Multiphase transport of hydrogen within the porous rock: relative permeability

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Pumped Hydro Energy Storage

The principle of Pumped Hydro Storage (PHS) is to store electrical energy produced by renewables by using potential energy of water. During low demand cycle and high availability of power, plant pump water from the lower reservoir to the upper reservoir using electricity. In times when demand is high and electricity is more expensive, this stored potential energy is converted back into electrical energy: water from the upper reservoir is released back into the lower reservoir. This mechanical action rotates the turbine to produce electricity (Fig 1.2) The installed power range from 10 MW – 3.0 GW when there is no limitation factor. It efficiency is about 70% to 80%. The quick response for energy demands (few seconds to minutes) is an important advantage when using this technique. PHS is currently the electricity storage technology providing the largest storage capacities. There are over 170 GW of pumped storage capacity in operation worldwide. Europe the second biggest zone, with 57GW, accounting for approximately 33% of the market (Kruck et al., 2013; European Association for the storage of energy, 2016).

Geothermal energy storage

Geothermal underground resources range from shallow resources, through deep permeable aquifers, hot springs, fumaroles, geysers, travertine deposits, chemically altered rocks to hot dry rocks. It integrates into various usage like heating, cooling, and electricity production options, depending on the local needs, possibilities, and geological conditions. Despite the good overall understanding of the subsurface, several unknown factors remain vicious for successful geothermal exploitation due to geological heterogeneity, anisotropy, faults, diagenesis reducing porosity and permeability, scaling, and corrosion. Until recently, geothermal power systems have exploited only resources where naturally occurring heat, water, and rock permeability are sufficient to allow energy extraction. Enhanced Geothermal System technologies have allowed to exploit new geothermal resources in hot dry rocks (Kruck et al., 2013).

Hydrogen gas storage

Hydrogen could account for almost one-fifth of total final energy consumed by 2050. A prospective Mackenzi study showed that by 2050, hydrogen in France will represent: 20% of the energy demand, 18% of the vehicles market, and a 55 millions of tons reduction of 𝐶𝑂2 emissions. By this time, this industry would represent a turnover of 40 billion euros and more than 150,000 jobs (Air Liquide, 2018). On the European side, Hydrogen usage will reduce annual 𝐶𝑂2 emissions by roughly 6 gigatons compared to today’s levels, and contribute roughly, up to 20% of the abatement required to limit global warming to 2°C (Air Liquide, 2017). Hydrogen gas is considered green; it combustion produces only water. Hydrogen exists as natural ressources. The first prospects were discovered at the bottom of the sea in the 1970s and more recently on land. Also, it can be produced by steam methane reforming. Although this process emits CO2, the gas could possibly be captured and stored to produce carbon-free hydrogen. Instead of natural gas, the use of biomethane (methane from the fermentation of biomass) is also a solution. other known techniques to produce hydrogen is coal gasification or combustion but this process emits a lot of CO2 and CO, and considered as very pollutant. Thus, the most efficient technique is the electrolysis of water by the electricity generated by renewable energy like windmills. The electrolysor separates a water molecule into hydrogen and oxygen. Hydrogen produced is considered green. A wind turbine can produce a maximum of 12 MW of electricity and an efficient electrolysor needs 0.04 MWh in average (Bertuccioli et al., 2014). Hydrogen fuel will lift-off as a new vector of transition in the world of energy. The next chapters, will discuss the importance of hydrogen storage in energy transition process.

