# Design Considerations for the Liquid Air Energy Storage System Integrated to Nuclear Steam Cycle
## 2 Analysis Methodology  
### General Code  
The first goal of this research is to reproduce the model proposed in the reference [15] with the KAIST Closed Cycle Design code (KAIST-CCD). This work gives an insight to how the LAES system performs and how each design parameter will influence the round-trip efficiency. After the model is verified to produce similar results to the previous study, the model can be modified to optimize the operating conditions of the LAES system with APR1400 under more realistic conditions. To test the LAES system under realistic conditions, three design parameters were modified from the reference [15]. 1. Pinch temperature of heat exchanger: The pinch temperature for heat exchangers in the reference [15] is 2K pinch. However, when designing a heat exchanger, typically 5K or larger values are assumed for the pinch due to economic reason and increased pressure drop for excessively low pinch design condition. Therefore, in this paper, the pinch temperature in the heat exchangers is changed to 5K. 2. Pressure drop: Pressure drop in components and piping always occurs. Due to this pressure drop, the pressure of fluid decreases while flowing through the system. This generally influences the overall performance of the system. 3. Ambient temperature: In the realistic system, the ambient temperature is always changing. As an LAES system is an open system that takes in air from the atmosphere, the temperature of ambient air affects the performance of the system. The KAIST-CCD is a MATLAB based code used to calculate and optimize thermodynamic processes. It can be separated into two main subroutines: the layout section and the design parameter section. The layout section determines the process layout of a thermal system, and it gives the information on how components are connected to each other. In the design parameter section, it provides the design conditions for the layout code: the pressure and temperature for ambient air, the efficiency, and operating conditions for each component. The properties of fluid are obtained from REFPROP developed by NIST [17]. The layout adopted for code modelling is depicted in Figure 1. It is separated into two parts: before the liquid air tank and after the liquid air tank. The layout before the liquid air tank is the storage part of the system (i.e., charging mode) and the layout after the liquid air tank is the system for discharge operation. The code calculates the charging system first, until the result converges in the charging system and then starts to calculate the discharging system with the results from the charging system. The algorithm of the code is shown in Figure 2. The following describes the thermodynamic for constructing the model of the proposed system. The calculation in the components follows the fundamental laws  
Figure 1: LAES system with a reference nuclear power plant (NPP) system with design limitations adapted from [15]. of general thermodynamics. However, certain components follow the calculations below for better accuracy. The specific parameters for calculation are stated in Tables 1 and 2. \begin{table}
\begin{tabular}{c c} \hline \hline
**Variables** & **Values** \\ \hline Thermal power from NPP (MW) & 250 \\ NPP inlet steam pressure (kPa) & 7093 \\ NPP inlet steam temperature (K) & 560 \\ Thermal efficiency of the NPP (\%) & 31 \\ Ambient pressure (kPa) & 101 \\ Ambient temperature (K) & 288 \\ Liquid air storage pressure (kPa) & 101 \\ Operational period in energy storage mode (hours/day) & 8 \\ Operational period in energy release mode (hours/day) & 1 \\ Temperature approach of heat exchangers (K) & 2 \\ Isentropic efficiency of the air turbines (\%) & 92 \\ Isentropic efficiency of the cryogenic turbine (\%) & 88 \\ Isothermal efficiency of air compressors (\%) & 90 \\ Isentropic efficiency of the cryogenic pump (\%) & 70 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters for LAES Calculation data from [15].