**2. Materials and Methods**

### *2.1. Selection of the Modeling Basis*

Although only a handful different types of liquefaction process are used in current operating LHL plants, a wide range of improved processes have been proposed. In the present study a comprehensive review of the various improved liquefaction technologies is outside the scope of work. Instead, a single, representative, improved process was selected to be used as the basis for the present study. The details of the selection process are described below.

Because the results from this study are intended to support further research in future low-carbon energy supply and, specifically, how different supply chain configurations affect efficiency, the improved concepts of most relevance are those technologies likely to be used in the near future. Taking the techno-economic analysis of Cardella et al. [30] as a basis, the improved technology that fits best with the aim of the study is the use of a mixed refrigerant (MR) for pre-cooling of the hydrogen feed stream.

Most current, and much improved, hydrogen liquefaction processes are based on the division of the overall process into two parts: a pre-cooling step and a cryogeniccooling step. In conventional LHL plant designs, the pre-cooling stage often uses liquid nitrogen (LIN) as a refrigerant, whereas the cryogenic-cooling step uses either helium in a Brayton cycle, or hydrogen in a Claude cycle [18]. In the cryogenic step, the hydrogen feed is generally cooled from below around −90 ◦C to the final liquefaction temperature. Although the break-point temperature between the pre-cooling and the cryogenic step, *T*p, is potentially an optimization variable, the present study assumes that the impact of ambient temperature on operating parameters in the cryogenic step is small and, therefore, that *T*p can be fixed.

Typical of the concepts for improved energy consumption using MRs is the process studied in the work of Skaugen et al. [17], which is based on a Claude cycle in cryogeniccooling step and a MR in the pre-cooling step. In this process the pre-cooling step and the portion of the cryogenic step that operates above *T*<sup>p</sup> are not integrated. This allows the present study to consider the optimization of the pre-cooling process independently from the operation of the cryogenic-cooling process. In addition, because the details of the composition and operating conditions for the proposed MR cycle are clearly set-out in the work of Skaugen et al. [17], the present study uses the work of Skaugen as the basis for model development and validation.

Although the operating parameters in the cryogenic-cooling step are assumed fixed in the present study (i.e., they are not affected by ambient temperature), the energy consumption of the cryogenic-cooling cycle compressor is still affected by the exit temperature that the inter and after-coolers, *T*c, are designed to operate with, which would normally be set relative to the ambient temperature of the seawater, or air, used as the heat-sink. Because of this, modelling of the performance of the cryogenic cycle compressor as it varies with *T*c does form part of the present study.

Another important factor in the design and optimization of hydrogen liquefaction processes is the conversion of ortho to para hydrogen. This process releases a significant quantity of heat, affecting both the process design and the selection of optimum operating parameters. The conversion of the ortho isomer during liquefaction is typically promoted using a catalyst. The effectiveness of the catalyst and the residence time in the heat exchangers affects the approach to the equilibrium concentration and, subsequently, the temperature profile in the heat exchangers. However, across the range of temperatures experienced in the pre-cooling process, the equilibrium concentration of para hydrogen varies by less than 5% [21]. Moreover, as in the study of Skaugen et al. [17]—which is a reference case for this study—catalytic conversion is assumed after the pre-cooling process. This will result in a low approach to the equilibrium conversion in the pre-cooling process and, therefore, in this study the modelling of the conversion of ortho to para hydrogen is set outside the scope of work.

## *2.2. Process Model Development*

As described above, the process model used in this study consists of two separate parts: a model of the MR pre-cooling step, and a model of the cryogenic-cooling step cycle compressor. The development of these two models is described below. A block diagram showing the relationship between the cryogenic-cooling step and the pre-cooling step is also presented in Appendix A.

Figure 1 illustrates the process flow scheme used for the MR pre-cooling process, which is based on the flow scheme used in the reference study of Skaugen et al. [17]. The main equipment items shown in Figure 1 are a compressor (comprising RC-1 and RC-2), two process coolers (PC-1 and PC-2), a MR separator (VV-1), a pump (PP-1), and the main heat exchanger (HX-1). The MR compressor comprises two stages (RC-1 and 2), both with after-cooling (PC-1 and 2) to *T*c. Any liquids condensed liquids after the first stage are separated in VV-1. Liquids separated in this way are pumped (PP-1) to the compressor discharge pressure—bypassing the second stage of compression (RC-2)—and mixed with the vapor stream entering the main heat exchanger (HX-1). The main heat exchanger is modelled as a multi-stream type heat exchanger with two hot streams: H2 and high-pressure MR, and one cold stream: low-pressure MR. The low-pressure MR stream exiting the main heat exchanger returns to the MR compressor. Hydrogen leaving HX-1 is cooled to *T*p.

