Applicability of the common equations of state for modeling hydrogen liquefaction processes in Aspen HYSYS

1. 1.   Introduction

Liquid hydrogen demands have experienced rapidgrowth in the past decades' thanks to the increased applications (Ohlig & Decker, 2014). Hydrogen has wide applications in the petroleum and chemical industries, including hydrodealkylation, hydrodesulfurization, and hydrocracking (Qian, Jaubert, & Privat, 2013). Hydrogen could be used as a storage system for renewable energy sources faced with fluctuation during a day, such as solar and wind (Ahmadi, Mirghaed, & Roshandel, 2014). Moreover, hydrogen has been introduced as a promising fuel for internal combustion engines because of its renewability, efficient combustion, and nearly zero greenhouse gas emissions (Bai-Gang, Dong-Sheng, & Fu-Shui, 2012). Using hydrogen is involved with many challenges due to the low energy density (Berstad, Stang, & Nekså, 2009). Therefore, it should be solved by different methods such as liquefaction and compression. The boiling temperature of hydrogen is as low as 20 K and nearly one-third of its energy contents will be consumed in the liquefaction process (Yuksel, Ozturk, & Dincer, 2017). By the way, it seems to be the best method; therefore, many pieces of research are focused on this method (Asadnia & Mehrpooya, 2017; Berstad et al., 2009; Hammad & Dincer, 2018; Matsuda & Nagami, 1997; Mehrpooya, Sadaghiani, & Hedayat, 2020; Nandi & Sarangi, 1993; Sadaghiani & Mehrpooya, 2017; Valenti & Macchi, 2008; J.-H. Yang et al., 2019; Yuksel et al., 2017). Hydrogen clean energy sector, including using hydrogen in cars, buses, etc. are proliferated, so liquid hydrogen will likely play a significant role in transportation (Ohlig & Decker, 2014; Rösler, van der Zwaan, Keppo, & Bruggink, 2014). Liquid hydrogen is used directly by the aerospace industry as a fuel, and electronics and metallurgical sectors for specific production processes. Besides end-use, the liquid form of hydrogen for transportation and storage is economical, especially over long distances (Sherif, Zeytinoglu, & Veziroǧlu, 1997).

For the development of hydrogen industries, accurate predictions of the thermodynamic properties of hydrogen are essential (Sakoda et al., 2010). Thermodynamic models employ the equation of state (EOS) as the relationship between pressure, temperature, and density (McCarty, Hord, & Roder, 1981) to determine how the fluid behavior deviates from that of an ideal (J.-H. Yang et al., 2019). EOS's desired criteria are accuracy, consistency, computational speed, robustness, and predictive ability outside of the fitted domain (Wilhelmsen et al., 2017).

At low temperatures and high densities, hydrogen exhibits quantum behavior; therefore, in cryogenics applications, EOS must be modified appropriately to consider this context (Sadus, 1992). One of these modifications for cubic EOSs is volume translation, which had been used since the pioneering work of André Péneloux to improve the description of volumetric properties. This technique is widely applied in process and product design, where an EOS is used to estimate densities and other thermodynamic properties (Frey et al., 2007; Jaubert, Privat, Le Guennec, & Coniglio, 2016). The calorimetric and volumetric properties of fluids for processes like compression, expansion, and heat exchange in the cryogenic region are essential (Jacob W Leachman, Jacobsen, Lemmon, & Penoncello, 2017). The change of heat capacity and enthalpy influences the calorimetric properties, which affects the overall efficiency of the liquefaction process. The volumetric properties, such as vapor pressure and density affect the pressure changer equipment (J.-H. Yang et al., 2019). To conduct a precise simulation of the hydrogen liquefaction process, choosing a proper EOS that could yield satisfying thermodynamic properties results, is essential. Therefore, in this study, the choice of appropriate EOS for hydrogen liquefaction processes, which are simulated using Aspen HYSYS, is investigated.

