Research into the Kinetics of Hydrogen Desorption from the MNTZV-159 Metal Hydride Storage Tank in the Operating Conditions of a Low-Pressure Refuelling Station

Abstract

A form of long-term hydrogen storage with high volume efficiency is hydrogen absorption into the host lattice of a metal or an alloy. Unlike high-pressure hydrogen storage, this form of storage is characterised by a low operating pressure. By employing metal hydride (MH) materials in a low-pressure refuelling station, it is possible to significantly increase the safety of hydrogen storage and, at the same time, to facilitate the refuelling of external devices that use MH storage tanks without the necessity of using a compressor. In this article, a methodology for the identification of the mathematical correlations among the hydrogen pressure in the storage tank, the hydrogen concentration in the alloy and the volumetric flow rate of hydrogen is described. This methodology may be used to identify the kinetics of the process and to create simplified simulations of the hydrogen release from an absorption-based storage tank by applying a finite difference method. The mathematical correlations are based on measurements of hydrogen desorption, during which hydrogen was released from the storage tank at stabilised pressure levels. The resulting mathematical description facilitates the identification of the approximate hydrogen pressure, depending on its flow rate, for a particular MH storage tank, while respecting the complexity of its internal structure, heat transfer and the hydrogen’s passage through a porous powder MH material. The identified mathematical dependence applies to the certified MNTZV-159 storage tank at pressures ranging from 7 to 29.82 bar, with hydrogen concentrations ranging from 0.223 to 1.342%, an input temperature of 59.5 °C and a cooling water flow rate of 4.36 L·min⁻¹. This methodology for the identification of a correlation between the flow rate, pressure and hydrogen concentration applies to this particular type of storage tank, and it depends not only on the alloy used and the quantity of this alloy but also on the internal structure of the heat exchanger.

1. Introduction

A hydrogen refuelling station, as a component of the infrastructure for the hydrogen refuelling of hydrogen fuel cell vehicles, is a very important part of hydrogen energy utilisation [1]. In this article, an analysis is provided with regard to the metal hydride storage system of an atypical low-pressure refuelling station that is used to supply green hydrogen for metal hydride technologies, with the operation adjusted to the particular requirements of metal hydride (MH) alloys. Unlike the storage tanks installed in high-pressure refuelling stations, the alternative described in this article facilitates significant reductions in the energy required for the process of hydrogen compression to a high pressure [2,3,4]. Moreover, compared to the current developments in the market, low-pressure hydrogen storage in the form of metal hydrides facilitates the storage of hydrogen directly from an electrolyser, without the use of pressure multipliers [5,6,7]. Metal hydride storage tanks also facilitate an increase in the safety of the operations of refuelling stations, as well as the long-term storage of high-purity hydrogen at lower pressures, not exceeding the operating pressures of 3–5 MPa [8,9,10,11]. The reduction in the operating pressure results in a reduction in the hydrogen escape speed at rupture, while the kinetics of hydrogen desorption from the MH alloy prevents the instant release of the entire amount of gas to the surrounding environment. The application of such storage tanks in the decentralised system of a hydrogen supply, with the technology installed in a compact container, may accelerate the process of introducing hydrogen technologies into practice.

Refuelling stations that are based on, and intended for, filling storage tanks with metal hydrides constitute a specialised form of infrastructure in the field of hydrogen engineering. Unlike conventional hydrogen refuelling stations (HRSs), which refuel vehicles with compressed or liquified hydrogen, refuelling stations that store hydrogen in MH alloys are designed to facilitate the reversible supply and release of the hydrogen [12,13]. This process significantly depends on the kinetics of the absorption–desorption cycle [14,15].

The basic principle of the operation of an MH station is, in the first step, to ensure the efficient transfer of hydrogen from a pressure tank or an electrolyser into a metal hydride storage system in the refuelling station, where the process of hydrogen absorption into a metal matrix is accompanied by an exothermic reaction. This process requires precise control of the pressure, temperature and time, since the storage kinetics strongly depends on these factors. In a refuelling station, a sufficiently high pressure (usually 10–30 bar for MH technologies) and optimal kinetics must be maintained in order to maximise the rate of hydrogen absorption. Therefore, a thermal management system is a crucial component of such refuelling stations, as it removes the heat generated during hydrogen absorption from the system, while, during hydrogen desorption, it provides efficient heating to prevent the slowing down or even arrest of the fuel release kinetics [16,17,18].

