Hydrogen Gas Compression for Efficient Storage: Balancing Energy and Density

1. Introduction

Hydrogen, as widely acknowledged, serves as a crucial energy carrier, and its role in the energy transition is intricately tied to the ability to store energy harnessed from renewable sources. There is significant emphasis on hydrogen and its relevance. However, the prevailing perception is that the debate tends to be overly general, initially encompassing broad elements while potentially overlooking some crucial technical aspects (Ajanovic et al. 2024, [1]). The discussion about hydrogen has been ongoing for over 40 years, yet the lack of compelling solutions for widespread applications is still tied to certain technical aspects related to materials and intrinsic challenges of hydrogen. Additionally, it’s important to clarify that hydrogen is a carrier and as such needs to be integrated into an energy chain where energy balances must be respected, and the overall process efficiency must be acceptably high. The recent interest in hydrogen is primarily associated with its potential integration with the increasing penetration of renewable energy in energy systems. As outlined in Figure 1, illustrating how hydrogen can be integrated into a complex energy system, hydrogen can effectively complement the energy chain, providing an additional opportunity to further incorporate renewable sources, especially intermittent ones like wind and PV solar. Figure 1 illustrates a potential integration of hydrogen, highlighting the significance of energy storage as well. It is imperative, therefore, to maintain a comprehensive understanding of all components within the entire value chain.

Figure 1. Potential role of hydrogen storage in the energy chain.

Figure 1. Potential role of hydrogen storage in the energy chain.

2. Thermophysical properties of hydrogen and gas compression storage requirements

From the analysis of hydrogen’s thermophysical properties, it is evident that gas-phase compression is thermodynamically advantageous. Liquid-phase compression, on the other hand, requires at least the same amount of work, but since the fraction of liquid separated is smaller, as depicted in the figure for a generic Linde compression cycle, a significant portion of the calorific power would be subtracted from the process. This is shown in a schematic way in Figure 2.

Table 1. Energy content of hydrogen and other fuels at environmental temperature and pressure.

Table 1. Energy content of hydrogen and other fuels at environmental temperature and pressure.

Fuel	Energy per liter [MJ/l]
Hydrogen (ambient pressure)	0,0107
Natural gas (ambient pressure)	0,0364
Methane (ambient pressure)	0,0378

Thinking about a generic gas like hydrogen, in the T-p diagram, during Joule-Thomson transformations, there is a zone where the derivative of temperature with respect to pressure, while keeping enthalpy constant (a quantity called the Joule-Thomson coefficient μ), is positive. It represents the rate of change of temperature with respect to pressure for a fluid undergoing throttling or expansion without external work or heat transfer.

(1)

The thermophysical properties of hydrogen are so disadvantageous that even high-pressure gas compression and liquefaction bring them closer to conventional fuels, albeit still at a certain distance. As can be observed from an analysis of Figure 2, the energy content of hydrogen expressed in MJ/l, even with a compression level of 700 bar, is still about 1/7 of that available with the main liquid fuels typically used in the energy sector. Even liquefaction, despite all the highlighted issues, does not solve the problem. The issue of compressing hydrogen in gaseous form encompasses various aspects, including the significant consideration of storage vessels. Historically, certain pressure levels, such as 350 bar and 700 bar, have been identified as structurally feasible, with four distinct types of containers available for storage. A paper from Barthelemy, [12], provides a historical and technical overview of hydrogen storage vessels and discusses the challenges and constraints of hydrogen energy applications. It explores the storage of hydrogen as a compressed or refrigerated liquefied gas, detailing the evolution of storage methods from seamless steel cylinders to aluminum cylinders and hoop-wrapped metallic cylinders. The development of fully wrapped composite tanks for high-pressure hydrogen storage is examined, along with the specific issues associated with these technologies. Additionally, the storage of hydrogen in liquid form is discussed, tracing the use of cryogenic vessels since the 1960s. The topic of compressed hydrogen structures is certainly of great importance and is inherently linked to the determination of storage pressures, but it is not elaborated on in this work.

Figure 2. Hydrogen compression as a gas or in liquid form.

