Parameter Identification for a Slug Test in a Well with Finite-Thickness Skin Using Extended Kalman Filter

Yeh and Chen (J Hydro 342(3–4):283-294, 2007) integrated a slug test solution for a well having a finite-thickness skin with the simulated annealing (SA) to determine the hydraulic parameters of the skin zone and formation zone. Some results obtained in positive-skin scenarios are however not accurate if compared with the target values of the parameters. This study first employs the sensitivity and correlation analyses to quantify the relationship between two normalized sensitivities and analyze the resulting errors in parameter estimates. It is found that the inaccuracy in parameter estimates can be attributed to following two problems: (1) the normalized sensitivities of the skin thickness and hydraulic conductivity are highly correlated and (2) the SA algorithm is very sensitive to round-off error in well-water-level (WWL) data. A parameter identification approach is thus developed based on the extended Kalman filter (EKF) coupled with the solution used by Yeh and Chen (J Hydro 342(3–4):283-294, 2007) to determine the parameters in six positive-skin scenarios where the parameters were not accurately determined before. We show that previous two problems can be overcome by the proposed approach because it is designed to account for uncertainties of measurements. Moreover, the EKF can save 99.8% and 99.9% computing time when compared with the results using the SA in analyzing 20 WWL data and 47 WWL data, respectively.