H 2 -Quartz and Cushion Gas-Quartz Intermolecular Interactions: Implications for Hydrogen Geo-Storage in Sandstone Reservoirs

Emissions of carbon dioxide (CO 2 ) from fossil fuel usage continue to be an incredibly challenging problem to the attainment of CO 2 free global economy; carbon Capture and Storage (CCS) and the substitution of fossil fuel with clean hydrogen have been identi�ed as signi�cant primary techniques of achieving net zero carbon emissions. However, predicting the number of gas trapped in the geological storage media effectively and safely is essential in attaining decarbonisation objectives and the hydrogen economy. Successful underground storage of carbon dioxide and hydrogen depends on the wettability of the storage/cap rocks as well as the interfacial interaction between subsurface rocks, the injected gas, and the formation of brine. A key challenge in determining these factors through experimental studies is the presence of con�icting contact angle data and the di�culty of accurately replicating subsurface conditions in the laboratory. To address this issue, molecular dynamics simulations offer a microscopic approach to recreating subsurface conditions and resolving experimentally inconsistent results. Herein, we report the molecular dynamics simulation results for hydrogen (H 2 ) and cushion gas ( e.g., CO 2 and N 2 ) on quartz surfaces to understand the capillary and trapping of these gases in sandstone formations. The results of these three gasses were compared to one another. The simulation predictions showed that the intermolecular interactions at the CO 2 -quartz surface area are more substantial than at the N 2 and H 2 -quartz interface, suggesting that the quartz surface is more CO 2 -wet than N 2 and H 2 -wet under the same circumstances. In addition, it was found that CO 2 has a substantially higher adsorption rate (~ 65 Kcal/mol) than N 2 (~ 5 Kcal/mol) and H 2 (~ 0.5 Kcal/mol). This phenomenon can be explained by the fact that CO 2 density is substantially larger than N 2 /H 2 density at the same geo-storage conditions. As a result, CO 2 could be the most favorable cushion gas during underground hydrogen storage (UHS) because a higher CO 2 residual is expected compared to H 2 . However, due to the Van der Waal Interaction force with quartz, only a small amount of H 2 can be withdrawn.


Introduction
The global energy demand is increasing and could outpace supply soonest because the world population and pace of industrialization are rising in geometric progression.The world has relied on fossil fuels for several years [1,2].Due to the continued depletion of petroleum resources and growing global concern for reducing carbon emissions and combatting the effects of global warming, the search for alternative sources of energy as well as sustainable and environmentally friendly solutions remains high [3,4].
Presently, almost 36 billion tons of anthropogenic CO 2 emissions are produced by fossil fuel oxidation, suggesting that continued reliance on carbon-based fossil fuel is in de ance of the actualization of a net zero emission goal (carbon neutrality) by 2050 [5].
The adverse environmental effects of CO 2 emission as a signi cant greenhouse gas can be curtailed by underground storage of carbon dioxide and the execution of a hydrogen economy [6].Presently, there is insu cient information on underground hydrogen storage compared to underground CO 2 storage.
Successful storage of large quantities of hydrogen is crucial in implementing the hydrogen economy chain and substituting fossil fuels with hydrogen as the principal global energy source.Hydrogen can be stored at the surface and subsurface.Still, underground storage is more promising because of the enormous amounts of surface storage tanks required for surface storage, the safety challenges, and the cost of construction storage facilities.The volumetric density of hydrogen is very low, and up to 60 kgH 2 /m 3 volumetric density or 1.14 x 10 10 m 3 surface storage space will be required to attain the net-zero emission goal [7].
Moreover, the subsurface storage facilities erected for gas transportation and storage in major oilproducing nations can be reused for hydrogen storage.The promising underground facilities for hydrogen and CO 2 have been identi ed as, depleted hydrocarbon reservoirs saline aquifers, and salt caverns.The depleted hydrocarbon reservoirs are well-known geological structures due to the prior experience acquired from methane and natural gas storage [8].However, successful geological storage of hydrogen and carbon dioxide is signi cantly impacted by various physio-chemical parameters, mainly the wettability of brine/H 2 and brine/CO 2 systems on the rock, the rock/ uid interfacial tension and uid ow dynamics in the porous system.The rock-wetting behaviors regulate the uid distribution, the H 2 /CO 2 injection, and the withdrawal of stored hydrogen [9][10][11].
