A mathematical study of the viability of the polymer injection process: a simplified model

Abstract

 It is well known that adding some water soluble polymer into water can enhance the oil recovery factor in the waterflood recovery method. However, this polymer solution increases the injection cost. Not only in reason of the polymer cost itself, but also because of the time for production should be longer in order to reach the water breakthrough. In this work, to study this behavior, we use a simple PDE system that models the flow of water with polymer into a one directional porous media previously filled with oil. Under suitable simplifications, we prove that the system’s solution projects to a single scalar equation which we use to create a profit functional. The profit functional allows the study of the economical viability of the polymer injection. This study presents a simple new way to deal with this class of problems where we dynamically obtain regions to optimize the defined functional solution.