The demand for accurate and efficient simulations in order to test the geomechanical effects is a reality for the entire geoscience community. The motivation that arises from that need is the development and the evolution of modelling methods to study these effects. Deep understanding of any problem in fine scale is crucial, especially when it extends to much coarser scales. In this work the finite volume method (FVM) is used for mechanical modelling of deformation in elastic media. The momentum balance equation is solved as the governing equation for mechanics, assuming linear elasticity for the stress tensor. Here, displacement is mapped onto a vertex-centred grid in three dimensions (3D). A set of eight trilinear basis functions are used to locally interpolate the value of displacement within each grid cube. In the finite volume method, the discretized form of the equations are obtained by integrating the governing equation over control volume surfaces, since in 3D the control volume is a cube. Hence, discretized forms are obtained by considering 24 surfaces, which form between a displacement node and its neighbouring displacement cells. This required extensive derivation. The implementation of the numerical model was carried out by writing a code in MATLAB. Several numerical test cases are presented to demonstrate the capability of this model. In the first place, the consistency of the model is checked through comparison with synthetic analytical solutions, which are compared to the numerical solutions. Furthermore, the simple test case of uniaxial compression, has been carried out with this model, but also compared to the results with a 2D FVM model and a 3D finite element (3D FEM) one. In another test case, ground plain strain subsidence is studied in a real hydrocarbon field with a heterogeneous map for elasticity parameters. It is shown that 3D FVM is in close agreement with 3D FEM in predicting the subsidence due to field depletion. Last but not least, displacement and stresses, in a faulted reservoir in which fluids are injected, are modelled and the results are shown to coincide with a robust analytical solutions for the system. Finally, the aim of this work is to shed some more light on the finite volume method for mechanics and bring it closer to the audience of science.

The Netherlands will need to transform her traditionally fossil fueled energy system in the coming decades to achieve the goal of reducing CO2 emissions to net-zero in 2050. Therefore, an increase in renewable energy sources as solar and wind energy in the overall energy mix will be essential. However, due to the highly variable energy production patterns of these renewable energy sources, a primary need for energy storage is created. Since electricity can not be stored on a large enough scale to balance significant energy fluctuations, the need for a gaseous CO2 neutral energy carrier is created. In The Netherlands, this role could potentially be fulfilled by green hydrogen gas. Green hydrogen can be stored in geological formations such as depleted gas reservoirs. Due to the immense storage volumes and frequent occurrence in the Dutch subsurface, depleted gas reservoirs could be an excellent opportunity to serve as large scale energy storage sites. Moreover, underground natural gas storage in gas reservoirs is a proven and used technique in The Netherlands. Utilizing a natural gas reservoir as a hydrogen storage site comes with several challenges. This report provides a full overview of all the challenges with underground hydrogen storage in geological formations as aquifers, depleted gas reservoirs and salt caverns based on literature. In this way, the full potential and risks of using depleted gas reservoirs for this technique is clearly highlighted. Using this overview, a priority scheme for the usage of different geological formations as storage facilities for hydrogen is proposed. In combination with possible meteorological conditions combined with different Dutch policy scenarios, a minimum seasonal storage need of 16 TWh through the use of hydrogen is identified. Using the priority scheme, rock salt caverns are used as much as possible to fulfill the minimal need for seasonal hydrogen storage. By performing an analysis on the potential subsurface storage capacity in The