Numerical Modelling of Gas Mixing in Salt Caverns During Cyclic Hydrogen Storage

Abstract

This study presents the development of a robust numerical model for simulating underground hydrogen storage (UHS) in salt caverns, with a particular focus on the interactions between original gas-methane (CH₄) and injected gas represented by hydrogen (H₂). Using the Schlumberger Eclipse 300 compositional reservoir simulator, the cavern was modelled as a highly permeable porous medium to accurately represent gas flow dynamics. Two principal mixing mechanisms were investigated: physical dispersion, modelled by numerical dispersion, and molecular diffusion. Multiple cavern configurations and a range of dispersion–diffusion coefficients were assessed. The results indicate that physical dispersion is the primary factor affecting hydrogen purity during storage cycles, while molecular diffusion becomes more significant during long-term gas storage. Gas mixing was shown to directly impact the calorific value and quality of withdrawn hydrogen. This work demonstrates the effectiveness of commercial reservoir simulators for UHS analysis and proposes a methodological framework for evaluating hydrogen purity in salt cavern storage operations.

1. Introduction

Decarbonization of the energy sector is a cornerstone of the European Green Deal. In this way, hydrogen will play the main role as a raw material, a fuel, and, above all, an energy carrier [1], which helps balance seasonal fluctuations in supply and demand [2,3]. The European Commission, as well as national governments, including that of Poland, anticipate a rapid growth of hydrogen production, distribution, and storage infrastructure to meet these ambitions [4,5,6].

The widespread deployment of hydrogen, however, depends on the development of robust, efficient, and safe storage technologies [1]. While above-ground storage options, such as high-pressure gas tanks, are well-known, they present many limitations in terms of capacity, cost, and economic feasibility for seasonal and large-scale applications [7,8,9]. In contrast, underground storage in geological formations offers the potential for cost-effective, long-duration storage of much more energy, making it highly attractive for balancing and energy system flexibility [3,10,11,12,13].

One of the major challenges of large-scale underground gas storage (UGS) and UHS is gas mixing. In addition to mixing, other processes such as CO₂ hydrate formation and clay mineral (e.g., kaolinite) alterations may also occur and affect storage performance [14,15]. The interaction between the injected hydrogen and the original or residual gases, primarily CH₄, leads to dilution and reduces the purity of the withdrawn H₂ [16]. In volumetric terms, admixture of CH₄ increases the calorific value per unit volume [17] of the withdrawn gas, but at the same time decreases hydrogen purity, which is critical for end-use applications. Therefore, additional separation processes may be required, increasing the costs of hydrogen storage operations [4,18,19]. The phenomenon of gas mixing has been the subject of extensive theoretical and experimental studies. The classical description of dispersion in flowing systems was introduced by Taylor [20] for one-dimensional tube flow. Aris [21] later extended Taylor’s work by examining two-dimensional flow. Laboratory flow experiments demonstrated the existence of diffusion and dispersion during density-driven convection, supported by visualization techniques [22]. Arekhov [23] measured the effective diffusion coefficients of H₂–CH₄ gas mixtures in reservoir rocks using rock cores. The results revealed that the observed transport effects are a combination of molecular diffusion and physical dispersion, and their contribution varies with pressure conditions and rock properties. Another study by Lester, Metcalfe, and Trefry [24] utilized pore models to demonstrate that flows in real media can lead to chaotic advection, a phenomenon in which particles follow unpredictable trajectories. This chaotic flow significantly intensifies dispersion compared to classical models. The influence of this phenomenon was also described and presented through the example of modelling hydrogen storage in a porous medium [16].

Feldmann et al. [18] conducted an investigation into gas mixing processes in depleted porous gas reservoirs through numerical methods. Azin et al. [25] examined how the cyclical operation of gas stored in a partially depleted gas reservoir affected the composition of withdrawn gas through simulation approaches. In a related study, Lysyy et al. [26] analysed seasonal hydrogen storage in a depleted oil and gas reservoir, emphasizing the operational feasibility and the challenges associated with large-scale applications in porous structure. Additionally, Hogeweg et al. [19] benchmarked various simulation methodologies for porous UGS/UHS.

All of these studies share a common focus: they were conducted on porous rocks.

Salt caverns have been widely used for gas storage around the world [27,28,29]. Among the various geological storage options, salt caverns stand out due to the low permeability of their surrounding rocks and their proven tightness over decades of gas storage operations in many countries [6,30]. In addition, salt caverns offer high injection and production rates, making them particularly suitable for balancing the intermittent nature of renewable energy sources [31,32].

In Poland, Kaliski et al., Filar et al., and Zeljaś [12,33,34] documented domestic cavern operations. Other publications confirm the technical potential of salt caverns for future hydrogen storage, both domestically and across Europe [3,6,27,29,35]. In this study, we build on these existing facilities and represent the cavern as a simplified storage domain without modelling the leaching process or construction details.