Understanding the conditions for geological rock wettability alteration is critical for ensuring the containment safety of the stored H 2 /CO 2 , keeping the buoyant gas in storage formations, and preventing gas diffusion across the caprocks.Wettability is a uid's relative ability to spread over a solid surface when additional uids are present [12].Some recent publications have already addressed the impact of rock/brine/CO 2 and rock/brine/H 2 wettability on residual and structural trapping of storage rocks and caprocks [9,[13][14][15][16][17][18][19][20].Their results showed that the residual/capillary trapping of storage/caprocks depends on pressure, temperature, salinity, and organic acid contaminations [21][22][23].Residual trapping of storage rocks and capillary trapping of caprocks were predicted to be higher as the rock becomes less gas (CO 2 /H 2 ) wet at a higher temperature, lower pressure, and decreasing concentration of organic acids [6,9,20,24].H 2 /rock and CO 2 /rock reactions also signi cantly in uence rock storage potentials, with carbonate formations found to be less favorable for carbon dioxide and hydrogen storage due to considerable/signi cant reactions between the carbonate minerals [25], particularly calcite and dolomite, and the stored gas [26].Rock petrophysical properties are modi ed due to the occurrence of dissolution, precipitation, and compaction resulting from carbonate-rock interactions/reactions [27].The creation of ow routes and the widening of cracks in the reservoir will allow for pore throat expansion, increased permeability, and porosity [28,29], During sequestration, CO 2 is permanently stored in the geo-storage media.In contrast, hydrogen is stored temporarily during UHS to be withdrawn during critical energy needs to offset the balance between the demand and supply.To guarantee the safe withdrawal of stored gases, cushion gases are required to maintain formation pressure.Such cushion gases have been suggested as gases with a high tendency to wet the rock, such as carbon dioxide, hydrogen, and methane.Recent studies have demonstrated that the order of increasing gas contact angle and residual for CO 2 , N 2 , and H 2 is as follows: CO 2 > N 2 > H 2 [19,[30][31][32].Researchers suggested that these results could be attributed to the impact of gas density.However, these insinuations have not been investigated.
To the author's knowledge, no one has investigated and compared the effects of CO 2 /H 2 /N 2 gas density on the quartz wetting phenomenon and gas sorption/adsorption on the quartz surface.Quartz is a typical silicate crystal primary foremost signi cant in geological studies since oxygen and silicon are signi cant elements of the Earth's crust.Understanding the kinetics of the quartz-water-gas interaction is critical for understanding the geochemical interaction during UHS and the alteration of host-rock porosity via dissolution and gas sorption [26,33].The study aims to determine the impact of hydrogen density on the wettability of H 2 /brine systems and H 2 sorption/adsorption on the quartz surface.The results will then be compared with carbon dioxide/brine and nitrogen/brine systems to evaluate the dependence of quartz wettability and gas sorption/adsorption on uid (H 2 , N 2, or CO 2 ) density.The attendant implications of our results on underground hydrogen storage and CO 2 storage will be emphasized.
2. Computational procedure 2.1.Simulation of the adsorption characteristics of H 2 , N 2, and CO 2 gas on quartz surface The construction of quartz mineral complex models was done using two specialized modules -the Materials Visualizer module and the Amorphous Cell module.These tools enabled the creation of detailed, three-dimensional models of quartz mineral structures.To simulate the adsorption of H 2 , N 2, and CO 2 gas on the quartz surface, the COMPASS program (Version 2.8) was utilized.This program was chosen for its advanced capabilities in molecular dynamics simulations.A force eld was used to represent the intermolecular interactions between the gas molecules and the quartz surface.This allowed the simulation to accurately model the adsorption behaviour of the gases on the quartz surface.
The quartz surface was created by cleaving the unit cell of quartz along the (1 1 1) face.This was done with a depth of 6 layers, allowing for a comprehensive analysis of the interactions between the gas molecules and the quartz surface [33,34].Having created the mineral surface models, the Amorphous Cell and Packing module were employed to assemble mineral-gas systems with dimensions of 7.6Å × 7.6Å × 7.6Å.To accurately simulate the electrostatic interactions between the mineral and gas, a charge force eld was assigned using the Ewald summation method with a precision of 0.001 kcal/mol.The charge group cut-off was set at 12.5Å with a 0.5Å buffer.The van der Waals terms were calculated using an atom-based approach and a truncation method of the cubic spline with a cut-off distance of 12.5Å.The simulation was conducted using the Monte Carlo method.The BIOVIA Materials Studio software was utilized to design and model the system, providing the capability to predict and comprehend the relationship between the atomic and molecular structure properties of the material and its behavior within the system [35,36].The parameters for the simulation process were set according to the COMPASS force eld module.This module applied a charge force eld using a robust calculation method to evaluate the electrostatic and van der Waals forces and an optimized Ewald and atom-based approach.The simulation involved loading stages of 100,000 kcal/mol, three heating cycles, and 15,000 steps per cycle.The energy force eld used was COMPASS with charge force eld parameters set to a cut-off of 12.5Å and a buffer width of 0.5Å.The temperature was xed at 393k [37].The component for the simulation shows in Fig. 1.