Netherlands, it becomes clear that the Dutch subsurface can not realize more than 12.1 TWh of potential hydrogen storage capacity by only utilizing salt caverns. Since depleted gas reservoirs are identified as the best alternative for underground hydrogen storage, a minimum need for hydrogen storage from Dutch depleted gas reservoirs is estimated at 3.9 TWh in 2050. In this thesis, all physical and chemical aspects that are important during the subsurface storage of hydrogen in porous media are addressed. This leads to the identification of potential losses of hydrogen during the storage of the gas in the depleted gas reservoir. Analyzing all the possible methods leading to potential hydrogen loss shows that on the long term, bacterial conversion seems to be the biggest challenge if no measures against this conversion are taken. Using numerical reservoir simulation as a quantification and sensitivity analysis tool, the hydrodynamic behaviour of hydrogen in contact with other gasses is described. This is done by introducing a dimensionless gravity number. The interpretation of this number shows if the displacement process is either dominated by viscous or gravitational forces. Furthermore, the displacement efficiency of hydrogen towards other gasses is analyzed. Displacement of hydrogen towards residual gasses in porous media dominated by viscous forces proves to be more efficient than the displacement dominated by gravitational forces. By performing cyclic storage simulations, the overall efficiency of injecting and reproducing hydrogen from a depleted gas reservoir is examined. This is done for both homogeneous and heterogeneous reservoirs. By performing a sensitivity analysis on the input parameters of the simulator, an overview is given of the parameters that will have the most positive or negative impact on the cycle efficiency. The results of the simulation show a regular cycle efficiency that is estimated at roughly 70%. Applying a higher difference in injection and production pressure leads to a lower cycle efficiency whereas using a more elongate reservoir as storage site shows to have a positive effect on the overall cyclic efficiency.

This thesis contributes to increasing the technology readiness level of hydrogen storage in gas reservoirs, which will be required when hydrogen has become a major energy carrier in the future Dutch energy system. It addresses the mixing processes with resident gases that occur during hydrogen storage operations in gas fields, and analyzes their implementation in a reservoir simulator. The CMG GEM reservoir simulator allows incorporation of mechanical dispersion and effective molecular diffusion into its simulations, while solving the advection dispersion transport equation fully implicitly, as well as gravitational segregation and other macro scale mixing phenomena. Mechanical dispersion is quantified by its main parameter dispersivity, for which a large uncertainty exists in the literature. Dispersivity represents pore scale fluid velocity differences caused by microscale heterogeneities in a porous medium. Due to the lack of adequate hydrogen dispersivity experiments, a range of dispersivity values is collected from literature on (groundwater) dispersivity experiments in sandstones. A sensitivity analysis is conducted, in which the influence of the different mixing processes on the mixing between working gas and cushion gas is analyzed. For this, a conceptual reservoir model (radial and homogeneous), with properties based on Dutch sandstone gas fields was built in CMG GEM. The effect of molecular diffusion on mixing proves to be negligible compared to mechanical dispersion at typical reservoir flow rates. Furthermore, the results of the simulations prove to be significantly influenced by numerical dispersion, which is a calculation error, dependent on grid size and time step. The effect of numerical dispersion compared to mechanical dispersion is quantitatively analyzed, after which various options are introduced to deal with numerical dispersion in a way that the physical processes are most realistically represented. The work in this thesis demonstrates the challenges of realistically implementing hydrogen storage mixing processes in a reservoir simulator, and should be regarded as a foundation for further research.

