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Potential of New Business Models for Grid Integrated Water Electrolysis
Feb 2018
Publication
Grid integrated water electrolysers have the potential of coupling electric power systems subjected to high shares of renewable energy sources with sectors of hydrogen demand thus contributing to European decarbonization goals in future. We therefore investigate the business potential of future electrolyser applications in cross-commodity arbitrage trading by applying a complex power market simulation method for future scenarios and different European countries. Based on this we evaluate the potential of additional provision of grid services towards grid operators in order to increase the electrolyser utilization ratio. For this we use a method that identifies measures of transmission grid operators in order to ensure secure grid operation. In this context uncertain hydrogen prices and different sectors of hydrogen demand are addressed through sensitivities of different hydrogen sales prices. The analysis shows a high dependency of business model efficiency on the hydrogen price. While cross-commodity arbitrage trading can achieve profitability for the transportation sector applications for the industry sector and natural gas system are less efficient. The results however indicate that for these less efficient applications grid service provision can be an option of increasing the electrolyser utilization ratio thus increasing its profitability.
Research Efforts for the Resolution of Hydrogen Risk
Jan 2015
Publication
During the past 10 years the Korea Atomic Energy Research Institute (KAERI) has performed a study to control hydrogen gas in the containment of the nuclear power plants. Before the Fukushima accident analytical activities for gas distribution analysis in experiments and plants were primarily conducted using a multidimensional code: the GASFLOW. After the Fukushima accident the COM3D code which can simulate a multi-dimensional hydrogen explosion was introduced in 2013 to complete the multidimensional hydrogen analysis system. The code validation efforts of the multidimensional codes of the GASFLOW and the COM3D have continued to increase confidence in the use of codes using several international experimental data. The OpenFOAM has been preliminarily evaluated for APR1400 containment based on experience from coded validation and the analysis of hydrogen distribution and explosion using the multidimensional codes the GASFLOW and the COM3D. Hydrogen safety in nuclear power has become a much more important issue after the Fukushima event in which hydrogen explosions occurred. The KAERI is preparing a large-scale test that can be used to validate the performance of domestic passive autocatalytic recombiners (PARs) and can provide data for the validation of the severe accident code being developed in Korea
A Fundamental Viewpoint on the Hydrogen Spillover Phenomenon of Electrocatalytic Hydrogen Evolution
Jun 2021
Publication
Hydrogen spillover phenomenon of metal-supported electrocatalysts can significantly impact their activity in hydrogen evolution reaction (HER). However design of active electrocatalysts faces grand challenges due to the insufficient understandings on how to overcome this thermodynamically and kinetically adverse process. Here we theoretically profile that the interfacial charge accumulation induces by the large work function difference between metal and support (∆Φ) and sequentially strong interfacial proton adsorption construct a high energy barrier for hydrogen transfer. Theoretical simulations and control experiments rationalize that small ∆Φ induces interfacial charge dilution and relocation thereby weakening interfacial proton adsorption and enabling efficient hydrogen spillover for HER. Experimentally a series of Pt alloys-CoP catalysts with tailorable ∆Φ show a strong ∆Φ-dependent HER activity in which PtIr/CoP with the smallest ∆Φ = 0.02 eV delivers the best HER performance. These findings have conclusively identified ∆Φ as the criterion in guiding the design of hydrogen spillover-based binary HER electrocatalysts
Assessing Uncertainties of Life-Cycle CO2 Emissions Using Hydrogen Energy for Power Generation
Oct 2021
Publication
Hydrogen and its energy carriers such as liquid hydrogen (LH2) methylcyclohexane (MCH) and ammonia (NH3) are essential components of low-carbon energy systems. To utilize hydrogen energy the complete environmental merits of its supply chain should be evaluated. To understand the expected environmental benefit under the uncertainty of hydrogen technology development we conducted life-cycle inventory analysis and calculated CO2 emissions and their uncertainties attributed to the entire supply chain of hydrogen and NH3 power generation (co-firing and mono-firing) in Japan. Hydrogen was assumed to be produced from overseas renewable energy sources with LH2/MCH as the carrier and NH3 from natural gas or renewable energy sources. The Japanese life-cycle inventory database was used to calculate emissions. Monte Carlo simulations were performed to evaluate emission uncertainty and mitigation factors using hydrogen energy. For LH2 CO2 emission uncertainty during hydrogen liquefaction can be reduced by using low-carbon fuel. For MCH CO2 emissions were not significantly affected by power consumption of overseas processes; however it can be reduced by implementing low-carbon fuel and waste-heat utilization during MCH dehydrogenation. Low-carbon NH3 production processes significantly affected power generation whereas carbon capture and storage during NH3 production showed the greatest reduction in CO2 emission. In conclusion reducing CO2 emissions during the production of hydrogen and NH3 is key to realize low-carbon hydrogen energy systems.