The design of the molecular structures was optimized using a combination of Non-local Density Approximation (ND) and the Discrete Density Approximation (DDA) method, implemented in the Dmol3 module of Materials Studio 8.0.The optimization process followed the Perdew-Burke-Ernzerhof (PBE) level and was based on the generalized gradient approximation (GGA) method [38].The simulation considered all core and valence electrons and utilized the double numerical plus polarization (DNP) basis set, which expanded the electronic eigenstates with a cut-off radius of 4.4 Å.The self-consistent eld (SCF) convergence was set to 10 − 6 with convergence criteria of 1 × 10 − 5 Ha for energy, 2 × 10 − 3 Ha/Å for maximum force, and 5 × 10 − 3 Å for maximum displacement.The gas molecule models were introduced into the quartz mineral system and optimized through a geometry optimization process using a smart algorithm with a convergence tolerance of 10 − 4 kcal/mol.The molecular dynamic simulation was conducted in the constant number of particles, volume, and temperature (NVT) ensemble with a time step of 1.0 fs.The simulation was controlled in terms of temperature with the use of the Nosé-Hoover [39,40] thermostat with a Q ratio of 0.01 to maintain a temperature of 393K.The electrostatic interactions and van der Waals forces were taken into account through the utilization of the Ewald summation and Atom-based summation methods.Once the density distribution of the gas and quartz minerals were recorded for two separate 50 ps intervals and found to be the same, the system was deemed equilibrated.An additional 1.0 ns simulation (106 steps, every 1 fs) was then carried out for analytical purposes, and the interaction energy calculation was based on the con guration with the lowest energy, which represents the best adsorption model, as shown in Fig. 2.

Analysis of Adsorption Process of Gases along Quartz Surface
We used simulations to explore the adsorption behaviors of gases on quartz minerals to assess the in uence of each gas's adsorption and the change in wettability.For this work, we used N 2 , H 2 , and CO 2 gas; Fig. 3 shows the results of the adsorbate-adsorbent structural arrangement for each gas.The simulation results indicated e signi cant immense size and considerable activation energy with the penetration of CO 2 on the quartz crystals, which leads to heat transmission within the environment (Fig. 3).Prior to exploring the concepts of physisorption and chemisorption, it is crucial to comprehend what adsorption is.It refers to the accumulation of molecular species on a surface instead of in the solid or liquid bulk.A classic example of this phenomenon is the drying of air with silica gel, where water molecules get adsorbed on the gel's surface.Adsorption is the bonding of gas or liquid molecules, atoms, or ions to a surface.Physisorption, also known as physical adsorption, is a type of adsorption that is exothermic and has a modest adsorption enthalpy range of 20 to 40 kJ/mol.Physical adsorption, or Physisorption, involves the buildup of gas molecules on a solid surface through weak forces such as Van der Waals.Unlike Chemisorption, Physisorption is not speci c to any particular gas and can be reversed as the adsorbed gas molecules can be displaced by the solid [41].Chemical adsorption, also referred to as chemisorption, is a type of adsorption that takes place through the formation of chemical bonds between the adsorbent and adsorbate.This leads to a strong and speci c connection between the two, which is why chemisorption is known for its high speci city.Unlike physical adsorption, chemisorption is irreversible and is favored under high-pressure conditions.The chemical bonding involved in chemisorption results in a high enthalpy of adsorption, with values ranging from 80 to 240 kJ/mol [42].A temperature rise can cause a shift from physisorption to chemisorption for a gas that was previously adsorbed at a lower temperature.Based on the results obtained, we had physisorption in all three (3) gases used, implying that the gas-lled all the pores of the quartz, which might be owing to the quartz's piezoelectric qualities creating electric potential when mechanical stress is applied.Based on the data, H 2 has adsorption energy of -1.94 Kcal/mol, N 2 has adsorption energy of -6.55 Kcal/mol, and CO 2 has adsorption energy of -67.58 Kcal/mol (Table 1).
The adsorption energies of CO 2 show a stronger interaction with the surface than with water.The gases that have higher stickiness to quartz are CO 2 and N 2 gas.The bulk density of a gas refers to the density of its molecules without taking adsorption into account.An increase in bulk density signals a reduction in the amount of gas that is adsorbed on the surfaces of the pores, re ecting a decrease in the overall adsorption impact [43].In the case of the adsorb gases, the pressure increases as pore size decreases, which can be interpreted as the Van der Waals forces intensifying at high pressure and leading to an increase in the adsorption of gas molecules.The results indicate that nitrogen (N 2 ) has a weaker attraction to the fully coordinated quartz surface compared to carbon dioxide (CO 2 ) and hydrogen (H 2 ).This is likely due to N 2 's weaker van der Waals interactions.The weaker interactions lead to two practical effects.Firstly, N 2 has a lower density compared to CO 2 and H 2 at equal pressures, meaning fewer N 2 molecules compete with water for the fully-coordinated quartz surface.Secondly, N 2 's attraction to the surface is weaker compared to CO 2 .These factors greatly improve the surface wettability of water when N 2 is present.Based on our simulations of N 2 /water/silica contact angles, using N 2 to assess residual trapping would not be an accurate comparison and would also overestimate the capillary breakthrough pressure in structural entrapment.However, it is important to note that N 2 may still be useful for fracture identi cation, which is beyond the scope of this current study.
