Methods of analyzing fluid flow in a formation include defining physical boundaries of a porous geological formation reservoir and parameters related to a process of injection of fluid over a period of time, and configuring a reservoir simulator that characterizes transport of the fluid as solute within the physical boundaries of the reservoir in accordance with the fluid injection process. The reservoir simulator utilizes at least one upscaled equation describing advective transport for the solute. Output of the simulator may be viewed. The parameters related to the injection process including one or more of an injection rate, a location of injection, and a time length of injection can be optimized.