The Accuracy of Aspen HYSYS has been proved in many studies around hydrogen liquefaction and similar areas (Ansarinasab, Mehrpooya, & Mohammadi, 2017; Ghorbani, Hamedi, Shirmohammadi, Hamedi, & Mehrpooya, 2016; Nouri, Miansari, & Ghorbani, 2020; Sadaghiani, Mehrpooya, & Ansarinasab, 2017; Seyam, Dincer, & Agelin-Chaab, 2020; Skaugen, Berstad, & Wilhelmsen, 2020; Taleshbahrami & Saffari, 2010; Thomas, Ghosh, & Chowdhury, 2011). Therefore, it is selected as the simulation tool here. Aspen HYSYS is developed by Aspen Tech and includes a set of subroutines to estimate physical properties and liquid-vapor phase equilibrium, heat and material balances, and simulating chemical engineering equipment (Belkadi & Smaili, 2018). It contains over 30 thermodynamic models and has extensive databank and powerful methods for fluid properties computation (Asadnia & Mehrpooya, 2017).

In 1949, Redlich and Kwong (Redlich & Kwong, 1949) introduced one of the most successful PVT relationships. Later, Soave (Soave, 1972) modified the Redlich-Kwong (RK) EOS successfully. The Soave-Redlich-Kwong (SRK) EOS has found widespread applications in the chemical and petroleum industries.  Krasae-In et al. (Krasae-In, Stang, & Neksa, 2010) proposed a large-scale hydrogen liquefaction plant using a multi-component refrigeration system. They adopted the SRK as EOS because of its popularity, simplicity, and fast computation through the PRO/II software package. They found that the SRK model is quite the same as that of REFPROP[1] V.8 and claimed that the SRK model is adequate for the cryogenic regions. Krasae-In (Krasae-in, 2014) simulated a large-scale liquefaction plant using SRK while he confirming that Peng-Robinson (PR) yields quite similar results. Krasae-in et al. (Krasae-in, Bredesen, Stang, & Neksa, 2011) simulated a hydrogen liquefaction test rig utilizing SRK as a fluid package. Moreover, the SRK equation of state has been applied to many studies around liquid natural gas (Hammer et al., 2003; J. B. Jensen & Skogestad, 2006; Myklebust, 2010; Nogal, Kim, Perry, & Smith, 2008).

PR is the most widely used Cubic EOS in the industry. Since its publication in 1976, PR has been adopted as one of the most useful models for thermodynamic and volumetric calculations in both industrial and academic fields (Lopez-Echeverry, Reif-Acherman, & Araujo-Lopez, 2017). Many pieces of research are concentrated on the correction of PR for different materials and conditions (Abudour, Mohammad, Robinson Jr, & Gasem, 2013; Feyzi, Seydi, & Alavi, 2010; Haghtalab, Mahmoodi, & Mazloumi, 2011; Le Guennec, Lasala, Privat, & Jaubert, 2016; Le Guennec, Privat, & Jaubert, 2016; Lin & Duan, 2005). Yin et al. (Yin & Ju, 2020) presented a new cycle for hydrogen liquefaction. They used Aspen properties databanks and PR as thermo-physical properties and EOS, respectively. A novel hydrogen liquefaction process was investigated by (Asadnia & Mehrpooya, 2017). They simulated the process using Aspen HYSYS and adopted PR as EOS. Sadaghiani et al. (Sadaghiani & Mehrpooya, 2017; Sadaghiani et al., 2017) used PR as a fluid package for simulation of hydrogen liquefaction through Aspen HYSYS. Ghorbani et al. (Ghorbani, Mehrpooya, Aasadnia, & Niasar, 2019) developed a novel structure for liquefaction of 290 TPD hydrogen that consists of an absorption refrigeration system, organic Rankine cycle, and parabolic solar dishes beside the basic liquefaction cycle. They simulated the process in Aspen HYSYS V.9 and used PR as a fluid package. Ebrahimi et al. (Ebrahimi, Ghorbani, & Ziabasharhagh, 2020) performed pinch and sensitivity analyses for the hydrogen liquefaction process in a hybridized system, including biomass gasification and air separation. They applied the pinch method on each multi heat exchanger (HX) of the hydrogen liquefaction process. Aspen HYSYS and MATLAB were used for simulation, and PR was adopted as EOS. Moreover, PR has been chosen as EOS in many other studies around  hydrogen liquefaction (Mehrpooya et al., 2020; Seyam et al., 2020).

