the reservoir. Rapid depressurization regimes lead to early maximum rates of hydrate dissociation and gas production, while the maximum rates occur at the end of the production test for the cases of slower depressurization. Shut-ins do not appear to have a significant impact on water production, as the cessation of production is followed by higher rates production when depressurization resumes. Similarly, (a) the fraction of produced CH 4 originating from exsolution from the water, (b) the water-to-gas ratio, and (c) the rate of replenishment of produced water by boundary inflows do not appear significantly affected by shut-ins, the effects of which seem to be temporary in the majority of the cases. The study confirmed the superiority of multi-step depressurization methods as the most effective strategies for hydrate dissociation and gas production and showed that two observation wells (located at distances of 30 and 50 m from the production well) are appropriately positioned and both able to capture the P, T, and S G behavior during the fluid production and shut-ins in any of the eight cases we investigated.

03 NATURAL GAS↗

Oil in Alaska North Slope Gas Hydrate Reservoir: Micro-CT and Flow Simulation Insights into Permeability

Gas hydrate-bearing sands on the Alaska North Slope (ANS) host minor volumes of crude oil whose impact on formation permeability has never been quantified relative to a gas hydrate reservoir system. Here, we combine in situ pressure-core microcomputed-tomography (μ-CT), thermogravimetric analysis (TGA), gas-chromatography–mass-spectrometry (GC–MS), scanning-electron microscopy coupled with energy-dispersive spectroscopy (SEM-EDS), and Stokes-flow simulation to (i) quantify oil saturation, (ii) infer its source, and (iii) evaluate its influence on permeability after gas-hydrate dissociation. μ-CT and SEM-EDS imaging identify the host sediment as silty, with some grain-coating clay present. Eight representative 3003-voxel subvolumes extracted from a preserved pressure core (Core 15P-3c, from the B1 sand (unit B), HYDRATE 02 Geo Data Well (GDW), 886.96–887.29 m measured depth, MD) exhibit porosities of 0.34–0.37 and an average oil saturation of 0.09 ± 0.03, in comparison to an independent TGA-based estimate of 0.16. GC-MS fingerprints obtained from an adjacent depressurized core (Core 17P-1, 891.37–891.44 m MD), together with oil pore habit revealed by μ-CT, suggest that the oil is partly native but also includes contributions from mineral oil-based drilling fluid contamination. Further analysis of oil–porewater interactions and flushing tests confirms that native oil saturation in the analyzed samples ranges from 0.04 to 0.08 with an average of approximately 0.06, and the oil is highly immobile. Flow simulations demonstrate that the native oil saturation of ≈0.06 reduces permeability by approximately 50% due to both pore blockage and increased flow-path tortuosity. These findings reveal the potential presence of native oil within the ANS gas hydrate reservoir and suggest that future simulation models may need to account for its impact on permeability to improve long-term performance predictions of gas and water production.

02 PETROLEUM↗

Surface Dynamics of Selective Hydration of Rutile TiO 2 : A Kinetic Monte Carlo Approach

The utility of atomic layer deposition (ALD) continues to expand beyond conformal thin-film fabrication to include area- or site-selective ALD. We previously identified a strategy for site-selective ALD (SS-ALD) via the evaluation of thermodynamically preferred hydration of rutile TiO 2 surfaces, as deduced from electronic structure calculations. Here, we report a novel kinetic Monte Carlo (KMC) model that allows for the investigation of surface dynamics and kinetics that improves our understanding of and intuition for the selective hydration strategy. Here we demonstrate the validity of the strategy with respect to step-edge defects for the lowest energy (110) facet as well as report results for the other common facets which agree with experimental STM observations. The results here indicate that the selective hydration strategy is feasible both thermodynamically (evaluated in our previous publication) and kinetically (from the KMC model). Because diffusion has a slower rate than others, we find that any proximity effects between terrace and defect sites are unlikely to affect the selective hydration strategy for rutile TiO 2 . The KMC model further provides relevant timescales for achieving selectivity experimentally and establishes the kinetic viability of the selective hydration approach to SS-ALD.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Combined Machine Learning and Molecular Dynamics Reveal Two States of Hydration of a Single Functional Group of Cationic Polymeric Brushes