The explanation provided earlier has given a thorough account of why hydrogen (H 2 ) has a stronger attraction to water than the other two gases.The degree of roughness on the surface plays a crucial role, as the surface may undergo chemical changes during cleaning and the experiment.Our simulations evaluated a fully coordinated quartz surface.In real-life situations, however, a quartz surface in a reservoir is likely to have silanol groups.This observation led us to investigate the effect of silanol groups on contact angle by constructing a hydroxylated surface.The rock and uid characteristics of quartz can signi cantly vary with temperature, including the impact of temperature on uid-uid interactions (surface tension), rock-uid interactions (wettability), and uid property (viscosity ratio), which can have a signi cant effect on two-phase gas/liquid relative permeability.The geometry of an adsorption con guration can be used to identify a solid's wetting state.At maximum saturation pressure, the amount of vapor that can be adsorbed onto a high-energy solid surface is limitless.This leads to a substantial increase in the area under the adsorption isotherm.This phenomenon is known as complete wetting, where the vapor at saturation pressure forms a macroscopically dense layer that covers the solid surface.Conversely, for low-energy surfaces, the region beneath the saturation isotherm is limited, resulting in a relatively modest amount of vapor adsorption.Partial wetting, on the other hand, occurs when a thin lm (the equivalent of one or a few single layers) forms during saturation.The results indicated that electrostatic forces play a crucial role in the adsorption of amines onto quartz surfaces.Additionally, the hydrogen bonding between quartz and the collectors was computed based on the adsorption con guration, aligning with prior studies.
Between charged particles, electrostatic interactions occur.Because both the porous media, including organic matter, and mineral surfaces are often negatively charged, repulsion is the signi cant primary electrostatic interaction in microbial movement.Based on our ndings, electromagnetic phenomena that occur on the quartz surface when subjected to gas adsorption indicate that there are no moving charges -that is when a static equilibrium has been formed on the quartz Fig. 4 and Table 1.Because the electric force is so strong, charges quickly achieve their equilibrium locations.
The total energy is the sum of various energy forms, such as kinetic and potential energy.Van der Waals energy refers to the attractive and repulsive forces between atoms, molecules, and surfaces and their interactions with other intermolecular forces.This is distinct from covalent and ionic bonding, which arises from uctuations in polarizations or nearby particles.Electrostatic energy, on the other hand, is the result of interactions that govern the formation of bonds between ions and give rise to the ionic character of these bonds.Finally, intermolecular energy encompasses the interactions between atoms within a single molecule.Our study evaluates the impact of electrostatic, Van der Waals, and intermolecular energies on the interaction of N 2 , H 2 , and CO 2 gases with the quartz surface and the resultant change in wettability.The results showed that CO 2 exhibits the strongest adsorption energy with 63.1 Kcal/mol, followed by N 2 with 8 Kcal/mol, and H2 with − 1.623 Kcal/mol as illustrated in Fig. 5.
The absolute adsorbed quantity includes the adsorbed molecules in both adsorbed and gas phases.The adsorbed molecules are dispersed across the adsorption zone, and the excess adsorption capacity only comprises the adsorbed molecules in the form of adsorbed phases (Fig. 5).Because of the little difference between the bulk gas phase density and the adsorption phase density when the adsorption pressure is low, the excess adsorption capacity and total adsorption capacity are essentially the same.
The negative (-) sign implies that the matching adsorbed state is more thermodynamically stable than the unbound state, indicating an exothermic process.Adsorption reduces the stresses on the sandstone surface, resulting in a decrease in surface energy [33].The van der Waals interaction is the driving force behind these intermolecular forces.When two neutral molecules of the same substance are brought together, their non-bonding electrons overlap, resulting in a repulsive force due to the presence of surface electrons.This creates a permanent dipole, which induces the development of partially charged dipoles.Electrostatic attraction causes these opposing dipoles to be drawn towards each other, which is known as dipole-dipole interaction.As demonstrated in our results, all the adsorbed gases have a negative value, implying a strong attraction between the gases and the quartz surface (as seen in Fig. 6 and Table 1).