The kinetics of hydrogen absorption and desorption is a key parameter in the process of assessing the efficiency and practical applicability of metal hydrides [19]. The rate at which a metal absorbs and then releases hydrogen directly affects the operating performance of a low-pressure refuelling station that is used to refuel mobile and stationary hydrogen-powered devices. From a practical point of view, an ideal hydride material is one that facilitates high rates of absorption and desorption at the lowest possible energy cost [20,21]. In reality, however, a compromise must be found in relation to the capacity, thermodynamic stability and kinetics.

Jana et al. present experimental studies on a tube bundle reactor (TBR) designed for metal hydride (MH)-based hydrogen storage systems. The TBR, comprising 19 MH tubes, is designed to operate at a low temperature and moderate pressure (273–353 K, up to 95 bar) with a projected storage capacity of ~385 g hydrogen. A promising desorption regime was identified as 323–343 K, necessitating an average heating rate of only 0.8–1.7 kW. The estimated energy efficiency of hydrogen storage was in the range of 58–64% [22]. Hydrogen desorption from metal hydrides is a key process in refuelling hydrogen-powered systems, primarily in applications where an MH storage tank is used as a source of hydrogen for the refuelling of storage tanks in vehicles containing a fuel cell, as well as other equipment. The ability to achieve the smooth, fast and reliable release of hydrogen is dependent on a thorough understanding and the optimisation of the desorption characteristics of MH storage tanks [23,24]. With regard to the system’s integration, a challenging prerequisite is to ensure a balance between the supply of heat and the required hydrogen flow rate [25]. When a vehicle is refuelled, the supply of hydrogen from an MH storage tank must exhibit a level at which a stable pressure can be maintained during the refuelling process (ranging from several minutes to several dozens of minutes, depending on the thermal management system installed in the equipment that is being refuelled), which requires a fast response in the thermal management system. The refuelling process is therefore longer than the process in which compressed hydrogen is used, while the system weight of MH tanks remains a limiting factor for mobile applications.

The identification of the current volume of fuel in the primary storage tank of a refuelling station, as well as measures aimed at ensuring a sufficient hydrogen flow rate, are more complex than those applied in the case of conventional high-pressure refuelling stations. With a high-pressure storage tank, it is sufficient to know the pressure in the storage tank in order to identify the residual amount of fuel in the primary storage tank [26], and the released amount of fuel is identified using a flow meter; however, refuelling hydrogen-powered equipment from a storage tank in which hydrogen is stored in a metal hydride depends on a number of variables (the hydrogen pressure, hydrogen concentration, hydrogen release kinetics, etc.). In order to predict the current stock of fuel in the primary storage tank and to ensure the required volumetric flow rate of hydrogen to supply hydrogen for MH technologies, it is necessary to identify the mathematical correlations among the pressure of the hydrogen in the storage tank, the concentration of hydrogen in the alloy and the volumetric flow rate of the hydrogen. Therefore, the present article provides a description of a methodology for the identification of the mathematical correlations among the hydrogen pressure in the storage tank, the hydrogen concentration in the alloy and the volumetric flow rate of hydrogen.

2. Description of the Storage and Measurement System

The low-pressure metal hydride hydrogen storage tank that was used for the storage and recovery of green hydrogen produced from solar energy using the Nitidor bipolar H₂ electrolyser, which is part of a low-pressure refuelling station, was designed following the STN EN 13 322-2/A1 standard [27]. It is a double-shell pressure vessel filled with a powder MH material—Hydralloy C5. The wall of the internal pressure vessel, containing the powder alloy, is 4.5 mm thick. The external diameter of the pressure vessel is 159 mm. The cylindrical part of the pressure vessel ends with a bottom on each side, with each bottom having an opening in the centre with an internal ¼ NPT thread. During the process of hydrogen absorption, heat is removed from the volume of the metal hydride alloy using an aluminium intensifier (a heat exchanger), which ensures the homogeneity of the thermal field of the storage tank and the more efficient distribution of thermal energy to the surrounding environment, and vice versa. The designed shape of the intensifier is subject to intellectual property rights (Patent: SK 289187 B6). Its walls have a basic thickness of 1 mm. Active cooling of the pressure vessel with a heat-carrying medium is ensured using a 2 mm thick shell heat exchanger, which is welded to the basic pressure vessel. The inlet and outlet openings for the heat-carrying medium have an external 3/8 thread to connect the cooling circuit to the MH storage tank. The pressure vessel is connected to the hydrogen circuit through a ¼ NPT thread, while the opening on the opposite side of the pressure vessel is used to attach a heat sensor, which directly measures the temperature in the centre of the metal hydride alloy during experiments. The operating temperature of the storage tanks ranges from −50 to 80 °C. The operating pressure of the MNTZV-159 storage tank ranged from −1 to 45 bar, which was determined by the tank’s strength and structure. Hydralloy C5 may only be exposed to higher operating pressures with the use of a tank with a different design that would ensure its resistance to higher pressures. Based on the tests that were conducted, the storage tank ruptures at a pressure exceeding 300 bar. The storage tank contained 46.07 kg of a metal hydride alloy with an initial grain size of 0–2 mm.

