A new approach for saturation height modelling in a clastic reservoir using response surface methodology and artificial neural network

Abstract

• Brook-Corey's function was the best conventional water saturation prediction model. • The RSM model gave a better prediction fit than the conventional methods. • The independent variables had an influence on water saturation via 3D response surface plots. • Mathematical links improved the RSM model's performance in design space. • The RBFNN model was superior compared to the RSM model with mathematical links. Saturation Height Modelling (SHM) is an important reservoir characterization method for estimating the water saturation component which is a fraction of the total reservoir fluids in porous media. Although several methods have been used in calculating water saturation, little or no research has employed Response Surface Methodology (RSM) in predicting water saturation in field cores. In this paper, well datasets were tested with four conventional curve fitting models including Lambda, Thomeer, Leverette J, and Brooks-Corey of which Brook-Corey gave the best fit with an R 2 of 0.485. The RSM with the Central Composite Design (CCD) was used to obtain the mathematical and statistical relationship between the predictors and target as well as the variables’ interactions optimization. The model was analysed using Analysis of Variance (ANOVA) which validated the correlations with an F-value of 4.96, a p-value less than 0.05, and a Lack of Fit-value of 0.76 implying that the model developed was statistically significant. The RSM model gave a better fit with an R 2 value of 0.817 with mathematical links, almost twice that predicted by the conventional methods. Then, the testing performance of the RSM model was compared to the standard radial basis function neural network model ( R 2 of 0.9779). The results proved that both RSM and RBFNN models’ performance was accurate and reliable and could give a precise prediction of water saturation without any conventional curve fitting parameters.