Keywords

1 Introduction

Hydrogen energy is an essential renewable energy carrier that provides a critical technical pathway to achieve low-carbon goals. Liquid hydrogen, with its high storage density and low storage pressure, is a crucial component of building hydrogen energy storage and transportation systems. As future hydrogen consumption gradually increases, the design of the liquefaction process is becoming a widely researched topic in liquid hydrogen production technology.

Hydrogen consists of two spin isomers, which are ortho-hydrogen and para-hydrogen, and their concentration ratio varies with temperature [1]. The common conversion of ortho- to para-hydrogen is an exothermic reaction that can occur with the help of catalyst, but this phenomenon can also occur in liquid hydrogen without the catalyst. In order to reduce the vaporization of liquid hydrogen products caused by conversion heat, catalytic conversion is arranged in multiple temperature ranges of the liquid hydrogen production process. Catalytic conversion reaction can be categorized as adiabatic convention, isothermal convention and continuous convention. It is challenging to integrate the catalyst in the heat exchanger to realize the multistage continuous reaction. However, continuous reaction consumes the least amount of work, so it is more suitable for large-scale hydrogen liquefaction plant.

Despite being commercially available, current software lacks a heat exchanger model integrated with the ortho to para conversion reaction. Therefore, effectively and accurately designing a hydrogen liquefier with continuous conversion is the focus of researchers' attention. Son et al. [2] adopted an equivalent heat exchanger model using a conversion reactor unit to simulate the catalytic reaction, but the limitation of this work is that if a large amount of ortho- is converted to para-hydrogen, the results will be infeasible. Guocong et al. [3] replaced the module with a heater and heat exchanger, which is more suitable for adiabatic conversion. Meanwhile, Berstad et al. [4] used equilibrium hydrogen to optimize the design process. However, in the above design process, these methods have some limitations. Furthermore, if the hydrogen in the outlet of heat exchangers can’t reach the equilibrium hydrogen,there is still a lack of a mature solution. In the present study, we provide a new design method for a hydrogen liquefier with ortho- and para-hydrogen conversion heat exchanger based on the Aspen Hysys V12.1. This will not only improve the calculation accuracy, but also provide a reference for other similar processes.

2 Hydrogen Liquefaction Process Model

2.1 Liquefaction Process Description

To assess the suitability of Aspen Hysys for simulating hydrogen liquefaction systems with continuous conversion, a 5 TPD (ton per day) liquefier system was chosen for the study. Different working media, such as hydrogen, helium, neon, and mixed working media, were evaluated for the pre-cooling component of the system.Considering the technical maturity, complexity and energy consumption, liquid nitrogen pre-cooling and helium cryogenic cooling scheme was ultimately selected, as shown in Fig. 1. Therefore, The system consists of a compressor, a liquid nitrogen pre-cooling section, a turbo-expander pre-cooling section, and a liquid hydrogen storage system. Hydrogen gas is gradually cooled in heat exchangers (HEX1-7) from 300K to 20K through throttling valves, with HEX3-7 containing a catalyst.HEX3 is designed as the thermosiphon heat exchanger where hydrogen undergoes isothermal conversion. HEX4-5 is used for near-continuous conversion.In this scheme, there are the following characteristics: (1) the cooling path and the liquefaction path are relatively independent. (2) the cooling medium is inert working medium, resulting in higher safety levels, and non-explosion compressors can be used to reduce initial equipment investment. (3) a thermosiphon heat exchanger is used for isothermal conversion in the liquid nitrogen temperature zone. Under the temperature of 80K, the continuous convection with catalytic filled heat exchangers were used. (4) two throttling valves are employed to further utilize the J-T effect of hydrogen.