Fundamentals and Principles of Solid-State Electrochemical Sensors for High Temperature Gas Detection
Dec 2021
Publication
The rapid development of science technology and engineering in the 21st century has offered a remarkable rise in our living standards. However at the same time serious environmental issues have emerged such as acid rain and the greenhouse effect which are associated with the ever-increasing need for energy consumption 85% of which comes from fossil fuels combustion. From this combustion process except for energy the main greenhouse gases-carbon dioxide and steam-are produced. Moreover during industrial processes many hazardous gases are emitted. For this reason gas-detecting devices such as electrochemical gas sensors able to analyze the composition of a target atmosphere in real time are important for further improving our living quality. Such devices can help address environmental issues and inform us about the presence of dangerous gases. Furthermore as non-renewable energy sources run out there is a need for energy saving. By analyzing the composition of combustion emissions of automobiles or industries combustion processes can be optimized. This review deals with electrochemical gas sensors based on solid oxide electrolytes which are employed for the detection of hazardous gasses at high temperatures and aggressive environments. The fundamentals the principle of operation and the configuration of potentiometric amperometric combined (amperometric-potentiometric) and mixed-potential gas sensors are presented. Moreover the results of previous studies on carbon oxides (COx) nitrogen oxides (NOx) hydrogen (H2 ) oxygen (O2 ) ammonia (NH3 ) and humidity (steam) electrochemical sensors are reported and discussed. Emphasis is given to sensors based on oxygen ion and proton-conducting electrolytes.
World Energy Issues Monitor 2020: Decoding New Signals of Change
Oct 2020
Publication
ISSUES MONITOR 2020: DECODING NEW SIGNALS OF CHANGE
The annual World Energy Issues Monitor provides unique insight into what energy policymakers CEOs and leading experts identify as Critical Uncertainties and Action Priorities. New this year the Issues Monitor also provides readers with the views of the individual customer detailing their perceptions of their role in the overall energy system. The Issues Monitor report includes a global issues map 58 country maps and six regional maps as well as perspectives from Future Energy Leaders (FEL) and energy innovators.
GLOBAL PERSPECTIVES
The 2020 global map incorporates all survey responses representing the views of over 3000 energy leaders from 104 countries. In this era of transition defined by decentralisation digitalisation and decarbonisation energy leaders must pay attention to many different signals of change and distinguish key issues from the noise. The Issues Monitor identifies shifting patterns of connected issues shaping energy transitions.
A NEW PULSE
The focus for the 2010s was about trying to automate and upgrade the energy system and set targets to move the energy transition forward. Digitalisation accelerated the transition of all sectors towards a more customer-centric environment. New policies and regulations were introduced to facilitate this transition and empower consumers. As a result the 2020s may very well be about realising those targets through a transition from activism to action.
TREND TRACKING: CCS
In comparing response from the Oil & Gas sector in 2015 with 2019 we found that almost half of respondents identified Carbon Capture & Storage (CCS) as a high impact issue in 2019 up from about a third in 2015. CCS is increasingly being viewed as an essential option for continued hydrocarbon use although governmental support is needed to enable scalability and cost effectiveness.
A DIFFERENCE IN OPINION: NUCLEAR
Opinions remain polarised but in many European countries nuclear power is increasingly recognised as a carbon-free energy source and potentially an integral part of the future energy mix. In December 2019 the European Commission set a target of net-zero carbon emissions by 2050. There is qualified support among energy leaders to include nuclear energy to help create a carbon neutral continent and enable a just energy transition.
The annual World Energy Issues Monitor provides unique insight into what energy policymakers CEOs and leading experts identify as Critical Uncertainties and Action Priorities. New this year the Issues Monitor also provides readers with the views of the individual customer detailing their perceptions of their role in the overall energy system. The Issues Monitor report includes a global issues map 58 country maps and six regional maps as well as perspectives from Future Energy Leaders (FEL) and energy innovators.