In recent years, significant progress has been made in terms of modelling and analysing salt caverns as underground hydrogen storage facilities. Höpken [36] developed an operational model to assess the impact of future energy demand on cavern performance parameters. This work emphasizes the importance of adapting simulations to account for variable market scenarios [36]. Jeannin et al. [37] introduced a numerical model that integrates heat transfer and some parameters of strategy development, allowing for different scenarios of cavern cyclic performance [37]. Complementing these efforts, Ruiz-Maraggi and Moscardelli [38] launched the open-source GeoH2 Salt Storage and Cycling App, which models storage capacities with the injection/withdrawal of hydrogen cycles for salt caverns [38].

Another crucial area of research addresses the integrity and geomechanical stability of caverns, as well as potential gas storage losses. For example, Ghaedi [39] focused on salt cavern integrity, particularly concerning leakage through cavern seals, and reported that such losses are typically very small, equalling less than 0.5% of the maximum capacity over 30 years of storage operation [39]. While such geomechanical and integrity issues are critical for UHS, the present work deliberately focuses on transport processes, namely mixing by dispersion and diffusion, because they directly affect hydrogen purity and calorific value during cyclic operation.

In a wider context, Qian et al. [40] provided a comprehensive review of hydrogen storage and its technological benefits, limitations, and critical aspects related to safety, microbiology, and operational constraints [40].

One of the most important areas is gas mixing in salt caverns. It is a critical challenge for maintaining hydrogen purity or for predicting calorific value during the withdrawal of stored gas. From a Polish perspective, Budak and Szpunar [4] examined the changes in hydrogen–methane gas composition during cavern operations, revealing that mixing processes can significantly affect the calorific value profile and, more importantly, reduce hydrogen purity. As a result, additional separation may be required before the gas can be sent out to the gas system [4]. More recently, Wallace et al. [41] conducted numerical studies comparing hydrogen and gas mixtures in salt cavern storage. Their findings indicated that hydrogen has greater fluctuations in pressure and temperature as well as a lower effective energy storage capacity compared to any other gas composition with methane [41]. These operational characteristics increase the risks associated with gas mixing during cyclic injection and withdrawal. In addition to this, Hu et al. [42] examined the effects of cushion gas pressure and operating storage parameters on hydrogen storage capacity in lined rock caverns (LRC) [42]. They found that lower cushion gas pressure increases the hydrogen injection total, while higher injection rates accelerate temperature increases. These factors can indirectly affect mixing dynamics by altering thermal and pressure gradients.

In addition to mixing processes, UHS in salt caverns also involves a range of other challenges, such as geomechanical stability, cavern shape evolution, and safety management [43,44,45]. These aspects are crucial for long-term operation but remain outside the scope of this study. Here, we focus exclusively on modelling physical dispersion by numerical dispersion and diffusion that directly influence the purity and calorific value of the withdrawn H₂. Classical transport models such as the Maxwell–Stefan equations, the Presentation-De-Buthane theory, and the dusty gas model [46,47] provide the theoretical foundation for gas mixing. Experimental approaches, including the capillary and point–source methods, have also been applied to quantify binary diffusion. The present work complements these efforts by demonstrating how commercial reservoir simulators can be used to parametrize dispersion–diffusion processes under cyclic cavern operation.

Overall, these studies indicate that the phenomenon of gas mixing plays a crucial role in accurately predicting the composition of gas during UGS/UHS. Salt caverns are particularly suitable for the purpose as they offer proven tightness, a high rate of injection/withdrawal, and extensive operational experience from decades of gas storage. However, despite these advancements, there has been no systematic investigation, to the best of the authors’ knowledge, on the combined effects of dispersion and diffusion in salt caverns and their impact on the composition of the withdrawn gas during storage operations. The issue of gas mixing has not been adequately addressed in the commercially available reservoir simulators used to model multiple processes occurring during the transport of reservoir fluids (oil, gas, water). The best example proving the validity of this thesis is the world’s most popular reservoir simulator, Eclipse by GeoQuest (Schlumberger), in both the Black Oil and Compositional versions. Since numerical modelling of reservoir processes (including the production and operation of underground gas storage, UGS) has become a widely accepted standard, its users, including the authors of this work, are forced to use special methods based on the unique features of standard reservoir simulators, which cause the appearance of phenomena analogous to the physical mixing processes of gases flowing through a porous medium. The phenomenon in question that occurs in nature is physical dispersion, while the numerical mechanism used to model it is numerical dispersion. Previous works [48,49] presented the determination of a difficult-to-measure reservoir parameter, physical dispersion [20] for a porous medium, while in the present work, research and analyses will be carried out for salt caverns [19,31,50,51]. In addition to a systematic analysis of the effects of physical dispersion modelled by controlling numerical dispersion, the impact of molecular diffusion [18] on the simulation results will also be investigated.