The state of a material is determined by the balance of kinetic energy between individual particles (molecules or atoms) and intermolecular forces.The temperature of the material determines its kinetic energy, which keeps the molecules apart and in motion.Meanwhile, intermolecular interactions strive to draw the particles together.Figure 4, 5, 6, and 7 shows the connections between the energy of the H 2 , N 2 , and CO 2 gas adsorption system on the quartz surface.We discovered that the valence terms in uenced gas adsorption in quartz in each simulation.Non-bonding interactions, on the other hand, add to the overall energy of the adsorption system.
Additionally, our ndings revealed that the Van der Waals (vdW) term energy plays a crucial role in determining the total energy of the adsorption system.The electrostatic interaction energy was found to be zero in non-bonding contacts, meaning that it has no effect on the adsorption process in each simulation.However, the Van der Waals (vdW) term energy has a signi cant impact on the overall energy of the adsorption system [44].
Furthermore, that contribution is independent of pressure and pore size, indicating that the process of each gas adsorption in each simulation includes a physical adsorption process.When physical adsorption processes occur in an adsorption system, heat is produced.As a result, the system's energy will be reduced.We may deduce from Figs. 4, 5, 6, and 7 that the system's energy will decrease as the pressure rises.Furthermore, there is no link between the adsorption system's total energy in the pore size increase.
3.2.Sorption analysis of the H 2 , N 2, and CO 2 gas on quartz surface for wettability alteration Examining the underlying molecular-scale processes is motivated by proof of wettability variation, like changes in water-wet surfaces known to impact reservoir productivity [45].These ndings are crucial for assessing eld-scale possibilities for developing ecologically friendly subsurface uid recovery or storage techniques.One of the critical issues impacting pore space accessibility for conveying subsurface uids in this context is the self-assembly of CO 2 storage components, commonly known as asphaltenes.Some unfavorable gas and water injection effects include precipitation, self-assembly, and gas deposition on mineral surfaces.Deposition of gas on rock surfaces can alter their wetting characteristics, causing a shift from water-wet to gas-wet.This can result in the formation of hydrophobic surfaces and ultimately lead to the degradation of the reservoir.Experiments have demonstrated that the addition of gas molecules on mineral surfaces modi es the surface's topographical features.However, due to the relatively short time scales involved with these events, the wettability undulation of various mineral surfaces, such as quartz and calcite, caused by gas adsorption has not been well understood.However, this study concentrated on the surface of silica, utilizing three distinct gas adsorption and sorption analyses to identify which gas had the best diffusivity and wetting to the silica surface.Additionally, the pressure also affects the residual.The increase in contact angle with increasing pressure observed in our result, suggest that change in the wettability of the quartz surface to gas.It quanti es the degree to which a droplet of liquid or gas spreads or beads up on the surface.A smaller contact angle indicates a higher degree of wetting, where the droplet spreads out more on the surface, while a larger contact angle indicates a lower degree of wetting, where the droplet beads up and does not spread as much.
The BET equation [46], the V/-t technique (developed by de Boer in 1958), and the a-method [47] are commonly used to analyze sorption data for non-microporous (mesoporous) adsorbents.These methods are built on the principles of surface coverage and the potential for interactions between adsorbates, leading to the formation of multiple layers.The Langmuir adsorption isotherm model is frequently utilized to interpret adsorption data in various situations.The Langmuir sorption model assumes a single layer of localized sorption, where the number of adsorbed sorbate molecules has a direct correlation to the number of sorption centers of equal strength, with a ratio of 1:1 [29].The Langmuir adsorption isotherm model is frequently utilized to interpret sorption data in several circumstances.The model is built on the idea of a single layer of localized sorption, where the number of adsorbed sorbate molecules has a direct correlation with the number of sorption sites, each of equal a nity.
The gas contact angle rose as pressure concentrations in the quartz surface increased.This behavior can be attributed to the enhanced hydrophobicity of the quartz surface and the higher degree of chemisorption of the gas on the substrate surfaces as the pressure concentration rises.Furthermore, when pressure increased, the gas contact angle increased increasing with H 2 wettability (Fig. 8).As with other gases, the increase in contact angle observed for H 2 gas is related to its increased density with increasing pressure [48].Based on this discovery, we hypothesize that greater H 2 density cause's enhanced solvation forces/adhesion at the H 2 /rock contact, enhancing H 2 wettability.