The Benedict-Webb-Rubin (BWR) expressions are based on the pioneering work of Benedict, Webb, and Rubin (1940, 1942) (Reid, Prausnitz, & Poling, 1987). The Modified Benedict-Webb-Rubin (MBWR) and Benedict–Webb– Rubin–Starling (BWRS) are two modifications of BWR (Reid et al., 1987). MBWR originally is proposed by Jacobsen and Stewart for nitrogen (Jacobsen & Stewart, 1973) and employed by Younglove (Younglove, 1982) for hydrogen. Although using the BWR series encounters some difficulties in the computation process, it is preferred in some cases because of its high precision (Thomas, Dutta, Ghosh, & Chowdhury, 2012). This EOS was implemented in the three past releases of REFPROP. Valenti and Macchi (Valenti & Macchi, 2008) used the BWRS for all hydrogen forms, in their work on a large-scale hydrogen liquefier. They used Aspen Plus for simulation and validated the results against the existing hydrogen liquefier operating parameters located in Ingolstadt, Germany. Absorption properties of hydrogen, including fugacity and compressibility factor, were evaluated by Zhou and Zhou (Zhou & Zhou, 2001) using the SRK (Soave, 1972) and BWR (Benedict, 1940).

Yang et al. (J. C. Yang & Huber, 2008; Zheng et al., 2010) used REFPROP for analyzing processes containing hydrogen. Valenti and Macchi (Valenti, Macchi, & Brioschi, 2012) investigated the influence of thermodynamic models. They developed a fluid file for REFPROP and used it as a reference case for comparison against four other considered modeling alternatives. Cardella et al. (Cardella, Decker, & Klein, 2017; Cardella, Decker, Sundberg, & Klein, 2017) used PR for hydrocarbons and nitrogen and REFPROP for pure helium, neon, and the isomeric forms of hydrogen.

Sakoda et al. (Sakoda et al., 2010) conducted a review on the thermodynamic properties of hydrogen, based on the existing equations. Thermodynamic properties of hydrogen are studied by investigating eleven EOSs to predict different properties (Nasrifar, 2010). Ghanbari et al. (Ghanbari, Ahmadi, & Lashanizadegan, 2017) performed a comparison between the most successful cubic EOSs, i.e., PR and SRK from the modification perspective. Thermodynamic and transport properties of normal hydrogen and parahydrogen are reviewed by Jacobsen et al. (Jacobsen, Leachman, Penoncello, & Lemmon, 2007; Jacob W Leachman, Jacobsen, Penoncello, & Huber, 2007). Thomas et al. (Thomas et al., 2012) investigated the applicability of some simpler EOSs for modeling helium systems and compared the results to the MBWR.

In this research, four common EOSs in the literature, including two cubic EOSs, PR and SRK, and two non-cubic EOSs, MBWR, and BWRS are investigated to determine the best  EOS for the future studies which are conducted by Aspen HYSYS. Although utilization of the volume translation method is provided in Aspen HYSYS for cubic EOSs through the “generalized cubic equation of state (GCEOS),” it is not applied here. The main goal is to compare the default EOSs implemented in the Aspen HYSYS without additional manipulating as they are employed to the common researches in this field (Ansarinasab et al., 2017; Asadnia & Mehrpooya, 2017; Ebrahimi et al., 2020; Ghorbani et al., 2019; Mehrpooya et al., 2020; Sadaghiani & Mehrpooya, 2017; Sadaghiani et al., 2017). The research's novelty is in the complete investigation of the common EOSs, which has been used for simulation of hydrogen liquefaction through different studies using Aspen HYSYS, the most popular simulation tool for hydrogen liquefaction processes. Due to the occurring heat exchange between MR streams and hydrogen streams through heat exchangers, investigating the mere effect of the EOS that is applied to the hydrogen streams is not normally possible. On the other hand, employing a unit EOS to MR and hydrogen isomers could not yield desirable results. Moreover, using a unit EOS for the whole process impose more restrictions on the simulation. In this study, an innovative, simplified configuration is developed to be able to capture the mere effect of EOS on essential performance parameters such as coefficient of performance (COP) and specific energy consumption (SEC). Therefore, it may be possible to survey the mere effect of the EOS that is dedicated to hydrogen and parahydrogen, separately.

REFPROP is considered as the base case for comparison since its accuracy has been validated through different studies (Cardella, Decker, Sundberg, et al., 2017; Valenti et al., 2012). The deviation of the estimated properties by different EOSs to the corresponding reference properties is crucial. This index has been termed as “deviation” in the rest of the paper and is defined as follows:

where  and  stand for the desired property and the estimated property in order.