The aim of this article is to present the challenges and methodological approaches associated with modelling hydrogen storage in salt caverns, with particular emphasis on the processes of gas mixing and the simulation of physical dispersion and molecular diffusion. The analyses presented here are intended to contribute to the development of more accurate and reliable modelling tools supporting the safe and efficient storage of natural gas and hydrogen in the context of the energy transition.

2. Materials and Methods

2.1. Salt Cavern Model

For a better understanding and description of the phenomena occurring during the H₂ storage process in a salt cavern, a three-dimensional model of such a structure was used, built based on data from domestic and foreign literature [4,5,29,52]. The base model is based on a grid of blocks with dimensions of 60 × 60 × 300, composed of 235,792 active blocks that form a cylinder with hemispheres at the bottom and top (Figure 1a). A single simulation block has a cross-section of 1 × 1 m, and the height of each block is also 1 m. All active model blocks are characterized by a uniform porosity of ≈100% and a permeability of 10,000 mD. Due to the specific properties of the salt cavern, a uniform distribution of these parameters was assumed. The model blocks form a volume with a total height of 200 m, while the radius of the cylinder is 20 m, so the resulting volume of the salt cavern model is 237,375 Rm³ (reservoir cubic meters). A cross-sectional view of the model used in the following procedures is shown in Figure 1b.

2.2. Fluid Properties

To model the mixing of the original gas, i.e., CH₄, with the injected gas, i.e., H₂, the fluid model described by the Peng–Robinson (PR) equation of state (EOS) was used. In this study, the PR EOS was applied as a simplified two-component CH₄-H₂ system, with all parameters kept at their default values (

Table 1. Parameters of Peng–Robinson equation of state for fluid of variable composition.

Component	Molecular Weight [kg/kmole]	Tcrit [K]	Pcrit [bar]	Vcrit [m3/kg-mole]	Zcrit [-]	Vol Shift [-]	Acentric Factor [-]	Parachor [dyne/cm]	Omega A [-]	Omega B [-]
H2	2.016	33.2	12.97	0.065	0.3054	0	−0.22	34	0.4573	0.0778
C1	16.043	190.6	46.00	0.099	0.2874	0	0.013	77	0. 4573	0.0778

). No additional calibration was performed, as the focus of this study was on transport phenomena (dispersion and diffusion) rather than on detailed phase equilibrium modelling.

The initial cavern content was assumed to be 100% CH₄ (cushion gas), representing a typical case of converting an existing UGS facility into UHS.

2.3. Phase Permeability

For the modelling of gas flows in the salt cavern, the absence of water in the model (S_w = 0, S_g = 1) and the gas relative permeability K_rg(Sg) = 1 was assumed.

2.4. Model Initialization

Based on the literature data [4,5,52], the initial pressure Pini = 140 bar was assumed and T = 57 °C.

2.5. Simulation Model Validation

The Eclipse commercial reservoir simulator was created to model flows in a porous medium that take place following Darcy’s law. By being careful about the limitations of this program, it can also be used to model flows in a salt cavern [19,31,32,50,51] described in the same way as a porous medium, but with a very high porosity value (100%) and a very high permeability value at which flow resistance will be negligible. Therefore, to determine the value of permeability, for which the flow resistance will be negligible (i.e., no resistance, as in a cavern), a forecast of the H₂ storage operation was carried out for five models of the salt cavern (differing in permeability, from k = 10 mD to k = 100,000 mD), consisting of the following:

• Precycle, i.e., original gas withdrawal (CH₄),
• H₂ injection phases,
• Withdrawal of gas from the cavern (H₂ with CH₄).

The daily injection and withdrawal rates applied in this study (500,000 and 600,000 Nm³/d, respectively) were estimated to represent the filling and emptying of a single cavern of typical size reported in the Polish literature [5,33].

Figure 2 shows the bottom pressure in the injection–production (IP) well, where it is possible to observe, among others, a pressure drop in the CH₄ withdrawal phase, which is much faster for models with a permeability of 10 and 100 mD than for other models, which means that the CH₄ withdrawal rate decreases faster (Figure 3). Therefore, the use of a model with a permeability of 1000 mD is sufficient to achieve flow conditions in the cavern.

On the other hand, as a result of the analysis of the concentration of H₂ in the withdrawn gas (Figure 4), differences of this magnitude were observed between the models with a permeability of 1000 and 10,000, which resulted from a relatively small, but longer-lasting gas extraction withdrawal for models with a permeability of 10, 100, and 1000 mD (the condition of extraction withdrawal at P_{bhp, min} = 40 bar).

Taking into account the differences in the course of the gas withdrawal efficiency, bottom pressures, and H₂ concentration of the extracted gas, which resulted from the applied permeability of selected models, we decided to use a model with a permeability of 10,000 mD for further research. It should be noted that the upper permeability value of 100,000 mD does not correspond to natural reservoir rocks but was introduced as a numerical abstraction to reproduce the negligible flow resistance characteristic of an open cavern volume. Similar approaches have been reported in the literature, where the cavern volume is represented as an artificial domain with porosity ≈ 1.0 and very high permeability, effectively mimicking an open space with negligible flow resistance [53]. Lower permeability values (e.g., 10–100 mD) were included only to demonstrate the artificial effect of flow resistance and are not intended to represent cavern conditions. This simplification does not explicitly resolve turbulence and boundary-layer phenomena; instead, their effect on mixing is approximated implicitly through numerical dispersion of the finite-difference scheme. A more detailed resolution would require Computational Fluid Dynamics (CFD) modelling.

