Impulse functions applied to compute pressure change during injectivity tests

Analytical solutions to compute the pressure change during injectivity tests are desired, as they are useful to interpret pressure transient data. Currently, impulse functions (or Green’s functions) for single-phase flow are already known. However, these formulations are not applicable for injectivity tests, as they cannot handle two-phase flow. Instead, the existing analytical solutions for pressure change during injectivity tests assume that flow-rate within the swept region remains constant, which is not necessarily true for multilayer reservoirs. Therefore, the main novelty of this work is to obtain an impulse function for two-phase flow in single-layer reservoirs with vertical wells. The proposed formulation, which accounts for a flow-rate transient inside the flooded region, employs a radially composite reservoir approach to depict the waterfront propagation and assumes a piston-like fluid displacement. Then, we apply the proposed impulse function to determine pressure change in multilayer reservoirs with different layer properties and in single-layer reservoirs with horizontal wells. To the best of our knowledge, the solutions developed in this work have not been presented in literature before. This work also aims to estimate individual layer permeabilities based on the pressure and flow-rate data computed using the developed formulation. A computational implementation of the models proposed in this work was developed and compared to previously existing solutions and to a commercial flow simulator. Results showed a good agreement, and evidenced that a layer flow-rate transient occurs at the wellbore in multilayer reservoirs. Moreover, layer permeabilities were estimated with decent accuracy.