Research on an Analytical Model of Unsteady Flow in Water Injection Well and Its Application

Produced water in oil field is generally recycled back to the formation, and the dynamic analysis of formation pressure during water injection has always been a research hotspot. It is difficult, however, to apply current numerical models to formation pressures analysis during water injections due to the models' complexity. Furthermore, actual formation conditions are quite different from the generic analytical models that assume homogeneous and circular boundaries. Therefore, this paper takes the anisotropy of formation into account for the first time and establishes a mathematical model for unsteady flow when water injection well is located at any position of a rectangular formation. This paper also considers the well as line source instead of point source, and this research adopts an orthogonal transformation method to deduce the exact solution of the model. It is of great significance to easily and exactly analyze formation pressure behaviour during water injection. Calculation program is compiled to analyze the key factors affecting formation pressure during water injection. Results show that: initial injection bottom hole pressure is proportional to time on semi-log scales, and the pressure increases rapidly, but the increase slows down later on in time, the model correctly reflects the propagation mechanism of pressure-wave, which can be applied to analyze the pressure behaviour of reservoirs during water injection.