The selected cycle frequency and daily injection/withdrawal rates were chosen to ensure methodological clarity in the numerical simulations. These values were estimated based on the reported injection and withdrawal gas volume of a specific underground gas storage facility that uses salt caverns in Poland, as well as the assumed duration of the injection and withdrawal periods [5,33,54]. It is important to note that the actual operating parameters of salt caverns can vary depending on local conditions and the design of the facility. A detailed analysis of these parameters is beyond the scope of this study.

2.6. Dispersion

2.6.1. Physical and Numerical Dispersion

Physical dispersion occurring in hydrocarbon structures [55] is the process of blurring the concentration profile of reservoir fluids caused by the inhomogeneity of the convection velocity field, resulting from the complex flow through a porous medium. An analogous effect is also the result of the occurrence of molecular diffusion, resulting solely from the concentration gradient.

The vast majority of commercially available reservoir simulators using the finite difference method are burdened with the problem of numerical dispersion. On the one hand, it requires a detailed analysis and evaluation of the magnitude of numerical dispersion effects in the results of calculations with such simulators for most processes where physical dispersion does not occur. On the other hand, it makes it possible to take into account the effects of physical dispersion by modelling them through numerical dispersion in the processes in which it occurs. In this case, the problem boils down to the quantitative control of numerical dispersion in a situation where it is not a simple result of changing the relevant parameter, because it does not exist, but depends in a complex way on other parameters of the model, such as the size of its blocks [49].

2.6.2. Numerical Dispersion Analysis

To find the dependence of the numerical dispersion intensity on the flow velocity and the size of the model blocks, the distribution of H₂ concentration along the axis of symmetry of the salt cavern was analysed. Since the flow and, thus, the concentration of H₂ in the part of the cavern described by the cylinder was studied, the height of the blocks was modified in this part of the model, so that the volume of the salt cavern was identical in all models (Figure 5). H₂ was injected into a CH₄-filled UGS with a constant injection rate (q_g,inj = 600,000 Nm³/d) through an IP well providing access to the cavern in its upper part (Figure 5). Due to the closed nature of the storage operation, it was not possible to maintain the conditions of stationary H₂ flow along the analysed A-A’ cross-section (Figure 5).

The results of the simulation in the form of the distributions of H₂ concentration along the analysed model axis for different times, t, were confronted with the analytical model described below.

Due to the complex nature of the flow of injected H₂ in the cavern, the convection–dispersion equation was used, having an analytical solution in one dimension for the following boundary and initial conditions [56]:

$$u\left(x,t=0\right)=0 \mathrm{for} \mathrm{x}\ge 0,$$

(1)

$$u\left(x=0, t\right)=1,\mathrm{for} \mathrm{t}\ge 0,$$

(2)

$$u\left(x=, t\right)=0,\mathrm{for} \mathrm{t}\ge 0.$$

(3)

This solution takes the form of [56]:

$$u\left(x,t\right)={\displaystyle \frac{1}{2}}erfc\left({\displaystyle \frac{x-vt}{2\sqrt{Dt}}}\right)+{\displaystyle \frac{1}{2}}exp\left({\displaystyle \frac{vx}{D}}\right)erfc\left({\displaystyle \frac{x+vt}{2\sqrt{Dt}}}\right),$$

(4)

where erfc is the so-called complementary error function:

• v—velocity of convection [m/d],
• x—distance from the structure ceiling [m],
• D—dispersion–diffusion coefficient [m²/d],
• t—time [d].

For further analysis, due to the high values of the argument of the complementary error value function, a modified solution of this equation was used:

$$u\left(x,t\right)={\displaystyle \frac{1}{2}}erfc\left({\displaystyle \frac{x-vt}{2\sqrt{Dt}}}\right)+{\displaystyle \frac{1}{2}}exp\left({\displaystyle \frac{vx}{2D}}-{\displaystyle \frac{x^2}{4Dt}}-{\displaystyle \frac{v^{2}t}{4D}}\right)\left({\displaystyle \frac{1}{\sqrt{\pi }}}\right)\left({\displaystyle \frac{1}{z}}\right)\left(1-{\displaystyle \frac{1}{2z^2}}\right)+{\displaystyle \frac{3}{4z^4}}-{\displaystyle \frac{15}{8z^6}},$$

(5)

where $z=\left({\displaystyle \frac{x+vt}{2\sqrt{Dt}}}\right)$.

