Wang et al. [4] experimentally investigated the pull-down performance of a −80˚C ultra-low temperature freezer. They concluded that the volumetric efficiency of high temperature cycle (HTC) compressor deteriorated more obviously during the pull-down process, and had higher potential for performance improvement compared with that of LTC. Ustaoglu et al. [5] optimized the performance of a vapor compression cascade refrigeration cycle by considering the statistical analysis methods, Taguchi and ANOVA approaches. They concluded that the COP and exergy efficiency within the range of the operating parameters in the evaluation were found to be 3.274% and 37.63%. Rui et al. [6] proposed a novel ternary mixture, R600a/R23/R14, for ARC systems for 190 K (−83˚C) applications. Their results demonstrated the feasibility of the proposed R600a/R23/R14 ternary mixture as an environmental benign alternative for Auto-Refrigeration cascade systems. Roy and Mandal [7] numerically investigated energetic, exegetic, economic and environmental performances of a 50-kW cooling capacity cascade refrigeration system using four different refrigerant pairs, namely R41/R404A, R170/R404A, R41/R161 and R170/R161. They conclude that the COP and exergetic efficiency of the system to be maximum with R41/R161 refrigerant pair followed by R170/R161 for the same operating conditions.

Roy and Mandal [8] conducted a numerical study of cascade refrigeration system using two different refrigerant pairs, namely, R41/R404A and R170/R161. They concluded that R170/R161 is in higher optimal COP as well as exergetic efficiency for system compared to R41/R404A system. The refrigeration performance parameters of two binary azeotropic mixtures of R170/R23 and R170/R116 and a ternary azeotropic mixture of R170/R23/R116 were measured systematically in the low-stage loop of a two-stage cascade system by Gong et al. [9]. They concluded that these mixtures show good potential as low-temperature stage refrigerants for applications in the −80˚C temperature range. Zou et al. [10] experimentally investigated the heat transfer coefficients for saturated flow boiling in a horizontal tube of the binary mixtures of R170/R290. They conclude that the comparison of the experimental heat transfer coefficient with the predicted value shows that the total mean deviation is 15.97% for R170/R290 mixtures. Zhuang et al. [11] compared experimental data with various well-known correlations of condensation heat transfer coefficient and pressure drop of R170 in a horizontal tube with inner diameter of 4 mm. Chen et al. [12] conducted a theoretical study on a modified vapor compression refrigeration cycle (MVRC) with zeotropic mixture R170/R290 for freezers. They concluded that the proposed cycle has potential advantages for application in the freezers. Park and Jung [13] presented the thermodynamic performance of R170/R290 mixture on a heat pump bench test in an attempt to substitute R22. They conclude that the coefficient of performance (COP) and capacity of R290 are up to 15.4% higher and 7.5% lower, respectively than those of R22 for two conditions. Sun et al. [14] presented a comparative analysis of thermodynamic performance of cascade refrigeration systems (CRSs) for refrigerant couples R41/R404A and R23/R404A to discover whether R41 is a suitable substitute for R23. They concluded that the theoretical analysis indicates that R41/R404A is a more potential refrigerant couple than R23/ R404A in CRS. Sun et al. [15] investigated the suitability of using R23, R41 and R170 in the low-temperature cycle (LTC) and R32, R1234yf, R1234ze, R161, R1270, R290 and R717 in the HTC refrigerant in CRS. They recommended R161 for use in HTC, and R41 and R170 for use in LTC. Nawaz et al. [16] evaluated the performance of R290 (propane) and R600a (isobutane) as substitutes for R134a (a HFC) for heat pump water heating (HPWH). They concluded that a significant reduction in system charge and lower condenser discharge temperatures as additional benefits. Liu and Yu [17] proposed the using of an ejector subcooling refrigeration cycle (ESRC) with zeotropic mixture R290/R170 for low temperature freezer applications. They conclude that the performance characteristics of the proposed cycle demonstrate its potential applications in low-temperature freezers. Aktemur et al. [18] proposed using R41 in low-temperature circuit (LTC), and using R1243zf, R423A, R601, R601A, R1233zd (E) and RE170 for a high-temperature circuit (HTC). They concluded that there is a maximum COP improvement of 13.05% compared to studies in the literature. Turgut and Turgut [19] presented a comparative investigation on performance analysis of cascade refrigeration systems using R744/R717, R744/R134a, and R744/R1234yf refrigerant pairs. Das and Samanta [20] conducted a comparative analysis on energy and exergy of cascade refrigeration system using different pairs of refrigerants. They concluded that R744/R717 attained the highest COP value equivalent to 7.848, and the highest ECOP value of 0.9838 was also attained by R744-R717. Xie et al. [21] proposed using the pairing consists Hydrocarbons, such as R170 and R290 as natural working fluids instead of R22/R23 in cascade refrigeration cycles. They concluded that R290/R170 can be used as the substituting refrigerants to R22/R23 in the cascade refrigeration cycle. Wang et al. [22] investigated the performance of a single-stage Linde-Hampson refrigerator (LHR) operating with six different binary refrigerants (R23/R134a, R23/R227ea, R23/R236ea, R170/R290, R170/R600a and R170/R600) with ozone depletion potentials (ODPs) of zero was conducted using a new approach at the temperature level of −60˚C. They introduced two useful new parameters, the entropy production per unit heat recuperated and the ratio of heat recuperating capacity to the power consumption of the compression. Fatouh and El Kafafy [23] conducted an investigation on Liquefied petroleum gas (LPG) of 60% propane and 40% commercial butane to substitute for R134a in a single evaporator domestic refrigerator with a total volume of 10 ft³ (0.283 m³). Their results reveal that lower on-time ratio and energy consumption of LPG refrigerator are observed by nearly 14.3% and 10.8%, respectively, compared to those of R134a refrigerator were achieved. They conclude and proposed using LPG as an appropriate long-term candidate replacing R134a in the domestic refrigerators, except capillary tube length and initial charge.