Fig. 1.
figure 1

Flow chart of hydrogen liquefaction

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2.2 Simulation Method

Equivalent catalyst-filled heat exchanger model

Fig. 2.
figure 2

Flow chart of hydrogen stream in HEX3-5

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In the process shown in Fig. 1, HEX1-2 are typical plate-fin heat exchangers, and their calculations can be done using the LNG heat exchanger model in Aspen Hysys. As for the hydrogen properties, normal hydrogen (o-H2:75%, P-H2:25%) from NIST is used for HEX1-2. On the other hand, HEX3-7 are filled with a catalyst, so the hydrogen properties used in these heat exchangers employ the equilibrium hydrogen physical property method. This method can be obtained by modifying the heat capacity of the para hydrogen from NIST. By using these properties in Aspen Hysys, we can relative accurately simulate the performance of the heat exchangers in the hydrogen liquefaction process. Since Aspen Hysys doesn’t have a built-in heat exchanger model for ortho-para H2 conversion, equivalent heat exchanger models need to be customized to simulate this process in catalyst-filled heat exchangers like HEX3-7. In cases where the para hydrogen content at the outlet doesn’t reach the equilibrium state, the non-equilibrium conversion efficiency is used to calculate the actual exit para hydrogen fraction. This is done by dividing the exit para hydrogen fraction by the equilibrium hydrogen fraction. The difference between the equilibrium and non-equilibrium conversion heat is then calculated and set as the heat loss in the heat exchanger. This can be implemented in Aspen Hysys using spreadsheets to perform the necessary calculations and provide a more accurate model of the heat exchanger’s performance. The specific implementation process can be further explained as shown in Fig. 2, which shows a schematic diagram of the catalyst-filled heat exchanger and the attached hydrogen stream. The cutter is placed between HEX1 and HEX3 to convert the property package model of hydrogen. This is necessary because the hydrogen properties used in HEX1 and HEX3-7 differ due to the ortho-para H2 conversion process taking place in the catalyst-filled heat exchangers. The hydrogen outlet temperature of each heat exchanger is represented by T1-T6. At each temperature, the corresponding equilibrium hydrogen content is represented as Xeq1−Xeq6. After conversion through the catalyst-filled heat exchangers, the para hydrogen content is represented as X′1−X′6. By using these values, we can calculate the non-equilibrium conversion efficiency as the ratio of the para hydrogen content after conversion to the equilibrium hydrogen content at the corresponding temperature. The difference between the equilibrium and non-equilibrium conversion heat is then calculated and set as the heat loss in the heat exchanger, which can be implemented using spreadsheet tools. This allows for a more accurate simulation of the heat exchanger performance in Aspen Hysys.

In Fig. 2, the temperature decreases from left to right, so the corresponding para hydrogen content increases. The blue line represents the conversion heat that is released as the ortho-para H2 conversion takes place in the catalyst-filled heat exchangers. \({\text{H}}_{{\text{ignored }}}\) in HEX3 represents the heat duty difference between the enthalpy of normal hydrogen and the equilibrium hydrogen at T1, which needs to be taken away in HEX3. In each stage of heat exchanger, the equilibrium hydrogen enthalpy change is denoted as \({\text{Stream dH}}\left( {\text{i}} \right)\), where the H represents the mass enthalpy in kJ/kg, as shown in Eq. 1.

$$ {\text{Stream dH}}\left( {\text{i}} \right) = {\text{H}}_{{{\text{Xeq}}\left( {{\text{T}}_{{{\text{i}} + 1}} } \right)}} - {\text{H}}_{{{\text{Xeq}}\left( {{\text{T}}_{{\text{i}}} } \right)}} {\text{ for i}} = 1 - 6 $$
(1)

When the actual outlet para hydrogen content X′(i) does not reach the equilibrium content Xeq(i) at stage i, it creates an excess heat difference in the heat exchanger, \({\text{H}}_{{{\text{excess}}\left( {\text{i}} \right)}}\) represents the influence of this part which is shown in Eq. (3).

$$ {\text{H}}_{{\text{ignored }}} = {\text{H}}_{{{\text{Xeq}}\left( {{\text{T}}_{1} } \right)}} - {\text{H}}_{{\left( {{\text{T}}_{1} ,0.25} \right)}} $$
(2)
$$ {\text{H}}_{{{\text{excess}}\left( {\text{i}} \right)}} = 2\left( {{\text{X}}_{{{\text{eq}}\left( {\text{i}} \right)}} - {\text{X}}_{{\text{i}}}{\prime} } \right) \times {\text{H}}_{{{\text{reaction}}\left( {\text{i}} \right)}} \quad {\text{for}}\, i = 2 - 6 $$
(3)

where the \(H_{{{\text{reaction}}\left( {\text{i}} \right)}}\) is the reaction heat duty at temperature Ti. In addition to the excess heat term, the heat duty at each stage of the heat exchanger also includes the equilibrium hydrogen enthalpy change, \({\text{Stream dH}}\left( {\text{i}} \right)\). Equations (4) and (5) represent the actual heat duty and the heat correction value of the heat exchanger that needs to be added to the actual heat duty to account for any deviations from the expected heat transfer performance of the heat exchanger, respectively.