The state of hydration of a macromolecular system regulates a plethora of different properties of such a system. In this article, we develop a novel machine learning (ML) approach, based on the unsupervised clustering algorithm, for probing the hydration behavior of the {N(CH 3 ) 3 } + functional group of the PMETAC [Poly(2-(methacryloyloxy)ethyl trimethylammonium chloride] polyelectrolyte (PE) brush system. The PE brushes and the brush-supported water molecules and counterions (chloride ions) are first described using all-atom molecular dynamics (MD) simulations. The simulation data is subsequently used in our ML framework to identify that (1) the {N(CH 3 ) 3 } + functional groups of the PMETAC brushes have two distinct hydration states with one state (state 1) being characterized by less structured water molecules and the other state (state 2) being characterized by more structured water molecules and (2) an enhancement in the brush grafting density leads to the progressive dissapparenace of state 2. An increase in the grafting density increases the number of chloride counterions in a given volume around the {N(CH 3 ) 3 } + functional group and increases the number of shared water molecules between the {N(CH 3 ) 3 } + and Cl - . The chloride counterions are associated with a hydration layer with much less structured water molecules. Therefore, with an increase in the grafting density, an increase in the percentage of shared water molecules leads to the prevalence of the hydration state [of the {N(CH 3 ) 3 } + moiety] with less structured water molecules. Finally, we explain how the present findings are commensurate with two key previous related results, namely a significantly large chloride ion mobility inside the PMETAC brush layer and the {N(CH 3 ) 3 } + -Cl - average distance remaining independent of the PMETAC brush grafting density. Furthermore, we anticipate that the combined ML-MD-simulation approach proposed in this study can be adapted to probe other soft matter systems to reveal new insights of the underlying mechanisms of emergent phenomenon.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Hydration-Controlled Proton Transport in Respiratory Complex I

Proton pumping by respiratory complex I is one essential element for generating the proton motive force that drives ATP synthesis in mitochondria. Although it is understood that electrons from NADH reduce ubiquinone at the peripheral arm and that four protons are transferred in the membrane domain, the mechanism by which this redox reaction initiates proton translocation remains unclear. A lateral pathway linking the quinone binding site to the membrane domain via ND1, ND3, and ND4L subunits has been proposed as a possible initial path of an excess proton. However, experimental structures indicate that the hydration connectivity between D66 ND3 and E34 ND4L is comparatively weaker than in neighboring segments, suggesting a potential regulatory point for proton transfer. Using multiscale reactive molecular dynamics (MS-RMD) and a water wire connectivity metric, we directly simulate proton transport through this region as coupled to the hydration by water molecules. Our results reveal that proton transfer is thermodynamically feasible when transient hydration aligns with the presence of an excess proton, revealing the strong coupling between hydration and proton transfer (PT) in this region of Complex I. These findings support a model where proton injection enhances local hydration, dynamically opening the pathway for proton transfer and regulating the onset of proton pumping in Complex I.

Chemical structure↗

A hybrid machine-learning approach for analysis of methane hydrate formation dynamics in porous media with synchrotron CT imaging