1. Ortho-para Conversion

Bonhoeffer and Harteck, about the same time as Eucken and Hiller, observed changes in property values in the samples of hydrogen, which were held at low temperatures for several hours. Since they were nearly isolated, the only possible cause was a conversion of the molecules from one spin state to another spin state (Jacob William Leachman, Jacobsen, Penoncello, & Lemmon, 2009). This observation came to no surprise when Heisenberg and Hund explained the existence of two different spin states for helium, orthohelium, and parahelium and postulated a similar occurrence for hydrogen (Farkas, 1935). Bonhoeffer and Harteck chose the names of orthohydrogen and parahydrogen. Variation in the properties of hydrogen isomers is attributed to the orientation of the nuclear spin (Jacob William Leachman et al., 2009). In general, more substantial discrepancies in the properties of orthohydrogen and parahydrogen occurs in those related to specific heat capacity such as enthalpy and entropy (Jacobsen et al., 2007). The equilibrium composition of orthohydrogen and parahydrogen varies with temperature. At room temperature and above, hydrogen has a composition of 75 % orthohydrogen and 25 % parahydrogen, which is called normal hydrogen (Farkas, 1935).

The ortho-para conversion is very slow, and if not catalyzed, the natural conversion could not proceed with proper speed. In this situation, the portion of orthohydrogen is higher than the equilibrium concentration; therefore, conversion occurs in the storage vessel. Typically, hydrogen liquefiers are designed to produce liquid hydrogen with a parahydrogen content of more than 95% (Gupta, Basile, & Veziroglu, 2016). The ortho-para conversion at the normal boiling point generates heat of conversion equal to 703 kJ/kg. Thus, when hydrogen gas with a parahydrogen concentration of 25% is liquefied and stored, ortho–para conversion gradually occurs, generating heat of conversion equal to 527kJ/kg. Since liquid hydrogen’s latent heat of vaporization is 446 kJ/kg, substantial boil-off occurs during the long-term storage, which means that normal liquid hydrogen might be vaporized entirely even in a perfectly insulated vessel (Gupta et al., 2016; Verfondern, 2008). Orthohydrogen does not exist as pure fluid and its maximum fraction could reach 75%. The proper EOS for the orthohydrogen can just be estimated from mixing rules (Sakoda et al., 2010). In most studies conducted in the field of hydrogen liquefaction, only parahydrogen and normal hydrogen are involved. The Ortho-para conversion achieves technically by packing the hydrogen side of the heat exchangers with an appropriate catalyst (Asadnia & Mehrpooya, 2017), so theoretically, conversion of the ortho-para could be simulated through a conversion reactor as defined in equation 1  (Asadnia & Mehrpooya, 2017; Noh et al., 2017; Sadaghiani & Mehrpooya, 2017; Sadaghiani et al., 2017).

The conversion progress depends on the hydrogen temperature (Asadnia & Mehrpooya, 2017 and is considered as follows(Asadnia & Mehrpooya, 2017):

where ,  and  are conversion coefficients, and  T is hydrogen temperature (K).

The conversion coefficients are adjusted, such that the fraction of parahydrogen in the output reactor equals experimental data (J. Jensen, Stewart, Tuttle, & Brechna, 1980).Table 1 lists the temperature and parahydrogen concentration in the inlet of convertors. Moreover, the equilibrium concentration of the parahydrogen in the outlet of converters and the conversion coefficients are indicated.

Table 1. Conversion coefficient applied to the conversion reactors used for modeling ortho-para conversion

1. 3.   Methodology

Here the capability of four common EOSs available in the Aspen HYSYS, including; PR, MBWR, BWRS, and SRK, are investigated for predicting volumetric and calorimetric properties of hydrogen and parahydrogen, including density, vapor pressure, specific heat capacity, enthalpy, and entropy. Volumetric behaviors of parahydrogen and hydrogen are the same (Pitzer, Lippmann, Curl Jr, Huggins, & Petersen, 1955) since where the volumetric properties are discussed, just the properties for one of them are reported (J.-H. Yang et al., 2019).