The aspects of underground hydrogen storage

The production of electricity from renewable energies is green and sustainable but intermittent and does not always succeed in meeting unpredictable market needs. Power-to-X models are business models based on the transfer of energy from the electricity grid to the gas storage grid. The main objective is to store electricity during the season of high production – low demand and to reuse it during the season of scarcity. One promising response is the conversion of electricity into hydrogen, a green and versatile energy carrier gas. This is done by electrolysis technology that decomposes water into oxygen and hydrogen gas using the electricity produced from renewables. Hydrogen gas can be used as energy carrier for combustion and power production. Hydrogen fuel cells are not new to utilities. It started in 1997 to power the forklifts batteries for industrial usage. Now upscaling this technology is a must because of it multiple advantage over electricity storage. Like for example, transportation loss is much lesser if using a gaseous carrier (<0.1%) compared to using the power network (8%) on the grid (Davison et al., 2010; Michalski et al., 2017; Zivar et al., 2021).
Hydrogen storage can be physically as either a gas or a liquid. Hydrogen gas can be stored above or underground in high-pressure tanks (350–700 bar). It storage as a liquid requires gas cooling at very low cryogenic temperatures considering that it boiling point is −252.8°C at atmospheric pressure ( blog, 2021). Hydrogen in light weight solids is also a new storage technique, especially for mobile and rapid usage. The molecule can combine with solids like coal either physically or chemically by adsorption and absorption. It density is preserved and the volumetric losses of liquefaction and compression are avoided by this method (Prachi et al., 2016).
For long term storage, deep ground geological formation enables large volumes of gas stocking at an adequate pressure in a small land parcels (Davison et al., 2010; Michalski et al., 2017; Zivar et al., 2021). Depending upon the way it is produced but also its final usage, hydrogen can be stored in a mixture with other different gases (such as carbon dioxide, carbon monoxide, methane, and nitrogen) or as a pure hydrogen (Zivar et al., 2021). According to its application, hydrogen is stored according to power-to-mobility model for automation ; fuel cell electric vehicles (FCEVs), power-to-industry model for industrial feedstock, power-to-power model to feed fuel cells for electricity generation and compensate shortage during low generation periods and can be also used for urban heating (Robinius et al., 2017). In addition, there is the power-to-gas model, which consists in injecting directly the produced renewable hydrogen into the city gas network in a small proportion to enhance the energetic mix. An alternative is based on the conversion of hydrogen in the storage by a reaction with the CO2 into renewable methane and water, under the influence of microbial activity or in presence of other catalyzers. Renewable methane can be then injected in the natural gas network without limitations to enhance the calorific value (Haeseldonckx & D’haeseleer, 2011; Gahleitner, 2013). There are two storage types of facilities for geological hydrogen storage:
– Cavern storage, in which the gas is contained in excavated or solution-mined cavities of dense rock like salt rock. Those salt rocks can be dome salt or thick beds of salt.
– Porous media storage, in which the gas occupies the naturally occurring pore space between mineral grains or crystals in sandstones or carbonate formation.

