## 3 Numerical Analysis
### Steam Chamber Development  
Figure 4 compares the steam chamber development between the SAGD process (Figure 4a) and the bottom-up assisted pressure drive process (Figure 4b) in typical oil sand reservoirs with multiple shale barriers. It is obvious that the steam chamber characteristics determined in the two processes are taken at different times of operation. In the first 6 months of SAGD operation, the steam chamber grows upwards, which is similar to typical steam chamber development. This is the reason that the existence of shale barrier I does not affect the steam chamber. As the steam chamber grows vertically, shale barrier II behaves like the boundary, and then the steam chamber grows laterally at 9 months of operation. Meanwhile, the impact of shale barrier I on steam chamber development takes into effect, as seen at 12 months of operation. In the typical SAGD process, once the steam encounters shale barriers, steam changes its migration due to the properties of shale (low permeability and low thermal conductivity). Therefore, the oil above the shale barrier cannot be effectively heated and drained by gravity. The observed  
Figure 3: Schematic of the grid systems in (**a**) the SAGD process and (**b**) the bottom-up assisted SAGD process with respect to the well locations and shale barriers distribution. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Properties** & **Unit** & **Value** \\ \hline Horizontal permeability & mD & \(10^{-3}\) \\ Vertical permeability & mD & \(10^{-4}\) \\ Porosity & - & 0.08 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Properties of shale barriers in the numerical model. characteristics of steam chamber development are the same as those investigated in the literature [8; 16; 38]. Steam chamber development characteristics in the bottom-up assisted pressure drive process are depicted in Figure 4b. With the initiation of the steam injection, a steam chamber connecting the injector and producer is first developed (as seen in the steam chamber at 3 months of operation). With the continuous injection of the steam, the steam chamber moves from the bottom upwards with relatively flat horizontal front (as seen in the steam chamber at 6 months of operation). Compared to the steam chamber volume in the early stage of operation (i.e., 3 months and 6 months of operation), it is obvious that the steam chamber in the bottom-up assisted pressure drive process is much greater than that in the SAGD process. Meanwhile, the large contact area between steam and oil contributes to high oil production. Steam chamber development is affected by shale barrier I at 9 months of operation and shale barrier II at 12 months of operation. Because of the low permeability of shale barriers, the steam chamber grows laterally. Together with the pressure drive between  
Figure 4: Comparison of steam chamber development between (**a**) SAGD processes and (**b**) bottom-up assisted pressure drive at different times of operation. the injector and producer, the oil above the shale barriers can be displaced efficiently, as shown at 24 months of operation. Different from the SAGD process, the pressure difference between the injector and producer of the bottom-up assisted pressure drive process is greater due to the long distance between the injector and producer. Therefore, the pressure drive provides another driving force. This feature is beneficial for oil production, especially in reservoirs with shale barriers. In the bottom-up assisted pressure drive process, although the presence of shale barriers affects the steam chamber development, the oil above the shale barriers moves to the production well by the force of the pressure drive. In addition, there is an amount of oil in the middle of two well pairs. This region is hardly swept by the steam chamber in the SAGD process (i.e., 24 months of SAGD). The infill well is usually drilled to recover these resources.