Salt caverns formed by solution mining may cause soil subsidence, because the surrounding adapts to fill the void (cavity) created in the strata. The cavern volume is hence not only a function of salt extraction (estimated from mass balance) but also a function of salt creep. The cavern size can be measured by sonar, but a less costly way would be to correlate cavern volume to cavern compressibility. The size of the cavern can be obtained by a compressibility test. The compressibility test consists of injecting brine or fresh water into the cavern, causing a pressure build-up. The pressure increase depends on the cavern volume and compressibility. Bérest et al. (2006) [1] derived an equation that expresses the pressure response to injection of a volume V of fresh water. The equation includes creep that can be derived from a separate geometric creep model that relates the strain to the stress history using the Norton-Hoff law for describing an Arrhenius type of response model, and thermal expansion effects influenced by the geothermal temperature. It also considers Darcy flow and leakage through the permeable salt cavity. This thesis investigates the sensitivity related to the various mechanisms in the Bérest and Van Sambeek (2005) model. It also extends the model by introducing chemical dissolution of salt effects and taking into account the impact of the sump (insoluble precipitates at the bottom of the cavern). We state the model equations and solve them for an example of interest. We can also compare the calculated pressure response to the results of a pressure test. In this pressure test a given volume of fresh water is injected above the sump and produced at the top of the cavity. The produced salt concentration is also one of the parameters measured in the test. There are at least two widely used methods to obtain or predict cavern size of active salt solution mining caverns, namely sonar surveys and leaching simulators. However, these data can be flawed due to uncertainties of the methods and the accuracy of measuring devices like flow meters. The compressibility test can then be used as an additional survey method. The test execution is simple and inexpensive, making it possible to be performed more frequently than a sonar survey. The cavern volume is obtained from a compressibility test data by using a solution that includes not only the injection volume, but also volumes introduced by other phenomena. These other phenomena are caused by thermal, hydraulic, mechanical, and chemical influences. Previous work has attempted to introduced solutions incorporating these influences for idle caverns. The proposed solution incorporates these effects in an active leaching salt cavern. It also introduces the impact of sump (insoluble on cavern bottom) to be included in the model. The proposed solution is then tested against field data. The work here differs from previous work that it presents a comprehensive description of the various methods used in the literature and practice. Where current models predict cavity volumes with a mean absolute percentage error of 33% (Thiel’s method for BAS3O) to 127% (Bérest et al. for BAS4) for the studied caverns (BAS3O and BAS4), the model here, which includes the presence of insoluble particles, and a well-established creep model is able to predict cavity volumes to an accuracy of 33% (proposed model for BAS3O) to 12% (proposed model for BAS4).

Multiscale computational homogenization is an efficient method to upscale the microstructural behavior of micro-heterogeneous materials. In this method, a representative volume element (RVE) is assigned to a macroscale material point and the constitutive law for the macroscopic model at that point is obtained by solving a boundary value problem on the RVE. Among the conventional boundary conditions, the so-called strong periodic boundary conditions tend to converge faster towards the actual microstructural response. Nonetheless, applying strong periodic boundary conditions to a batch of 48 fiber-matrix RVEs under uniaxial load with varying orientations introduces a dependency between the average ultimate principal stress (σ1) and the orientation angle (θ). This treatise investigates the effects on this dependency by applying so-called weak periodic boundary conditions instead. These boundary conditions soften the strong requirement of periodicity of displacements at the RVE boundary by coarsening the traction mesh and requiring periodicity to hold only in an average sense over this coarser mesh. Three main questions are asked: Do weak periodic boundary conditions alleviate the dependency between σ1 and θ? Is this dependency the result of RVEs prone to localization under shear? Do smaller coarsening factors widen the range of θ over which localization with a single shear band is permissible? Overall, it is concluded that only the weakest form of weak periodic boundary conditions reduces the dependency between σ1 and θ, which is indeed caused by RVEs that are prone to strain localization under shear, particularly towards θ = 45o. Increasing coarsening factors quickly introduce stricter periodicity requirements, thus limiting the possibility of strain localization with a single shear band at angles other than θ = 45o. Recommendations are provided to alleviate the dependency between σ1 and θ as well as how to more realistically model the behavior of RVEs used in this research.

