Oil production from a fractured reservoir, composed of a gas cap and an oil zone, is usually accomplished using surface or submersible pumps. The production method is called controlled gravity drain age (CGD). In the CGD mode of production, the pumps usually operate under a constant withdrawal rate until gas breakthrough, at which time the pumping rate would be influenced by the presence of gas at the production well In this paper, we describe immiscible displacements in fractured porous media to have a better understanding of the process. Oil-gas CGD displacements were conducted using a laboratory flow apparatus in the fractured glass bead systems. A detailed dimensional analysis was conducted to scale up the experimental results based on the physics of the CGD process and experimental findings. Dimensional analysis of immiscible two-phase flow in porous media allows for quantification of the influences of petrophysical properties of the fractured media and physical properties of test fluids on some important aspects, such as critical pumping rate and recovery factor at gas breakthrough. In this work, an empirical model based on the dimensional groups of the system obtained from the Buckingham pi theorem was employed to investigate the gravity drainage process in a fractured porous medium. A model was developed to predict the critical pumping rate, maximum withdrawal rate, distance between the gas-liquid (G-L) interface positions within the matrix and fractures, and recovery factor just before gas breakthrough for fractured porous media undergoing the CGD processes. The model was tested against experimental and field data of oil production under CGD. The results demonstrate that the model gives satisfactory prediction for the oil-gas drainage systems. The procedure outlined in this paper also has potential applications in modeling immiscible displacements.