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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Isotope effects in molecular structures and electronic properties of liquid water via deep potential molecular dynamics based on the SCAN functional

Here, Feynman path-integral deep potential molecular dynamics (PI-DPMD) calculations have been employed to study both light (H 2 O) and heavy water (D 2 O) within the isothermalisobaric ensemble. In particular, the deep neural network is trained based on ab initio data obtained from the strongly constrained and appropriately normed (SCAN) exchange-correlation functional. Because of the lighter mass of hydrogen than deuteron, the properties of light water are more influenced by nuclear quantum effect than those of heavy water. Clear isotope effects are observed and analyzed in terms of hydrogen-bond structure and electronic properties of water that are closely associated with experimental observables. The molecular structures of both liquid H 2 O and D 2 O agree well with the data extracted from scattering experiments. The delicate isotope effects on radial distribution functions and angular distribution functions are well reproduced as well. Our approach demonstrates that deep neural network combined with SCAN functional based ab initio molecular dynamics provides an accurate theoretical tool for modeling water and its isotope effects.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Nuclear quantum effects in molecular liquids across chemical space

Abstract Nuclear quantum effects (NQEs) influence many physical and chemical phenomena, particularly those involving light atoms or occurring at low temperatures. However, their impact has been carefully quantified in few systems-like water-and is rarely considered more broadly. Here we use path-integral molecular dynamics to systematically investigate NQEs on thermophysical properties of 92 organic liquids at ambient conditions. Depending on chemical constitution, we find substantial impact across thermal expansivity, compressibility, dielectric constant, enthalpy of vaporization, and notably molar volume, which shows consistent, positive quantum-classical differences up to 5%; similar, less pronounced trends manifest as isotope effects from deuteration. Using data-driven analysis, we identify three features-molar mass, classical hydrogen density, and classical thermal expansivity-that accurately predict NQEs and facilitate understanding of how characteristics like branching and heteroatom content influence behavior. This work highlights the broad relevance of NQEs in molecular liquids, while also providing a conceptual and practical framework to anticipate their impact.

Science & Technology - Other Topics↗
DOE OSTI2021

Phonon gas model for thermal conductivity of dense, strongly interacting liquids

Developing predictive thermal property models for liquids based on microscopic principles has been elusive. The difficulty is that liquids have gas-like and solid-like attributes that are at odds when considering the frameworks of microscopic models: Models for gases are simple due to randomness and low density, whereas models for crystalline solids rely on symmetry and long-range order for easier calculation. The short-range order in liquids does, however, provide structure to neighboring molecules similar to amorphous solids, and there have been recent advances indicating that collective vibrational modes store heat in liquids. Models combining Debye approximations from solid-state physics and Frenkel’s theory of liquids can accurately predict the heat capacity of liquids. Phonon-like dispersions in liquids have also been widely observed in neutron scattering experiments. These developments motivate us to propose a model where high-frequency vibrational modes, which travel at the speed of sound and have a mean free path on the order of the average intermolecular distance, conduct heat in liquids. We use this liquid phonon gas model to calculate the thermal conductivity of liquids with varying intermolecular interaction energies from strongest to weakest—Coulomb, hydrogen-bonding, Keesom, and London dispersion energy. Generally, the model is more accurate as the intermolecular interaction energy and density of liquids increase. The calculated thermal conductivity of Coulombic-bound molten sodium nitrate and hydrogen-bonded water is within 1.46% and 2.98% of the experimentally measured values, respectively, across their entire temperature ranges. Further modal analysis of the velocity and the mean free path of collective vibrations could establish the liquid phonon gas model as an accurate model for weakly interacting liquids as well.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Importance of nuclear quantum effects on the hydration of chloride ion

Path-integral ab initio molecular dynamics (PI-AIMD) calculations have been employed to probe the nature of chloride ion solvation in aqueous solution. Nuclear quantum effects (NQEs) are shown to weaken hydrogen bonding between the chloride anion and the solvation shell of water molecules. As a consequence, the disruptive effect of the anion on the solvent water structure is significantly reduced compared to what is found in the absence of NQEs. Additionally, the chloride hydration structure obtained from PI-AIMD agrees well with information extracted from neutron scattering data. In particular, the observed satellite peak in the hydrogen-chloride-hydrogen triple angular distribution serves as a clear signature of NQEs. The present results suggest that NQEs are likely to play a crucial role in determining the structure of saline solutions.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Isotope effects in x-ray absorption spectra of liquid water

