Study on the fitting function form in the "JBN method" for measuring relative permeability

As one of the main indicators for evaluating reservoirs, relative permeability is an important production data for oilfield production, and the accuracy of its value is closely related to the accuracy of predicting oilfield production data. The "JBN method" established by Johnson, Bossler, Navman and other scholars is one of the important methods to give the relative permeability of oil-water phases through unsteady-state displacement experiments. The calculation formula is based on the one-dimensional Buckley-Leverett two-phase displacement theory, and is mathematically analytically derived. In the "JBN method", from the unsteady-state displacement experimental data to the calculation results of the relative permeabilities, there are two terms in the equations that differentiate the data. Therefore, in order to obtain the entire relative permeability curve, it is necessary to perform function fitting on the data first and then perform derivation, so the fitting accuracy of the function has an important impact on the experimental determination of the relative permeability curve of water and oil phases. Starting from the unsteady-state displacement experiment of the "JBN method", this paper analyzes the essence of the physical phenomenon of the displacement, starts from the first and second derivatives of the data to be fitted, fully considers the mathematical characteristics required for the function to be fitted, and effectively improves the fitting accuracy of the two physical quantities, so as to improve the accuracy of the relative permeability curve of water and oil phases.