Figure 2. Hydrogen compression as a gas or in liquid form.

Figure 3. Volumetric energy content of different fuels in different operating conditions.

Figure 3. Volumetric energy content of different fuels in different operating conditions.

To better understand the issues associated with hydrogen compression, whether aimed at maintaining it in liquid or gaseous conditions, it is necessary to have a clear idea of the orders of magnitude associated with the two phases. The thermophysical properties of hydrogen can be quantitatively visualized in the graph depicted in Figure 4, rearranged, and readapted from Grestein and Klell, in [13] and Klell, [14], representing the temperature range from 0 K up to a temperature of 325 K. To understand the pressure that need to be reached, next table elucidates various density values achievable through the judicious manipulation of pressure and temperature variables. A discernible pattern emerges, showcasing a substantial upswing in density with the application of higher pressure and the simultaneous reduction in temperature. This correlation underscores the dynamic interplay between these thermodynamic factors, providing valuable insights for optimizing hydrogen storage and utilization strategies. Table 2 presents various density values achievable by NIST webbook database, [15] strategically combining pressure and temperature.

Figure 4. Hydrogen thermophysical properties in a T-s diagram. (Readapted and Rearranged from the original reported by Grestein and Klell, [13] and Klell, [14]).

Figure 4. Hydrogen thermophysical properties in a T-s diagram. (Readapted and Rearranged from the original reported by Grestein and Klell, [13] and Klell, [14]).

Table 2. Hydrogen density (kg/m3) at Different Temperatures (°C) and Pressures (MPa).

Table 2. Hydrogen density (kg/m3) at Different Temperatures (°C) and Pressures (MPa).

T [°C]	0,1 MPa	1 Mpa	5 Mpa	10 Mpa	30 Mpa	50 Mpa	100 Mpa
-100	0,1399	1,3911	6,7608	12,992	32,614	46,013	66,660
-75	0,1223	1,2154	5,9085	11,382	29,124	41,848	62,322
-50	0,1086	1,0793	5,2521	10,141	26,336	38,384	58,503
-25	0,0976	0,9708	4,7297	9,1526	24,055	35,464	55,123
0	0,0887	0,8822	4,3036	8,3447	22,151	32,968	52,115
25	0,0813	0,8085	3,9490	7,6711	20,537	30,811	49,424
50	0,0750	0,7461	3,6490	7,1003	19,149	28,928	47,001
75	0,0696	0,6928	3,3918	6,6100	17,943	27,268	44,810
100	0,0649	0,6465	3,1688	6,1840	16,883	25,793	42,819
125	0,0609	0,6061	2,9736	5,8104	15,944	24,474	41,001

Figure 5. Hydrogen density as a function of temperature and pressure.

Figure 5. Hydrogen density as a function of temperature and pressure.

Density experiences a significant increase with higher pressure and lower temperatures. The compressibility factor (Z) of a gas is a dimensionless quantity that reflects how much the gas deviates from ideal behavior. For an ideal gas, the compressibility factor is always equal to 1. However, real gases, including hydrogen, deviate from ideal behavior under certain conditions. In the case of hydrogen, the compressibility factor tends to increase with increasing pressure and decreasing temperature. The deviation from ideal gas behavior is more pronounced under conditions where the gas particles are closer together and experience stronger intermolecular forces, such as at high pressures or low temperatures. So, your observation aligns with the non-ideal behavior of hydrogen, and the increasing compressibility factor signifies that hydrogen exhibits deviations from ideal gas behavior, especially under conditions of elevated pressure and reduced. Compressed hydrogen storage encompasses a spectrum of pressure levels tailored for diverse applications. Small-scale storage, utilizing spherical vessels, commonly operates at 20 bars. Medium-scale storage in pipelines typically involves a pressure of 100 bar, while industrial-scale storage utilizes pressures in the range of 200–300 bar. Operational pressures for hydrogen fuel cells in light- and heavy-duty road transport span from 350 bar to 700 bar. Hydrogen refueling stations, servicing both light- and heavy-duty road transport, necessitate storage at 1000 bar.