Pan et al. [24] provided a literature review of the cascade refrigeration system (CRS) to achieve an evaporating temperature as low as −170˚C. Jain et al. [25] developed a thermodynamic model for cascaded vapor compression–absorption system (CVCAS) which consists of a vapor compression refrigeration system (VCRS) coupled with single effect vapor absorption refrigeration system (VARS). They use the first and second laws of thermodynamics to perform their comparative study for a design capacity of 66.67 kW. The results show that the for CVCAS the electric power consumption is reduced by 61% meanwhile the COP of vapor compression cycle is improved by 155%. Cheng et al. [26] conducted a novel double internal auto-cascade two-stage compression system suitable for refrigerant mixtures, which can effectively modulate the concentration of the refrigerant going to the evaporator and the injection port, drive the refrigerant rich in high-pressure composition to enter the evaporator, thereby improving the system performance. Dixit et al. [27] investigated the proposal of integration of a two-stage absorption refrigeration system with a compression refrigeration system for utilizing low-temperature heat and reducing electric energy consumption. They compared this proposed system with vapor compression system from the viewpoint of energy, exergy, environment and economics. The proposed system reduces the electricity consumption by 89.3%.

Bulula et al. [28] proposed to use Medical Store Department (MSD) to the Expanded Program on Immunization (EPI) to reduce costs of the vaccine supply chain responsibilities in Tanzania. Zhao et al. [29] conducted their study on a mixed solution of tetradecane (TD) and lauryl alcohol (LA) was selected as the base liquid. They developed a new type of cold storage equipment for vaccine, which can monitor the temperature of the vaccine in real time on the user’s mobile phone. They stated that coupling the developed low temperature phase change material with the cold storage equipment can ensure that the vaccine is always in the required low temperature environment. Recently, Holm and Poland [30] stated that it is important for providers to be familiar with the practicalities of vaccine packaging, storage, preparation, and administration. Several of these vaccines require ultra-cold or have cold-storage requirements that are different than what vaccine administrators are prepared for. More recently, Mouneer [31] conducted many case studies on health and safety applications to highlight the importance of sustainable development under COVID-19 in Egypt. These cross sectional studies included the COVID-19 transportation and vaccination plan in many countries.