The isotope effects in x-ray absorption spectra of liquid water are studied by a many-body approach within electron-hole excitation theory. The molecular structures of both light and heavy water are modeled by path-integral molecular dynamics based on the advanced deep-learning technique. The neural network is trained on ab initio data obtained with SCAN density functional theory. The experimentally observed isotope effect in x-ray absorption spectra is reproduced semiquantitatively in theory. Compared to the spectrum in normal water, the blueshifted and less pronounced pre- and main-edge in heavy water reflect that the heavy water is more structured at short- and intermediate-range of the hydrogen-bond network. In contrast, we find the isotope effect on the spectrum is negligible at post-edge, which is consistent with the identical long-range ordering in both liquids as observed in the diffraction experiment.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Quantum Simulations of Vibrational Strong Coupling via Path Integrals

A quantum simulation of vibrational strong coupling (VSC) in the collective regime via thermostated ring-polymer molecular dynamics (TRPMD) is reported. For a collection of liquid-phase water molecules resonantly coupled to a single lossless cavity mode, the simulation shows that as compared with a fully classical calculation, the inclusion of nuclear and photonic quantum effects does not lead to a change in the Rabi splitting but does broaden polaritonic line widths roughly by a factor of 2. Moreover, under thermal equilibrium, both quantum and classical simulations predict that the static dielectric constant of liquid water is largely unchanged inside vs outside the cavity. Furthermore, this result disagrees with a recent experiment demonstrating that the static dielectric constant of liquid water can be resonantly enhanced under VSC, suggesting either limitations of our approach or perhaps other experimental factors that have not yet been explored.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Pilot-Scale Algal Oil Production

The main objective of the project is complete: development of a preliminary planning and design for a pilot-scale algal oil cultivation and processing facility, FEL-3 design with -5% / +15% cost estimate accuracy, and conversion of the algal oil to biofuel in an off-site existing bio-oil refinery. The design basis includes 10 tons per day of dried algae cultivated with CO 2 supplied by direct air capture, electricity supplied solar power, well water supply, zero liquid discharge, off-site extraction, and off-site conversion of oil to biofuel. The design and permitting package is an important milestone in the path to commercialization of algal biofuels and bioproducts as it provides the preliminary design, permitting path, long-term land lease, planning documents, and team needed for success in future engineering, construction, start-up and operations of a pilot-scale farm at a site in Paso Robles, CA. Outcomes of the business assessment include (i) identification of a product spectrum for economical algal biofuels using co-products with markets that are commensurate with production of 6-7 billion gallons per year of sustainable aviation fuel (SAF), renewable diesel, and renewable gasoline, (ii) a path toward near-term contribution of algae oil to SAF, and (iii) an approach for long-term operation of a pilot-scale farm.

09 BIOMASS FUELS↗
DOE OSTI2022

Influence of the Nature of Aliphatic Hydrophobic Physical Crosslinks on Water Crystallization in Copolymer Hydrogels