A considerable contribution to the greenhouse effect originates from landfills. This contribution originates from the degeneration of waste in the landfill. The gas which is created during the degeneration consists of 40 to 60% methane. One mole of methane has a global warming potential which is 28 times higher than that of carbon dioxide. Therefore, emissions of methane should be reduced. One method which can be used to reduce this emission is the oxidization of methane to carbon dioxide. This can be done by the construction of a cover soil with methanotrophic bacteria in the soil. These bacteria oxidize methane as their source of carbon and energy. This oxidation process discriminates against the heavier isotopes present in the gas, this shifts the isotope signature. A method to determine the oxidation efficiency of the methane is based on the evaluation of this change in isotope signature over the cover soil. Next to the fractionation of isotopes due to oxidation, fractionation also occurs due to diffusion. However, fractionation due to diffusion is generally assumed to be negligible. Mostly, this assumption is valid, since the dominant part of transport is advective; which does not discriminate against an isotope. In this thesis the effect of compaction and saturation on two sands are evaluated. Using this evaluation, the criteria during which diffusion becomes an important transport phenomena are determined. This is determined by a series of experiments, where the concentration of methane is monitored while the gas diffuses through a soil sample. In this thesis the effect of the soil matrix on the fractionation of methane is also evaluated. This is evaluated by performing isotope spectrometry on samples of gas, taken at different times during the experiments. These two aspects are combined to evaluate if the oxidation efficiency can still be determined using fractionation of stable methane isotopes when diffusion plays a considerable role in gas transport. During the experiments the decrease of methane in the chamber was measured. Spread over two soils, for a total of 18 variations in compaction or saturation the decrease of methane over time was measured. The results of the experiments show that for diffusion no distinction between variation in compaction and saturation needs to be made. Compaction and saturation can be described together for both soils using the air-filled porosity. The relation between the air-filled porosity and the effective diffusion coefficient is linear for both soils. Due to the large sand fraction the share of coarse pores is high for the whole range of compaction, meaning that no significant increase of tortuosity is visible in the relation between air-filled porosity and the effective diffusion coefficient. When the effective diffusion coefficients are compared to effective permeability values of these soils, it showed that the diffusion is more important for drier and more compacted soils. Thus, diffusive transport becomes important for gas transport over a cover soil when the pressures are lower, the soil is drier, and the soil is more compacted. The fractionation factors due to diffusion, which have been determined for a selection of experiments, showed no trend with any other measured parameters. The precision of the measured values from which the fractionation factors are determined is high. Thus, the confidence in the fractionation factors is high. The lack of a trend present means that in sand the soil matrix has no effect on the fractionation factor. This means that the fractionation factor due to diffusion in soil is the same as in free air. For the calculation of the oxidation efficiency with a relevant diffusive flux the ratio of diffusive to advective flux needs to be determined but the fractionation factor due to diffusion is constant. Before the oxidation efficiency can be calculated, first the load needs to be corrected for any loss through hot-spots. Next, the advective flux and diffusive flux are combined, this is done by adding the fluxes together. The fluxes can be added because there are no interdependent effects, each flux only increases the total flux. Thus, the oxidation efficiency can be calculated using the changes in isotope signatures, even when a significant diffusive flux is present.

The effect of conductive heat transfer recharge originating from the surrounding conduction dominated geothermal system on the geothermal reservoir lifetime has been reviewed during its development, by studying the effect of multiple reservoir and production parameters. A two dimensional (2D) finite volume implicit coupling strategy, using a direct solver method, is applied on a non-isothermal lumped-parameter model to simulate reservoir development over a period of 35 years. Two test cases are investigated, modelled after the low temperature geothermal fields of Middenmeer in The Netherlands and Soultz-sous-Forêts in France. Resulting produced thermal water temperature and thermal energy flow rate profiles are simulated with and without consideration of the geothermal system. A resolution of 200×200 equidistant structured cells is applied to cover an integrated (reservoir and surrounding) domain that extends 2 km vertically and 10 km horizontally. The reservoir domain extends 200 m vertically and 1 km horizontally, covered by a computational grid resolution of 20×20. Sensitivity analysis show that this is the best resolution that can be applied without losing simulator stability and accuracy. Results show that the conductive heat transfer recharge originating from the surrounding geothermal system has a significant effect on reservoir lifetime by reducing temperatures after thermal drawdown up to 26.5% in the first test case and up to %22.6 in the second test case. In addition, it lead to an increase in the average annual thermal energy production, up to %12.5 and %14.3 respectively. The consideration of the conductive recharge from the surrounding domain shows a significantly increased lifetime estimate for low temperature geothermal reservoirs. Furthermore, permeability, rock thermal conductivity and (re-)injection temperature are the reservoir and production parameters that can greatly influence the reservoir lifetime.