Fast multi-phase processes in methane hydrate bearing samples pose a challenge for quantitative micro-computed tomography study and experiment steering due to complex tomographic data analysis involving time-consuming segmentation procedures. This is because of the sample's multi-scale structure, which changes over time, low contrast between solid and fluid materials, and the large amount of data acquired during dynamic processes. Here, a hybrid approach is proposed for the automatic segmentation of tomographic data from time-resolved imaging of methane gas-hydrate formation in sandy granular media, which includes a deep-learning 3D U-Net model. To prepare a training dataset for the 3D U-Net, a technique to automate data labeling based on sample-specific information about the mineral matrix immobility and occasional fluid movement in pores is proposed. Automatic segmentation allowed for studying properties of the hydrate growth in pores, as well as dynamic processes such as incremental flow and redistribution of pore brine. Results of the quantitative analysis showed that for typical gas-hydrate stability parameters (100 bar methane pressure, 7°C temperature) the rate of formation is slow (less than 1% per hour), after which the surface area of contact between brine and gas increases, resulting in faster formation (2.5% per hour). Hydrate growth reaches the saturation point after 11 h of the experiment. Finally, the efficacy of the proposed segmentation scheme in on-the-fly automatic data analysis and experiment steering with zooming to regions of interest is demonstrated.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

A Geomechanical Model for Gas Hydrate Bearing Sediments Incorporating High Dilatancy, Temperature, and Rate Effects

The geomechanical behavior of methane hydrate bearing sediments (MHBS) is influenced by many factors, including temperature, fluid pressure, hydrate saturation, stress level, and strain rate. The paper presents a visco-elastoplastic constitutive model for MHBS based on an elastoplastic model that incorporates the effect of hydrate saturation, stress history, and hydrate morphology on hydrate sediment response. The upgraded model is able to account for additional critical features of MHBS behavior, such as, high-dilatancy, temperature, and rate effects. The main components and the mathematical formulation of the new constitutive model are described in detail. The upgraded model is validated using published triaxial tests involving MHBS. The model agrees overly well with the experimental observations and is able to capture the main features associated with the behavior of MHBS.

15 GEOTHERMAL ENERGY↗

Estimation of Sorption Behavior of Europium to Calcium Silicate Hydrate by Thermal Analysis - 20172

High-level radioactive waste generated from reprocessing processes will be disposed in a geological disposal that is deep underground. Calcium silicate hydrate is formed as a secondary mineral in the repository via the reaction of calcium ions leaching from the cement and the silicic acid dissolved from the host rocks. In this study, the sorption behavior of europium, which is also known as a chemical analog of americium, on calcium silicate hydrate was examined. The solid phase was analyzed via thermogravimetry- differential thermal analysis, differential scanning calorimetry, Raman spectroscopy, fluorescence spectroscopy, and fluorescence lifetime analysis. To understand the behavior of calcium silicate hydrate under conditions saturated with groundwater, the study samples were analyzed using the above methods, except for deferential scanning calorimetry, without a drying process. The results of the differential scanning calorimetry analyses showed that the temperatures for the endothermic peaks of calcium silicate hydrate for the lower Ca/Si ratios were larger than those for the higher Ca/Si ratios for coexistent conditions of europium ions. Hence, the relationships of the temperatures of the endothermic peaks and the Ca/Si ratios were reversed by the addition of europium ions. These study results suggest that calcium silicate hydrate can immobilize europium ions, thus preventing the production of colloidal forms. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

Analysis of short‐ and long‐term system response during gas production from a gas hydrate deposit at the UBGH2‐6 site of the Ulleung Basin in the Korean East Sea

Abstract This study is a continuation of an investigation into the feasibility of long‐term production from a marine hydrate accumulation that has the properties and conditions of the UBGH2‐6 (UBGH2, Ulleung Basin Gas Hydrates 2; 2 is the number of the scientific expedition) site at the Ulleung Basin in the Korean East Sea. The 12.7 m‐thick system is in deep water (2157 m), but at 140 m below the seafloor. It is characterized by alternating hydrate‐free clays and muds and hydrate‐rich sand layers. The layered stratigraphy and the presence of mud layers favours the use of vertical wells rather than horizontal wells for production. The analysis indicates that production from such a hydrate accumulation is technically feasible, but the gas production rates are generally low. Water production accompanying gas production from this deposit appears manageable under all the scenarios investigated in this study, however, the water‐to‐gas ratio is high. Subsidence at the ocean floor at the end of a 14 day test is quite limited. However, there is significant uncertainty in the predictions of the geomechanical system's behaviour because they are not based on measured system properties but only on estimates/assumptions from analogues. The long‐term production potential of the reservoir at the site investigated here appears challenging because of the limited effectiveness of dissociation and large water production, in addition to substantial subsidence.