The research objective is to compare different pairs of refrigerants included hydrocarbon refrigerant pair Propane/Ethane namely (R290/R170) to be used in cascade refrigeration systems (CRS) to cool down the evaporating temperature to store COVID-19 vaccines which may need keeping temperature either during transportation or during storage processes at low temperature reaches to −80˚C. The aims of this objective is to evaluate the thermodynamic analysis on both the first law for COP values and the second law for exegetic efficiencies for the proposed alternatives consist of lower side and higher side refrigerant vapor compression cycles, which work together to achieve the cooling down the cold stores for COVID-19 vaccines along its journey through cold supply chain either in cold storage in cold in hospitals and clinics or in transportation via refrigerated tucks, ships, and aviation.

Holm and Poland [30] reported that each vaccine has different packaging and requirements for storage, preparation, and administration, as reported by. Recently, Shervani et al. [32] presented useful data and very important results in containing, treating and eliminating pandemic COVID-19. They Classified the COVID-19 vaccines according to its production companies, dosing, and storage requirements. More recently, Williamson [33] reported in one article on BBC that UK government have classified the COVID-19 vaccines into seven types of vaccines based on their origin countries in the as follows: 1) Oxford University AstraZenca of UK, 2) Moderna (mRNA−1273), 3) the Pfizer-BioNTech (BNT162b2), 4) Gam-COVID-Vac Sputnik V, the Russian vaccine, 5) CoronaVac (Sinovac), the Chinese vaccine, 6) Novavax, the American vaccine, and 7) Johnson & Johnson (JNJ-78436735), as reported in BBC by Williamson [33], as can be seen in both Figure 2(a) and Figure 2(b). Figure 2(a) depicts the COVID-19 classification in tabulated form as shown in Figure 2(a). Meanwhile, Figure 2(b) compares between the final prices for most of these vaccines, using the bar chart for the cost per jab of COVID-19 vaccine candidates, presented by

McCarthy [34]. Figure 2(c) shows the HIV vaccine enterprise for COVID-19 vaccine research as reported by AVAC [35]. Figure 3 shows the classification of the COVID-19 vaccines. Figure 3(a) displays the transportation container used to keep the COVID-19 vaccine in −80˚C, meanwhile Figure 3(b) shows the standard COVID-19 vaccine bottle. The first vaccine type, produced by the company Moderna named (mRNA−1273), which also acts on the mechanism of mRNA. It has dosing schedule consists of two doses, 28 days apart. This type requires Frozen between −13˚F to 5˚F (−25˚C to −15˚C). It can be stored refrigerated from 36˚F to 46˚F (2˚C to 8˚C) for up to 30 days prior to first use. Sinopharm’s vaccine can be stored at 2 to 8˚C (36˚F to 46˚F), or a normal refrigeration temperature. The second vaccine is produced by Sino pharm company (China) named CoronaVac or SinoVac, as shown in Figure 3(e). The third vaccine type produced by two joint venture companies Pfizer/BioNTech named (BNT162b2), as can be seen in Figure 3(c), acts on the mechanism of mRNA. It has dosing schedule consists of Two doses, 21 days apart. This type requires Ultra-cold freezer works between −112˚F to -76˚F (−80˚C to −60˚C) for up to 6 months. The fourth vaccine is Russian vaccine and it has named Sputnik V. The fifth vaccine is produced by Johnson & Johnson/Janssen (JNJ) companies and it has named JNJ-78436735, as shown in Figure 3(d). It has one dosing schedule and two-dose regimen is under evaluation. It is stable for 2 years at −4˚F (−20˚C) but can be stored for at least 3 months at typical refrigeration temperatures of 36˚F to 46˚F (2˚C to 8˚C). The sixth vaccine is the American vaccine and it is produced by Novavax company.

Figure 4 presents the cold stores and freezers for transportation and storage for the COVID-19 vaccines. The vaccine refrigerators and refrigeration machines can be classified into three types according to energy sources as follows: 1) vapor compression units which are electric power driven machines as can be seen in Figure 4(a) and Figure 4(b), 2) photovoltaic units which use solar energy driven machines as can be seen in Figure 4(c), and 3) absorption units which named bottled gas or kerosene driven machines as can be seen in Figure 4(d). Ice-lined refrigerators are the preferred option where there is reliable mains electricity for at least eight hours per day. Even with periodic breaks in electricity, the inner lining of the unit can preserve the +2˚C to +8˚C holdover time. A few models are available that can operate effectively on as little as four hours of