The sorption result of CO 2 on the quartz surface at 500 Psi, 1000 Psi, 1500, 2000, and 2500 Psi is shown in (Fig. 9) First, gas molecules are evenly mixed and co-adsorbed on the surface at 500 psi.Second, at 1000 pressure, CO 2 gas molecules slowly dissolve into the quartz phase while the remaining CO 2 molecules are adsorbed on the quartz surface, leading to the diffusion of the two mixed components.Finally, from 1500 to 2500 psi (equilibrium pressure), the CO 2 molecules are equally distributed on the quartz surface, resulting in total adsorption and a change in wettability on the quartz, which changes the density eld (Fig. 11) and density structure of the quartz (Fig. 12).To measure the CO 2 distribution, the density pro les of all three gas components were estimated as standard to the quartz surface, as shown in Fig. 10.We can observe from this graph that a single-density peak of CO 2 is positioned around 8.0 Å above the silica surface.With a distance of 26.5 Å, this result shows that it is near the silica surface.However, when the distance is around 17.2 Å, the density eld of N 2 is close to 3.8.Å a density peak of H2 develops at roughly 1.6 Å, below the silica surface.When the distance exceeds 11.1 Å, the curve attens out.These ndings suggest that gas molecules are uniformly distributed on the quartz surface.
The concentrations of the most prevalent rock-forming minerals are astonishingly close.Bulk densities are frequently in uenced more by porosity and cementation than mineral composition.The densities of a few popular gases in quartz are listed in Table 2 below.To fully comprehend the mechanism of quartz, it is critical to investigate the effects of liquid nitrogen on gas sorption.As a result, a model that can re ect the quartz structure should be developed.The quartz density model is built in this text at various temperatures.The density structure is built here using the quartz macromolecular structure.The size of the quartz may be changed to match the sizes of macropores, mesopores, and micropores in the quartz pores, which can better explain the gas ow in the quartz.The interaction of quartz with nitrogen gas and the characteristics of quartz under liquid nitrogen should be investigated using microscopic molecular simulations.Based on the ndings of the isothermal adsorption curve, the thermodynamic properties of sorption were computed and analyzed, and the effects of densities and pressure on sorption/adsorption capacity, adsorption heat, and adsorption entropy were investigated.The computations in this work were done using a grand canonical Monte Carlo (GCMC) simulation with the Sorption module in Materials Studio.The simulated temperature was 393 K, while the pressure ranged from 500-2500 psi (Fig. 10).The adsorbent was a quartz-alpha type with N2 molecules present in equal amounts.
Quartz is a nonporous material.Quartz surfaces have 0% porosity due to their composition, according to materials experts at Cosentino, a Spanish quartz company famed for producing slabs that appear exactly like white Carrara marble.Quartz slabs are made up of more than 90% natural quartz shards combined with sophisticated resins that work as bonding agents and generate the cohesiveness anticipated of solid building material, resulting in high-density slabs with no porosity.The principal pore size, however, was a nanometre micropore (300 nm).In this work, micropore models for 1 or 2 nm and a mesopore model for 4 nm were constructed depending on the quartz's real condition and the computer's computing ability.The 5 *5 *2 supercell is shown in Fig. 2 to re ect the scenario before the adsorption simulation.That super cell was formed, and vacuum layers of 1, 2, and 4 nm were added.The quartz model's structure was z optimized.Furthermore, the geometry optimization module of Forcite, the molecular dynamics module, and the molecular dynamics module are utilized to optimize the model's structure [49].The initial design was a low-energy optimized quartz model with no adsorbate molecules.The Metropolis operating criteria were then used to approve or reject the modi cation for constructing a new con guration depending on the change in energy.In three dimensions, a periodic boundary condition was utilized, and the cell parameters were as follows: a = 21.500013,b = 21.500013,c = 18.32809, and = 900 = 1200 = 90°.
As seen in Fig. 10, the amounts of N 2 in the system steadily rose as the pressure increased.Figure 10 shows that most of the N 2 molecules were concentrated on the quartz surface, with just a minor percentage of the gas molecules free.Figure 10 indicates that under varied pressures, N 2 molecules were concentrated in the hole wall surfaces and were dispersed roughly parallel to the hole wall surfaces.Some of the H 2 and N 2 molecules were scattered within the pores in a location distant from the pore wall.
At lower pressures, the distributions of H 2 , CO 2 , and N 2 molecules close and away from the wall were sparse (Figs. 8, 9, and 10).The number of molecules closes and far from the whole walls grew as pressure increased.Among these molecules, the N 2 molecules collected mostly along the quartz wall surfaces.
Furthermore, the majority of the N 2 was clustered on the quartz molecules.This suggested that the interaction between the quartz surface and the N 2 gas was substantial at the quartz surface's proximity.
The system had a large number of free-state H 2 O and N 2 molecules.The amount of H 2 O was signi cantly more than that of N 2 , indicating that the contact between the quartz surface and the H 2 O and N 2 molecules was weak and did not impact the H 2 O and N2 molecules.As a result, H 2 O and N 2 molecules distant from the quartz surface did not merge.