Figure 6 shows examples of fitting the above model to the simulation results in the form of H₂ concentration, with c_H2 as a function of position, x along the A-A’ profile (Figure 5) for selected time steps, and t = 10, 20, 30, 40, and 50 days from the start of injection.

The very good fit of the model to the simulation results described above justifies the correctness of the adopted procedure. As illustrated in Figure 6, the numerical dispersion reproduced by the simulation results effectively mimics physical dispersion, which is described by the one-dimensional convection–dispersion equation used in the analytical model.

The procedure of fitting the model to the simulation results was repeated for the three other models differing in block heights (Figure 5). For each of these models and for each time step, the convection velocity coefficient, v, and the dispersion–diffusion coefficient, D, were adjusted. Figure 7 shows the decreasing dependence of the adjusted vertical velocity component, v, for the subsequent time steps, i.e., 10, 20, 30, 40, and 50 days from the start of injection. The decrease in the value of the speed of H₂ movement over time can be explained primarily by the increasing pressure in the UHS. It should be noted that the different block sizes in the analysed models have a relatively small effect on the convection velocity.

The second adjusted quantity is the dispersion–diffusion coefficient, the value of which decreases nonlinearly at lower and lower velocities, which may be due to the lack of stationarity of the flows due to the varying pressure in the cavern (Figure 8).

2.7. Diffusion

2.7.1. Molecular Diffusion

Diffusion is a special case of dispersion at zero fluid flow velocity. The two fundamental components of dispersive mixing are molecular diffusion and physical dispersion. Molecular diffusion takes place due to the concentration gradient, regardless of the presence or absence of flow. In the phenomenon of gas displacement by another gas under typical conditions of porous media and for the vast majority of the flow velocities of these fluids, physical dispersion is the dominant process responsible for the observed mixing of gases, while molecular diffusion may be important (from the point of view of reservoir engineering) during stand-ups performed between the gas injection and withdrawal phases.

2.7.2. Diffusion Coefficients

The analytical Chapman–Enskog formula was used to determine the binary diffusion coefficients for both gases [23]:

$$D_{diff,ij}=\left({\displaystyle \frac{0.0018583}{P{\sigma }_{ij}^2{\mathsf{\Omega }}_{ij}}}\right)\sqrt{T^3\left({\displaystyle \frac{1}{M_{w,i}}}+{\displaystyle \frac{1}{M_{w,j}}}\right)}$$

(6)

where D_diff—binary diffusion coefficient [cm²/s],

• P—pressure [bar],
• σ—medium molecular size,
• Ω—Lennard-Jones potential,
• T—temperature [°C],
• Mw—molecular mass [g/mol].

Thanks to the binary diffusion coefficients in the CH₄-H₂ system (for fixed conditions P, T) taken from the literature [23], the above formula has been reduced to the following form:

$$D_{diff,ij}=\left({\displaystyle \frac{A}{P}}\right)\sqrt{T^{3}B}$$

(7)

where A and B are fixed coefficients.

Table 2. Estimated values of binary diffusion coefficients in CH₄-H₂ system.

T [°C]	P [bar]	D [m2/d]
28	40	0.1547
57	40	0.4492
57	155.14	0.1158
57	221.1	0.0811
57	301.89	0.0595

presents the diffusion coefficients in the CH₄-H₂ system, the first value is an example from the literature, while the next one is estimated for the reservoir temperature and selected pressures according to the above formula:

Similar to the models with different vertical block sizes, a simulation forecast of H₂ injection was made for the selected model (with blocks with vertical dimensions, h = 1 m) to which binary diffusion coefficients were implemented, D_diff = 0.1 m²/d.

In contrast to numerical physical dispersion, which is modelled indirectly in the simulator by numerical dispersion, the molecular diffusion coefficient can be explicitly specified as an input parameter in Eclipse 300. This allows users to have direct control over gas mixing during simulations.

2.7.3. Gas Diffusion Analysis

Based on the results of the simulation, the concentration profile of injected H₂ was adjusted to the UHS for the same time steps as in the previous models. The values of the convection velocity obtained as a result of fitting the convection–dispersion model to the results of the simulation were compared with the values obtained from the model without diffusion (Figure 9). No significant differences were found.

While the introduction of diffusion did not affect the speed of movement of the injected H₂ front, its inclusion affected its blurring, which is expressed by an increase in the dispersion–diffusion coefficient, D, determined from the convection–dispersion model (Figure 10).

2.7.4. Diffusion Effects During Stand-Ups

Since the dominant phenomenon determining the blurring of the front during the flow (injection of H₂ into the UHS) is physical dispersion, simulation models were prepared to show the effect of diffusion on the blurring of this front, in which the course of operation of the cavern consisted of an injection phase lasting until the H₂ front moved to the middle of the cavern height, followed by the so-called stand-up for about 600 days.

For the results of simulations of models differing in diffusion, the H₂ concentration profile during stand-up after injection was analysed for selected time steps (Figure 11).