The measurement system consisted of the hydrogen circuit and a thermal circuit. The hydrogen circuit contained regulation elements, mechanical valves, filters, a check valve and the Bronkhorst IN-FLOW flow meter (D-Ex Instruments Bratislava, Bratislava, Slovakia), series F-113AI-M50-ABD-HH-V-0C, with a maximum flow rate of 8.2 L·s⁻¹. The components were interconnected with 10 mm pipes, the walls of which were 1 mm thick. The system was composed of an ATEX pressure BD sensor DX10-DMP 333l NG (with a range of 0–60 bar, BD Sensors, Buchlovice, Czech Republic). The temperature of the MH storage tank was monitored using NTCC-10K temperature sensors(TME Electronic Components, Łódź, Poland), while the temperature of the water was monitored using an NTC B57301K0103A001 temperature sensor (TME Electronic Components, Łódź, Poland). During the experiment, the tested MH hydrogen storage tank was connected to a pressure vessel with a pressure of up to 200 bar and purity of 99.999%, in order to prevent the potential contamination and oxidation of the MH alloy during the use of the electrolyser.

Figure 1 shows a connection diagram of the apparatus used to measure the flow rates and thermodynamic parameters of the hydrogen and water circuits.

Active cooling of the metal hydride storage tank was provided using a fully automated thermal management system, combining a heating system comprising an accumulation tank to heat the water and an active cooling system to cool the storage tank during hydrogen absorption. The flow rate of the cooling/heating water was measured using the YF-B1 water flow sensor with a frequency output. The cooler was controlled and regulated by a datalogger, which also recorded the flow rates, temperatures and pressures in the hydrogen circuit, and we stored the measured values in an external data storage device.

3. Experiment and Discussion

The MNTZV-159 metal hydride storage tank (Faculty of Mechanical Engineering, TUKE, Košice, Slovakia), installed in a low-pressure refuelling station, was connected to the water and hydrogen circuits. The measurements were conducted in three consecutive phases. The first phase was the activation of the storage tank, which facilitated the initiation of the absorption process. It consisted of three refuelling cycles, in which hydrogen was vacuumed for 1 h with a vane vacuum pump, which facilitated the achievement of the threshold absolute pressure of 5 Pa, while the hydrogen was filled up to a pressure of 4.5 MPa for 90 min.

Following the activation step, the storage tank was vacuumed for 3 h and the hydrogen absorption process was carried out. Figure 2 shows the curve of the pressure and temperature in the storage tank as a function of time. As the pressure increased, the average surface temperature of the MH storage tank sharply increased (Figure 2) as a result of the increasing equilibrium temperature of the metal hydride.

The shapes of the curves of the pressure and temperature were determined by the significantly high flow rate in the initial phase of absorption (Figure 3), exceeding the value of 7 L·s⁻¹. The reaction heat that was generated in a significant amount during the absorption process was removed through accumulating the thermal energy into the storage tank mass, which was supported by the use of the water cooling system; however, after achieving the maximum pressure of 45 bar and the equilibrium temperature of 70 °C, heat removal was only provided by the water cooling system, and this led to a sudden regulated reduction in the hydrogen flow rate to avoid exceeding the maximum pressure limit.

Upon integrating the hydrogen flow rate over time, the total volume of the absorbed hydrogen amounted to 6.878 m³ (Figure 3). With the weight of the MH alloy at 46.07 kg, the total hydrogen concentration was 1.342%.