Investigation of the quartz surface at various pressures of (500, 1000, 1500, 2000, and 2500 psi), and the temperatures are (298, 343, 353, 363, 373, and 393k).According to the simulation ndings, a and r both rise with pressure, with a = 38° and r = 15° at and T = 289 K [32] Fig. 12 and Fig. 13.The rise in a and r with increasing pressure was also found for simulations at T = (343, 353, 363, 373, and 393) K, which is consistent with the majority of the literature data and molecular dynamics (MD) simulations [50].Iglauer et al. [30] interpreted this behavior as an immediate increase in CO 2 density with pressure, which enhances the intermolecular contacts between CO 2 and quartz, resulting in the de-wetting of the quartz.
According to the research, pressure signi cantly impacts the CO 2 wettability of rock surfaces.This observation appears relevant for H 2 wettability independent of the type of gas utilized for rock substrate.
This behaviour might be explained by increased intermolecular interactions between the solenoid group of the rock substrates and H 2 at higher pressures, similar to those seen at CO 2 -quartz contacts.For example, in the presence of H 2 at higher pressures (2500psi), all recorded gas adsorption/sorption are more extensive than those obtained at lower pressures (500 psi) but lower than those simulated in the presence of CO 2 (Fig. 8, 9, and Fig. 10).The result of those intermolecular interactions at the CO 2 -quartz surface is more substantial than at the N 2 , and H 2 -quartz interface, suggesting that the quartz surface is more CO 2 -wet than N 2 and H 2 -wet under the same circumstances.This phenomenon may be explained by the fact that CO 2 density is substantially more prominentand more signi cant than N 2 /H 2 density under storage settings (for example, CO 2 , N 2, and H 2 at 1000 psi and 343 K are 6g/Cm − 3 , respectively).
The thermo-dynamical relationship between vapor adsorption and wetting can be analysed using the Gibbs adsorption equation.The surface pressure generated by vapour adsorption on a solid is computed using a vapor adsorption isotherm.In the vapor-liquid-solid system, the surface pressure is connected to the spreading tension and the contact angle.The disparity between the interfacial tensions of a solid and a solid-liquid interface can be calculated by considering both the surface pressure at the saturated vapor pressure and the liquid's interfacial tension.Knowing the value of K for two immiscible liquids allows for forecasting the wettability in a liquid-liquid-solid system.
Adsorption on a solid alters the interfacial Gibbs energy, with the extent of change depending on the type and amount of adsorbing molecules.The effect on the interfacial tension (surface pressure) caused by adsorption can be either positive or negative, depending on the type of adsorption.For vapor adsorption on a solid, the surface pressure , is positive, de ned as the difference between the interfacial tension of the clean (in vacuum) solid surface , denoted .recent times, there has been a growing interest in studying Maxwell's diffusion and transport diffusion coe cients, as they play a crucial role in explaining macroscopic mass transfer phenomena.Most studies on the microscopic diffusion process for the three gases mentioned above have been done using molecular simulations and experimental characterizations.Several papers have previously been published in the recent decade that explores the self-and transport diffusion processes.Based on the reservoir components, we studied the diffusion coe cient of CO 2 , H 2 , and N 2 on a quartz surface (Fig. 14).The discovery indicated that the diffusion coe cient of CO 2 was signi cantly greater, by one to two orders of magnitude, compared to H 2 and N 2 .This discrepancy may be attributed to the different diameters of the gas molecules in their dynamic motions.Furthermore, it was noted that the diffusion coe cient decreased as pressure and temperature increased.
Self-diffusion is powered by the random thermal motion of micro-particles and adheres to Einstein's principles, which are independent of pressure and concentration gradients.Many researchers focus on self-diffusion and use molecular simulations to determine the diffusion coe cient.While this coe cient can effectively describe the motion of diffusion particles at the microscale, it serves as a basis for macroscopic mass transfer.However, research into Maxwell's diffusion and transport diffusion coe cients has gained attention because they are crucial for understanding macroscopic mass transfer.Studies of the microscopic diffusion process for CO 2 , H 2 , and N 2 have utilized molecular simulations and experimental characterizations.There have been numerous papers published in recent years exploring both self-diffusion and transport diffusion processes.This study analysed the diffusion coe cient of CO 2 , H 2 , and N 2 on quartz surfaces based on the components of the reservoir (Fig. 14).It was discovered that CO 2 's diffusion coe cient was one to two orders of magnitude higher than those of H 2 and N 2 , potentially linked to the molecular diameter of the gas.Additionally, the diffusion coe cient decreases with rising pressure and temperature [23].