**Figure 1.** Flow diagram for the MR H2 pre-cooling process.

To allow the calculation of process energy consumption a simplified model of the process presented in Figure 1 was developed in MATLAB [31] with the TREND software package [32] used to calculate thermo-physical properties. Table 1 presents the set of fixed modelling parameters, MP, used in the model of the MR pre-cooling process. In general, the parameters in Table 1 were selected to reflect those used in the reference study [17].


**Table 1.** Summary of MR process fixed modelling parameters.

\* Isentropic efficiency.

For simplicity, the pressure-loss in the main heat exchanger was scaled linearly with temperature and the two MR streams were assumed to be mixed before entering the heat exchanger and the combined MR stream enters the main heat exchanger at the H2 feed temperature.

The temperature profiles for the combined hot streams and the cold stream in HX-1—the hot and cold composite curves—were estimated by splitting the heat exchanger into *n* equally sized temperature intervals, each sized (*T*in − *T*out)/*n* and stream enthalpies calculated for each temperature point (*n* + 1, total). Then the heat exchanger duty was also split into *n* equally sized intervals (*Q*HX−1/*n*), and the hot and cold composite temperatures, *T*HC and *T*CC, interpolated at each point (*n* + 1, total) using linear interpolation of the temperature-enthalpy data. Finally, the temperature approach was calculated for each point, Δ*T* = *T*HC − *T*CC. In both cases, *n* was set to 50 to give a high degree of accuracy to the calculations.

Figure 2 provides a sketch of the cycle compressor (comprising H2-1 to 4) for the cryogenic-cooling step which forms the basis of the present study. The stream LP H2 represents the low-pressure hydrogen stream returning from the liquefaction process. This stream is compressed in two compressor stages (H2-1 and H2-2) before blending with medium-pressure hydrogen. The combined stream is then compressed in two further compressor stages (H2-3 and H2-4) before being passed-back to a multi-stream heat exchanger (HX-2), which cools the HP stream down to *T*p. The compressor inter-stage pressures are calculated assuming equal stage pressure ratios.

**Figure 2.** Flow diagram of the cryogenic-cooling step H2 cycle compressor.

The model of the cryogen-cooling step compressor shown in Figure 2 was also developed in MATLAB using the same basis as the MR process model. Table 2 presents the fixed modelling parameters used in the study performance of this compressor, which are based on the reference model [17]. The outlet temperature of the four after-coolers (PC-3 to 6) were assumed equal to *T*<sup>c</sup> and the inlet temperature of the LP and MP streams to the compressor was assumed to have a 2 ◦C approach to *T*<sup>c</sup> in all cases.


**Table 2.** Summary of fixed modelling parameters for the cryogenic-cooling cycle compressor.

Isentropic efficiency.

In addition to the cycle compressor, the reference study describes several turboexpanders within the cryogenic cooling step. These produce 2.8 MW of shaft power, which is assumed in the reference study to be recovered as electrical energy with as efficiency of 80% [17]. Assuming, as before, that the parameters in the cryogenic process remain constant with varying *T*c, this recovered energy equates to a specific energy production for the expanders, SECEx, of approximately 0.43 kWh/kg, which is a constant value for all cases studied in this work.

Where operating parameters were not available in the reference study, they have been inferred from the data that is presented there. Because of this, it cannot be claimed that there is any direct equivalence between the results presented here and the reference model.

#### *2.3. MR Pre-Cooling Model Validation*

An important aspect of successful optimization is the minimization of temperature differences in HX-1, and since the targeted minimum approach temperature is only 1 K, the accuracy of the property predications used in the process model is very important. In the TREND software package, several properties methods are available; to select the basis that is most appropriate for the present work, three of these were compared against results from the reference study: Peng Robinson (PR), Soave-Redlich-Kwong (SRK) and the TREND Helmholtz free energy model. Tables 3 and 4 present the parameters used in the validation work. The results of the validation work were used to select the properties method used in the later optimization work.

**Table 3.** Validation case MR composition.


**Table 4.** Validation case MR modelling parameters.