This study aims to characterize the variation in stomatal conductance and leaf water potential of corn plant in height over time on a diurnal time-scale and on a seasonal time-scale, under well-watered and water stressed conditions. An additional objective was the development of a protocol for plant-water relation measurements in radar experiments. Field experiments were done to measure the leaf water potential by conducting pre-dawn measurements three times a week, evening measurements once a week and a mid-day measurement in the beginning and at the end of the growing season. The stomatal conductance was measured multiple times per day for three days a week, given that there was no precipitation. As the research is part of a larger project, additional hydrological data, soilmoisture data and sap flow data were collected. For the stomatal conductance a clear variation over height was observed. This variation was caused by limited solar radiation for the lower leaves. The leaves that received full solar radiation had clear diurnal cycle in stomatal conductance and a high variation in stomatal conductance. In water-stressed conditions, it is expected to see a change in stomatal behaviour in these leaves. For the leaf water potential, no values were reached that have been connected to water stress in the literature. Also, no water stress coping mechanisms were observed in the corn. From this it can be concluded that no water stress took place during this experiment for the days on which data was collected. In the leaf water potential data a clear influence of the soil water potential was observed. For the leaf water potential, no values were reached that have been connected to water stress in the literature. Also, no water stress coping mechanisms were observed in the corn. From this it can be concluded that no water stress took place during this experiment for the days on which data was collected. In the leaf water potential data a clear influence of the soil water potential was observed.

English: Landfills have been indicated as a major methane source. Methane oxidation systems are `low technology' systems that can treat these methane emissions. Yet, methane oxidation systems are herein still sub-optimal and leave room for improvement. A numerical model was established to research the effective gas permeability ratio between the gas distribution layer and the methane oxidation layer, and the centre-to-centre distance of the gas inlet points, necessary to achieve a spatial homogeneous methane load. In order to relate the permeability ratio to the design choice for the materials, laboratory experiments were performed to asses the influences of compaction level, hydraulic conditions and physical properties of a soil on the effective permeability of that soil. Overall, it is concluded that the effective permeability is predominantly influenced by the compaction level and soil texture. The water saturation only has a significant influence at near saturated levels. This means that the choice of suitable material and adequate construction practice has more effect on the effective permeability than seasonal changes in saturation levels in moderate climates. Furthermore, it is concluded that there are two parameters that govern the spatial homogeneity of the methane fluxes from the gas distribution layer into the methane oxidation layers: the permeability ratio between these layers, and the centre-to-centre distance between the inlet points. The required permeability ratio increases quadratically with an increasing centre-to-centre distance. Nederlands: Stortplaatsen zijn aangeduid als een belangrijke bron van methaanemissies. Methaanoxidatiesystemen zijn technisch simpele systemen die het stortgas kunnen saneren. Op dit moment zijn de bestaande methaanoxidatiesystemen nog weinig efficiënt en is het noodzakelijk om de homogeniteit van de laterale distributie van het stortgas te optimaliseren. Er is een numeriek model gegenereerd om inzicht te geven in de benodigde ratio tussen de effectieve permeabiliteit voor gas van de gasdistributielaag en van de methaanoxidatielaag, en in de maximale hart-op-hartafstand tussen de gasinlaatpunten om deze lateraal homogene methaan distributie te bereiken. Om de effectieve permeabiliteitsratio te relateren aan de materiaalselectie zijn er laboratoriumexperimenten uitgevoerd, die de invloeden van het compactieniveau, de hydraulische condities en de fysieke grondeigenschappen op de effectieve permeabiliteit voor gas vaststellen. Al met al kan worden geconcludeerd dat de effectieve permeabiliteit hoofdzakelijk wordt beïnvloed door het compactieniveau en de grondtextuur. Het watergehalte blijkt alleen significante invloed te hebben onder bijna verzadigde omstandigheden. Dit betekent dat een geschikte materiaalkeuze en adequate constructie de effectieve permeabiliteit voor gas meer beïnvloeden dan de seizoensgerelateerde veranderingen in het watergehalte in gematigde klimaten. Daarnaast kan worden geconcludeerd dat twee parameters bepalend zijn voor de laterale homogeniteit van de methaanstroom van de gasdistributielaag naar de methaanoxidatielaag: de ratio tussen de effectieve permeabiliteit voor gas tussen deze twee lagen, en de hart-op-hartafstand van de gasinlaatpunten. De benodigde permeabiliteitsratio neemt kwadratisch toe bij een toenemende hart-op-hartafstand.