Moridis, George J.↗

Coupled THM modeling of bentonite heating and hydration in tank tests with a new temperature-dependent water retention model

This study presents a coupled thermo-hydro-mechanical (THM) model for simulating the heating and hydration behavior of bentonite, a buffer material in deep geological repositories (DGRs). The model incorporates a new temperature-dependent soil water retention curve which captures the thermal-induced shift in water retention behavior. It also distinguishes between liquid and gas permeability, modeling intrinsic gas permeability as a function of accessible porosity to improve vapor transport and desaturation predictions. The model was validated against two large-scale tank tests, demonstrating good agreement with measured temperature, relative humidity, and water inflow data. It revealed a complex porosity evolution driven by thermal expansion, vapor movement, vapor condensation, and hydration-induced swelling during heating and hydration processes. The simulation results also suggest that the permeability of the hydration layer plays a critical role in controlling water intake. Clogging of this layer can significantly reduce the volume of water inflow during the hydration phase. Furthermore, while the model effectively captures key THM behavior, further development of the mechanical constitutive law is required to account for possible thermo-elasto-plastic volume changes and microstructural effects. Overall, the model provides a robust tool for evaluating the evolution of bentonite-based barrier material in DGRs.

Guo, Guanlong [Lawrence Berkeley National Laborato↗

Vibrational spectroscopy of uranium tetrafluoride hydrates

Uranium tetrafluoride (UF 4 ) is an important intermediate in the production of UF6 and nuclear fuel. Historical characterization of UF 4 with Raman spectroscopy was plagued with ambiguity until the first accurate Raman spectrum was published by our group in 2016. Although generally considered to be relatively stable, UF 4 can hydrolyze to form numerous UF 4 hydrates that may play a role in future uranium waste forms. In contrast to anhydrous UF 4 , the hydrates, with their OH stretch and HOH bending modes, can be spectroscopically characterized by the type and degree of water bonding in the crystal lattice, which can yield additional information about their crystal structure. Herein, vibrational spectroscopy (Raman and infrared) was used to characterize three different UF 4 hydrates: UF 4 (H 2 O) 0.33 , U 3 F 12 (H 2 O), and UF 4 (H 2 O) 2.5 . Spectra show the different hydrates vary in the number of observed bands, full-width half-maximum of the bands, and band intensity. These differences are due to varying interactions between the OH stretch and HOH bending modes with UF 4 and the polymeric UF 4 structure in the crystal lattice. These vibrational data, in combination with spectral fitting and crystallographic structures measured with powder X-ray diffraction and single crystal X-ray diffraction, provide unique details on the location of water molecules in the crystal lattice of hydrated UF 4 , and provide an interesting contrast to the vibrational spectra of anhydrous UF 4 .

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Surface Hydration and Hydroxyl Configurations of Gibbsite and Boehmite Nanoplates

Discontinuation of the bulk structure at the interface between metal oxide particles and water leads to altered bonding characteristics and unique facet-dependent molecular environments. Surface hydration and consequent hydroxylation adds further complexity to the interface, details that for metal (oxy)hydroxides are especially difficult to isolate from the background signal of bulk structural hydroxyls. Here we probe for the first time the hydroxylation and hydration structures on basal surfaces of gibbsite (?-Al(OH)3) and boehmite (?-AlOOH) nanoplates at ambient conditions, using the interface-sensitive technique vibrational sum frequency generation spectroscopy (VSFG). Hydroxyl stretching modes at the interfaces with adsorbed water layers compared directly to Raman and infrared bulk modes show that while gibbsite surface frequencies were sharp and nearly identical to those in the bulk, boehmite surface hydroxyls displayed a very different broad spectrum of states. Ab initio molecular dynamics simulations of both basal surfaces with and without hydration waters reveal that gibbsite surface hydroxyls interact only weakly with overlying hydration waters remaining essentially unperturbed, whereasthose on boehmite can interact more strongly facilitated by higher configurational degrees of freedom at the interface. The findings clearly unveil substantial differences in the hydrated interfacial dynamics of these two otherwise similar materials, with implications for their interfacial chemistry and wettability.

