WExp 2: Work output for Exp 2

The R/G fraction, which is the ratio of the re-liquefied flow rate to the BOH generation flow rate, is estimated using Equation (2). The SEC is defined by Equation (3) to evaluate the energy required to re-liquefy the 1 kg of BOH. Because the re-liquefaction system utilizes the cold energy of the hydrogen, the SEC varies with the R/G fraction.

$$\text{R/G fraction} = \frac{\dot{\text{m}}\_{\text{re-liquefaction}}}{\dot{\text{m}}\_{\text{BOH}-\text{generation}}} \times 100 \text{ \%} \tag{2}$$

$$\text{SEC} = \frac{\dot{W}\_{\text{net}}}{\dot{\text{m}}\_{\text{re}-\text{liquefaction}}} \tag{3}$$

. mBOH−generation: Mass flow rate of the generated BOH . mre−liqeufaction: Mass flow rate of the re-liquefied BOH

In thermodynamics, physical flow exergy refers to the maximum useful work delivered to an external user as the stream reaches the dead state [30]. Considering refrigeration systems, it refers to the reversible and minimum work required for refrigeration to occur at a certain state. The physical flow exergy of stream can be estimated using Equation (4) [31]. In Equation (4), subscripts S and 0 refer to present state of the stream and dead state, respectively. Subscript \*\* means state that has same temperature with the dead state and same pressure with the present state. The first two terms in Equation (4) corresponds to thermal exergy, which is the physical exergy from the temperature difference of the stream with the dead state. The last two terms represent mechanical exergy, which is the physical exergy from pressure difference of the stream with the dead state.

$$\mathbf{E\_{S}} = \mathbf{E\_{T}} + \mathbf{E\_{M}} = (\mathbf{H\_{S}} - \mathbf{H\_{\*\*}}) - \mathbf{T\_{0}}(\mathbf{S\_{S}} - \mathbf{S\_{\*\*}}) + \mathbf{T\_{0}}(\mathbf{S\_{0}} - \mathbf{S\_{\*\*}}) - (\mathbf{H\_{0}} - \mathbf{H\_{\*\*}}) \tag{4}$$

ES: Physical flow exergy of stream

ET: Thermal exergy of stream

EM: Mechanical exergy of stream

HS: Enthalpy of stream at present state

H∗∗: Enthalpy of stream at state \*\*

H0: Enthalpy of stream at dead state

SS: Entropy of stream at present state

S∗∗: Entropy of stream at state \*\*

S0: Entropy of stream at dead state

T0: Ambient temperature

During re-liquefaction, the irreversibility between processes causes exergy loss. To calculate this exergy loss, the physical exergy difference between inlets and outlets of a component can be used [32]. This exergy loss makes the system less efficient and require more work than an ideal system. From this point of view, the system exergy efficiency can be estimated using the numerical indicator *ηex* via Equation (5).

$$\eta\_{\text{ex}} = \frac{\dot{\mathcal{E}}\_{\text{re}-\text{liquefaction}-\text{in}} - \dot{\mathcal{E}}\_{\text{re}-\text{liquefaction}-\text{outlet}}}{\dot{\mathcal{W}}\_{\text{net}} + \dot{\mathcal{E}}\_{\text{BOH to PEMFC}-\text{in}} - \dot{\mathcal{E}}\_{\text{BOH to PEMFC}-\text{out}}} \tag{5}$$

. Ere<sup>−</sup>liquefaction<sup>−</sup>in: Physical flow exergy of Stream 102 . Ere<sup>−</sup>liquefaction<sup>−</sup>outlet: Physical flow exergy of Stream 105 . EBOH to PEMFC−in: Physical flow exergy of Stream 106 . EBOH to PEMFC−out: Physical flow exergy of Stream 108

### *3.2. Economics*

CAPEX is defined as the initial investment required to construct a plant [33], and it consists of the direct project expenses, indirect project expenses, contingency and fee as depicted in Figure 2. The direct expenses encompass the equipment costs, material costs, and labor costs required to install the equipment. The indirect project expenses include the freight costs, insurance, and taxes. They also include the overhead costs required to construct the plant. The contingency is the cost that covers unforeseen circumstances, while the fee is related to the contractors. Among these costs, the sum of the direct and indirect costs is called the bare module cost. The contingency and fee are assumed as 15% and 3% of the bare module cost, respectively. The bare module cost for each component is estimated using the Aspen Capital Cost Estimator V11.

**Figure 2.** Composition of CAPEX.

OPEX is defined as the costs associated with the day-to-day operations of a plant [33]. OPEX consists of direct manufacturing costs, fixed manufacturing costs, and general manufacturing expenses as depicted in Figure 3. The direct manufacturing costs are the operating expenses, which vary with the production rate. They include raw materials costs, utilities costs, and operational labor. The fixed costs are independent of changes in the production rate. They include taxes and insurance. The general expenses are overhead costs that are necessary to carry out business functions. They include administration, distribution and selling costs, as well as costs for research and development. Equation (6) [33] is used to estimate OPEX. Table 2 shows the specific values used to estimate CAPEX and OPEX.

$$\text{OPEX} = 0.18 \,\text{CAPEX} + 2.73 \,\text{C}\_{\text{OL}} + 1.23 \,\text{(C}\_{\text{UT}} + \text{C}\_{\text{WT}}\text{)}\tag{6}$$

COL: Cost of the operator salary CUT: Cost of utilities CWT: Cost of the cooling water

**Figure 3.** Composition of OPEX.

**Table 2.** Cost values for CAPEX and OPEX estimation.


The life cycle cost (LCC) is defined as the total costs required to install and operate the system during the life cycle [33]. It is estimated using Equation (7). The specific life cycle cost (SLCC) is defined as the LCC required for 1 kg of BOH, which is estimated using Equation (8). Additionally, the cost difference is defined as the difference between the LH2 production cost and SLCC, as expressed by Equation (9).

$$\text{LCC} = \text{CAPEX} + (\text{LifeCycle}) \times \text{OPEX} \tag{7}$$

$$\text{SLCC} = \frac{\text{LCC}}{\dot{\mathbf{m}}\_{\text{re-liquefaction}}} \tag{8}$$

(Cost difference) = (LH2 production cos t) − SLCC (9)