$$ {\text{Q}}_{{\text{actual duty}}} = {\text{Stream dH}} + {\text{H}}_{{{\text{excess}}\left( {\text{i}} \right)}} - {\text{H}}_{{{\text{excess}}\left( {{\text{i}} + 1} \right)}} $$
(4)
$$ {\text{Heat}}\,{\text{loss}} = {\text{H}}_{{{\text{excess}}\left( {\text{i}} \right)}} - {\text{H}}_{{{\text{excess}}\left( {{\text{i}} + 1} \right)}} $$
(5)

For i = 1–6,when i = 1, \({\text{H}}_{{{\text{excess}}\left( 1 \right)}} = {\text{H}}_{{\text{ignored }}}\)

Validation of the equivalent heat exchanger

In Aspen HYSYS, the stand-alone conversion process of O-H2 to P-H2 can be achieved through a conversion reactor. The conversion reactor is modeled by setting the reactants, feed rates of reactants, reaction conditions (such as pressure, temperature, and catalyst), and reaction kinetics models. To validate the accuracy of the conversion heat value achieved by the equivalent heat exchanger unit, comparisons with data are performed in this study. Following the model shown in Fig. 2, a calculation model for the conversion reactor can be established as shown in Fig. 3 which shows a calculation model for the conversion reactor, which consists of feed-in streams for normal hydrogen and catalyst, a reactor, and an outlet stream for non equilibrium hydrogen.

Fig. 3.
figure 3

Conversion reactor units to model the process of o-p hydrogen in HEX3-5

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The conversion heat that is released during the conversion process is calculated based on the inlet and outlet conditions of the reactor. In order to ensure consistency between the conversion reactor and heat exchanger models, the parameters needed during the reaction process, such as temperature, pressure, flow rate, and other data, can be transferred to the corresponding variables in Fig. 3. Besides, the conversion rate in the conversion reactor can be calculated using the actual para-hydrogen content, which is obtained from the calculations in the equivalent heat exchanger model. The conversion rate is shown in Eq. (6):

$$ {\text{Conversion}}\,{\text{ rate}}\% = \frac{{{\text{X}}_{{{\text{i}} + 1}}^{\prime} - {\text{X}}_{{\text{i}}}^{\prime} }}{{1 - {\text{X}}_{{\text{i}}}^{\prime} }} \times 100\% $$
(6)

In this equation, \({\text{X}}_{{\text{i}}}^{\prime}\) represents the para hydrogen content at the inlet of stage i, and \({\text{X}}_{{{\text{i}} + 1}}^{\prime} \) represents the para hydrogen content at the outlet of stage i + 1. The conversion rate calculation takes into account the fact that not all of the normal hydrogen is converted to para hydrogen in the conversion reactor due to equilibrium limitations.

As shown in Table 1, the results of heat duty of hydrogen stream calculated by the conversion reactors and customized heat exchanger models are compared with the HEX3-7. The results show that the customized models were able to produce accurate predictions for the heat duty of the hydrogen stream, with errors ranging from 0.84 to 5.55%. These errors are within an acceptable range and indicate that the customized models can be used to simulate the performance of the hydrogen liquefaction process.

Table 1. Heat duty compared with the conversion reactor and customized heat exchanger
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Process optimization

The performance of the hydrogen liquefaction cycle is influenced by the process organization and operating parameters. The behavior of these parameters is complex, and can be difficult to understand without the help of a process simulator. In this study, a commercial process simulator, Aspen Hysys V12.1, was selected to model and analyze the hydrogen liquefaction process. Aspen Hysys is a widely used process simulator that allows for the simulation and optimization of a range of chemical and physical processes. The use of a process simulator allows for the analysis of how different operating parameters and process organization can affect the performance of the hydrogen liquefaction process. By simulating the process under different conditions, we can optimize the design and operation of the process to achieve maximum efficiency and performance.

