To configure the BOG re-liquefaction system for an ammonia fueled ship, the size of the fuel tank was first determined. Even for the same ship type, the size of the fuel tank may vary depending on the ship owner's requirements and the ship's route. In this paper, the capacity of the fuel tank was calculated based on the size needed for a 60-day voyage at the normal power output (NCR) of the main engine applied to a 320, 000 dwt VLCC, and the tank size was set to 15, 000 m³ considering the loading limit [13]-[15]. The process design for the BOG treatment system can be carried out by knowing the amount of BOG that needs to be treated. Calculations were performed by referring to the surface area and insulation thickness information of the Type-A tank applied to the actual project [16]. The IMO type-A tank is primarily used in VLGC and VLAC for actual project. The calculation was performed based on spray-type insulation, which has recently been widely used as insulation for Type-A tanks in ships, and the thickness of the insulation was set at 125 mm, the same as the thickness of insulation for LPG and ammonia carriers [17][18]. According to research by Marina Gravit et al., the thermal conductivity of PUF (polyurethane foam) and PIR (polyisocyanurate) insulation materials, which are commonly used in Type-A independent tanks of ships, varies depending on the supplier. In this study, the boil-off rate (BOR) was calculated using the thermal conductivity of BASF’s PUF material, as shown in the equation (1) below [17].

Where Q represents total heat flow rate, ρ represents density of fluid, HV represents evaporation latent heat of fluid, and VL represents tank volume of fluid.

The BOR of the tank was calculated using Equation (1), based on a thermal conductivity of 0.028 W/m·K[17], resulting in a BOR of 0.065%/day.

The values applied in the calculation are shown in Table 1, and the capacity of the evaporative gas treatment system was calculated by adding a 30% design margin, considering heat inflow from the pipe to the evaporative gas generation amount of 267.7 kg/h, resulting in 348.0 kg/h.

The configuration of ammonia BOG re-liquefaction process is as shown in Figure 1.

Figure 1: 
Configuration of ammonia re-liquefaction system

The evaporation gas generated from the fuel tank is supplied to the (1) compressor. At this time, a knockout drum (9) can be placed in front of the compressor to remove liquid droplets that may be contained in the evaporation gas. The compressor type is a three-stage reciprocating compressor, primarily used for ammonia and LPG carriers. Although the three-stage reciprocating compressor is more expensive compared to the screw type, it is widely used on actual ships because there is no contamination by lubricant in the gas handling system. The gas compressed in the first stage of the compressor is mixed with the side stream from the (2) heat exchanger and supplied to the second stage of the compressor. The side stream fluid is fed through (6) Joule-Thomson valve, resulting in additional cooling of the ammonia in the (2) heat exchanger. The subsequent expansion of the fluid through the (5) Joule-Thomson valve into the tank decreases the vapor fraction. The gas compressed in the second stage is supplied to the third stage of the compressor through (7) a heat exchanger for cooling the gas on the second stage discharge side. The pressurized gas in stage 3 is supplied to the (4) receiver tank through the (3) condenser. Cooling medium of the system is glycol water which is supplied from ship’s utility system. Ammonia supplied to the receiver tank is basically in a supercooled state, so no evaporation gas is generated, but gases generated by nitrogen, air, etc., are discharged through the pressure control valve (8).

The ammonia tank's BOG treatment system does not need to consider various substances and only needs to address the discharge of ammonia and a small amount of nitrogen that may be included during operation. Thus, the process system can be configured more simply than the LPG re-liquefaction system.

The coolant for cooling and condensing ammonia is 32°C seawater and 36°C glycol water. Since the amount of BOG that needs to be reliquefied is 348.0 kg/h and the flow rate is not large, glycol water was considered as the coolant, and the minimum approach temperature for the heat exchanger was used. When calculated at 3°C, ammonia could be cooled to 40°C in the condenser. The saturation pressure of ammonia at 40°C was 14.5 bar based on the application of the e-NRTL equation of state, which can be expressed as Equation (2) below [19][20].

Where γ_i represents activity coefficient of component i, τ_ji represents interaction parameter for component between components j and i, x_j represents Mole fraction of component j, G_ji represents Gibbs energy of component j with respect to component i.

