## 1 Introduction  
In the middle and late stages of a natural gas field's development, the reduction in formation pressure often renders the gas incapable of autonomously removing the accumulated formation water. This frequently results in a decline in the production capacity of the gas wells, potentially leading to their abandonment [1]. Therefore, to effectively address this issue, plunger lift technology has been widely adopted as a cost-effective artificial lift method [2]. This technique involves deploying a plunger in the wellbore to facilitate efficient gas-liquid separation and liquid discharge [3]. Current research on gas-lift plunger performance primarily employs experimental measurements and numerical simulations, both of which have inherent limitations. Experimentally, the process involves high costs and complex equipment setup, often requiring on-site trials. Experiments are constrained by actual gas well conditions, making it difficult to replicate various operating conditions, thereby limiting the general applicability of the results. Additionally, experiments are time-consuming, especially when repeated under different conditions. Due to environmental influences on measurement, experimental results often contain significant errors. Particularly in gas-lift plunger experiments, the small gap between the plunger and the pipeline makes it challenging to measure physical quantities within the gap, which are crucial for characterizing the plunger's flow field. For numerical simulations, the reliance is on established models and assumptions, which may not fully reflect real-world scenarios. The flow field around a gas-lift plunger, characterized by high velocities, large gradients, small gaps, and curved streamlines, complicates the flow, necessitating the use of appropriate turbulence models to accurately describe turbulence structures and their impacts. The Reynolds-averaged Navier-Stokes (RANS) method, blending theory and empiricism, is a viable simulation technique. However, its turbulence model accuracy relies on specific model constants, usually calibrated with standard flows like flat plate boundary layers and free shear flows, which may be inadequate for predicting complex flow fields in gas-lift plungers [4]. Traditional computational fluid dynamics (CFD) techniques, such as Direct Numerical Simulation (DNS) and Large Eddy Simulation (LES), can effectively model gas flow. However, their requirement to handle high Reynolds number turbulence necessitates substantial computational resources, which in turn limits their practical engineering applications [5]. Currently, the Reynolds-averaged Navier-Stokes (RANS) equations remain the mainstream choice for engineering applications due to their favorable balance between computational cost and predictive accuracy. Given these limitations, there is a clear need to develop more accurate and efficient modeling techniques for gas-lift plunger systems. Accurate modeling not only enhances the fundamental understanding of near-wall turbulence and flow resistance within narrow annular gaps but also enables the optimization of plunger geometry and operating parameters through numerical tools. Furthermore, improved modeling fidelity provides a basis for digital twin technologies and intelligent well management systems. In geosciences, data assimilation (DA) has been developed as a technique to address potential shortcomings in experimental and numerical simulations, establishing it as a fourth central analytical approach alongside theoretical, experimental, and numerical methods [6]. DA is a method that integrates mathematical models with observational data, considering the uncertainties of both. It combines measured data with predictive models to adjust the model's evolution, optimize performance, and enhance accuracy. Data assimilation was initially proposed by [PERSON] to optimize weather forecasting [7]. Subsequently, this approach has been applied to system monitoring, hydrology, and geology, among other fields [8].