Sassi, Michel JPC↗

Influence of Water Sorption on Ionic Conductivity in Polyether Electrolytes at Low Hydration

Ion-containing polymers are subject to a wide range of hydration conditions across electrochemical and water treatment applications. Significant work on dry polymer electrolytes for batteries and highly swollen membranes for water purification has informed our understanding of ion transport under extreme conditions. However, knowledge of intermediate conditions (i.e., low hydration) is essential to emerging applications (e.g., electrolyzers, fuel cells, and lithium extraction). Ion transport under low levels of hydration is distinct from the extreme conditions typically investigated, and the relevant physics cannot be extrapolated from existing knowledge, stifling materials design. In this study, we conducted ion transport measurements in LiTFSI-doped polyethers that were systematically hydrated from dry conditions. A semiautomated apparatus that performs parallel measurements of water uptake and ionic conductivity in thin-film polymers under controlled humidity was developed. For the materials and swelling range considered in this study (i.e., <0.07 g water/g dry polymer electrolyte), ionic conductivity depends nonlinearly on water uptake, with the initial sorbed water weakly affecting conductivity. With additional increases in swelling, more significant increases in conductivity were observed. Remarkably, changes in conductivity induced by water sorption were correlated with the number of water molecules per lithium ion, with the normalized molar conductivity of different samples effectively collapsing onto one another until this unit of hydration exceeded the solvation number of lithium ions under aqueous conditions. Furthermore, these results provide important knowledge regarding the effects of trace water contamination on conductivity measurements in polymer electrolytes and demonstrate that the lithium-ion solvation number marks a key transition point regarding the influence of water on ion transport in ion-containing polymers.

36 MATERIALS SCIENCE↗

Influence of Seawater Salts on Magnesium Oxide Hydration: Implications for Carbonation

The effects of individual component salts on MgO hydration and subsequent carbonation have not been systematically investigated despite the increase in utilization of seawater and other brines in the production of MgO-containing next-generation cements, fire retardants, and sorbents for CO2. Here, we present a study of MgO hydration in the presence of individual saltwater cations at a range of concentrations, as well as binary mixtures at seawater concentrations, and subsequent carbonation. We observed that the presence of the cations increased MgO dissolution rates and that the subsequent carbonation extent of the hydrated material remained constant or even increased. Since the presence of these salts during hydration does not show negative effects on subsequent carbonation in our experimental study, the application of seawater and other brines containing high concentrations of these salts to hydrate MgO in industrial processes is likely feasible.

Evans, Barbara [ORNL] (ORCID:0000000225742567)↗

Selective ion transport through hydrated micropores in polymer membranes

Abstract Ion-conducting polymer membranes are essential in many separation processes and electrochemical devices, including electrodialysis 1 , redox flow batteries 2 , fuel cells 3 and electrolysers 4,5 . Controlling ion transport and selectivity in these membranes largely hinges on the manipulation of pore size. Although membrane pore structures can be designed in the dry state 6 , they are redefined upon hydration owing to swelling in electrolyte solutions. Strategies to control pore hydration and a deeper understanding of pore structure evolution are vital for accurate pore size tuning. Here we report polymer membranes containing pendant groups of varying hydrophobicity, strategically positioned near charged groups to regulate their hydration capacity and pore swelling. Modulation of the hydrated micropore size (less than two nanometres) enables direct control over water and ion transport across broad length scales, as quantified by spectroscopic and computational methods. Ion selectivity improves in hydration-restrained pores created by more hydrophobic pendant groups. These highly interconnected ion transport channels, with tuned pore gate sizes, show higher ionic conductivity and orders-of-magnitude lower permeation rates of redox-active species compared with conventional membranes, enabling stable cycling of energy-dense aqueous organic redox flow batteries. This pore size tailoring approach provides a promising avenue to membranes with precisely controlled ionic and molecular transport functions.