The above analysis confirmed the small effect of diffusion on the simulation results during flows caused by pressure changes in UHS, with its high significance for gas mixing during the so-called stand-ups (no flows caused by the pressure gradient). The analysis of the concentration course for the non-diffusion model additionally showed the lack of significant influence of phenomena related to gravitational segregation on selected gas components. However, in some cases diffusion can play a decisive role, as demonstrated by Miłek, Szott, and Gołąbek [57], who indicated that CH₄ displacement by injection of acid gas into water influenced the composition of the withdrawn gas.

3. Results

3.1. Assumptions of Storage Operation

To present the effects of mixing of selected gases on the purity of H₂ received from the salt cavern, simulation forecasts were prepared consisting of the so-called precycle, i.e., the preparation of UHS by collecting previously stored CH₄, and nine subsequent cycles of H₂ injection and withdrawal.

Other basic assumptions of storage operation are as follows:

−

Composition of the injected gas, c_H2 = 100%,

−

Injection and production (withdrawn) well providing access to the cavern top (Figure 5),

−

Two phases of H₂ injection per year, i.e., 1.01–14.02, 1.07–14.08,

−

Two phases of H₂ withdrawal per year, i.e., 15.03–14.05, 15.09–14.11,

−

Stand-ups between the above-mentioned phases,

−

H₂ injection rate, q_g,inj = 500,000 Nm³/d,

−

H₂ withdrawal rate, q_g,prod = 600,000 Nm³/d,

−

Initial pressure in UHS, P_ini = 140 bar,

−

Storage temperature, T_res = 57 °C,

−

Maximum bottom pressure in the pumping phase, P_bhp,inj,max = 160 bar,

−

Minimum bottom pressure in the gas withdrawal phase, P_bhp,prod,min = 40 bar.

It should be emphasized that the applied rates correspond to a single Polish cavern case. UGS facilities, however, often consist of multiple caverns, or in some cases, very large individual caverns. This explains why the Western European literature frequently reports much higher injection and withdrawal capacities, in the range of several million Nm³/d (where Nm³ denotes gas volume at normal conditions: 0 °C, 1.01325 bar) at the facility scale [35]. The values used in this study are, therefore, consistent with domestic cavern-scale operation.

3.2. Results of Simulation Forecasts

The dispersion–diffusion coefficient utilized in the simulations represents the combined effects of numerical dispersion, which models physical dispersion (Section 2.6), and molecular diffusion (Section 2.7). This approach ensures that the results take into account both mixing mechanisms that are relevant to H₂-CH₄ interactions in the cavern model.

Based on the above assumptions, multivariate simulation forecasts were made for models differing in terms of the dispersion–diffusion coefficient and the predetermined molecular diffusion coefficient (D_diff(P = 160 bar, T = 57 °C) = 0.11). Figure 12 illustrates that greater numerical dispersion (higher block of simulation grid) leads to stronger front blurring of the H₂ and, consequently, to more intensive mixing with the CH₄. As a result of greater numerical dispersion, the amount of H₂ withdrawn in each subsequent cycle decreases and the CH₄ contamination of the withdrawn gas increases (Figure 13).

As a result of the lower amount of H₂ that was withdrawn and, thus, the larger amount of H₂ remaining in the cavern, the amount of H₂ injected decreased in the subsequent cycles of each of the models (Figure 14). On the other hand, as a result of the decreasing amount of CH₄ remaining in the UHS, the capacity to receive previously injected H₂ gradually increased (Figure 15).

Detailed results are presented in

Table 3. H₂ withdrawal in subsequent UHS cycles for models differing in dispersion–diffusion coefficient (block height).

Cycle\Block Height	Hydrogen Withdrawal [kg mole]
	1 m	2 m	4 m	8 m
2	948,717	936,696	924,471	903,182
3	954,342	944,787	934,760	919,090
4	955,813	946,493	937,789	924,867
5	956,214	947,087	939,170	927,630
6	957,226	946,999	939,294	928,545
7	955,878	946,672	939,113	929,974
8	955,521	946,315	939,005	931,303
9	954,779	945,546	939,193	932,127
10	953,913	945,088	938,802	932,545

,

Table 4. H₂ injection in successive UHS cycles for models differing in dispersion–diffusion coefficient (block height).

Cycle\Block Height	Hydrogen Injection [kg mole]
	1 m	2 m	4 m	8 m
2	974,788	974,448	971,842	970,326
3	972,519	972,091	966,308	962,151
4	969,844	967,395	962,818	958,425
5	966,208	964,552	959,864	953,802
6	966,246	961,505	957,996	951,384
7	965,321	960,804	954,627	949,282
8	962,665	958,235	952,327	947,089
9	961,115	956,023	951,722	945,857
10	959,554	955,680	950,075	944,233

,

Table 5. H₂ contamination in subsequent UHS cycles for models differing in dispersion–diffusion coefficient (block height).