GLOBAL PERSPECTIVES
The 2020 global map incorporates all survey responses representing the views of over 3000 energy leaders from 104 countries. In this era of transition defined by decentralisation digitalisation and decarbonisation energy leaders must pay attention to many different signals of change and distinguish key issues from the noise. The Issues Monitor identifies shifting patterns of connected issues shaping energy transitions.
A NEW PULSE
The focus for the 2010s was about trying to automate and upgrade the energy system and set targets to move the energy transition forward. Digitalisation accelerated the transition of all sectors towards a more customer-centric environment. New policies and regulations were introduced to facilitate this transition and empower consumers. As a result the 2020s may very well be about realising those targets through a transition from activism to action.
TREND TRACKING: CCS
In comparing response from the Oil & Gas sector in 2015 with 2019 we found that almost half of respondents identified Carbon Capture & Storage (CCS) as a high impact issue in 2019 up from about a third in 2015. CCS is increasingly being viewed as an essential option for continued hydrocarbon use although governmental support is needed to enable scalability and cost effectiveness.
A DIFFERENCE IN OPINION: NUCLEAR
Opinions remain polarised but in many European countries nuclear power is increasingly recognised as a carbon-free energy source and potentially an integral part of the future energy mix. In December 2019 the European Commission set a target of net-zero carbon emissions by 2050. There is qualified support among energy leaders to include nuclear energy to help create a carbon neutral continent and enable a just energy transition.
A Fracture Analysis of Ti-10Mo-8V-1Fe-3.5Al Alloy Screws during Assembly
Oct 2016
Publication
Titanium screws have properties that make them ideal for applications that require both a high strength-to-weight ratio and corrosion resistance such as fastener applications for aviation and aerospace. The fracture behavior of Ti-10Mo-8V-1Fe-3.5Al (TB3) alloy screws during assembly was explored. Besides visual examination other experimental techniques used for the investigation are as follows: (1) fracture characteristics and damage morphology via scanning electron microscopy (SEM); (2) chemical constituents via energy dispersive spectroscopy (EDS) and hydrogen concentration testing; (3) metallographic observation; (4) stress durability embrittlement testing; and (5) torsion simulation testing. Results show that the fracture mode of the screws is brittle. There is no obvious relation to hydrogen-induced brittle. The main reason for the fracture of titanium alloy screws is internal defects around which oxygen content is high increasing brittleness. The internal defects of screws result from grain boundary cracking caused by hot forging.
The Effect of the Temperature and Moisture to the Permeation Properties of PEO-Based Membranes for Carbon-Dioxide Separation
Jun 2021
Publication
An increased demand for energy in recent decades has caused an increase in the emissions of combustion products among which carbon-dioxide is the most harmful. As carbon-dioxide induces negative environmental effects like global warming and the greenhouse effect a decrease of the carbon-dioxide emission has emerged as one of the most urgent tasks in engineering. In this work the possibility for the application of the polymer-based dense mixed matrix membranes for flue gas treatment was tested. The task was to test a potential decrease in the permeability and selectivity of a mixed-matrix membrane in the presence of moisture and at elevated temperature. Membranes are based on two different poly(ethylene oxide)-based polymers filled with two different zeolite powders (ITR and IWS). An additive of detergent type was added to improve the contact properties between the zeolite and polymer matrix. The measurements were performed at three different temperatures (30 60 and 90 °C) under wet conditions with partial pressure of the water equal to the vapor pressure of the water at the given temperature. The permeability of carbon-dioxide hydrogen nitrogen and oxygen was measured and the selectivity of the carbon-dioxide versus other gases was determined. Obtained results have shown that an increase of temperature and partial pressure of the vapor slightly increase both the selectivity and permeability of the synthesized membranes. It was also shown that the addition of the zeolite powder increases the permeability of carbon-dioxide while maintaining the selectivity compared to hydrogen oxygen and nitrogen.