Science & Technology - Other Topics↗

Recognition competes with hydration in anion-triggered monolayer formation of cyanostar supra-amphiphiles at aqueous interfaces

The triggered self-assembly of surfactants into organized layers at aqueous interfaces is important for creating adaptive nanosystems and understanding selective ion extraction. While these transformations require molecular recognition, the underlying driving forces are modified by the local environment in ways that are not well understood. Herein, we investigate the role of ion binding and ion hydration using cyanosurf, which is composed of the cyanostar macrocycle, and its binding to anions that are either size-matched or mis-matched and either weakly or highly hydrated. We utilize the supra-amphiphile concept where anion binding converts cyanosurf into a charged and amphiphilic complex triggering its self-organization into monolayers at the air–water interface. Initially, cyanosurf forms aggregates at the surface of a pure water solution. When the weakly hydrated and size-matched hexafluorophosphate (PF 6 - ) and perchlorate (ClO 4 - ) anions are added, the macrocycles form distinct monolayer architectures. Surface-pressure isotherms reveal significant reorganization of the surface-active molecules upon anion binding while infrared reflection absorption spectroscopy show the ion-bound complexes are well ordered at the interface. Vibrational sum frequency generation spectroscopy shows the water molecules in the interfacial region are highly ordered in response to the charged monolayer of cyanosurf complexes. Consistent with the importance of recognition, we find the smaller mis-matched chloride does not trigger the transformation. However, the size-matched phosphate (H 2 PO 4 - ) also does not trigger monolayer formation indicating hydration inhibits its interfacial binding. These studies reveal how anion-selective recognition and hydration both control the binding and thus the switching of a responsive molecular interface.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DEHP− extractant binding to trivalent lanthanide Er3+: Fast binding accompanied by concerted angular motions of hydration water

Solvent extraction of trivalent rare earth metal ions by organophosphorus extractants proceeds via binding of phosphoric acid headgroups to the metal ion. Water molecules in the tightly bound first hydration shell of the metal ions must be displaced by oxygen atoms from phosphoric acid headgroups. Here, we use classical molecular dynamics simulations to explore the event in which a fully hydrated Er3+ binds to its first phosphoric acid headgroup. Approach of the headgroup into the region between the first and second hydration shells leads to a fast ejection of a water molecule that is accompanied by reordering of the hydration water molecules, including discretization of their angular positions and collective rotation about the metal ion. The water molecule ejected from the first shell is located diametrically opposite from the binding oxygen. Headgroup binding places a headgroup oxygen closer to Er3+ than its first hydration shell and creates a loosely bound water that subsequently exchanges between the first shell and its environment. This second exchange of water also occurs at discrete angular positions. This geometrical aspect of binding may be of relevance to understanding the binding and transport of ion–extractant complexes that are expected to occur at the organic–aqueous liquid–liquid interface used in solvent extraction processes.

Chemistry↗

Pore occupancy of gas hydrate

Methane hydrate deposits are one of the largest fractions of hydrocarbons in the Earth's crust. They are found mainly in ocean sediments, and the configuration of the deposits—at the largest (kilometer) and smallest (micrometer) scales—determines how and when gaseous methane is released. Here, in this work, using thermodynamic arguments, we show how the confined spaces of the sediment allow methane hydrate to coexist with both water and gas to create a three-phase region. We find that the hydrate pore occupancy changes depending on the depth of the three-phase region, due to changes in methane density of the gas phase. We estimate the thickness of three-phase regions (hydrate, gas, and water) within ocean sediments. We further show how this directly predicts how the presence of hydrate affects the flow properties of gaseous methane and water through porous media.

flows in porous media↗