Abstract

A pressure transient test for tracking the advancement of a water front during the early stages of waterflooding is the primary contribution of this work. A composite, elliptical reservoir model is developed and utilized to provide for two distinct regions in which the flow behavior resulting from an induced fracture is elliptical rather than radial. A relationship between the increasing elliptical distance to the waterfront and the resulting change in the apparent (total) skin factor is obtained. Through the analysis of successive pressure falloff tests, this relationship may be used to monitor the advancement of the front provided the cumulative volume of injected water is known. The fluid saturations and the mobilities of the swept and unswept regions are assumed to be unknown and are obtained from the data using existing transient interpretation techniques.

The proposed procedure relies on the transient response of a vertically fractured injection well. The pressure response due to the presence of an infinite-conductivity vertical fracture is determined by solving the diffusivity equation in elliptical coordinates. The solution is then extended to a composite elliptical system to provide for the different fluid banks present during water injection. Computational issues which became evident during the verification stage of our work are also discussed. The solutions have been developed in the Laplace domain to facilitate the addition of multi-layer flow, a common characteristic of Indonesia's reservoirs.

The value of the methods developed here is that the position of the water/oil interface may be accurately determined and monitored over time whether the front is advancing radially or, in the more common case, elliptically. In addition, information vital to the success of the waterflood may be determined such as sweep efficiency, permeability anisotropy and residual oil saturation. Finally, we present new, efficient methods for computing Mathieu functions which may be used in any situation requiring elliptical geometry; notably fractured wells and anisotropic reservoirs.