electricity per day. Ice-lined refrigerators can expose vaccines to freezing temperatures if vaccines are not loaded properly. Solar energy refrigerators (photovoltaic units) are more expensive to buy and install than electric refrigerators, but they have no running costs, apart from cleaning and preventative maintenance. There are two types for solar refrigerators which are: 1) solar-battery units connected to a battery bank, which is charged by the solar panels, and 2) solar direct-drive units that are powered directly by the solar panels. Absorption units Bottled gas (or kerosene) refrigerators may be necessary in places where there is insufficient sunshine for a solar-powered unit. Gas-powered units are better than kerosene models because they need less maintenance and have better temperature control. Bottled gas and kerosene refrigerators can expose vaccines to freezing temperatures. Keeping vaccines in the +2˚C to +8˚C range is particularly difficult with kerosene refrigerator. Another classification for refrigerators and their types is presented according to mobility and transportation as follows: 1) Cooling stores (rooms) as can be seen in Figure 4(e), and 2) Portable (Mobile) fridge as can be seen in Figure 4(f). Outdoor events that affect vaccine can be a major concern without adequate cold storage containers with necessary cooling capacity. This is the very reason pharma companies recommend to use mobile fridge and cold storage solutions. Several refrigerated compartments and buildings were designed for storage vaccine in an environment below the outdoor temperature. Many vaccines must be stored at low temperatures, some below −15˚C (between −25˚C and −15˚C), and others between 2˚C and 8˚C. If vaccines are not stored correctly, they can lose their effectiveness.

A cascade refrigeration cycle can be considered as a multi-stage compression thermodynamic refrigeration cycle. In the cascade refrigeration system, more than one vapor compression cycles (two or more) with more than one refrigerant are circulated as primary refrigerants. The evaporating and the condensing temperatures of both cycle are sequentially lower with some overlap to achieve the desired total temperature drop, with carefully selected refrigerants to efficiently work in the desired temperature range they have been designed to provide it together. The low temperature cycle absorb heat from the cold store to be cooled down using the low temperature cycle evaporator, then it transfers this removed heat to a heat exchanger, namely cascade condenser, is cooled by the evaporation of the refrigerant of the high temperature cycle. Therefore, the high temperature cycle transfers this amount of heat to the condenser of the high temperature cycle, to carry the rejected heat outside of the cascade refrigeration system, either using air cooled condenser associated with fans, or water cooled condenser associated with cooling water pumps and cooling towers. In the current thermodynamics analysis, a two-stage cascade system uses two pairs of compressor plants, working individually with different refrigerants, connected among themselves so that evaporator one system is used to serve as the capacitor to a lower temperature of the system (i.e. the evaporator with the first unit cools the condenser of the second unit). In practice, an alternative approach utilizes a common capacitor with a booster circuit to provide two separate temperature of the evaporator. Clearly, diagram in two stages of the cascade refrigerating system, as shown that the compressor is reduced and the amount of cooling load (capacity) in the evaporator increases as a result of the cascade. Figure 5 depicts the Cascade Refrigeration System (CRS), which is proposed in the current study as innovative refrigeration system for COVID-19 vaccines transportation and storage. Figure 5(a) and Figure 5(b) demonstrate the presentation of cascade refrigeration cycle (CRS) with its both individual cycles consists of low temperature cycle (LTC) and high temperature cycle (HTC) on T-s diagram and p-h diagram, respectively, as presented by Aktemur et al. [18], for both cycles LTC and HTC. Figure 5(c) shows line diagram for cascade refrigeration cycle with LTC and HTC, as presented by Alhamid et al. [36]. They conducted a study to investigate the characteristics and COP of cascade refrigeration system using hydrocarbon refrigerant (Propane, Ethane) and CO₂ at LTC. Their study constructed a prototype cascade refrigeration machine using the environmentally friendly hydrocarbon refrigerants (Propane, Ethane) and CO₂. Their results are that the characteristics of the pressure and temperature of each component and the COP value at low temperature circuit of load variations using an electric heater at 90 W, 120 W and 150 W result in a COP value of 0.35, 0.48 and 0.60, respectively.