Generally, in order to understand changes in the flow rate and temperature, it is necessary to know the thermal balance of an MH storage tank. Hydrogen is absorbed into a metal hydride material, while reaction heat is released during the process. The thermal balance of the storage tank may be described using the heat output supplied through the inletting hydrogen, the heat output generated during hydrogen absorption (reaction heat), heat losses through the insulation and thermal bridges, the heat flow removed through the water cooling system and the accumulated heat flow that heats the storage tank. The correlations among the heat flows may be expressed using an energy equation relative to a time unit:

$$P_{\mathrm{H}2}+P_{\mathrm{G}}=P_{\mathrm{hl}}+P_{\mathrm{C}}+P_{\mathrm{a}} \text{(W)}$$

(1)

wherein P_H2 is the heat output supplied through the inletting hydrogen (W); P_G is the heat output generated in the MH alloy during hydrogen absorption (W); P_hl is the heat loss in the storage tank (W); P_C is the heat output removed through the cooling system (W); and P_a is the accumulated thermal energy per time unit (W). By adjusting and modifying these relationships, Equation (1) may be rewritten as follows:

$$\begin{array}{l}{Q}_v\cdot {\rho }_{H2}\cdot c_{p,\mathrm{H}2}\cdot \left(T_{\mathrm{in},\mathrm{H}2}-T\right)+{\displaystyle \frac{q_{\mathrm{MH}}\cdot m_{\mathrm{MH}}}{{\rho }_{\mathrm{H}2}}}\cdot {\displaystyle \frac{\mathrm{d}{c}_{{\mathrm{H}}_2}}{\mathrm{d}\tau }}=\\ =h_t\cdot A\cdot \left(T-T_{\mathrm{a}}\right)+Q_{v,\mathrm{w}}\cdot {\rho }_w\cdot c_{p,w}\cdot \left(T_{\mathrm{out},\mathrm{w}}-T_{\mathrm{in},\mathrm{w}}\right)+\sum \left(m\cdot c_p\right)\cdot {\displaystyle \frac{\mathrm{d}T}{\mathrm{d}\tau }}\end{array}$$

(2)

wherein Q_v is the hydrogen flow rate (L·s⁻¹); ρ_H2 is the hydrogen density (kg·m⁻³); c_p,H2 is the thermal capacity of hydrogen (J·kg⁻¹·K⁻¹); T_in,H2 is the hydrogen temperature at the inlet into the MH storage tank (K); T is the temperature of the MH storage tank (K); q_MH is the reaction heat produced during hydrogen absorption and desorption in the MH material (J·m⁻³); m_MH is the mass of the metal hydride (kg); c_H2 is the hydrogen concentration in the MH material (-); τ is the time (s); h_t is the overall heat transfer coefficient of the MH storage tank (W·m⁻²·K⁻¹); A is the surface area of the storage tank (m²); T is the temperature of the storage tank (K); T_a is the ambient temperature (K); Q_v,w is the volumetric flow rate of the cooling water (m³·s⁻¹); ρ_w is the water density (kg·m⁻³); c_p,w is the thermal capacity of the water (J·kg⁻¹·K⁻¹); T_out,w is the temperature of the water at the outlet (K); T_in,w is the temperature of the water at the inlet (K); and ∑(m·c_p) is the total thermal capacity of the storage tank (J·K⁻¹).

Equation (2) describes the power balance of the MH storage tank when taking into account a homogeneous thermal field at a particular moment in time. Such an assumption applies in the case of the infinitely high thermal conductivity of the MH material and the storage tank. Since the thermal conductivity of the MH alloy used was very low, amounting to 0.5–1 W·m⁻¹·K⁻¹, the thermal field of the storage tank exhibited large differences. They caused uneven absorption and impaired heat removal. As a result, the total efficiency of the water cooling system was reduced and the hydrogen refuelling time was longer. In order to eliminate large temperature differences in the alloy, a heat transfer intensifier was installed in the storage tank. This intensifier was composed of aluminium and exhibited high thermal conductivity. Nevertheless, the identification of changes in the storage tank temperature using the equation above was only approximate. However, it still facilitated an understanding of the identification of the hydrogen flow rate in the refuelling process that was sufficient to avoid exceeding the maximum pressure limit in the storage tank.