Hydrogen storage in salt caverns

Storage options are dictated by the regional geology and operational needs. Salt caverns storage is considered very practical because of salt tightness, favorable mechanical properties of salt and resistance to chemical reactions. Also the high saline condition restricts the hydrogen stock losses by microbial consumption. A prerequisite for the construction is a suitable geological salt deposits in the form of salt domes or bedded salt with a sufficient thickness and extent at a favorable depth. Mining technique for salt cavern is leaching, also called solution mining. It consists of injecting into a saline cavern freshwater through the string to the well bottom. Freshwater having a lower density than the brine flows out of the string to the cavern roof and saturates gradually with salt within the process. Brine is discharged out of the cavern via the leaching string. After this process, the salt cavern is finished when its shape and volume meet the requirements for storage. Most of the caverns are cylindrical. Eventually, the leaching string is replaced by a gas withdrawal tube above the cavern and the brine string is placed on the sump to empty the cavern while the first filling of gas is done (Kuntsman, 2007). The physical characteristics of the storage type must meet its economical capacities and containment for a suitable application. Two of the most important characteristics of a ground facility are the gas storage capacity and the rate at which gas can be withdrawn known as deliverability rate. Therefore, we define cushion gas as the unrecovered gas volume required in a reservoir for management purposes and to maintain minimum pressure for gas delivery. It is important for the stability of the reservoirs. Also, we can define the working gas volume as the gas in the storage plant above the cushion gas volume, withdrawn or injected compatibly to legal and technical limitations. In salt caverns, capacity is given by the chamber volume and sealing is provided by the impermeable host rock surrounding the cavern. Because most rock lithology cannot be considered to be absolutely impermeable, the limiting pressure for almost all forms of underground storage is related to the hydrostatic pressure gradient of 0.1 bar/m below the water table. While the overburden pressure or the confinement pressure is between 350-450 bar, every storage facility operates below those limits or slightly above, stays in safety range of 0.16 bar/m to avoid hydraulic fracking. As the storage pressure increases, less void volume is required for a given quantity of stored gas. Therefore, salt caverns provide very high deliverability rate considering their working gas volume. They have relatively low cushion gas requirements (about 25%), compared to gas-oil depleted reservoirs and aquifers characterized by their large storage capacities (Ozarslan, 2012).However, hydrogen density is nearly one-third of natural gas. Thus, for storage it needs to be compressed to 20 MPa and above for and efficient stock of gas. For example, taking a salt cavern at around 1000m of depth having a geometrical volume of 700,000 m3, the gas storage capacity would be at around 6 million kg of hydrogen, at a maximum operating gas pressure level while the cushion gas remaining after the operational pressure reaches its minimum is 3 million kg of hydrogen. So, based on construction conditions, salt caverns for a sufficient storage of gaseous hydrogen can be built up to 2000 m deep, 1,000,000 m3 volume, 300-500 m height, and 50-100 m diameter (Michalski et al., 2017; Zivar et al., 2021).

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Thermophysical properties

At STP conditions, hydrogen is in a gaseous state. At atmosphere pressure, hydrogen can liquefy at -252.87°C, the second-lowest boiling point among all elements after helium. Its solidification temperature is –259.34°C. That is why hydrogen is not used as primary fuel and why it is hard to store it under STP conditions compared to other liquefied gases. When pressure increases, the boiling point increases up to –253.15°C at 13 atmospheres and stops at this value even if pressure increases (Ebrahimiyekta, 2017).
Hydrogen has a very low density in the gaseous state and the liquid, ie. about 7% of the air density and 8 times denser than natural gas at room temperature. It is a challenging property for storage that requires compressing the hydrogen before any use. Its density is 0.08988 g / l in the gaseous state and 70.8 g / l in the liquid state (Züttel, 2003).
The model of ideal gas is generally used to estimate gas density. However, the behavior of hydrogen deviates significantly from the thermophysical principles of gas at high pressure (above 100 atm). It is mainly because hydrogen molecule is highly polarised.The attraction forces between molecules slightly change the gas partial pressure resulting in gas compression at higher pressure. Ideal gas overestimates gas density at a presure higher than 400 bars (Fig 1. 4) . So, other models are used like Van der Waals, Virial function, Berthelot equation to predict accurately the hydrogen behavior. Integrating the energy content in those models and the calorific factors can somehow overcome the inacuracy at high pressure (Klotz & Young, 1964; Tzimas et al., 2003) (Fig 1.4).