The local environment within a hydrogel influences the properties of water, including the propensity for ice crystallization. Water-swollen amphiphilic copolymers produce tunable nanoscale environments, which are defined by hydrophobic associations, for the water molecules. In this work, the antifreeze properties for equilibrium-swollen amphiphilic copolymers with a common hydrophilic component, hydroxyethyl acrylate (HEA), but associated through crystalline (octadecyl acrylate, ODA) or rubbery (ethylhexyl acrylate, EHA) hydrophobic segments, are examined. Differences in the efficacy of the associations can be clearly enunciated from compositional solubility limits for the copolymers in water (<2.6 mol % ODA vs ≤14 mol % EHA), and these differences can be attributed to the strength of the association. The equilibrium-swollen HEA-ODA copolymers are viscoelastic solids, while the swollen HEA-EHA copolymers are viscoelastic liquids. Cooling these swollen copolymers to nearly 200 K induces some crystallization of the water, where the fraction of water frozen depends on the details of the nanostructure. Decreasing the mean free path of water by increasing the ODA composition from 10 to 25 mol % leads to fractionally more unfrozen water (66–87%). The swollen HEA-EHA copolymers only marginally inhibit ice (<13%) except with 45 mol % EHA, where nearly 60% of the water remains amorphous on cooling to 200 K. In general, the addition of the EHA leads to less effective ice inhibition than analogous covalently crosslinked HEA hydrogels (19.9 ± 1.8%). These results illustrate that fluidity of confining surfaces can provide pathways for critical nuclei to form and crystal growth to proceed.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Insights into the thermo-hydraulic properties of compacted MX80 bentonite during hydration under elevated temperature

In high-level radioactive waste geological repositories, compacted bentonite undergoes coupled thermo-hydraulic processes due to heat released from a central waste canister and groundwater imbibition from the surrounding host rock. An understanding of these processes is essential for long-term simulations of radionuclide migration and canister corrosion, which requires an understanding of temperature effects on the coupled thermo-hydraulic properties governing these processes. In this study, a tank-scale radial infiltration test was used to investigate water imbibition processes in compacted bentonite under a central heater temperature of 200 °C that simulates high thermal gradients in a repository. Interpretation of this test focuses on evaluation of the liquid water wetting front during hydration and the interpretation of the temperature-dependent transient soil water retention curve (SWRC), thermal conductivity function (TCF), and hydraulic conductivity function (HCF). The SWRC during imbibition follows a temperature-dependent wetting path. Temperature effects on the hydraulic conductivity of bentonite in saturated conditions had the greatest effect on the shape of the HCF, with minimal temperature effects at higher suctions. The transient thermal conductivity data matched well with a new TCF linked with the SWRC shape. Although the bentonite layer was restrained, local deformations during hydration may have affected the shapes of the TCF and HCF.

Engineering↗
DOE OSTI2025

FY24 Task 4: Studies of Phosphate and Fluoride Solubility for Dissolution of High Phosphate Tank Waste

Knowledge gaps have been identified in phosphate solubility in almost every single- and multi-component system, and particularly for aluminate in phosphate/hydroxide, where uncertainties in predicted values of aluminum solubility are greater than 50%. Solubility data of multicomponent, aqueous electrolytes containing sodium hydroxide, sodium fluoride, sodium phosphate, sodium nitrite, sodium nitrate, and dissolved gibbsite are also sparse. For example, for solutions of (i) sodium nitrate and sodium phosphate, data are only available at 30 and 50 °C, and for (ii) dissolved gibbsite in sodium hydroxide and sodium phosphate, only two data points are available at 20 and 40 °C. There is no data available on mixtures of sodium hydroxide, sodium phosphate, sodium fluoride, and dissolved gibbsite. These knowledge gaps were identified in a technical review of waste solubility data and the impact of dilution on solution stabilities and will be addressed in this work to predict aluminum hydroxide and sodium phosphate solubility in multicomponent electrolytes upon dilution, and upon variation of temperature. Results will provide the technical basis to develop accurate models for (i) gibbsite solubility and mass transfer of aluminum between solid and liquid forms following the sluicing of sludge and saltcake with water; and (ii) further blending of these suspensions with bismuth from bismuth phosphate waste, and zirconium and uranium left from the fuel decladding. This work will be essential to developing a disposition path for retrieval solutions from bismuth phosphate wastes. This effort would also support sludge washing to further reduce phosphate concentration if that process were to be added back to the flowsheet in the future.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2022

Water balance model (WBM) v.1.0.0: a scalable gridded global hydrologic model with water-tracking functionality