Experimental measurements were performed in order to identify the cooling power Pc. The curve of its values, measured during the absorption process, is shown in Figure 4. Cooling was provided with the use of a water cooling system, and the heat was removed into the surrounding environment using a cooler. The average water flow rate was 4.2 L·min⁻¹ and the water temperature at the inflow into the storage tank was 45.3 °C. The cooling system was not regulated, and the cooling process was carried out as shown in Figure 4, corresponding to the real-life conditions of the low-pressure refuelling station prototype.

At the initial sharp increase in temperature, caused by massive hydrogen absorption, the most efficient heat removal was observed from the MH material located in close proximity to the cylindrical shell, where a large temperature gradient also existed between the MH material and the cooling water. Subsequently, hydrogen was also absorbed into the material that was nearer to the storage tank axis; however, the heat removal was less efficient in this area and, as a result, the cooling power was lower.

With a known hydrogen concentration in the MH material, the hydrogen desorption was measured at an average water heating temperature of 59.5 °C and a flow rate of 4.36 L·min⁻¹. All curves of the physical parameters, as well as the corresponding mathematical interpretations of the results, were expressed in relation to this temperature and flow rate.

Figure 5 shows the curve of the volume of the desorbed hydrogen as a function of time. Hydrogen was released from the storage tank in four doses, with a gradual regulated reduction in hydrogen pressure, while the hydrogen flow rates were measured in a steady state. The difference between the pressure values identified by the measurements at a single dose was approximately 5 bar. Since the data were analysed by applying multiple regression analysis, it was not necessary to apply a constant pressure step during the measurements; instead, it was sufficient to maintain an approximately even reduction in pressure within the tested range. The initial pressure in the measurement of every dose decreased while the hydrogen was being released.

By deducting the amount of desorbed hydrogen, shown in Figure 5, from the initial concentration of hydrogen in the storage tank, generated during the absorption process, it was possible to draw a curve of the hydrogen concentration in the MH material as a function of time (Figure 5). This curve clearly shows that, when hydrogen was gradually released from the tank, the hydrogen concentration decreased from the initial value of 1.342% to the final value of 0.223%.

The purpose of these measurements was to mathematically express the correlations among the hydrogen flow rate, pressure and concentration in the storage tank. Therefore, the hydrogen was released at a regulated pressure in order to achieve pressure stabilisation. As a result, the hydrogen flow rate was also stabilised (the blue region in Figure 6). At the subsequent pressure drop, the procedure was repeated; however, due to the lower pressure, the flow rate of the hydrogen was higher (the green region). The desorption process was also monitored during the following dose of desorption (Figure 7, Figure 8 and Figure 9).

The measurement procedure described above facilitated the identification of stabilised flow rates and pressures with a gradually decreasing hydrogen concentration, while, as early as at the first desorption dose, it was possible to obtain a sufficient amount of data to identify the mathematical correlations among the flow rate, pressure and concentration of hydrogen. The obtained series of measured data was subjected to multiple regression analysis, during which a number of potential mathematical correlations were examined. The aim was to find those that described, as accurately as possible, changes in the hydrogen flow rate as a function of the hydrogen pressure and concentration Q_v = f(p,c) (

Table 1. Comparison of the mathematical models for the prediction of the hydrogen flow rate with a known stable pressure and the current concentration of hydrogen.

	Model	Estimated Model Parameters		M.S.E.
1.	$Q_v={\displaystyle \frac{k_0\cdot p\cdot c}{1+k_1\cdot c+k_0\cdot k_2\cdot p\cdot c}}$	k0 = 0.1667 k1 = −3.9653 k2 = 2.5332		22.78
2.	$Q_v={\displaystyle \frac{k_0\cdot p\cdot c}{1+k_1\cdot c+k_2\cdot p}}$	k0 = −0.0930 k1 = 0.0695 k2 = −0.1815		0.29
3.	$Q_v=k_0\cdot c^{k_1}\cdot p^{k_2}$	k0 = 19.6820 k1 = 0.7737 k2 = −1.1134		0.11
4.	$Q_v=k_0+{\displaystyle \frac{k_1}{c}}+{\displaystyle \frac{k_2}{p}}$	k0 = 0.8966 k1 = −0.5702 k2 = 10.9650		0.10
5.	$Q_v=k_0\cdot c^{k_1}\cdot p^{k_2}$	k0 = 100.48766 k1 = 0.6172 k2 = −1.6705 Valid for pressure from 15 to 35 bar	k0 = 2.6285 k1 = 0.8924 k2 = −0.1781 Valid for pressure from 7 to 15 bar	0.05

M.S.E.—mean squared error.