Effective mean stress influence on salt rock mechanical behavior

The influence of effective pressure on the permeability of rock salt has been little treated in the literature.
Peach (1991) has shown that the permeability measurements carried out on the Asse salt, under different confinement pressures, can be reproduced with the Walsh model. He observed that any variation in permeability results essentially from a change in the opening of cracks. The author assumed an elastic matrix and a random topography of cracks involved in the flow. He calculated the variation in hydraulic conductivity of a crack under mean stress. This allows him to obtain the evolution of rock permeability induced by cracks connection uniformly distributed in the porous network. The relationship obtained between the permeability k and the mean effective stress ‘ can be expressed as: 3 where k0 is cracks permeability, and a0 mean half-opening diameter of cracks (with respect to the reference effective stress state σ0’); h the square root of the mean of the squares of the distribution of the heights of the indentations on cracks surface. So, the effective mean stress verifies the condition of poroelastic coupling according to Biot coefficient (Eqs. 2.11 and 2.12). During slow hydraulic loading of a sample, the progressive closure of cracks causes a progressive increase in the drained compressibility modulus KS, inducing a decrease in the Biot coefficient, as shown by the theoretical expression (Equation 2.12). Salt effective compressibility KS decreases with hydrostatic pressure and reaches a constant value attributable to the residual porosity which remains after the sample was healed (Sutherland & Cave, 1980; Stormont & Daemen, 1992b). So, permeability (k) recovery is related to porosity reduction due to cracks closure and both are related to the effective hydrostatic stress by the proportional relationship explicitly explained below:  log ‘ y k (2.12).
where y is a constant (y = 1 fitting the salt data) (Walsh, 1965; Stormont & Daemen, 1992). Hence, a risk of enhancing stably the volumetric creep rises at small stress when dilatancy boundary is crossed and stiffness stability of the material is lost. So, this might increase permeability and dilated salt grains will act as flow path for gas (Schulze et al., 2001; Cosenza et al., 1999).

Advection or permeation concept

Advection is a macroscopic phenomenon of general fluid transport in porous media under the influence of a pressure gradient effect. The fluid viscosity is inversely proportional to pressure. Fluid flow follows the Darcy’s law 2.14. The equation relates the fluid flow rate and the pressure gradient (Lefebvre, 2006; Boulin, 2008; De Marsily, 2004; Bear, 2013).
Note that gas viscosity is dependent of the square root of the temperature variation, and less dependent on the pressure variation. In hydrogen case, it varies only by 2% between 1 and 5 bar (Bear, 2013; Loeb, 2004; Boulin, 2008; Didier et al., 2012).

Table of contents :