Cycle\Block Height	Hydrogen Contamination [mol/mol]
	1 m	2 m	4 m	8 m
2	0.0311	0.0441	0.0552	0.0758
3	0.0204	0.0298	0.0368	0.0504
4	0.0159	0.0236	0.0291	0.0383
5	0.0136	0.0200	0.0242	0.0309
6	0.0123	0.0175	0.0210	0.0254
7	0.0108	0.0156	0.0184	0.0214
8	0.0098	0.0141	0.0164	0.0183
9	0.0091	0.0128	0.0148	0.0156
10	0.0085	0.0118	0.0133	0.0134

and

Table 6. Ratio of withdrawn to injected H₂ in subsequent cycles of UHS operation for models differing dispersion–diffusion coefficient (block height).

Cycle\Block Height	Ratio of Withdrawn to Injected Hydrogen in Subsequent Cycles [%]
	1 m	2 m	4 m	8 m
2	97.33	96.13	95.13	93.08
3	98.13	97.19	96.74	95.52
4	98.55	97.84	97.40	96.50
5	98.97	98.19	97.84	97.26
6	99.07	98.49	98.05	97.60
7	99.02	98.53	98.37	97.97
8	99.26	98.76	98.60	98.33
9	99.34	98.90	98.68	98.55
10	99.41	98.89	98.81	98.76

, which present the amount of H₂ withdrawn and injected in each cycle, the contamination of the received H₂, and an indicator displaying the proportion of injected H₂ in each cycle that was withdrawn in the next phase of its extraction.

3.3. Analysis of H₂ Saturation Distributions

During the first injection phase, the injected H₂ first fills the structure near the IP well, filling the top of the structure (Figure 16a). For models with smaller dispersion–diffusion coefficient values, the blurred front zone is relatively narrow, whereas a higher value of that coefficient results in a much wider blurred zone. During H₂ withdrawal the H₂ saturation zone decreases until the end of production, caused by a pressure drop in the production IP well (P_bhp,prod,min = 40 bar). As a result of gas mixing, some of the previously injected H₂ remains in the UHS (Figure 16b), most of it in the model with the highest dispersion, which is also confirmed by the results in the form of high CH₄ contamination of the withdrawn H₂ (Figure 13).

With each cycle, an increasing volume of H₂ remains in the cavern, which leads to a progressively advancing H₂ front (Figure 17a). In addition, the front becomes increasingly blurred, especially after the withdrawal phase (Figure 17b). In the case analysed, the position of the front and the extent of its blurring become less critical, primarily due to the purity and quantity of the H₂ withdrawn (Figure 12 and Figure 13). However, in the model with the highest dispersion, a pronounced shift in the position of the front as well as an extensive blurred zone could be significant if the IP well was located on the opposite side, i.e., at the bottom of the cavern (other uses of the cavern). The above observations indicate that the block size sensitivity can be interpreted as a practical control of numerical dispersion, applied here as a proxy for physical dispersion.

4. Discussion

The simulation results demonstrate that dispersion is the dominant mechanism governing gas mixing in a salt cavern during the operation of H₂ storage, while molecular diffusion plays a secondary but non-negligible role during stand-up phases. Physical dispersion, modelled numerically in the Eclipse 300 simulator, caused significant blurring of the hydrogen front and, in effect, an increase of CH₄ contamination of the withdrawn hydrogen. This directly impacts the calorific value and economic feasibility of hydrogen storage. In addition, additional separation processes may be needed [4,17,41]. The novelty of this study lies in its quantitative assessment of these phenomena under cyclic operation of the cavern. The simulations provide numerical estimates of hydrogen purity losses and their dependence on cycle number and numerical dispersion (as a proxy for physical dispersion), which, to our knowledge, have not previously been reported. These results are directly relevant for engineering practice, offering input for optimizing the completion of well placement and cycle design in order to maintain H₂ purity and storage efficiency.

The analysis demonstrates that the intensity of mixing depends strongly on the dispersion–diffusion coefficient. Higher values led to a broader front of H₂ spreading (Figure 16 and Figure 17) and greater dilution of H₂ with CH₄ (Figure 13). This observation aligns with classical theories of dispersion in porous media [20,21,55] as well as other numerical studies of underground hydrogen storage in porous formations [18,19].

The effect of gas mixing due to molecular diffusion had a very small influence on the purity of withdrawn gas, especially during active injection and withdrawal, but became noticeable during extended stand-up periods. In these cases, diffusion contributed to additional blurring even in the absence of flow, confirming earlier experimental observations by Arekhov et al. [23]. This indicates that extended stand-up periods may gradually degrade hydrogen purity. Generally, the diffusion coefficient is more sensitive to temperature (Table 2) and also varies with pressure. However, in the Eclipse simulator applied here, diffusion coefficients are treated as constant and were derived from Chapman–Enskog correlations at reference cavern conditions (57 °C, 140 bar). The operating pressure changes during stand-up periods also remained relatively stable between cycles. Under more variable storage conditions, pressure and temperature changes could further affect the diffusion coefficient and change the purity of the withdrawn gas, but this cannot be captured with the present model and should be addressed in future work.