The study has been performed on the basis of the following main assumptions:

  1. (1)

    The pressure drop of each streams in the heat exchanger is 5kPa;

  2. (2)

    The inlet and outlet helium state of the compressor are respectively 4bar, 298Kand 20 bar, 300K;

  3. (3)

    Liquid nitrogen gas holdup of the thermal siphon heat exchanger outlet is 0.2;

  4. (4)

    The temperatures difference of the heat exchangers in the same end is determined by set;

  5. (5)

    The nitrogen vent temperature is 298K;

  6. (6)

    Non-equelium conversion efficiency of the hydrogen is 95%;

  7. (7)

    The design mass flow rate of the hydrogen is 231kg/h.

Optimization objectives is in Eq. 7 and the optimization variables and variable bounds are showed in Table 2:

$$ {\text{f}}\left( {\text{x}} \right)_{{{\text{min}}}} = \left( {{\text{W}}1 + {\text{W}}_{{{\text{LN}}}} - {\text{W}}2 - {\text{W}}3 - {\text{W}}4} \right)/{\text{Q}}_{{{\text{LH}}}} $$
(7)

W1 is the power consumption of the compressor, kW; WLN is the power consumption of liquid nitrogen (0.6 kWh/Kg), kW; W2-W4 is the work of expander K-1, K-2, K-3,kW; QLH is the mass flow rate of liquid hydrogen, kg/h.

This paper uses the Eq. 7 without recover the turbine power as the objective function with the optimizer in Hysys and the equivalent heat exchanger model to optimize the process under the premise of the above variables and constraints.

Table 2. Optimization variables and variable bounds.
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3 Results

Specific power consumption is a crucial parameter in the design and operation of a hydrogen liquefier. It represents the direct operating cost of the process, and optimizing it is essential for maximizing the energy efficiency and reducing operating costs. The unit energy consumption of the optimized hydrogen liquefaction process was found to be12.61 kWh/kgLH2. From Fig. 4, the study found that the compressor and liquid nitrogen power consumption account for 68.34% and 31.66% of the total power consumption, respectively. This information is useful for identifying areas where energy efficiency can be improved. The total output power of the three expansion machines was found to be 104.4 kW, which accounts for about 3.58% of the total power consumption, so this part of power is not necessary to be recovered.

Fig. 4.
figure 4

The power of the critical components in the hydrogen liquefier

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Fig. 5.
figure 5

The heat load and minimum temperature difference of the heat exchanger

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To ensure that the heat exchangers operate efficiently and effectively, it is important to consider the temperature difference between the hot and cold fluids. By limiting the minimum temperature difference to 0.3-2K, the goal is to minimize the irreversible loss of energy. This requires careful consideration of the thermal characteristics of the system, including the design of the heat exchangers and the total investment. As shown in Fig. 5, HEX1 has the largest heat load among all the heat exchangers in the system and accounts for 78% of the total heat load. Therefore, its on-site installation limitations should be carefully considered in the actual design. HEX2 and HEX3, on the other hand, are designed as liquid nitrogen thermosiphon heat exchangers, which take advantage of the latent heat of evaporation of liquid nitrogen. This facilitates the provision of a cold source for isothermal conversion in HEX3. Below the liquid nitrogen temperature zone, the heat load of HEX4-7 decreases sequentially.

Fig. 6
figure 6

Conversion heat ratio and para hydrogen content of hydrogen stream from HEX3-7

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The conversion heat of HEX3 is the largest among all the heat exchangers in the system, accounting for about 50%, and the para hydrogen ratio is varied from 25 to 47%.The final exit para hydrogen content reaches 95%, meeting the requirements of the design requirement of the process, which shown in the Fig. 6.

4 Conclusion

In the process design of hydrogen liquefaction, the integral model of ortho and para hydrogen conversion heat exchanger is crucial to accurately calculate the process parameters. In this study, an equivalent heat exchanger model was constructed using Aspen Hysys to provide a new design method for hydrogen liquefaction, using the helium refrigeration hydrogen liquefaction model of 5tpd as an example. The method was validated through an analysis of the key process parameters. By using this simulation methodology, it is expected that future studies related to hydrogen liquefaction processes could be facilitated. This approach allows for a more efficient and accurate design of hydrogen liquefaction systems, which is crucial for the development of clean fuel technologies and the transition to a more sustainable energy future.