An Extension of Johnson, Bossler and Neumann JBN Method for Calculating Relative Permeabilities

Abstract

Abstract The Johnson, Bossler and Neumann (JBN) method is the industry standard for measuring relative permeabilities from field cores. Mitigating the numerical errors resulting from the numerical differentiation required by the method has been an area of interest over the years. There have been several modifications of this technique by many researchers in order to improve the results. Some of the researchers have used curve fitting and graphical approach. However, till date, the application of a numerical modeling technique to do the necessary numerical differentiation of the data required by the JBN method for improved results is yet to be established. This paper presents the application of cubic spline numerical modeling technique (CSNMT) on JBN method. Production data from field cores were used. The JBN technique was initiated procedurally. The necessary numerical differentiation of the production data required by the JBN method was done with cubic spline numerical modeling technique (CSNMT). Tridiagonal system of equations was formed and resolved. Different and continuous equations (polynomials) were derived for the contiguous intervals and then differentiated accordingly. The procedure was then accomplished. The technique shows good results which are close to those obtained when the numerical differentiation is done the traditional way, using an expression for an unequally spaced data gotten from the numerical differentiation of a second-order langrage interpolating polynomial for three data points. However, because of the oscillations induced and the difficulty in handling higher order polynomials numerically which leads to the use of second-order langrage interpolating polynomial instead of a polynomial of order one minus the number of the data points required, the results from the use of CSNMT are more reliable. In addition, the profiles of the production data are modeled in CSNMT. The reduction in the overall numerical error was reflected by the differences in the relative permeability values obtained by both approaches.