The application of the Kirchhoff transformation has proven to be a very effective tool in simplifying and solving complex diffusivity equations in reservoirs. Since its introduction by  in addressing the non-linear behavior of compressible fluids, it has seen many modifications and implementations in multiphase systems, from the Perrine type pseudo-pressure to the reservoir integral type pseudo-pressure also called the Mass balance Model (MBM) for pseudo-pressure as discussed by . Its applicability in addressing water influx from aquifers to oil and gas reservoirs has as of now not been addressed. Moreover, the models developed so far to address water influx such as the works of , , , have many limitations, such as imposing constant pressure at the reservoir–aquifer interface, single phase model used, no analytical approach of predicting excessive water cuts.
In this paper, the MBM pseudo-pressure is used to address water influx in reservoirs with two-phase flow (Gas/Water or Oil/Water). The model response is derived by developing diffusivity equations for the composite reservoir system to address the communication between the hydrocarbon reservoir and the aquifer. The non-homogenous nature of the diffusivity equation of each phase makes the derivation of the solutions to the equations cumbersome. Nonetheless, the reservoir integral type pseudo-pressure being a very powerful, can be incorporated in the diffusivity equations of the phases and solutions to the models can rigorously be derived. Defining the boundary conditions for each phase is very crucial as the hydrocarbons in the hydrocarbon reservoir depict a no-flow boundary at the aquifer interface, whereas the water phase and the total system response of the hydrocarbon reservoir depict mass conservation at the hydrocarbon reservoir-aquifer interface.
Using this approach, the solutions to the phases in the hydrocarbon and aquifer are readily obtained and its applicability in gas hydrate reservoirs highlighted. The effects of the water influx from the aquifer are clearly seen with increasing water cut at the sandface. The effects of different outer boundary conditions in the aquifer are investigated.
The novel approach introduced in this work will help tremendously to improve the characterization of the reservoir with multiphase flow, mostly especially for reservoirs with aquifer drive.