As can be seen on Figure 5(b), the p-h diagrams dramatically influence the performance of the selected refrigerant, due to its thermodynamic properties. Figure 6 depicts the methods can be used to classify the refrigerant either based on their chemical composition, as can be seen in Figure 6(a), or based on their working temperature ranges, as can be seen in Figure 6(b). The decision tree is shown in Figure 6(a). depends on classifying the refrigerants into three groups; which are; the first group is HCFC group, such as R22, R23, R32, and R410A, the second group is HFC group, such as R123, R134a, and R407c, and the third group is Halogen free refrigerant either pure hydrocarbon refrigerant such as R50 (pure Methane), R170 (pure Ethane), and R290 (pure Propane), or Inorganic such as NH₃, and CO₂. The hydrocarbon refrigerant may have active mixtures as mixture hydrocarbon refrigerants such as Propane/Iso-butane, as can be seen in Figure 6(a). On the other hand, Figure 6(b) classifies the refrigerant tested in the current article to achieve this research goals into three groups based on their working temperature ranges, which are high temperature ranges such as

R404, R407c, R410 and R507, Low temperature ranges such as R22 (used as base case only), R32, R123 and R134a, and Ultra Low temperature such as R170, and R290, as shown in Figure 6(b).

The research methodology aims to present a thermodynamic analysis on both first law and second law of thermodynamics for proposed cascade refrigeration systems using coupling of refrigerants. This cascade refrigeration system (CRS) is proposed to cool down the evaporating temperature to store COVID-19 vaccines which may need keeping temperature either during transportation or during storage processes at low temperature reaches to −80˚C. The numerically investigated cascade refrigeration machine consists of two refrigeration circuits, of low temperature cycle and high temperature cycle. The first refrigeration cycle is the high-temperature circuit (HTC) using several environmentally friendly refrigerants such as R22 as old reference commonly used since 1960s, R32, R123, R134a, R404, R407c, R410, and finally the most promising pure hydrocarbon refrigerant which is the propane namely as R290. On the other side, the second refrigeration cycle in the current study is the low temperature circuit (LTC) which uses also a pure hydrocarbon refrigerant namely Ethane (R170). Both systems are simulated to be interconnected to each other through the intermediate heat exchanger (also can be named cascade condenser), as can be seen in Figure 5(c). This intermediate heat exchanger is commonly used of the plate heat exchanger type. The different expansion devices of HTC and LTC are due to the fact that working pressures are not the same between the two circuits, as reported by Alhamid et al. [36]. The working principle between HTC and LTC are the same as a refrigeration cycle in general. The current research methodology focusses the interest on evaluating the commonly used parameters and metrics for both the energy analysis and the exergy analysis of the proposed CRS using different refrigerant pairs under different operating conditions by varying the intermediate temperature (T_inter) from −25˚C to +5˚C.

The results of the first law of thermodynamics for the coefficients of performance discharge temperatures for both LTC and HTC, T_{discharge, 2} and T_{discharge, 6}, respectively, are presented in Figures 7-9. The discharge temperatures for both LTC and HTC, (T_{discharge, 2} and T_{discharge, 6}), respectively, are plotted versus different intermediate temperature (T_inter) −25˚C, −15˚C, −5˚C, and +5˚C. The results of the specific power consumptions (SPCs) in kW/TR are presented in Figures 10-12, and discussed in the next subsection 4.2. Figure 7 shows the coefficients

of performance and discharges temperatures (T₆ at HTC) for three refrigerant pairs (R32/R170, R123/R170 and R134a/R170) versus different intermediate temperature (T_inter) −25˚C, −15˚C, −5˚C, and +5˚C. Figure 8 displays the coefficients of performance and discharges temperatures (T₆ at HTC) for three refrigerant pairs (R404/R170, R407c/R170, and R410/R170) versus different intermediate temperature (T_inter) −25˚C, −15˚C, −5˚C, and +5˚C. Figure 9 shows the coefficients of performance and discharges temperatures (T₂ at LTC and T₆ at HTC) for two refrigerant pairs (R22/R170 and R290/R170) versus different intermediate temperature (T_inter) −25˚C, −15˚C, −5˚C, and +5˚C.

