## 2 Materials and Methods
### CR Measurement  
The CR was measured in MPY using a commercial two-electrode LPR sensor (CR-200 Wireless LPR corrosion Rate Sensor, Pyxis, COSASCO(r), Santa Fe Spring, CA, USA) and a potentiostat (VSP potentiostat, Bio-Logic SAS, Grenoble, France). Figure 1 illustrate the experimental setup and specifications of the LPR sensor. This illustrates the setup of each test conducted in this study in single figure. The LPR sensor reading, immersion, and electrochemical tests were each conducted with independent experimental setups to prevent cross-influence between tests. The two-electrode LPR sensor used carbon steel electrodes (UNS K03005, COSASCO(r), Santa Fe Spring, CA, USA), identical to the material used for the specimens in this study, and transmitted MPY readings via Bluetooth every 5 min. For each factor combination, the sensor reading was averaged once measurements stabilized, typically between 30 min and 1 h.  
To validate the sensor data, several electrochemical techniques were employed, including three-electrode LPR, potentiodynamic polarization, and various amplitude sinusoidal micro-polarization (VASP) techniques. These tests were conducted using a three-electrode corrosion cell consisting of a working electrode (specimen with an exposed area of 0.48 cm\({}^{2}\)), a reference electrode (Ag/AgCl sat. KCl), and a counter electrode (graphite rod of \(\Phi\)3.2). The cell was placed in a 1 L water jacketed beaker containing 700 mL of 3.5% NaCl solution. The LPR test was performed to determine the polarization resistance (\(R_{p}\)). A small polarization was applied relative to the open-circuit potential (OCP), and the resulting current change was measured to calculate \(R_{p}\), which is the ratio of the current response (\(\Delta i\)) to the polarization (\(\Delta E\)), as shown in Equation (3) [18]. \[R_{p}=\ \Delta E/\Delta i \tag{3}\]  
Using the Stern-Geary equation (Equation (4)) [18], the corrosion current density (\(l_{corr}\)) was derived:  
\[I_{corr}=B/R_{p} \tag{4}\]  
Here, \(B\) is the Stern-Geary constant, which is calculated from the Tafel slope using Equation (5) [18]:  
\[B=(\beta_{a}\times\beta_{c})/2.3\cdot(\beta_{a}+\beta_{c}) \tag{5}\]  
Figure 1: Experimental setup for CR measurement in MPY using commercial LPR sensor, potentiostat, and immersion test coupon. where \(\beta_{a}\) and \(\beta_{c}\) represent the anodic and cathodic Tafel slope, respectively. The CR (MPY) was then calculated from \(I_{corr. }\) using [PERSON]'s law (Equation (6)) [18]:  
\[CR\ (MPY)=\ (0.13\times I_{corr.}\times EW)/\rho \tag{6}\]  
In this equation, the 0.13 is a constant used to convert \(I_{corr. }\) to CR (MPY). \(EW\) is the equivalent weight (27.93 g/equivalent for carbon steel), and \(\rho\) is the density (7.85 g/cm\({}^{3}\)). All MPY values in this study were rounded to one decimal place for consistency. The LPR test was conducted by sweeping the potential from cathodic to anodic regions within a range of \(\pm\)30 mV relative to the OCP, at a 0.5 mV/s scan rate. The \(I_{corr. }\) was converted to specimen CR as MPY. To complement the LPR data, the potentiodynamic polarization test was conducted by sweeping the potential across a broader range, specifically within \(\pm\)300 mV of the OCP at the same scan rate. This technique allowed for a more detailed analysis of corrosion behavior by extrapolating the anodic and cathodic Tafel slopes to determine \(I_{corr. }\)  
Lastly, the VASP technique [19] was employed to validate the corrosion data non-destructively. Like LPR, VASP provides non-destructive and instantaneous measurements, making it highly effective for real-time corrosion monitoring. However, VASP is a relatively new technique and has not yet been fully validated across a wide range of applications, which introduces uncertainties regarding its reliability. This technique, based on electrochemical impedance spectroscopy (EIS), uses low-voltage amplitude perturbation to determine both the CR and Tafel parameters without damaging the sample surface.