Abstract. This paper describes the University of New Hampshire Water Balance Model, WBM, a process-based gridded global hydrologic model that simulates the land surface components of the global water cycle and includes water extraction for use in agriculture and domestic sectors. The WBM was first published in 1989; here, we describe the first fully open-source WBM version (v.1.0.0). Earlier descriptions of WBM methods provide the foundation for the most recent model version that is detailed here. We present an overview of the model functionality, utility, and evaluation of simulated global river discharge and irrigation water use. This new version adds a novel suite of water source tracking modules that enable the analysis of flow-path histories on water supply. A key feature of WBM v.1.0.0 is the ability to identify the partitioning of sources for each stock or flux within the model. Three different categories of tracking are available: (1) primary inputs of water to the surface of the terrestrial hydrologic cycle (liquid precipitation, snowmelt, glacier melt, and unsustainable groundwater); (2) water that has been extracted for human use and returned to the terrestrial hydrologic system; and (3) runoff originating from user-defined spatial land units. Such component tracking provides a more fully transparent model in that users can identify the underlying mechanisms generating the simulated behavior. We find that WBM v.1.0.0 simulates global river discharge and irrigation water withdrawals well, even with default parameter settings, and for the first time, we are able to show how the simulation arrives at these fluxes by using the novel tracking functions.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Dimension-free path-integral molecular dynamics without preconditioning

Convergence with respect to imaginary-time discretization (i.e., the number of ring-polymer beads) is an essential part of any path-integral-based molecular dynamics (MD) calculation. However, an unfortunate property of existing non-preconditioned numerical integration schemes for path-integral molecular dynamics—including essentially all existing ring-polymer molecular dynamics (RPMD) and thermostatted RPMD (T-RPMD) methods—is that for a given MD time step, the overlap between the exact ring-polymer Boltzmann–Gibbs distribution and that sampled using MD becomes zero in the infinite-bead limit. This has clear implications for hybrid Metropolis Monte Carlo/MD sampling schemes, and it also causes the divergence with bead number of the primitive path-integral kinetic-energy expectation value when using standard RPMD or T-RPMD. We show that these and other problems can be avoided through the introduction of “dimension-free” numerical integration schemes for which the sampled ring-polymer position distribution has non-zero overlap with the exact distribution in the infinite-bead limit for the case of a harmonic potential. Most notably, we introduce the BCOCB integration scheme, which achieves dimension freedom via a particular symmetric splitting of the integration time step and a novel implementation of the Cayley modification [R. Korol et al., J. Chem. Phys. 151, 124103 (2019)] for the free ring-polymer half-steps. More generally, we show that dimension freedom can be achieved via mollification of the forces from the external physical potential. The dimension-free path-integral numerical integration schemes introduced here yield finite error bounds for a given MD time step, even as the number of beads is taken to infinity; these conclusions are proven for the case of a harmonic potential and borne out numerically for anharmonic systems that include liquid water. The numerical results for BCOCB are particularly striking, allowing for nearly three-fold increases in the stable time step for liquid water with respect to the Bussi–Parrinello (OBABO) and Leimkuhler (BAOAB) integrators, while introducing negligible errors in the calculated statistical properties and absorption spectrum. Importantly, the dimension-free, non-preconditioned integration schemes introduced here preserve ergodicity and global second-order accuracy, and they remain simple, black-box methods that avoid additional computational costs, tunable parameters, or system-specific implementations.

Korol, Roman (ORCID:0000000193076351)↗
DOE OSTI2021

Modeling Liquid Water by Climbing up Jacob’s Ladder in Density Functional Theory Facilitated by Using Deep Neural Network Potentials

