Modeling the Submergence Depth of Oil Well States and Its Applications

Obtaining the liquid storage state of oil wells in real time is very important for oilfield production. In this paper, under the premise of fully considering the transformation factors of full-pumping and nonfull-pumping states of oil wells, submergence depth models suitable for full- and nonfull-pumping wells are constructed. To reduce the application complexity of the models, parameter-reduction processing is performed to enhance the usability of the models. By analyzing the change trend of the submergence depth during the rising, maintaining, and falling of the oil well in the full-pumping state and nonfull-pumping state models, the judgment criteria for the transition of the oil well state are provided. On this basis, the application methods of nonlinear interpolation and least squares curve-fitting numerical solutions of submergence depth models are studied, and the unique existence of the solution of the corresponding one-variable nonlinear characteristic equation in the (0, 1) open interval is proven. Finally, the error estimation of the numerical solution is carried out, the calculation formula of the number of iterations for the numerical solution of the dichotomy is provided, and the error of the relevant numerical solution is verified.