The Equation (2) provided is used to calculate the natural logarithm of the activity coefficient (ln γ_i) of component i in a multicomponent system. This equation is typically used in thermodynamic models to describe non-ideal behavior in liquid mixtures. Each term in the equation has a specific role in determining how the interactions between different components affect the activity coefficient of the component in question [20].

Discharge pressure of the compressor was 15.5 bar, considering the design margin. Applicable compressors include piston compressors, screw compressors, and turbo compressors. Piston compressor is applied, and it was determined that a three-stage compressor would be suitable since the compression ratio of the compressor to be applied is 16.3. The process system design is shown in Figure 2.

Figure 2: 
HYSYS Simulation for ammonia re-liquefaction system

As shown, the evaporated gas generated in the fuel tank is routed to the compressor's suction side through a knockout drum and is then compressed to 15.5 bar using a three-stage compressor. The temperature of the side stream is 36°C, which means that the inlet of the second stage is above ambient temperature, necessitating the use of an intercooler at the discharge side of the second stage for cooling. The gas, compressed to 15.5 bar at the discharge side of the third stage, is then cooled and condensed to 40°C in the condenser.

The fluid supplied to the target process is essentially pure ammonia, and any nitrogen component that may be included in the evaporative gas immediately after ammonia fuel bunkering is discharged during relatively short-term operation. Therefore, in this optimization program, which aims at optimizing steady-state operation, nitrogen was not considered as a variable. Based on the process system modeling results, the supply pressure for the evaporative gas treatment system was set to an initial value of 0.1 bar, and the discharge pressure was set to 15.5 bar. Efficiencyrelated variables of the process system, such as power consumption, cooling capacity, and the COP, are shown in Table 2.

In the ammonia re-liquefaction process, the optimization objective is defined as minimizing the total power consumption of the entire process required to reliquefy the evaporative gas generated in the tank. Therefore, the optimization objective function was set to power consumption. Accordingly, as shown in Table 3, the discharge pressure of each stage of the compressor and the flow rate of the side stream were selected as variables.

To perform optimization, it is important to set each variable of the system so that the process system can be practically implemented. For example, if the minimum temperature approach (MTA) of the heat exchanger is optimized to be below 3°C, the system efficiency may be high, but the heat transfer area of the heat exchanger might become too large, or it might be impossible to design the heat exchanger in practice. And log mean temperature difference (LMTD) has a limitation as well due to similar reason. Therefore, constant variables like MTA and LMTD are decided based on engineering practice. For cooling water, although lower temperatures can increase system efficiency, the cooling freshwater temperature available on the ship is 36°C, so consideration of the cooling water temperature is necessary. The compression ratio for each stage of the compressor was set to be 3 or less, and the outlet temperature of each stage was set to be below 170°C. The temperature of the evaporative gas supplied to the re-liquefaction system was set to -20°C, considering the saturation temperature of the fuel tank and the temperature rise in the main gas pipe. The related variables were set as constraint variables, and the input values for each constraint variable are shown in Table 4.

This optimization problem is about finding the optimal values of decision variables that minimize or maximize an objective function under constraints. Constraints are conditions that the solution must satisfy, the objective variable is the target to be minimized or maximized, and decision variables are the variables whose values need to be determined.

- Black-box Optimization:The model to be optimized is configured based on the commercial simulation software Aspen HYSYS. The HYSYS tool itself inherently has several calculation functions capable of performing calculations related to heat, material, and energy. However, users cannot directly access the embedded equations nor obtain information about these equations, making it impossible to use them directly for optimization. Therefore, optimization of the target process becomes a type of optimization where some objective and constraint functions cannot be easily utilized, and the only information readily available to users is the output values for given input values. In other words, an optimization algorithm that only utilizes input and output values for calculations is needed for optimization.

- Optimization with Constraints:As mentioned earlier, there are several constraints associated with this process. In particular, the target process necessarily includes a heat exchanger, where physical constraints such as MTA and LMTD are typically used. These two constraints are the most important inequality constraints in this optimization and must be satisfied. Therefore, to find an optimal solution that does not violate these constraints, an algorithm capable of handling constraints is required. In this study, it was determined that applying the penalty function method, which converts constrained problems into unconstrained problems, is necessary.