In this paper the suitability of compressed hydrogen gas storage in salt caverns is analysed. The presence of microbial sulfate reducing bacteria create a contamination risk of H2S inside the cavern. Key cavern parameters that influence the production of H2S are highlighted by a chemical model. The model uses empirical data provided by Vattenfall, in order to predict what would happen inside an actual cavern. By doing so, it can be understood what cavern conditions are suitable for the storage of hydrogen. An analysis is done on the above ground process of a salt cavern storage plant to determine what extra separation steps are required to reach ISO limitations for hydrogen gas. The research is done by answering the following research questions: What are key cavern conditions that influence the suitability of hydrogen storage in salt caverns and for what purpose can the storage plant be implemented? The sub-research objectives are formulated as follows: 1. What are the potential process risks when storing hydrogen in salt caverns? 2. Are there substantial risks of contamination with subsurface hydrogen storage? What are the defining variables that contribute to said contamination? 3. How do these impurities build up when the salt cavern is used? 4. Is the equipment currently used in the gas storage facility in Epe useable for hydrogen gas storage? What changes should be made to the current storage process? When analysing future utilisation demands of hydrogen, one of the primary applications is energy con- version by fuel cells. There are severe limitations set by the International Organization for Standardization on the maximum amount of H2S in hydrogen gas used by fuel cells. This paper uses a chemical model based on PHREEQC to predict the chemical reactions in the cavern. In order to get close to actual results, the model input is constructed following empirical data of an existing salt cavern. With the chemical model different cases can be constructed each highlighting an important cavern constraint. What are the positive and negative forces on the production of H2S in salt caverns and what could be theoretically done to prevent H2S contamination? Primary aspects that positively contribute to H2S production, when the cavern is modelled as a batch reactor, sorted by significance are: • Bacterial growth and reduction rate • Brine volume and sulfate concentration. • Brine pH and ionic strength. • Cavern pressure and temperature. • Fe2+ and Fe3+ concentration. The chemical model only predicts what will happen in the cavern when there is no gas coming in or out, like a batch reactor. For this reason a dynamic model is constructed which predicts H2S outflow in the gas when applying different demand-cases to the cavern. The model results showed that with applying a maximum use case, which fluctuates between the maximum pressure and minimum pressure, there is still a minimum H2S output that is higher then the allowed limits. A demand curve is simulated where the cavern is used to power a hydrogen gas-turbine to profit from seasonal energy price changes. In this demand curve the cavern produces significantly less and less often, giving time for the H2S to build up. In two years, the H2S production reaches levels above the allowable limits set for hydrogen gas turbines. A gas process facility is required to eliminate H2S contamination, in order to size such a facility it was modelled in Aspen Hysys. The model is validated by using data from literature. After analyses of resulting process equipment and gas streams, the absorber tower’s efficiency is most dependant on its temperature its pressure and the absorbent flow rate. The water concentration is above ISO levels when withdrawn from the cavern. So to follow these limitations, an additional dehydration step is required. In conclusion the process is capable of accurately separating the H2S to below ISO limits. The process works using 6% of the potential chemical energy of hydrogen. The process is unable to purify the water concentrations. As a result of this research some conclusions can be made. When using salt caverns for long term hy- drogen storage can be a significant risk of H2S contamination as a result of microbial sulfate reduction. For the reference case the H2S concentrations reach above the levels set for fuel cell use and concentrations will increase in significance when utilisation of the cavern is decreased. For fuel cell application, a separation pro- cess based on MDEA gas sweetening can be used to get the hydrogen up to the demanded H2S purity. But a more economical solution would involve extensive testing of the cavern soil for any microbial activity. If there are no sulfate reducing bacteria there will be no problem. Other pre-process steps could involve increasing the pH of the brine in the cavern to avoid H2S production. As well as increasing the iron concentration in the brine.