For validation of the results, experimental data presented by Leachman et al. (Jacob W Leachman et al., 2017) and REFPROP, which its accuracy had been tested through different studies, are employed. Hydrogen in the liquefaction process normally experiences a continuous wide range of temperatures from 25  to -252.5 . However, the experimental data are reported only for the specific pressures and temperatures, so that it might tolerate some restriction on the range of data. By the way, as the first step, the data acquired from REFPROP are compared to the experimental data presented by Leachman et al. (Jacob W Leachman et al., 2017) for double-check. The results are shown in Table 2 and Table 3 for 1 MPa and 10 Mpa, through the common temperature range of hydrogen liquefaction processes; 20 K to 300 K.

Table 2. Enthalpy, entropy, and density from REFPROP and Ref. (Jacob W Leachman et al., 2017) for para-hydrogen.

Table 3. Enthalpy, entropy, and density from REFPROP and Ref. (Jacob W Leachman et al., 2017) for hydrogen.

As it could be seen in Table 2 and Table 3, for hydrogen and parahydrogen in the considered range, there exists a negligible discrepancy in the data such that the deviation is nearly less than 1% for the whole range except enthalpy and entropy in 20 K and 30 K for 1 MPa. Although the deviation could go higher in 20 K and 30 K, it could be ignored due to the low values of enthalpy and entropy in this range. As the temperature increases, the inconsistency is reduced to less than 0.1%. Since the results are compatible with experimental data of Ref. (Jacob W Leachman et al., 2017), it is found that REFPROP could be a useful tool for validation. It should be mentioned that REFPROP could yield data continuously while the experimental data are available just in the specific points. The data for density, vapor pressure, enthalpy, entropy, and specific heat capacity of the four considered EOSs are compared with the data extracted from REFPROP as the reference case.

3.1          Density

Estimated densities for the considered cases are compared to the reference case. The results are presented in Figure 1 and Figure 2. The estimated densities for parahydrogen and hydrogen using PR, SRK, and BWRS in low temperatures are not compatible with REFPROP, while the MBWR experiences excellent consistency in this zone. The density of the parahydrogen and hydrogen estimated by REFPROP and MBWR are the same, so here only the results for hydrogen are presented through Figure 1 and Figure 2 for 1 MPa and 10 MPa. It deserves to note that this is not true for the BWRS, PR, and SRK. In other words, these EOSs estimate different values for the parahydrogen and hydrogen density. The difference between the two estimated values could go up to 26% in low temperatures, such as 30 K, but it decreased to less than 1% at higher temperatures. 

Figure 1. Estimated densities for hydrogen in 1 MPa.

Figure 2. Estimated densities for hydrogen in 10 MPa.

For both 1 MPa and 10 MPa throughout the temperature range, MBWR leads to precise results for density such that the deviation is less than 0.05%. Among the three other EOSs, SRK performs better for estimating density in 1 MPa and 10 MPa. For the SRK, BWRS, and PR in 1 MPa, the deviation was reduced to lower than 1% in 50 K, 60 K, and 120 K, respectively. For 10 MPa, the deviation is higher, and it reaches less than 1 % for the SRK in 170 K and the BWRS and PR in 240 K. For PR, the deviation throughout the temperature range of 20-300 K is higher than 2%.

It could be seen that as the pressure increases or temperature decreases, the deviations increase, which is compatible with physical laws. The most significant deviation values in estimating density by Aspen HYSYS and considered EOSs, are for lower temperatures and higher pressures. As the temperature increases, the results for all three EOSs are getting more precise. In general, it could be said that all considered EOSs could perform well except in temperature lower than 40 K; however, throughout the range, the MBWR leads to more accurate results.

3.2   Vapor pressure

Vapor pressure for considered cases near the boiling point is reported in Figure 3. The data predicted by considered EOSs show excellent compatibility with experimental data. It should be noted that the deviation for BWRS is more prominent than other EOSs. For vapor pressure as a volumetric property, the hydrogen behavior is similar to parahydrogen (Pitzer et al., 1955), so here only the data related to parahydrogen are reported. 

Figure 3. Vapor pressure predicted for parahydrogen by four considered EOSs through Aspen HYSYS and experimental data.

3.3   Enthalpy and entropy

The enthalpy and entropy for considered EOSs are compared in Tables 4-7. For removing the effect of reference values in different models, the enthalpy and entropy increments (∆h & ∆s) are analyzed and reported. The enthalpy and entropy values are essential in energy and exergy analyses. At the same time, the other thermo-physical properties are not as crucial as these properties.