Table 3. Compressibility factor Z of Hydrogen at Different Temperatures (°C) and Pressures (MPa).

Table 3. Compressibility factor Z of Hydrogen at Different Temperatures (°C) and Pressures (MPa).

T [°C]	0,1 MPa	1 Mpa	5 Mpa	10 Mpa	30 Mpa	50 Mpa	100 Mpa
-100	1.0007	1.0066	1.0356	1.0778	1.2880	1.5216	2.1006
-75	1.0007	1.0068	1.0355	1.0751	1.2604	1.4620	1.9634
-50	1.0007	1.0067	1.0344	1.0714	1.2377	1.4153	1.8572
-25	1.0006	1.0065	1.0329	1.0675	1.2186	1.3776	1.7725
0	1.0006	1.0062	1.0313	1.0637	1.2022	1.3462	1.7032
25	1.0006	1.0059	1.0297	1.0601	1.1879	1.3197	1.6454
50	1.0006	1.0056	1.0281	1.0567	1.1755	1.2969	1.5964
75	1.0005	1.0053	1.0266	1.0536	1.1644	1.2770	1.5542
100	1.0005	1.0050	1.0252	1.0507	1.1546	1.2596	1.5175
125	1.0005	1.0048	1.0240	1.0481	1.1458	1.2441	1.4852

Figure 6. Hydrogen Compressibility (Z) at Different Temperatures and Pressures.

Figure 6. Hydrogen Compressibility (Z) at Different Temperatures and Pressures.

3. Gaseous hydrogen compression: analysis of technological solutions available

Small-scale storage using spherical vessels commonly operates at 2 MPa. Medium-scale storage in pipes typically involves a pressure of 10 MPa [16,17]. Industrial-scale storage utilizes pressures in the range of 20–30 MPa [18]. High operational pressures for light- and heavy-duty road transport span from 35 to 70 MPa [19]. Hydrogen storage in large production areas to hydrogen refuelling stations and/or industrial users may require compressing hydrogen up to 100 MPa. The isobaric and isenthalpic curves of interest for the storage of H₂ in compressed gaseous form are qualitatively represented in Figure 7.

Figure 7. Zone of interest for the storage of H₂ in compressed gaseous form: isobaric (red lines) and isenthalpic (blue lines) curves and aree of interest (green).

Figure 7. Zone of interest for the storage of H₂ in compressed gaseous form: isobaric (red lines) and isenthalpic (blue lines) curves and aree of interest (green).

Considering the data provided in Table 4 and referencing a total compression ratio of 350, the specific work associated with compression varies from approximately 10 MJ/kg for larger-sized compressors to over 26 MJ/kg for smaller-sized compressors. The nominal power of the various available models ranges from 4 kW up to 230 kW and the number of stages is from 3 to 5. Compressor with maximum output pressure of 700 bar are not available in the market.

Table 4. Specification of some compressor of the commercial type.

Table 4. Specification of some compressor of the commercial type.

Compressor type	Inlet pressure [bar]	Outlet pressure [bar]	Pressure ratio	Volumetric Flow rate [m³/h]	Nominal power [kW]	Specific work compression [MJ/kg]
3 stages	24-30	350-450	14.6-15	7-13	4-5.5	18.35-24.78
4 stages	1	350	350	26	15	25.02
4 stages	1	350	350	36	22	26.50
4 stages	1	350	350	76	38	21.68
5 stages	1 – 20	350	17.5-350	1000	132 – 230	5.72-9.98

Data for converting flow meter in kg/h: 1 m3/h (20°C, 1,013 hPa) = 0,083 kg/h.

4. Compression model and energy requirements for hydrogen compression: sensitivity analysis

Through mathematical modeling and simulation, we investigate how these deviations impact the energy requirements of hydrogen compression. By comparing the energy expenditure of idealized isothermal compression with real-world compression processes, we aim to quantify the efficiency losses associated with practical compression systems. This analysis provides valuable insights into the thermodynamic limitations and performance characteristics of hydrogen compression technologies. Considering a thermodynamic perspective, the process of isothermal reversible compression requires the least amount of work, and this can be computed under the assumption of ideal gas behavior with the following equation. [Zangh et al., 2005].

