A New Analytical Model of Pressure Performance in Water Injection Well and Its Application

Produced water re-injection is an important means of maintaining formation pressure and protecting the nature in oil field. Researchers have done a lot of work on predicting pressure behavior and analyzing the mechanism of injection pressure rise, but there are several kinds of problems. Firstly, actual formation conditions are quite different from the generic analytical models that assume homogeneous and circular boundaries. Secondly, the problems of water quality are usually regarded as the only cause of rapid rise of injection pressure, but the impacts of formation properties and processing factors also deserve in-depth study. Therefore, this paper establishes a practical mathematical model for unsteady flow when water injection well is located at any position of a rectangular formation. With the well being considered as line source instead of point source, it then adopts an orthogonal transformation method to deduce the exact solution of the model, which is of great significance to exactly analyze injection pressure behavior during water injection. Finally, a calculation program is compiled to analyze some key factors including formation properties and injection rate affecting injection pressure. Results show that: as permeability, porosity or total compressibility decreases, bottom hole injection pressure initially rises slightly and later rapidly, serious pollution or heterogeneity near well bore can cause excessive growth of injection pressure, the larger the injection rate is, the higher the injection pressure has to be, so it´s necessary to optimize the relationship between them.