This paper presents the effects of the top water-bearing zone on the performance of the steam and gas push, i.e., nitrogen as a non-condensable gas injected with steam into an oil sands deposit. The flow characteristics of fluid mixtures are examined in the presence of different-sized water-bearing formations overlying oil sands deposits, i.e., a finite aquifer with no-flow boundaries and an infinite aquifer with continuous mass flux. The performance efficiency is investigated by respectively implementing the cumulative steam to oil ratio, a simple thermal efficiency parameter, and the oil production on the surface. The top water-bearing area serves as a heat thief zone and negatively impacts bitumen recovery; furthermore, it increases the cumulative steam to oil ratio while decreasing the simple thermal efficiency parameter, as well as the oil production rate. When the steam chamber encounters the top aquifer, a severe heat loss occurs. As increasing mol % of nitrogen, the producing time with energy efficiency increases but the chamber growth is limited. The specific operational conditions would be possible for the finite-sized aquifer, while the continuous water influx and the significant heat loss obstructs the thermal processes for the infinite aquifer.