Gravity waterflooding (also known as “dumpflooding”) is a process in which water flows from a high pressure aquifer zone to a low pressure oil-producing zone using natural gravity. The water flows through a well connecting the two zones, enhancing the oil sweep into a producing well. This process is economically attractive due to the absence of injection surface facilities and injection fluid costs. This research quantifies the rate of fluid transfer from a high pressure aquifer zone to a low pressure oil producing zone. Detailed theoretical equations are derived to evaluate the rate of water injection from an aquifer into an oil reservoir with a gas cap by dumpflooding. Two cases considered are: (1) A finite aquifer injecting into a finite oil reservoir with a gas cap, and (2) An infinite aquifer injecting into a finite oil reservoir with a gas cap. A single-well model has also been built using an Excel spreadsheet to solve the ordinary differential equations using the bisection iterative technique.