Hybrid Hydrogen Home Storage for Decentralized Energy Autonomy
May 2021
Publication
As the share of distributed renewable power generation increases high electricity prices and low feed-in tariff rates encourage the generation of electricity for personal use. In the building sector this has led to growing interest in energy self-sufficient buildings that feature battery and hydrogen storage capacities. In this study we compare potential technology pathways for residential energy storage in terms of their economic performance by means of a temporal optimization model of the fully self-sufficient energy system of a single-family building taking into account its residential occupancy patterns and thermal equipment. We show for the first time how heat integration with reversible solid oxide cells (rSOCs) and liquid organic hydrogen carriers (LOHCs) in high-efficiency single-family buildings could by 2030 enable the self-sufficient supply of electricity and heat at a yearly premium of 52% against electricity supplied by the grid. Compared to lithium-ion battery systems the total annualized cost of a self-sufficient energy supply can be reduced by 80% through the thermal integration of LOHC reactors and rSOC systems.
Comprehensive Study on Hydrogen Production via Propane Steam Reforming Inside a Reactor
Feb 2021
Publication
In the proton exchange membrane fuel cells the required hydrogen must be produced in some way. The power generators in the path of these fuel cells generally include a steam reactor that through other fuels provides the needed energy to produce hydrogen. This study investigates a steam reactor powered by propane fuel consisting of a shell and tube heat exchanger. The shell contains a catalyst that receives the mixture of propane and steam and the tubes embedded inside the reformer contain hot gases that provide a suitable substrate for the reaction. Velocity and temperature fields inside the reformer species concentration control and reaction rate are studied. The conversion of reactants and yield of products are investigated according to the reaction rate. The results show that the hydrogen production yield can vary from 77.5 % to 92.2 %. The reaction rate can be controlled by the velocity and temperatures of the hot gases. However for the T=900 K full propane consumption is achieved at the reformer outlet.
Recent Research Progress in Hybrid Photovoltaic–Regenerative Hydrogen Fuel Cell Microgrid Systems
May 2022
Publication
Hybrid photovoltaic–regenerative hydrogen fuel cell (PV-RHFC) microgrid systems are considered to have a high future potential in the effort to increase the renewable energy share in the form of solar PV technology with hydrogen generation storage and reutilization. The current study provides a comprehensive review of the recent research progress of hybrid PV-RHFC microgrid systems to extract conclusions on their characteristics and future prospects. The different components that can be integrated (PV modules electrolyzer and fuel cell stacks energy storage units power electronics and controllers) are analyzed in terms of available technology options. The main modeling and optimization methods and control strategies are discussed. Additionally various application options are provided which differentiate in terms of scale purpose and further integration with other power generating and energy storage technologies. Finally critical analysis and discussion of hybrid PV-RHFC microgrid systems were conducted based on their current status. Overall the commercialization of hybrid PV-RHFC microgrid systems requires a significant drop in the RHFC subsystem capital cost. In addition it will be necessary to produce complete hybrid PV-RHFC microgrid systems with integrated energy management control capabilities to avoid operational issues and ensure flexibility and reliability of the energy flow in relation to supply storage and demand.
Magnetron Sputter Deposited NiCu Alloy Catalysts for Production of Hydrogen Through Electrolysis in Alkaline Water
Jul 2018
Publication
NiCu alloy catalysts with varying composition for electrolysis in alkaline water have been prepared by DC magnetron co-sputtering under Ar gas environment at substrate bias of 60 V. Nanocrystallinity lattice parameters and grain size of the NiCu alloys have been measured by grazing incidence X-ray diffraction (GIXRD). Elemental and microstructural analysis of the NiCu alloy have been done by field emission scanning electron microscopy (FESEM) as well as transmission electron microscopy (TEM). To analyze the NiCu alloys activity towards hydrogen evolution reaction (HER) cyclic voltammetry measurements have been done in a 6 M KOH at room temperature and further HER activities have been correlated with the varying Cu concentration in NiCu alloy catalysts.
Cross-regional Drivers for CCUS Deployment
Jul 2020
Publication
CO2 capture utilization and storage (CCUS) is recognized as a uniquely important option in global efforts to control anthropogenic greenhouse-gas (GHG) emissions. Despite significant progress globally in advancing the maturity of the various component technologies and their assembly into full-chain demonstrations a gap remains on the path to widespread deployment in many countries. In this paper we focus on the importance of business models adapted to the unique technical features and sociopolitical drivers in different regions as a necessary component of commercial scale-up and how lessons might be shared across borders. We identify three archetypes for CCUS development—resource recovery green growth and low-carbon grids—each with different near-term issues that if addressed will enhance the prospect of successful commercial deployment. These archetypes provide a framing mechanism that can help to translate experience in one region or context to other locations by clarifying the most important technical issues and policy requirements. Going forward the archetype framework also provides guidance on how different regions can converge on the most effective use of CCUS as part of global deep-decarbonization efforts over the long term.
