# Modeling the Submergence Depth of Oil Well States and Its Applications
## 1 Introduction  
In oilfield production, the submergence depth or dynamic liquid level depth of an oil well is an important index used to measure the fullness of the oil well pump, determine reasonable oil well production parameters, and formulate efficient production measures [1, 2]. The normal operation of the pumping unit requires a stable supply production balance, and a reasonable submergence depth measures whether oil wells can achieve this goal. This index is essential for oil well pumping management and is a key factor used to ensure the stable production, high efficiency, and low energy consumption of oil wells; additionally, it provides the premise for achieving the best economic benefits. For this reason, many researchers have conducted related studies on the submergence depth of oil wells or the state of the dynamic liquid level. [PERSON] and [PERSON] [3] aimed at the problem of unreasonable submergence depth of pumping units in China's oilfields; the optimization scheme of submergence depth was discussed with system efficiency and economic benefits as objective functions. [PERSON] et al. [4] believed that submergence depth is an important factor affecting liquid production and mechanical recovery efficiency. By establishing an objective function of comprehensive mechanical recovery performance with higher liquid production and efficiency, the optimal design of the submergence depth was achieved. [PERSON] et al. [5] determined the change trend in pump efficiencies by changing the pump efficiency value of the submergence depth according to the factors that affect pump efficiency to guide actual production. Using the relationship curve between pump efficiency and submergence depth, [PERSON] [6] analyzed the distribution of the submergencedepth of oil wells in normal production and, combined with production practice, provided the limit of the reasonable submergence depth of oil wells. [PERSON] et al. [7] believed that a reasonable submergence depth is directly related to oil well pumping efficiencies through the oilfield production experience. In a certain range, a high submergence depth can reduce the degree of pump leakage, which is conducive to improving pump efficiency. However, if the submergence depth is too high, the pump efficiency may be reduced due to the increased elastic expansion of the sucker rod. These studies showed the importance of a reasonable submergence depth for oilfield production. On this basis, various submergence depth- or dynamic liquid-level-related models have been developed. [PERSON] et al. [8] determined the mathematical model of submergence depth changes during pumping by studying the change characteristics of the submergence depth according to the similarity between the flow pressure change and the voltage change during capacitor discharge. This is only one step away from the theoretical derivation of the oil well pumping submergence depth model. [PERSON] et al. [9] proposed a venturi flow correction model based on system identification technology to improve the accuracy of downhole flow measurements. By analyzing the theoretical model and influencing factors of the traditional venturi, combined with the downhole flow conditions, a modified model of factors, such as flow coefficients and differential pressures, is established, which improves the accuracy of downhole flow measurements. To improve the simulation accuracy of the indicator diagram, the displacement coefficient, and the dynamic system parameters of oil wells with a low submergence depth and insufficient liquid supply, [PERSON] et al. [10] successively established a simulation model of the fluid-pumping law and instantaneous pressure in the pump barrel and improved the simulation model of the bottom boundary condition of the sucker rod string's longitudinal vibration, the dynamic simulation model of the oil well indicator diagram, and the simulation model of the oil well pump filling coefficient and leakage coefficient by comprehensively considering relevant parameters.