1. Contexte générale de la thèse
2. Objectifs
3. Le stockage d’Hydrogène dans les cavités salines
3.1 Problématique
3.2 Matériau et méthodes expérimentales
3.3 Résultats et discussions
4. Le Stockage d’Hydrogène dans les roches poreuses
4.1 Problématique
4.2 Description du dispositif expérimental
4.3 Résultats préliminaires
4.4 Conclusion
1.1.Environmental and economic problems of energy today
1.2.Assessment of underground energy storage
1.2.1.Pumped Hydro Energy Storage
1.2.2.Compressed air storage (CAES)
1.2.3.Geothermal energy storage
1.2.4.Hydrogen gas storage
1.3.The aspects of underground hydrogen storage
1.3.1.Hydrogen storage in salt caverns
1.3.3.Depleted oil and gas reservoirs
1.4.Hydrogen gas fundamentals
1.4.1.Hydrogen gas chemical aspect
1.4.2.Thermophysical properties
1.4.3.Energy Content
1.4.4.Hydrogen reactivity and solubility
1.5.Worldwide hydrogen storage examples in geological structures
1.6.Objectives of the thesis
2.1.Rock salt a polycrystalline material
2.1.1.Salt rock structure and mineralogy
2.1.2.Structure and mechanical properties of halite mineral halite NaCl crystal and beds joints
2.2.Rock salt mechanical properties and behavior
2.2.1.Salt crystal deformation types deformations by dissolution-recrystallization or cataclastic deformations
2.2.2.Salt mechanical properties evolution under instantaneous loading description properties of rock salt evolution under deviatoric stress: dilatancy boundary evolution under compressive deviatoric stress: the hardening effect
2.2.3.Salt mechanical properties under long-term loading description of salt creep creep characteristics relaxation processes
2.3.Salt poromechanical properties
2.3.1.General theory of poroelasticity
2.3.2.Effective mean stress influence on salt rock mechanical behavior
2.3.3.Anisotropy/isotropy of rock salt
2.4. Salt as a tight porous media
2.4.1. Definition of a porous media
2.4.2. Fluid flow dynamics and laws in porous media Advection or permeation concept Difference between diffusion and dispersion Pore-walls and gas interactions: impact on gas transport and Klinkenberg effect Fracture permeability
2.4.3. Fluid flow in rock salt reservoir: Gas permeability measurement methods
2.4.4. Mechanical influence on petrophysical properties of salt Hydrostatic effect on permeability: the healing process Deviatoric stress effect on permeability Experimenting the sealing capacity of rock salt
2.5. Thermo-mechanical loading effect
2.5.1. Security and geomechanical stability of salt cavern
2.5.2. Mechanical cycling effect
2.5.3. Thermal cycling effect
2.6. Conclusions
3.1. Abstract
3.2. Introduction
3.3. Material and methods
3.3.1. Material description and sampling
3.3.2. Microstructural characterization of initial material Porosity measurements X-ray 3D Computed Tomography (CT)
3.3.3. Theoretical considerations’s coefficient Measurement of ultrasonic P and S-wave velocities during compression test Apparent and intrinsic permeability
3.3.4. Experimental procedures for hydromechanical tests and permeability measurements
3.4. Microstructural characteristics of rock salt
3.5. Mechanical behaviour of rock salt
3.5.1. Behaviour under hydrostatic loading and poromechanical coupling
3.5.2. Behaviour under deviatoric loading
3.6. Permeability evolution during mechanical and thermal loadings
3.6.1. Intrinsic permeability and Klinkenberg effect
3.6.2. Evolution of apparent gas permeability with stress increase
3.6.3. Impact of mechanical and thermal fatigue on rock salt permeability Static (creep test) and dynamic (cyclic) mechanical fatigue Cyclic thermal fatigue
3.7. Conclusions
3.8. Acknowledgements
3.9. References
5.1. Challenges for hydrogen storage in porous rock
5.2. Flow and mass transport in porous rock:
5.2.1. Multiphase transport of hydrogen within the porous rock: relative permeability
5.2.2. Effects of saturation, wettability and mobility of fluids in porous rock
5.2.3. Mixing phenomena in gas-gas interaction
5.2.4. Miscibility of fluids: effect of hydrogen solubility in water
5.3. Hydrogen geochemical interactions in porous rock
5.3.1. Abiotic reactions of hydrogen
5.3.2. Physical properties of sandstone: a typical rock reservoir
5.4. Impact of bacterial activity on the storage in porous rock
5.4.1. Hydrogen biogeochemical Interactions and conversion
5.4.2. Hydrogenotrophic bacteria
5.4.3. Microbial Process The conditioning of the surface by the environment and bacteria adhesion Bacteria growth Growth stable phase and biofilm dispersion The decay phase
5.4.4. H2 consumption rate by biofilm degradation
5.4.5. The Shewanella bacteria
5.4.6. Flow-through test in literature
6.1. Introduction
6.2. Analog samples characterization: Vosges sandstone
6.3. Bacterial culture medium preparation
6.3.1. Batch experiments Preparation of the bacterial culture solution Preparation of the bacterial suspension Physicochemical analysis
6.3.2. Flow-through experiment mimicking the underground storage in aquifers apparatus Calibration of the micro-GC and the valve HP-LP Experimental procedure
6.3.3. Results and discussion
6.3.4. Results in batch Salinity impact on S. putrefaciens growth Hydrogen consumption evolution by the measurement of Fe2+ production S. putrefaciens bacterial cells count Some observations on hydrogen bacterial consumption in batch
6.3.5. Results of the feasibility tests of the experimental setup Experimental tests with hydrogen concentration of 70% and hydrogen reinjection for maintaining pressure equilibrium in the closed circuit Experimental test with hydrogen concentration of 5% and Argon reinjection for maintaining pressure equilibrium in the closed circuit
8.1. Hydrogen storage in salt cavern
8.2. Hydrogen storage in porous reservoir rocks


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