## 2 System Update and Optimization  
In the previous system process, the undecomposed HI solution and H\({}_{2}\)SO\({}_{4}\) solution from the decomposer outlet were recycled to the Bunsen tank to participate in the Bunsen reaction again. This significantly increased the system's energy consumption and hindered the Bunsen reaction. Therefore, in the optimized system, the undecomposed HI and H\({}_{2}\)SO\({}_{4}\) solutions are redirected to the purification tower, where they are mixed and purified with freshly separated liquid-liquid phases. As a result, a small cycle within the entire system was established to reduce the overall energy consumption. The undigested sulfuric acid and iodate solutions no longer return to the Bunsen reaction to participate in the overall system circulation, but undergo small cycles in the distillation and decomposition module circulation. Aspen Plus V12 software was utilized to design and optimize the process. For the thermochemical sulfur-iodine cycle, a typical polar non-ideal system, this study adopts a differentiated-property method selection strategy based on the material characteristics and processing conditions of different process modules. The research findings from [24] demonstrate that the ELECNRTL electrolyte model exhibits significant advantages in simulating such systems. This model boasts broad applicability, as it can handle electrolyte solutions across various concentrations and is equally suitable for mixed-solution systems. Its theoretical foundation rests on two core assumptions: First, mutual repulsion exists between ions of the same charge, with ions of opposite charge distributed around any central ion. Second, local electroneutrality is maintained, meaning the total charge of surrounding ions balances that of the central ion within its immediate vicinity. In terms of specific model construction, long-range ion interactions are characterized using a modified Pitzer-Debye-Huckel asymmetric model combined with the Born correction equation [25], while short-range molecular interactions are described by the Non-Random Two-Liquid (NRTL) model. This multi-scale modeling approach effectively integrates the influence mechanisms of long-range electrostatic interactions and short-range intermolecular forces. Consequently, the expression for calculating the excess Gibbs energy is formulated as follows:  
\[\frac{G_{m}^{*E}}{RT}\ =\ \frac{G_{m}^{*E,PDH}}{RT}+\frac{G_{m}^{*E,Born}}{RT}+ \frac{G_{RT}^{*E,NRTL}}{RT} \tag{4}\]The relationship between the corresponding activity coefficients can be obtained from this:  
\[ln\gamma^{*}\ =\ ln\gamma_{i}^{*PDH}+ln\gamma_{i}^{*Born}+ln\gamma_{i}^{*NRTL} \tag{5}\]  
The system flow is illustrated in Figure 1, while the corresponding stream components, temperature, and pressure are detailed in Table 1.  
For the entire system, a fully closed-loop operation is employed, requiring only 44.65 mol of water and an external energy input to produce 44.642 mol of hydrogen and 22.321 mol of oxygen. In the Bunsen reaction module, the reverse reaction products (streams 32 and 33) from the HI and H\({}_{2}\)SO\({}_{4}\) purification towers, along with the circulating streams (28 and 29) from the H\({}_{2}\)SO\({}_{4}\) and HI decomposition modules, are directed back to the Bunsen reaction. In the H\({}_{2}\)SO\({}_{4}\) module, to match the hydrogen production target, a portion of \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**Stream** & **Temperature (K)** & **Pressure (atm)** & & & & & & & & \\ \hline  & & HI & I\({}_{2}\) & H\({}_{2}\)O & SO\({}_{2}\) & SO\({}_{2}\) & H\({}_{2}\) & O\({}_{2}\) \\ \hline  
\hline \end{tabular}
\end{table} 
Table 1: The stream parameters of the system. Figure 1: Process flow diagram of the thermochemical iodine–sulfur cycle water splitting hydrogen production system. H\({}_{2}\)SO\({}_{4}\) stream 18 is recycled to the Bunsen reaction, while the remaining stream 7 is purified in the R2 purification tower at 418.15 K to remove HI and I\({}_{2}\).