Hydrogen in Grid Balancing: The European Market Potential for Pressurized Alkaline Electrolyzers
Jan 2022
Publication
To limit the global temperature change to no more than 2 ◦C by reducing global emissions the European Union (EU) set up a goal of a 20% improvement on energy efficiency a 20% cut of greenhouse gas emissions and a 20% share of energy from renewable sources by 2020 (10% share of renewable energy (RE) specifically in the transport sector). By 2030 the goal is a 27% improvement in energy efficiency a 40% cut of greenhouse gas emissions and a 27% share of RE. However the integration of RE in energy system faces multiple challenges. The geographical distribution of energy supply changes significantly the availability of the primary energy source (wind solar water) and is the determining factor rather than where the consumers are. This leads to an increasing demand to match supply and demand for power. Especially intermittent RE like wind and solar power face the issue of energy production unrelated to demand (issue of excess energy production beyond demand and/or grid capacity) and forecast errors leading to an increasing demand for grid services like balancing power. Megawatt electrolyzer units (beyond 3 MW) can provide a technical solution to convert large amounts of excess electricity into hydrogen for industrial applications substitute for natural gas or the decarbonization of the mobility sector. The demonstration of successful MW electrolyzer operation providing grid services under dynamic conditions as request by the grid can broaden the opportunities of new business models that demonstrate the profitability of an electrolyzer in these market conditions. The aim of this work is the demonstration of a technical solution utilizing Pressurized Alkaline Electrolyzer (PAE) technology for providing grid balancing services and harvesting Renewable Energy Sources (RES) under realistic circumstances. In order to identify any differences between local market and grid requirements the work focused on a demonstration site located in Austria deemed as a viable business case for the operation of a largescale electrolyzer. The site is adapted to specific local conditions commonly found throughout Europe. To achieve this this study uses a market-based solution that aims at providing value-adding services and cash inflows stemming from the grid balancing services it provides. Moreover the work assesses the viability of various business cases by analyzing (qualitatively and quantitatively) additional business models (in terms of business opportunities/energy source potential grid service provision and hydrogen demand) and analyzing the value and size of the markets developing recommendations for relevant stakeholder to decrease market barriers.
Improving Hydrogen Production Using Co-cultivation of Bacteria with Chlamydomonas Reinhardtii Microalga
Sep 2018
Publication
Hydrogen production by microalgae is a promising technology to achieve sustainable and clean energy. Among various photosynthetic microalgae able to produce hydrogen Chlamydomonas reinhardtii is a model organism widely used to study hydrogen production. Oxygen produced by photosynthesis activity of microalgae has an inhibitory effect on both expression and activity of hydrogenases which are responsible for hydrogen production. Chlamydomonas can reach anoxia and produce hydrogen at low light intensity. Here the effect of bacteria co-cultivation on hydrogen produced by Chlamydomonas at low light intensity was studied. Results indicated that however co-culturing Escherichia coli Pseudomonas stutzeri and Pseudomonas putida reduced the growth of Chlamydomonas it enhanced hydrogen production up to 24% 46% and 32% respectively due to higher respiration rate in the bioreactors at low light intensity. Chlamydomonas could grow properly in presence of an unknown bacterial consortium and hydrogen evolution improved up to 56% in these co-cultures.
Electric and Hydrogen Rail: Potential Contribution to Net Zero in the UK
Sep 2020
Publication
Electric trains (ET) and hydrogen trains (HT) are considered zero emission at the point of use. True emissions are dependent upon non-tailpipe sources primarily in energy production. We present UK carbon dioxide (CO2) operating emission model outputs for conventionally fuelled trains (CFT) ETs and HTs between 2017 and 2050 under four National Grid electricity generation scenarios.
Comparing four service categories (urban regional intercity and high speed) to private conventionally fuelled vehicles (CFV) and electric vehicles considering average distance travelled per trip under different passenger capacity levels (125% 100% 75% 50% and 25%).
