## 3 Results and Discussion
### Effects of Boundary Condition of the Top Water-Bearing Zone
Figure 4 illustrates the percentage of nitrogen regarding the gas (united steam and nitrogen) saturation at the end of the SAGP process (two years from the first oil), wherein the saturation distribution of the finite case (see Figure 4a) is compared with that of the infinite aquifer (see Figure 4b). For example, 40% nitrogen concentration means that 40% of nitrogen and 60% of steam comprise the gas volume in the grid cell since there is no gas phase except for nitrogen and steam. The nitrogen distribution shows the advantage of the non-condensable gas whereby it maintains the steam chamber, and in the finite aquifer, the screen of nitrogen is well developed by accumulating near the steam chamber edges. In the middle of steam chamber, the water influx could be unavoidable and thereby it reduces the energy efficiency and interrupts the desired chamber growth. At the same time of the water influx, the severe gas loss, especially the nitrogen, into the aquifer is observed. The injected fluid mixture, i.e., steam and nitrogen, moves vertically to the top aquifer and then spreads sideways due to the no-flow conditions at the upper area of the top aquifer. The released  
Figure 4: Nitrogen concentration to gas saturation at the end of production in the cases of: (**a**) the finite aquifer; and (**b**) the infinite aquifer. mass (gas movement from the steam chamber into the aquifer) increases the formation pressure of the aquifer so that the formation water is expelled to the lateral direction or it flows downward. The gas loss into the thief zone and the water influx into the steam chamber can occur simultaneously. All of the gas phases gather near the upper no-flow boundaries of the aquifer and spread sideways. As a result of the no-flow occurring on either side of the finite aquifer, the lateral movement of the fluids is limited regarding the formation water in the aquifer, and the steam is able to move to the steam chamber. Figure 5 describes oil saturation at the end of SAGP operation; Figure 5a shows the case of the finite aquifer and Figure 5b shows that of infinite case. This result represents how well the steam chamber can develop laterally; Figure 5a shows that the lateral growth of steam chamber is possible, notwithstanding that the water influx occurs in the middle of steam chamber, while Figure 5b explains that the thermal operation is unavailable due to dominant vertical flow and ineffective lateral flow, i.e., horizontal enlargement. The infinite aquifer provides continuous water influx with low temperature into the oil sands deposit and the steam chamber, and the gas phase with high temperature leaks out. These flow characteristics show the difficulties to develop the desired shape of the steam chamber, to maintain the chamber, and to enlarge the chamber in the horizontal direction without heat thief zones. These results can explain the transport of the steam and nitrogen that occurred during SAGP operation; furthermore, it can also support the production performances of Figures 2 and 3, whereby the finite case shows a higher energy efficiency and oil recovery. At the fixed-size water-bearing area, the objectives of the nitrogen injection can be achieved, since the injected nitrogen releases into the aquifer and forms a screen to prevent the water influx; however, a significant nitrogen loss is unavoidable, and the achievement of the desired efficiency is, consequently, difficult. The most important condition can be the determination of the optimal operations for the prevention of both the water influx and the heat loss. The unequal distribution of pressures in the steam chamber induces the co-occurrence of the water invasion into the steam chamber and the heat loss into the aquifer, as shown in Figure 4. If the fluids, i.e., steam and nitrogen, are injected with a higher pressure, the vertical growth of the steam chamber is dominant, and the steam chamber meets the aquifer at an early time as a result. The steam chamber encounters the aquifer at an early time so that the heat loss is significant.