Estimation of the production index of oil and gas from the reservoir into the well during under-balanced drilling (UBD) is studied. This paper compares a Lyapunov-based adaptive observer and a joint unscented Kalman filter (UKF) based on a low order lumped (LOL) model and the joint UKF based on the distributed drift-flux model by using real-time measurements of the choke and the bottom-hole pressures. Using the OLGA simulator, it is found that all adaptive observers are capable of identifying the production constants of gas and liquid from the reservoir into the well, with some differences in performance. The results show that the LOL model is sufficient for the purpose of reservoir characterization during UBD operations. Robustness of the adaptive observers is investigated in case of uncertainties and errors in the reservoir and well parameters of the models. (C) 2017 Elsevier Ltd. All rights reserved.