The first part of the thesis explores the process of homogenization, particularly for the permeability properties of rock samples. The Hill-Mandel postulate of energy consistency throughout the transitioning of scales is revisited since traditional homogenization methods rely on applying specific boundary conditions to enforce energy consistency. However, it is shown that the applied boundary conditions influence the effective physical parameter and provide upper or lower bound estimations. Recently, it is shown that these boundary conditions influence a layer near the boundary of the sample and that homogenization applied on the subsample away from this boundary layer is not affected by the boundary conditions. The research focuses on energy consistency by studying the evolution of the energy within the intrinsic subsample, away from the boundaries. With the help of Finite Element simulations of Stokes-flow through idealized structures, the energy of the fluid is traced without the influences of grain properties on the energy dissipation. By plotting the ratio of the energy dissipation of the macro- and micro-scale, it is shown that the energy consistency is not found within small subsamples. Yet, with a growing subsample, energy consistency is achieved naturally, without the enforcement of boundary conditions. As a result, it is concluded that the energy consistency is found at the Representative Elementary Volume (REV), which is a similar requirement as for traditional homogenization methods. The study of the natural energy consistency in idealized microstructures is extended to real microstructures, which include more natural heterogeneities, such as grain properties. It is shown that energy consistency is also found with the natural heterogeneities included, albeit with a slower convergence. For the homogenization of the permeability of a sample, the energy ratio is now known to be unitary, which can be used as an accurate indicator to determine the size of the REV. The second part of the thesis explores the process of determining the size of the REV, which is a common, yet essential practice in Digital Rock Physics. Currently, this is an extensive exercise, involving many and large-size simulations to trace the convergence of the physical property and requires a lot of computational resources and time. Numerical-statistical studies have shown that the convergence of the REV visualizes in a cone-like shape. By plotting the convergence for both the permeability and the energy dissipation ratio for idealized microstructures, this study analyses the shape and evolution of the cone of convergence. From this, the generic evolution law of the convergence is determined. It is shown that the asymmetrical convergence cone is described with a log-normal distribution, with a stable mean throughout the evolution of the cone and a variance for each sample size. The evolution of the variance is described with the law of large numbers, taking into account a reference value. This makes it possible to determine the size of the REV. Since the statistical method applies, information about the error of the fit, the error of the determined homogenized property, and the error of the size of the REV is provided. The study is extended to real microstructures to validate whether the determined evolution law applies when natural heterogeneities are included. It is shown that the evolution law still accurately describes the REV's convergence. Therefore, the REV's size of real rock samples can also be determined. Even when the REV is not included within the sample, the evolution law can provide an estimate of the size of the REV or the homogenized property. By using the cone of convergence, it is not necessary to run simulations on the full sample to find the REV, which is computationally expensive, instead running a number of simulations on small subsamples is sufficient, which saves both time and computational resources. It also unlocks the possibility to find the REV for high-resolution samples, as splitting the sample into subsamples allows for smaller simulations.

This study investigates the technical feasibility and economic viability of utilizing depleted offshore gas reservoirs in the Dutch North Sea for underground hydrogen storage (UHS) to buffer intermittent hydrogen production from offshore wind farms in the Dutch North Sea. The research aims to address the existing knowledge gap in integrating an offshore hydrogen storage platform while considering the maximum re-useability of existing natural gas infrastructure.