For parahydrogen, MBWR is the best choice. Although deviations for this EOS will increase for higher pressures and lower temperatures, it performs well enough through the whole range of temperature and pressure. The average deviation for MBWR is nearly less than 0.05% for both enthalpy and entropy. For 1 MPa pressure, the estimated enthalpies and entropies for the PR, BWRS, and SRK are almost identical. These models for both entropy and enthalpy could yield acceptable results in higher temperatures, while in low temperatures, they lead to high deviations. Although the pressure could affect the deviations proportionally, its effect is lower than that of the temperature. In 10 MPa, the PR and SRK are nearly the same and significantly better than the BWRS. In other words, pressure has a positive impact on the estimated results by the BWRS and a negative effect on the calculated results by the PR and SRK. For 1 MPa and 10 MPa in temperatures lower than 120 K, they lead to deviations higher than 5%.

Table 4. Estimated enthalpy and entropy increments for parahydrogen in 1 MPa.

Table 5. Estimated enthalpy and entropy increments for parahydrogen in 10 MPa.

Table 6. Estimated enthalpy and entropy increments for hydrogen in 1 MPa.

Table 7. Estimated enthalpy and entropy increments for hydrogen in 10 MPa.

Applying MBWR to hydrogen, the same as parahydrogen, leads to acceptable results throughout the whole temperature and pressure range. The estimated data for hydrogen using PR, BWRS, and SRK EOSs are nearly the same; they all experience high deviations for low temperatures such that for lower than 190 K, the deviations are higher than 5%. It should be noted that the deviations for hydrogen are higher in comparison to the parahydrogen.

3.4          Specific heat capacity and conversion enthalpy

Specific heat capacity (Cp) for hydrogen and parahydrogen estimated by considered EOSs through Aspen HYSYS are compared to the experimental data (Jacob W Leachman et al., 2017) in Figure 4 and Figure 5, respectively. As it is shown in Figure 4, the results for MBWR fit very well to the experimental data for the whole range of temperature typically met in the liquefaction processes. However, other EOSs could yield acceptable results only for temperature higher than 220 K. As the temperature approach to the boiling point, the deviation for MBWR increases and could reach 13%. For temperatures higher than 50 K, the deviation is less than 1%. 

Figure 4. Comparison of estimated values of heat capacity (Cp) for hydrogen by different EOSs to the experimental data.

For parahydrogen, the same as hydrogen, the results of MBWR fit very well with the experimental data. Three other EOSs yield acceptable results only for temperature higher than 120 K. The deviation for MBWR is less than 1% except for temperature lower than 50 K that could go up to 13%.

Ortho-para conversion is of great importance in the simulation of hydrogen liquefaction processes and could lead to inaccurate results if it is not simulated correctly. The results presented in the previous sections show that only MBWR could lead to desirable results in the whole range of temperature and pressure. Therefore, it deserves to compare the enthalpy of conversion based on the data obtained from Aspen HYSYS by MBWR with the experimental data. The results are shown in Figure 6.

To have a better understanding the results are presented in Table 8, from 20 to 280 K. Moreover, the difference between the two series of data is reported as a deviation in Table 8.  

Figure 5. Comparison of estimated values of heat capacity (Cp) for parahydrogen by different EOSs to the experimental data.

Figure 6. Comparison between results of Aspen HYSYS by MBWR and Experimental data (Jacob W Leachman et al., 2017).

Table 8. Comparison between results of Aspen HYSYS by MBWR and Experimental data from 20-280 K (Jacob W Leachman et al., 2017).

As it could be seen in Figure 6 and Table 8, the two curves are compatible very well. The difference between the two cases is in the range of 6-14 kJ/kg, which is ignorable in comparison to the power needed for liquefaction. The MBWR leads to a 1% deviation compared to the experimental data at the boiling point, which is ignorable. Although the deviation could go up to 14% at temperatures higher than 270 K, the value is lower than 8 kJ/kg and could be ignored. The results show that MBWR could estimate all the considered properties of the hydrogen and parahydrogen in the range of 20-300 K, which is typically met in the liquefaction processes.