The current numerical analysis applied by the first law of thermodynamics gives that the SPCs for CRS applications in the COVID-19 vaccines transportation and storage is starts from 4.8 kW/TR up to 6 kW/TR. The results of specific power consumptions (SPCs) in kW/TR are presented in Figures 10-12, for the three sets of refrigerant pairs versus different intermediate temperature (T_inter) of −25˚C, −15˚C, −5˚C, and +5˚C. Figure 9 depicts the SPCs per refrigerated tonnage in kW/TR for the refrigerant pairs (R32/R170, R123/R170 and R134a/R170) versus different intermediate temperature (T_inter) of −25˚C, −15˚C, −5˚C, and +5˚C. Figure 9 shows that the pair R123/R170 gives the minimum SPC at 4.8 kW/TR, numerically recorded for T_inter = −10˚C and −5˚C. For other pairs, which contain high temperature range as HTC, as can be seen in Figure 6(b), such as R404/R170, R407c/R170, and R410/R170, the results depicted from Figure 11 give that all of them have the highest three values of the specific power consumption from 5.5 to 6.6 kW/TR, numerically recorded for all T_inter temperature range from −25˚C to 5˚C, as can be seen in Figure 11. Therefore, it will be recommended to not use these three pairs tested in this article objective either in the presence of the COVID-19 pandemic or after this pandemic. However, Figure 12 shows that the base case used for this current study, which is R22/R170 gives the minimum specific power consumption at 5.2 kW/TR, numerically recorded for T_inter = −5˚C. Meanwhile, the highly recommended HC refrigerant pair in this article, which is depending on pure hydro carbon pair consists of both Ethane (R170) in LTC and Propane (R290) in HTC, gives almost constant and moderated value of the specific power consumption from 5.4 to 5.7 kW/TR, numerically recorded for all T_inter, as can be seen in Figure 12.

The exergetic efficiency (η_exergetic) is one of the most important parameters of the second law of thermodynamics. The current thermodynamic analysis gives that exergetic efficiencies (η_exergetic) for CRS applications in the COVID-19 vaccines transportation and storage starts from 25% up to 43%, as can be seen in Figures 10-12. Figure 10 depicts the η_exergetic for the refrigerant pairs (R32/R170, R123/R170 and R134a/R170) versus different intermediate temperature (T_inter) of −25˚C, −15˚C, −5˚C, and +5˚C. Figure 11 shows the exergetic efficiency (η_exergetic) for the refrigerant pairs (R404/R170, R407c/R170 and R410/R170) versus different intermediate temperature (T_inter) of −25˚C, −15˚C, −5˚C, and +5˚C. Figure 12 shows the exergetic efficiency (η_exergetic) for two refrigerant pairs (R22/R170, and R290/R170) versus different intermediate temperature (T_inter) of −25˚C, −15˚C, −5˚C, and +5˚C. Figure 10 presents the pair R123/R170 gives that the η_exergetic is recorded its numerically maximum value equal to 43%, at T_inter = −5˚C. Figure 11 presents that results of the three pairs of high temperature range as HTC, which are R404/R170, R407c/R170, and R410/R170 as classified in Figure 6(b), give that all of them have the lowest three values of the η_exergetic and its range starts from 25% to 32% and 39%, as can be seen in Figure 11. These findings confirm on the recommendations of applying the first law of thermodynamics by calculating the specific power consumption per refrigerated tonnage for CRS. Figure 12 shows that the base case used for this current study, which is R22/R170 gives a stable and relatively minimum values of the η_exergetic which starts from 30% to 32% as recorded for T_inter = −25˚C and −15˚C. On the other side, the most promising pair in future few decades, which is proposed in current article as well as R290/R170 gives almost constant and moderated value of the η_exergetic of 30% at T_inter = −25˚C, −15˚C, and +5˚C, however, it increases rapidly to 40% at T_inter = −5˚C, as can be seen in Figure 12.

These findings of both Energy and Exergy Analysis reveal the opportunity of using the pair consists of R290/R170 is highly recommended in these vaccine applications, besides, the unfeasibility of using some pairs in these transportation and storage applications such as R404/R170, R407c/R170, and R410/R170. The data and results presented in this article are very important and useful in providing the refrigeration solutions to containing the transportation and storage missions by production companies, and governments in many countries during the existing pandemic COVID-19.