(2)

So, considering the energy required to obtain a final pressure of 700 bar, starting from temperature of 300 K, it can be assumed to be about 8.17 MJ/kg, while it is about 7.30 MJ/kg for a compression between 1 and 350 bar.

(3)

In practical scenarios, the temperature of hydrogen undergoes a considerable increase even when utilizing advanced multi-stage intercooling technology during compression. As a result, it is more accurate to characterize the compression process as a polytropic compression. The energy consumption for this type of process can be roughly determined by the following equation, using a polytropic exponent, that accordingly with the most diffused textbooks of Thermodynamics can be assumed to be n=1.36.

(4)

Table 5. Specific work for ideal isothermal compression and polytropic compression (with n=1,36) of hydrogen from 300 K and 0.1 MPa to a final pressure.

Table 5. Specific work for ideal isothermal compression and polytropic compression (with n=1,36) of hydrogen from 300 K and 0.1 MPa to a final pressure.

Final H2 pressure [MPa]	Density [kgH2/m3]	wiT,id [MJ/kgH2]	wpol
2	1.6	3.73	4.28
10	7.8	5.74	13.05
20	14.7	6.61	20.55
30	20.8	7.11	26.70
35	23.8	7.30	29.48
70	40	8.17	51.71
100	50	8.61	57.52

Figure 8 shows the temperature-entropy diagram of an intercooled multi-stage compression with four stages of compression, where p1 is the initial pressure of hydrogen to store and p8 equals the storage pressure desired (p_st). The work of compression per kg of hydrogen in an intercooled multi-stage process (w_m-s) can be evaluated by the sum of the enthalpy changes between the stages. In an intercooled multi-stage compression, the specific work (w_m-s) can be evaluated, as schematically referred in Figure 5 by the isentropic efficiency (η_is) of the compressor, where referring to four compression stages:

$$w_{m-s}=\frac{\left(h_{2is}-h_1\right)+\left(h_{4is}-h_3\right)+\left(h_{6is}-h_5\right)+(h_{8is}-h_7)}{{\eta }_{is}}$$

(5)

and in general

$$w_{m-s}={(h}_2-h_1)+(h_4-h_3)+(h_6-h_5)+(h_8-h_7)$$

(6)

Figure 7. Temperature-entropy diagram of an intercooled four stages compression.

Figure 7. Temperature-entropy diagram of an intercooled four stages compression.

5. Analysis of the real compression work with respect to the various combination of initial and final pressure

Considering an isentropic compression efficiency of 0.8, along with the initial pressure of the hydrogen and the desired pressure at the end of the process, as well as the maximum temperature achievable due to structural constraints, it follows the need to determine the optimal number of compression stages. As observed in Table 6, in terms of the specific work required for gas compression, the difference between using 2, 3, or 4 compression stages is not particularly significant. However, what is noteworthy is the maximum temperature: while with two stages it reaches approximately 217 °C, 3 or 4 stages allow for much greater limitation of the maximum temperature. Similar considerations can be made in the case where the goal is to achieve a final gas pressure of 10 MPa; in this scenario, it is obviously not feasible to work with only two compression stages since the compression ratio would be approximately 10 (Table 7). The situation becomes more complicated if aiming to achieve a final pressure of 350 bar. In this case, maintaining reasonable value of maximum temperature requires 4 or 5 compression stages. The compression work required is on the order of 11 MJ/kg, a value that is approximately 10% of the fuel’s calorific value. Table 8 shows the data related to the two cases with 4 or 5 compression stages. Obviously, the specific energy required for compression increases as the isentropic compression efficiency decreases. Table 9 illustrates the scenario where the isentropic compression efficiency is reduced to 0.7. If the isentropic efficiency (ηis) decreases, the maximum temperature, and the specific work of compression increase.

Table 6. Specific work for multi-stage compression to 2 MPa (η_is=0.80): T_in = 20 °C, p_in = 0.1 MPa.