Results indicate by 2050 at 100% capacity CFTs produce a fifth of the emissions of CFVs per kilometre per person. Under two degree generation scenario by 2050 ETs produced 14 times and HTs produced five times less emissions than CFTs. Policymakers should encourage shifts away from private vehicles to public transport powered by low carbon electricity.
Comparing four service categories (urban regional intercity and high speed) to private conventionally fuelled vehicles (CFV) and electric vehicles considering average distance travelled per trip under different passenger capacity levels (125% 100% 75% 50% and 25%).
Results indicate by 2050 at 100% capacity CFTs produce a fifth of the emissions of CFVs per kilometre per person. Under two degree generation scenario by 2050 ETs produced 14 times and HTs produced five times less emissions than CFTs. Policymakers should encourage shifts away from private vehicles to public transport powered by low carbon electricity.
UKERC Research Atlas Landscape – Fuel Cells
Dec 2013
Publication
This UKERC Research Atlas Landscape provides an overview of the competencies and publicly funded activities in fuel cell research development and demonstration (RD&D) in the UK. It covers the main funding streams research providers infrastructure networks and UK participation in international activities.
Just Transition Commission
Mar 2021
Publication
The Just Transition Commission started work in early 2019 with a remit to provide practical and affordable recommendations to Scottish Ministers. This report sets out their view of the key opportunities and challenges for Scotland and recommends practical steps to achieving a just transition<br/><br/>Climate action fairness and opportunity must go together. Taking action to tackle climate change must make Scotland a healthier more prosperous and more equal society whilst restoring its natural environment. We want a Scotland where wellbeing is at the heart of how we measure ourselves and our prosperity. We know that the scars from previous industrial transitions have remained raw for generations. We know that some more recent aspirations for green jobs have not delivered on all the benefits promised for Scottish workers and communities. We need rapid interventions to fully realise the potential (and mitigate the potential injustice) associated with the net-zero transition.
The Hydrogen Storage Properties of MgH2–Fe7S8 Composites
Nov 2020
Publication
Nanostructured Fe7S8 was successfully synthesized and its catalytic effect on hydrogen absorption/desorption performance of MgH22 is systemically discussed. The MgH2 + 16.7 wt% Fe7S8 composite prepared by ball-milling method offers a striking catalytic activity for hydrogenation kinetics and also reduces the initial decomposition temperature for MgH22. The composite of MgH2–Fe7S8 can absorb 4.000 wt% of hydrogen within 1800 s at 473 K which is about twice that of pristine MgH2 (1.847 wt%) under the same conditions. The onset hydrogen release temperature of Fe7S8-modified MgH2 is 420 K which is 290 K lower than that of additive-free MgH2 (710 K). Meanwhile the doped sample could release 4.403 wt% of hydrogen within 1800 s at 623 K as compared to 2.479 wt% of hydrogen by MgH2. The activation energy for MgH2–Fe7S8 is about 130.0 kJ mol−1 approximately 36 kJ mol−1 lower than that of MgH2. The hydriding process of MgH2 + 16.7 wt% Fe7S8 follows the nucleation and growth mechanism. The prominent hydrogen storage performances are related to the reactions between MgH2 and Fe7S8. The newly formed MgS and Fe in the ball-milling process present a co-catalytic effect on the hydrogen storage performance of MgH22.
Hydrogen Permeation Under High Pressure Conditions and the Destruction of Exposed Polyethylene-property of Polymeric Materials for High-pressure Hydrogen Devices (2)-
Feb 2021
Publication
Aiming to elucidate physical property affecting to hydrogen gas permeability of polymer materials used for liner materials of storage tanks or hoses and sealants under high-pressure environment as model materials with different free volume fraction five types of polyethylene were evaluated using two methods. A convenient non-steady state measurement of thermal desorption analysis (TDA) and steady-state high-pressure hydrogen gas permeation test (HPHP) were used both under up to 90 MPa of practical pressure. The limit of TDA method of evaluation for the specimens suffering fracture during decompression process after hydrogen exposure was found. Permeability coefficient decreased with the decrease of diffusion coefficient under higher pressure condition. Specific volume and degree of crystallinity under hydrostatic environment were measured. The results showed that the shrinkage in free volume caused by hydrostatic effects of the applied hydrogen gas pressure decreases diffusion coefficient resulting in the decrease of permeability coefficient with the pressure rise.
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