## Permeability assignment to coarse cells One of the

In present work, we studied a reservoir with pre-defined permeability map and used the stated procedure by Hesami and Dabir (2013) to produce the Amlodipine measure map. The cut-off criterion was applied on energy measure to find high energy and critical regions.

2.2. Quantitative representation of key flow paths

Using key flow paths, to quantify the dynamic features of the reservoir has become of great interest. Streamlines are the usual indicator of flow paths defined as a curve in space in which each point is tangent to the local velocity vector. The time needed for its transverse along the streamline is called time of flight. The following is the procedure to calculate the time of flight in a two phase flow. The velocity is obtained using the concept of time of flight and an indicator for the element size is assigned for the whole region for finer gridding of the system. To calculate the time of flight, we used Pollock (1988) approach in which the velocity field varies linearly, represented as follows:equation(7)dxdt=Vx=Vx,0+mx(x−x0),mx=Vx,Δx−VxΔx