Within the framework of Kohn–Sham density functional theory (DFT), the ability to provide good predictions of water properties by employing a strongly constrained and appropriately normed (SCAN) functional has been extensively demonstrated in recent years. Here, we further advance the modeling of water by building a more accurate model on the fourth rung of Jacob’s ladder with the hybrid functional, SCAN0. In particular, we carry out both classical and Feynman path-integral molecular dynamics calculations of water with the SCAN0 functional and the isobaric–isothermal ensemble. To generate the equilibrated structure of water, a deep neural network potential is trained from the atomic potential energy surface based on ab initio data obtained from SCAN0 DFT calculations. For the electronic properties of water, a separate deep neural network potential is trained by using the Deep Wannier method based on the maximally localized Wannier functions of the equilibrated trajectory at the SCAN0 level. The structural, dynamic, and electric properties of water were analyzed. The hydrogen-bond structures, density, infrared spectra, diffusion coefficients, and dielectric constants of water, in the electronic ground state, are computed by using a large simulation box and long simulation time. For the properties involving electronic excitations, we apply the GW approximation within many-body perturbation theory to calculate the quasiparticle density of states and bandgap of water. Compared to the SCAN functional, mixing exact exchange mitigates the self-interaction error in the meta-generalized-gradient approximation and further softens liquid water toward the experimental direction. For most of the water properties, the SCAN0 functional shows a systematic improvement over the SCAN functional. However, some important discrepancies remain. The H-bond network predicted by the SCAN0 functional is still slightly overstructured compared to the experimental results.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Metastable precipitation and ion–extractant transport in liquid–liquid separations of trivalent elements

The extractant-assisted transport of metal ions from aqueous to organic environments by liquid–liquid extraction has been widely used to separate and recover critical elements on an industrial scale. While current efforts focus on designing better extractants and optimizing process conditions, the mechanism that underlies ionic transport remains poorly understood. Here, we report a nonequilibrium process in the bulk aqueous phase that influences interfacial ion transport: the formation of metastable ion–extractant precipitates away from the liquid–liquid interface, separated from it by a depletion region without precipitates. Although the precipitate is soluble in the organic phase, the depletion region separates the two and ions are sequestered in a long-lived metastable state. Since precipitation removes extractants from the aqueous phase, even extractants that are sparingly soluble in water will continue to be withdrawn from the organic phase to feed the aqueous precipitation process. Solute concentrations in both phases and the aqueous pH influence the temporal evolution of the process and ionic partitioning between the precipitate and organic phase. Aqueous ion–extractant precipitation during liquid–liquid extraction provides a reaction path that can influence the extraction kinetics, which plays an important role in designing advanced processes to separate rare earths and other minerals.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Observed and Simulated Variability of Droplet Spectral Dispersion in Convective Clouds Over the Amazon

Abstract In this study, the variability of the spectral dispersion of droplet size distributions (DSDs) in convective clouds is investigated. Analyses are based on aircraft measurements of growing cumuli near the Amazon basin, and on numerical simulations of an idealized ice‐free cumulus. In cleaner clouds, the relative dispersion , defined as the ratio of the standard deviation to the mean value of the droplet diameter, is negatively correlated with the ratio of the cloud water content ( ) to the adiabatic liquid water content ( ), while no strong correlation between and is seen in polluted clouds. Bin microphysics numerical simulations suggest that these contrasting behaviors are associated with the effect of collision‐coalescence in cleaner clouds, and secondary droplet activation in polluted clouds, in addition to the turbulent mixing of parcels that experienced different paths within the cloud. Collision‐coalescence simultaneously broadens the DSDs and decreases , explaining the inverse relationship between and in cleaner clouds. Secondary droplet activation broadens the DSDs but has little direct impact on . The combination of a rather modest DSD broadening due to weak collision‐coalescence with enhanced droplet activation in both diluted and highly undiluted cloud regions may contribute to maintain a relatively uniform within polluted clouds. These findings can be useful for parameterizing the shape parameter ( ) of gamma DSDs in bulk microphysics cloud‐resolving models. It is shown that emulating the observed relationship improves the estimation of the collision‐coalescence rate in bulk microphysics simulations compared to the bin simulations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

A Machine‐Learning‐Assisted Stochastic Cloud Population Model as a Parameterization of Cumulus Convection

