Submergence depth modeling of oil well reservoirs and applications

Abstract

In oilfield production, it is important to be able to acquire the reservoir status of oil wells in real time, especially for low or ultra-low permeability oil wells. In this paper, based on the reservoir percolation characteristics of the oil layer and combined with the oil well permeability, liquid pressure and oil well pressure formulas, the non-homogeneous linear differential equation for oil well pressure is derived, based on which a submergence depth model of oil well reservoirs is established. The parameter merging is applied to reduce the parameter dimension of the submergence depth model; this approach substantially reduces the parameter dimension and application complexity and effectively improves the model application range. The model not only conforms to the reservoir percolation law of the oil layer but also applies to the balance laws of other substances with potential energy balancing ability. The application methods studied (namely, the extraction of the greatest common divisor, the weighted dichotomy and least-squares curve fitting) successively reduce the calculation error and expand the application scope. The least-squares curve fitting method causes the submergence depth error to reach the minimum of the 2-norm, and the number of iterations can be accurately assessed by the convergence speed of halving the numerical calculation error in every iteration. This method is suitable not only for the zero submergence depth case in the initial state but also for non-zero submergence depth cases. The experimental results show that the proposed submergence depth model for oil well reservoirs accurately reflects the change laws of submergence depth and time. Combined with the proposed application methods, the corresponding submergence depth can be obtained at any time point. The model and application methods provide strong support for formulating scientific oil production plans and implementing reasonable production methods for oil wells.