Nanoclusters of quartz, carbon dioxide, nitrogen, and hydrogen gas were imported from the MS library to create a quartz atmosphere.An amorphous tool was employed as a building option to develop the needed shape, with 100 present loadings of quarts and one loading of carbon dioxide, hydrogen, and nitrogen gas.The molecules of these Nano clusters were optimized to occupy the cubic unit cell evenly by optimizing the shape, which includes using a smart minimization strategy to reduce the overall energy of the new microstructure.The system was rst run through the NVE ensemble before re-equilibrating using the NVT ensemble.The entire system was annealed before running the dynamics to remove the most undesirable structures created during the build-up, and then temperature variance was analysed.The same technique was used to examine the impact of pressure variation on CO 2 , H 2 , and N 2 diffusivity in the system, except for NVT, which was substituted with the NPT ensemble.Convergence was assured during geometry optimization, and the cell was built using the Ewald electrostatic addition technique with a cut-off diameter of 31A and 3D periodic boundary conditions.The system density was adjusted to 3g/cm 3 , the beginning temperature was 298K at a pressure of 2500psi, and the initial velocity of molecules was chosen at random using the Boltzmann distribution technique.CO 2 , H 2 , and N 2 diffusivity in quartz surface were determined at temperatures 343K, 353K, 363K, 373K, and 393K with a pressure range of 500psi to 2500psi.In contrast, the pressure was altered four times to examine its in uence on the diffusion coe cient at a constant temperature (393K) [51,52].
EMD simulations predict different thermo-physical characteristics of uids, including diffusion coe cients, by using molecules' movements in a representative uid ensemble under macroscopic equilibrium conditions.On the other hand, the outcomes of EMD simulations are highly dependent on the underlying force eld (FF), which de nes intermolecular and intermolecular interactions.The literature has a thorough foundational exposition of the theory of EMD simulations.An example of a connection between pressure and elapsed time owing to N 2 dissolution in quartz surface at 393k K is presented in Fig. 14.When the gas is put into the sorption cell, the pressure immediately rises from 0 to around 350 Psi.It then gradually falls to the nal pressure (345.83psi) owing to dissolution.The pressure decay is the difference in pressure between the calculated and measured values from the cell and quartz volumes.
The pressure measurements are used to calculate the solubility and diffusion coe cient.The solubility of both gases (N 2 , H 2 , and CO 2 ) increased almost linearly with pressure, but carbon dioxide dropped as temperature climbed.However, the solubility of nitrogen rose with temperature.Carbon dioxide solubility in lower molecular weight PP (M w =3.210 5 ) were found to be very close to those in higher molecular weight PP (M w =4.5110 5 ).For the ranges investigated in this study, the effect of molecular weight on solubility was determined to be minimal.
The mean square distribution of CO 2 molecules is determined at different temperatures; the results are shown in Figure (14).The maximum distribution is obtained when the temperature is 393K.At the same time, the lowest is recorded when the temperature is 298K, which has a direct (although not necessarily linear) impact on the predicted diffusion coe cients of CO 2 at different temperatures, as shown in Figure (14).Table 4 demonstrates the direct dependency of diffusivity on temperature gradient since the maximum diffusivity is recorded at the highest temperature value, making it a crucial parameter to consider during CO 2 sequestration [51].the success of these procedures depends on rock-wetting various behaviors, which is popularly evaluated through contact angle measurements.However, contact angle datasets obtained from experimental observations could be ambiguous and inconsistent, and molecular dynamics modeling can be highly valuable in improving our understanding of wettability on mineral surfaces for CO 2 /H 2 /N 2 gas systems.
Thus, we constructed a consistent hydroxylated α -quartz model that ts simulation observations to a Hereby, I Surajudeen Sikiru, Ahmed Al-Yaseri, Nurudeen Yekeen, Hassan Soleimani, Bonnia N.N, Mohammed Falalu Hamza, Mohammad Yeganeh Ghotbi consciously assures that for the manuscript H2-Quartz and Cushion Gas-Quartz Intermolecular Interactions: Implications for Hydrogen Geo-Storage in Sandstone Reservoirs the following ful lled: This material is the authors' own original work, which has not been previously published elsewhere.The paper is not currently being considered for publication elsewhere.The paper re ects the authors' own research and analysis in a truthful and complete manner.The paper properly credits the meaningful contributions of co-authors and co-researchers.The results are appropriately placed in the context of prior and existing research.All authors have been personally and actively involved in substantial work leading to the paper, and will take public responsibility for its content.

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3. 3 .
Diffusion coe cient of the H 2 , N 2, and CO 2 gas at different TemperatureThe mechanism behind self-diffusion is the result of the random thermal motion of individual particles, and it is governed by the principles set forth by Albert Einstein, which are unaffected by pressure differences or concentration variations.Many scientists focus their attention on studying the selfdiffusion process and they utilize molecular simulations to determine the diffusion coe cient.At the micro scale, this coe cient provides an accurate representation of the movement properties of the diffusing particles and serves as a basis for understanding macroscopic mass transfer.However, in r S γ

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Table 1
The value of adsorption of each gas on the quartz surface

Table 2
The density value of CO 2 , N 2 , and H 2 gases

Table 4
Diffusion coe cient of N 2 /H 2 /CO 2 in sandstone environment at different temperatures