).

The selection and evaluation of the prediction models was carried out by applying absolute, as well as relative, accuracy metrics: the mean error (M.E.), mean absolute error (M.A.E.), mean squared error (M.S.E.) and mean absolute percentage error (M.A.P.E.). The M.S.E. is determined here to be the most appropriate metric, since a greater emphasis is placed on larger deviations between the predicted and real values, and it is often used for optimisation purposes in regression models. The M.S.E. is also appropriate when analysing a bias–variance trade-off dilemma.

Model 5 describes the correlations among the variables using square dependence. A comparison of the M.S.E. values indicated that this was the best model (exhibiting the lowest mean squared error, equal to 0.05). The values of coefficients k₀ to k₂ as a function of the pressure were different for pressures ranging from 7 to 15 bar and from 15 to 35 bar. A comparison of the measured and predicted flow rates, based on Model 5, is shown in Figure 10.

The correlation between the flow rates exhibited relatively good concordance; however, in measurements 5, 6, 15 and 19, the deviations observed were larger. These points corresponded to pressures located in the lower section of the range (7 to 10 bar), wherein the model exhibited lower accuracy, i.e., a maximum absolute deviation of 41%. In the entire range of measurements, the average absolute deviation was 13%.

The prediction model facilitated the simulation of the output pressure of the storage tank with a defined flow rate at the outlet. The concentration may be identified by applying the finite difference time-domain method based on the values of the hydrogen flow rate, using Equation (3), which facilitated the identification of the pressure as a function of the flow rate and time.

$$c_{i+1}=c_i-{\displaystyle \frac{Q_{\mathit{vi}}\cdot \Delta {\tau }_i\cdot {\rho }_{\mathrm{H}2-\mathrm{n}}}{m_{\mathrm{MH}}}}$$

(3)

Equation (3) also describes the mass balance of hydrogen, while the concentration is expressed as a ratio of the mass of hydrogen absorbed (m_H2-abs) in the metal hydride to the mass of the metal hydride (m_MH). With the known values of the hydrogen flow rate (Q_vi) over time and a known concentration value at the beginning of the measurement (c₀), Equation (3) may be adjusted in order to calculate the mass of hydrogen that has been absorbed and released (m_H2-rel) over time τ:

$$m_{\mathrm{H}2-\mathrm{abs}}=c_i\cdot m_{\mathrm{MH}}$$

(4)

$$m_{\mathrm{H}2-\mathrm{rel}}=\left(c_0-c_i\right)\cdot m_{\mathrm{MH}}$$

(5)

It was assumed that the hydrogen was withdrawn from the storage tank as shown in Figure 11, with a maximum flow rate amounting to 1.2 L·s⁻¹, while the total simulation time was 7200 s. The initial value of the hydrogen concentration in the storage tank was 1.29%.

By applying Equation (3), it was possible to identify a predicted approximate curve of the pressure at the outlet from the storage tank, which is shown in Figure 12 together with the volumes of released hydrogen.

The created experiment-based mathematical model facilitates the prediction of the approximate pressure at the outlet from the storage tank as a function of the hydrogen concentration and flow rate. Hence, it describes the metal hydride storage tank during the dynamic withdrawal of gas. Since the model is based on measurements of a steady hydrogen flow rate and pressure, it cannot be used to describe the current pressure at a sharp change in the flow rate. However, when the flow rate is stabilised, the prediction of the real pressure is more accurate. For the purpose of comparing the model with real-life measurements of hydrogen desorption from the storage tank, independent measurements were conducted while hydrogen was released from the storage tank at an average flow rate of 1.2 L·s⁻¹ and at an initial concentration of 1.222%. Figure 13 shows the curve describing the decreasing pressure over a period of 2000 s.

In the initial phase, when the flow rate equalled zero and did not fall within the basic validity range, the model exhibited indefinite pressure values. In the phase preceding the measurement time of 250 s, the model exhibited poorer concordance with the experiment. The reason was that, in the model, a homogenous thermal field in the MH material was hypothesised. Better concordance was observed in the case of stationary hydrogen withdrawal, compared to sharp changes in the hydrogen flow rate. After the flow rate increased and was stabilised, the calculated pressure values were also more even and in relatively good concordance with the measured data. This was caused by the presence of only small changes in the flow rate and a gradual decrease in the hydrogen concentration in the MH, without any sharp changes in the model input values. For such conditions, the model exhibited a mean squared error of 0.927, with an average absolute deviation in the pressure amounting to 0.786 bar, compared to the data obtained by measurements.

