Solutions to the Curve Fitting Problem of Mathematical Correlation and SCAL Data

Abstract

Mathematical correlation has been widely used in oil and gas industry to model relative permeability and capillary pressure from water saturation. The application of mathematical correlation is essential especially in the absence of laboratory data. Additionally, the correlation is also applied to generate a refined relative permeability and capillary pressure table as the input to reservoir simulation.There are several correlations being used in the industry such as Corey, Skjaeveland and LET correlation. The focus in this paper is the LET correlation. The correlation offers more flexibility as well as accuracy in matching the responses from laboratory experiments.Having a representative correlation is the basic, but the curve-fitting to the experimental data is also indispensable. In a problem which involves a non-linear correlation, the attempt to find a solution which fits the experimental data becomes more complex. To overcome this problem, it is fundamental to have a search method which can fit the experiment data with the lowest possible residual errors.In this paper, different search methods of curve-fitting are investigated. In the last part of the paper we will compare the performance of each method. The main evaluation parameters are the residual error and the computational time. The methods studied in this paper are the Levenberg -Marquardt method, particle swarm optimization and mesh pattern search.