Abstract A machine‐learning‐assisted stochastic cloud population model is coupled with the Advanced Research Weather Research and Forecasting (WRF) model to represent fluctuations in the cloud‐base mass flux associated with the life cycles and interactions among cumulus convection cells. In this cloud population model, the size distribution and the associated cloud‐base mass flux of the convective cells are related to their previous state and to the change in the total convective area via a transition function. The convective area tendency in turn is assumed to depend on the cloud‐base mass flux that is resolved by the host WRF model. The transition function is represented by a single hidden‐layer neural network trained by the evolution of convective cell size distributions in a 1‐km grid‐spacing WRF simulation run over the Australian Monsoon region. At every grid point of the host model, the cloud population model predicts the cell size and cloud‐base mass flux distributions from which a random sample of cells is fed to an entraining parcel model that calculates precipitation as well as the associated liquid water potential temperature and total moisture tendencies. These tendencies are averaged over the cells and provided to the host model. Several regional simulations are performed over tropical and midlatitude domains to test this as a potential approach to scale‐aware parameterization. It is shown that such an approach could be a new promising path to simulating realistic precipitation statistics and propagation of precipitation associated with the Madden‐Julian Oscillation while maintaining realistic depictions of the diurnal cycle over both land and ocean.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Porous mesh manifold for enhanced boiling performance

High-performance electronics are continuously demanding cooling of higher heat fluxes. Phase-change cooling, including pool boiling, is a useful approach to address this challenge; however, competition between liquid and vapor flows generally limit the heat fluxes that can be dissipated. A range of strategies to control these flows have been investigated previously, including capillary guides. Here a manifold structure formed from a metallic mesh is investigated to control the disposition of liquid and vapor phases above a pool fed boiling surface enhanced with porous structures. Copper mesh forms defined liquid flow paths, using capillary action to guide and distribute liquid evenly over the heated surface, along with open channels to facilitate vapor escape. The mesh provides a novel structure for liquid guidance that imposes low resistance to liquid flow while occluding a minimal area of heated surface underneath. The manifold performance is characterized in boiling fed by a pool of water above a laser-textured aluminum nitride heat dissipation surface with pin–fin structures having heights of 110 µm and spacing of 30 µm with a heated area of 5 mm x 5 mm. A maximum heat flux of 490 W/cm 2 is reached with the manifold in the pool fed configuration, representing an increase of more than 65% over the porous pin fin surface alone. The maximum stable superheat observed for the manifold of 36K is 14K higher than that for the porous surface without the manifold. The factors limiting performance of the manifold are analyzed. High superheat is attributed to partial flooding of the boiling surface as suggested by the reduction in superheat using external suction. Similar systems and structures for enhanced two-phase cooling are compared.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Relative permeabilities for two-phase flow through wellbore cement fractures

Multiple fluids are likely to exist in fractures and flow paths associated with leaky wellbores, including liquids (e.g., crude oil) and gases (e.g., gas exsolved from liquid). These fluids occupy and move through different portions of the pore spaces within the fractures depending on many factors, including fluid properties, fracture size, and the amount of the different fluids. Upward leakage of any phase, through the fracture, can contaminate water-bearing formations, create hazardous surface conditions, and compromise the functionality of the wellbore. Early signs of wellbore leaks may be expressed by anomalous pressure behavior at surface monitoring points on cavern storage wells. These pressure anomalies are difficult to interpret, necessitating knowledge of the factors that affect the multiphase flow in fractures and porous media. These parameters are critical to modeling multiphase flow in fractures. This insight can guide further diagnosis and maximize leak remediation. Here, our study focuses on the relationship of the liquid–gas relative permeabilities for representative variable-aperture wellbore cement fracture. To obtain the relative permeability of each phase, two-phase flow tests were conducted where both fluids were flowing simultaneously through a fractured wellbore cement specimen under a range of factors, namely (1) aperture size, (2) capillary numbers, and (3) viscosity ratio. The flow experiments were conducted under a range of confining stresses and flow velocities, using nitrogen gas and silicone oils (of different viscosities) in a specially designed pressure vessel. The sum of gas and oil relative permeabilities were found to be less than one under all conditions, which indicates that the presence of one phase affects the permeability of the other phase, and vice versa. Since the gas phase flow conditions include a significant inertial flow component in addition to viscous flow, the inertial flow coefficients at different saturation states are presented. The factors affecting the relationship between the relative permeabilities are discussed in detail. A new mathematical model for estimating the relative permeability of wellbore cement fracture is presented and experimentally validated.

58 GEOSCIENCES↗