The model may only be used for the specific MNTZV-159 storage tank, used in combination with Hydralloy C5. With different types of alloys and tank designs, new measurements must be performed while taking into consideration the respective geometry, physical parameters and type of MH alloy.

4. Conclusions

In the present article, the process of hydrogen desorption from a low-pressure metal hydride storage tank of the MNTZV-159 type, filled with Hydralloy C5, used as an accumulation and distribution element in the decentralised system for hydrogen withdrawal, is described. The initial concentration of hydrogen in the alloy amounted to 1.342%, while, during the process of the regulated measurement of desorption doses, it gradually decreased down to a final value of 0.223%. The measurements were performed at a stable heating water temperature of 59.5 °C and a flow rate of 4.36 L·min⁻¹ in order to ensure stable gas release conditions. Desorption was carried out in four regulated doses with stabilised pressures, which ranged from 7.067 to 29.82 bar. At each dose, the stabilised volumetric flow rate of the hydrogen, as well as the corresponding pressure, was recorded, with the aim of creating a database of 12 points with a defined state regarding the pressure/concentration/flow rate coordinates. By applying multiple regression analysis, it was possible to identify the most accurate model—Model 5—with power dependence. Out of all the compared models, Model 5 exhibited the lowest M.S.E. value (the lowest error in the prediction of the results obtained with the model), i.e., a very good degree of concordance with the experimental data. It facilitates the retrospective identification of the current pressure in a storage tank based on a known hydrogen flow rate and concentration in the MH material. Furthermore, with the use of an equation derived by applying the finite difference time-domain method, it was possible to approximately identify the hydrogen concentration during a simulated withdrawal. As a result, it was possible to define the pressure as a function of the time and instantaneous flow rate.

In order to verify the predictive capabilities of the model, independent measurements were conducted, during which hydrogen was desorbed at an average flow rate of 1.2 L·s⁻¹ and an initial concentration of 1.222%. A comparison of the calculated and the experimentally identified values of the pressure at the outlet from the storage tank over a period of 2000 s showed a very good correlation. At a stabilised flow rate, the average absolute deviation in the pressure was 0.786 bar, and the M.S.E. of the model, compared to the real data, amounted to 0.927. Such a result confirms that the created model is suitable for practical implementation in real-life regulation systems. The application of the prediction model with the low-pressure refuelling station facilitates the regulation of the hydrogen flow rate with regard to maintaining the required level of pressure in the storage tank, with only a small deviation between the predicted and real pressures. The maximum value of the difference in the pressure identified in the individual measurements and the model values did not exceed 1.3 bar, with the operating pressure ranging from 7 to 30 bar.

From a technical point of view, one of the significant benefits offered by the research described in this paper is a measurement methodology that facilitates the identification of multidimensional dependences based on a single experimental cycle. This approach significantly saves time, while offering a sufficiently accurate tool to predict fuel release without the necessity of the continuous monitoring of its concentration. The created model is a robust tool for the simulation of the dynamic behaviour of MH storage tanks, especially in applications with the stable, or slightly changing, withdrawal of hydrogen, such as those found in stationary fuel cells, laboratory applications and autonomous power units. In combination with the thermal management system, it is possible to optimise the operation of an entire low-pressure refuelling station without the necessity of gas compression. This will reduce the energy costs and increase the safety of the system compared to those of a high-pressure system. The general energy savings relate to the use of lower pressure levels in MH technologies. In the process of refuelling MH storage tanks with the use of a high-pressure refuelling station, the compression work is thwarted in the subsequent gas supply reduction to lower pressure values.

The implementation of a dynamic model appears to be a suitable extension in future work, as it will take into consideration the transient states that occur in sudden changes during withdrawal, as well as nonlinear thermal fields in the MH material. Moreover, the created model may be used in hybrid systems with metal hydrides and composite storage tanks, in which the prediction of the pressure becomes a crucial factor for the management of the concurrent use of multiple sources and hydrogen accumulators.