Table 6. Specific work for multi-stage compression to 2 MPa (η_is=0.80): T_in = 20 °C, p_in = 0.1 MPa.

Number of stages	T2 [°C]	p2 [MPa]	T4 [°C]	p4 [MPa]	T6 [°C]	p6 [MPa]	T8 [°C]	wm-s [MJ/kgH2]
2	216.7	0.5	214.8					5.67
3	140.5	0.3	142.6	0.7	140.8			5.26
4	106.8	0.2	109.5	0.5	107.6	1.0	107.3	5.07

Table 7. Specific work for multi-stage compression to 10 MPa (η_is=0.80): T_in = 20 °C, p_in = 0.1 MPa.

Table 7. Specific work for multi-stage compression to 10 MPa (η_is=0.80): T_in = 20 °C, p_in = 0.1 MPa.

Number of stages	T2 [°C]	p2 [MPa]	T4 [°C]	p4 [MPa]	T6 [°C]	p6 [MPa]	T8 [°C]	wm-s [MJ/kgH2]
3	220.2	0.5	222.9	2.2	222.8			8.84
4	164.6	0.3	162.7	1.0	162.5	3.2	162.8	8.34

Table 8. Data for intercooled multi-stage compression (η_is=0.80) from 0.1 MPa and 20 °C to 35 MPa.

Table 8. Data for intercooled multi-stage compression (η_is=0.80) from 0.1 MPa and 20 °C to 35 MPa.

Number of stages	T2 [°C]	p2 [MPa]	T4 [°C]	p4 [MPa]	T6 [°C]	p6 [MPa]	T8 [°C]	p8 [MPa]	T10 [°C]	wm-s [MJ/kgH2]
4	209.5	0.4	211.4	1.9	211.4	8.1	212.5			11.34
5	164.6	0.3	167.0	1.0	166.7	3.4	166.7	10.9	167.6	10.86

Table 9. Optimized specific work of compression from 20 °C and 0.1 MPa. Multistage intercooled compression with η_is=0.70, varying the storage pressure and the number of stages.

Table 9. Optimized specific work of compression from 20 °C and 0.1 MPa. Multistage intercooled compression with η_is=0.70, varying the storage pressure and the number of stages.

pst [MPa]	Three stages		Four stages		Five stages
	Tmax [°C]	wm-s [MJ/kg]	Tmax [°C]	wm-s [MJ/kg]	Tmax [°C]	wm-s [MJ/kg]
2	160	6.0	122	5.8	100	5.7
10			185	9.5	147	9.2
20			214	11.4	171	10.9
30			232	12.5	185	12.0
35			242	13.0	191	12.4
70					219	14.5
100					235	15.8

This factor gains even more significance when considering that a portion of the energy has already been dissipated during the electrolysis process. It’s crucial to emphasize, however, that the energy expenditure during the compression phase does not escalate significantly in relation to the compression ratio. This implies that the selection of an optimal compromise between enhancing density and minimizing work input might be contingent on other critical factors. These factors include the maximum number of compression stages, the upper limit on compression temperature, and the maximum compression ratio associated with a single stage. Balancing these elements becomes pivotal in determining the overall efficiency and feasibility of hydrogen compression processes.

Table 10. Intercooled multi-stage compression (η_is=0.80) with five stages from initial condition of 20 °C and 3 MPa.

Table 10. Intercooled multi-stage compression (η_is=0.80) with five stages from initial condition of 20 °C and 3 MPa.

pH2 [MPa]	T2 [°C]	p2 [MPa]	T4 [°C]	p4 [MPa]	T6 [°C]	p6 [MPa]	T8 [°C]	p8 [MPa]	T10 [°C]	wm-s [MJ/kgH2]
35	75.9	4.9	75.9	8.0	76.0	13.1	76.2	21.4	76.6	4.29
70	92.1	5.6	92.9	10.5	93.4	19.7	94.5	37.1	95.9	5.87
100	100.9	6.0	102.3	12.1	102.8	24.4	103.7	49.2	106.8	6.82

6. Conclusions

Nomenclature

Subscripts, superscripts, acronyms and abbreviations

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