The aim in this work was to develop a method to draw our conclusions for the uncertain quantities of interest in a real problem in oilfield, namely the cuttings transport problem, given the limited data available. The cuttings transport process is subject to disturbances and is influenced by various factors in a stochastic and uncertain manner. In addition, the drilling environment is very complex to understand fully, and to model efficiently and accurately. An experiment was conducted to monitor the process in real-time via time-series measurements of distributed pressure transducers along the drillstring. A mathematical model describing the dynamic process of cuttings transport is developed, which aims to capture the dominant characteristics of the process, without attempting to model reality perfectly; modeling and measurement errors are represented by uncertainties in model inputs, parameters, and states. The proposed model is described in detail, and is incorporated in the Bayesian framework (via ensemble Kalman filtering) to make our best estimate about the location and amount of cuttings transported along the wellbore in real time, given the available data. The estimations of the uncertain process parameters are described. (C) 2017 Elsevier Ltd. All rights reserved.