In this paper, we used the Genetic Algorithm (GA), a method that represents possible solutions to the problem in a predefined data structure and gradually transforms them to produce increasingly better solutions, combined with the penalty function method.

The structure of the optimization program, as shown in Figure 3, is based on the process of inputting initial values into the HYSYS model and running Python code. The Python code then sends these values as inputs to HYSYS and receives the calculation results as outputs.

Figure 3: 
Schematic of Optimization process

The input and output values are handled by an optimization solver implemented in Python, which conducts the optimization process. Since continuous interaction with HYSYS is required to exchange input and output values, it is essential to maintain an organic connection with HYSYS and ensure that data is neither deleted nor lost. Once the optimal solution is obtained through the optimization solver, it is output along with the input and output values for each stage.

Optimization is implemented using Python as the programming language, with Python interfacing with Aspen HYSYS. After accessing the HYSYS library from Python to modify process variables, the modified HYSYS simulation results are read, and the optimization engine derives the next optimal point.

The optimization input and output interface is handled by Python code. By inputting the optimization variables into the Python code and executing it, the variables are entered into the Spreadsheet in HYSYS. After running the simulation, the optimization results are displayed in the Spreadsheet in HYSYS.

Figure 4 illustrates the flowchart of the ammonia re-liquefaction process optimization conducted in this study.

Figure 4: 
Flowchart of optimization program

First, the initial values to be optimized are input into the HYSYS modeling file through Python code, and it is determined whether these initial values satisfy the constraints. If the initial point violates the constraints, a penalty function is applied to ensure that the result is not considered an optimal solution, thus discarding it [21][22].

The reason for checking whether the initial values satisfy the constraints is that the genetic algorithm applied in this study is a global optimization technique. It uses the given initial values to create new values through selection, crossover, and mutation, and the process is repeated with these new values as inputs. The penalty function is applied to initial values that violate constraints to discard them [23][24].

The initial values are used as input genes to create individuals, which are then evaluated for fitness. Individuals that pass the constraints are selected as the parent generation, and through the creation of offspring generation individuals, mutation of individuals, and selection of elite individuals, the optimal solution is determined.

As shown in Figure 5, four individuals are created and evaluated for fitness. Only individuals A and D, which satisfy the constraints, are selected as the parent generation, while individuals B and C, which violate the constraints, are discarded. The parent generation individuals are crossed to create offspring individuals A and D, and some offspring are mutated to create mutated individual D”. The individuals generated so far constitute the first generation. Elite individuals are selected from the generated individuals and passed to the next generation. This process is repeated to find the optimal combination of variables.

Figure 5: 
Optimization process of ammonia re-liquefaction system

During the creation of individuals, the range for each variable was set from 1 to 2000. The developer set the initial value for individual A based on the developer's experience in process system development, which helped improve the speed of finding a global solution. Additionally, a mutation rate of 40% was applied to provide ample opportunities for exploring global solutions.

To determine whether the variables and constraints are satisfied, a spreadsheet embedded in HYSYS was used. The coordinates of each cell in the spreadsheet were linked with Python code to facilitate input, output, and evaluation.

When each variable is input, the objective function calculation is performed in HYSYS. Since the developer does not know the calculation formulas, these are defined as black-box functions, and a method to compute the target values that meet the constraints is applied. In this process, hyperparameters corresponding to the number of generations, crossover, and mutation probabilities for running the genetic algorithm were set as shown in Table 5.

When the constraints are exceeded or an error occurs that prevents calculation results from being obtained, the penalty function method is used to apply a value of negative infinity to the output values, thus excluding them.

The optimal combination of variables is found, and hyperparameters are applied to select the optimal individuals among those generated. Based on the mutation probability, genes are modified to create new offspring generations, and the process is repeated with increasing generations to find the optimal individual. Among the individuals in each generation, including parent generation, offspring generation, and mutated individuals, the combination of variables with the best objective function is selected as the elite individual. This elite individual is then used as the parent for the next generation, and the process is repeated.