RCP model, which is a general empirical equation, is being thoroughly used to simulate and investigate the performance of the oil wells completed by Autonomous Inflow Control Devices (AICD’s) and Autonomous Inflow Control valve (AICV). In this paper, a dimensionless version of the model was presented, and the parameters of the modified model were estimated. In addition, we demonstrated how the model and measurement uncertainties can be quantified within the Bayesian statistical inference framework. A Markov Chain Monte Carlo (MCMC) method known as Hamilton Monte Carlo (HMC) was used to estimate the joint posterior probability distribution. Results from the analysis confirmed that at the calibration step the model can describe most of the variations in the measurements. However, the results at validation step showed a slightly overprediction by the model in specific areas of the valve performance. The inadequacy in model could not be explained by the measurement noise or the uncertainty in the estimated parameters.