1. 4.   Result and discussion

MBWR yields the most accurate results, while PR is the most common EOS, which has been utilized in the field of hydrogen liquefaction processes. For more understanding, EOS’s effect on significant specifications of a sample liquefaction cycle, including COP and SEC, is investigated through applying MBWR and PR. For this purpose, the liquefaction concept proposed by Sadaghiani et al. (Sadaghiani & Mehrpooya, 2017), which includes two MR cycles, is considered. Due to the configuration of this concept, any change in the hydrogen streams, such as changing the dedicated EOS, could lead to unavoidable changes in the MR cycles. Therefore, it is impossible to capture EOS’s mere effect on the COP and SEC  using this concept. The considered concept is simplified to remove the interaction between MR cycles and hydrogen streams for solving this problem. The simplified concept and the original one are presented in Figure 7. It is not logical to reject heat from hydrogen streams using coolers since, in this situation, indexes like COP and SEC are not valid anymore. Although the simulation in the Aspen HYSYS is based on the simplified concept in Figure 7, for calculation of the COP and SEC, it is supposed that every cooler is served by a hypothetical independent refrigeration cycle to provide a cooling effect.

These refrigeration cycles are supposed to be based on the reversed­ Carnot cycle with an ambient temperature of 25 . COP for the reversed­ Carnot cycle is calculated as follows:

where , ,  and   stand for cooling effect (rejected heat from hydrogen stream), work input (for the all hypothetical reversed Carnot cycles), the temperature of the cold and warm space, respectively. For every cycle  is obtained from Aspen HYSYS simulation, and the  could be calculated as follows (Van Wylen, 2015):

The results are reported in Table 9 for two cases, with MBWR and PR as EOS.

Table 9. Cooling effect and work input for cases with PR and MBWR.

For the liquefaction cycle, the COP could be calculated using Equation (3) while the SEC is defined as:

The COP and SEC for the two considered cases are reported in Table 10.

Table 10. COP and SEC for cases with the PR and MBWR as EOS.

It is found that using MBWR leads to 10.63% lower SEC and 4.12% higher COP compared to PR. 

Figure 7. Schematic of the original sample liquefaction cycle (right) and simplified one (left).

1. 5.   Conclusion

Liquid hydrogen has a wide range of applications and particular usages due to its unique characteristics. Liquid hydrogen is expected to play an important role in the future of energy if it could be liquefied economically. The existing liquefaction plants have low efficiencies so many studies are dedicated to optimizing liquefaction processes and providing novel concepts. The accuracy of these studies is intensively dependent on the simulation tools and adapted models. Aspen HYSYS includes a rich data bank of physical properties and different implemented models and EOSs, so it has been chosen as the simulation tool in many pieces of research. The accuracy of the models developed by Aspen HYSYS and similar programs are crucially dependent on the selected EOS. In this study, four common EOSs, PR, MBWR, SRK, and BWRS, which had been utilized in many studies around hydrogen liquefaction, are investigated through a novel methodology to find their accuracy and the proper range of applications.

Although the results of the PR and SRK for density are acceptable through the whole range, the best results are gained by applying the MBWR. The use of the PR, SRK, and BWRS in estimating the enthalpy and entropy experience more deviations, especially in lower temperatures and higher pressures, so that they can be used only for temperature range far from the boiling point. It deserves to note that the effect of temperature on the accuracy of the results for a specified EOS is more than the pressure. The results show that MBWR is the best EOS, which could estimate essential properties, including density, vapor pressure, entropy, enthalpy, and specific heat capacity with acceptable deviations compared to the reference case, i.e., REFPROP. Moreover, the MBWR could yield fair values for conversion enthalpy through the whole range of temperature, so it could be the right choice for hydrogen liquefaction processes, especially the ones that include ortho-para conversion. The three other considered EOSs could present nearly acceptable results for higher temperatures but are not adequate for hydrogen liquefaction processes due to the low boiling point of hydrogen and high deviations for lower temperatures. If utilizing the MBWR is not possible thanks to the computational difficulties or the processes temperature, it seems that the PR, which is a simple EOS, could perform better than the two others and lead to more accurate results. Applying the PR and MBWR to a simplified concept for liquefaction of hydrogen shows that using PR compared to the MBWR leads to 10.63% and 4.12% deviation in SEC and COP, respectively. It is advised to use the MBWR for simulation of hydrogen liquefaction processes conducted by Aspen HYSYS. This could lead to more accurate and reliable results.