Another key finding is the cycle-dependent evolution of gas composition. CH₄ contamination in the withdrawn gas progressively decreased from cycle to cycle, as the ratio of H₂ to CH₄ in place increased. This implies that the initial operational cycles are very important for maintaining the purity of hydrogen. Strategies such as precycling or just the use of cushion gas may help maintain H₂ purity, as highlighted by Wallace et al. [41].

From a modelling point of view, this study demonstrated both the strengths and limitations of using a reservoir simulator for salt cavern applications. Modelling the cavern as an ultra-permeable porous medium and controlling dispersion effects through numerical block size allowed for effective alignment with analytical convection–dispersion solutions (Section 2.6.2). However, this approach relies on artificial representation of mixing processes, rather than explicitly resolving cavern-scale turbulent or chaotic advection phenomena [24]. Therefore, benchmarking for cavern simulators [37,38] should be considered in future studies to improve the reliability of predictions. Moreover, this and every simulation model should be verified based on operational data in order to confirm its usefulness for future simulation forecasts.

Finally, the operational utility of the results of this work is significant. The configurations of wells, particularly the relative placement of injectors and producers in the field, called the well pattern, can significantly influence mixing intensity, as indicated by the differences in front propagation observed in Section 3.3. Moreover, operational parameters such as cycle frequency, injection and withdrawal rates, and their duration directly affect the extent of dispersion and diffusion. Therefore, systematic optimization of these factors is essential to minimize hydrogen contamination, improve storage efficiency, and ensure the reliable performance of salt cavern facilities in the context of the energy transition. It should be emphasized that while the economic feasibility and scale of H₂ production and storage are crucial for large-scale deployment, these are system-level issues beyond the scope of this study. Instead, the present work provides a methodological framework for quantifying mixing processes and their impact on the purity of withdrawn H₂. These issues, particularly the optimization of well placement and operational parameters, will be investigated in future work. In addition, while this study focused on the H₂-CH₄ system, other gases such as N₂ or CO₂ may also be present in underground storage. Their concentrations in operational gas storage are generally negligible compared to CH₄, and their presence would not increase contamination of the withdrawn hydrogen. In the case of CO₂, biomethanation could even occur, which is currently being investigated by the authors in parallel research.

Limitations and Outlook

The present study has several limitations. Geomechanical effects such as deformation of the salt cavern’s shape and volume were not considered, nor were hydro-chemical processes such as salt dissolution at varying brine levels. Turbulent mixing phenomena, which can occur in open cavern geometries, were also not explicitly modelled. Their influence on gas mixing was only approximated indirectly through numerical dispersion of the finite-difference scheme used in the reservoir simulator. While this provides a practical approximation, it does not capture turbulence and boundary-layer processes explicitly. A comprehensive representation of such effects would require high-resolution CFD modelling, which is planned as a part of future research.

Another limitation is the lack of direct validation against laboratory or field data. This prevents an immediate assessment of model adequacy under real operating conditions. The present work should, therefore, be regarded as methodological, providing a systematic framework that can later be validated and complemented with laboratory-scale experiments and operational UGS/UHS data.

The presented methodology is intended as a first step, providing quantitative insights into dispersion–diffusion impacts that can be integrated with geomechanical and CFD-based models in subsequent studies.

5. Conclusions

• The Eclipse 300 commercial compositional simulator, developed by Schlumberger, has been confirmed to be effective for modelling the operation of UHS located in a salt cavern, represented as an ultra-permeable porous rock.
• For the simulations carried out, no significant influence of gravitational segregation on the modelling results was found.
• Physical dispersion modelled as numerical dispersion is identified as the primary driver of mixing during the operation of UHS. This phenomenon has a significant influence on the composition of withdrawn gas.
• Molecular diffusion does not have a significant impact on the modelling of flows caused by the pressure gradient in the cavern, but it may be important in a situation where there are no such flows, i.e., during the so-called stand-ups.
• Both of the above phenomena should be taken into account to properly model the operation of the UHS, especially to calibrate such a model before it is applied to forecast the future performance of a cavern as a UHS facility.
• The location of the injection and production wells, along with the well pattern, may be important for the simulation results, and should be the subject of further research.
• A research gap has been identified: to the authors’ best knowledge, no prior publication has systematically quantified the combined effects of dispersion and diffusion on the modelling of UHS operation or their impact on the composition of withdrawn gas during cyclic operations. This work provides a methodological framework for these assessments and practical guidance for forecasting the composition of withdrawn gas, which is crucial for the gas calorific value.
• From an operational perspective, the results offer valuable insights for cavern management, such as minimizing stand-up phases and optimizing well completion to maintain the purity of the withdrawn H₂ (Figure 16 and Figure 17).
• The study is subject to limitations (no geomechanical coupling, turbulence, or experimental validation), which will be addressed in future work by integrating dispersion–diffusion modelling with geomechanical analysis, CFD simulations, and laboratory/field data.