Maximum stabilized water-cut (WC), also known as ultimate water-cut in a reservoir with bottom-water coning, provides important information to decide if reservoir development is economical. To date, theory and determination of stabilized water-cut consider only single-permeability systems so there is a need to extend this concept to Naturally Fractured Reservoirs (NFRs) in carbonate rocks — known for severe bottom water invasion. This work provides insight of the water coning mechanism in NFR and proposes an analytical method for computing stabilized water-cut and relating to well-spacing design.
Simulated experiments on a variety of bottom-water hydrophobic NFRs have been designed, conducted, and analyzed using dual-porosity/dual-permeability (DPDP) commercial software. They show a pattern of water cut development in NFR comprising the early water breakthrough and very rapid increase followed by water cut-stabilization stage, and the final stage with progressive water-cut. The initial steply increase of water-cut corresponds to water invading the fractures. The stabilized WC production stage occurs when oil is displaced at a constant rate from matrix to the water-producing fractures. During this stage water invades matrix at small values of capillary forces so they do not oppose water invasion. In contrast, during the final stage (with progressing water cut) the capillary forces grow significantly so they effectively oppose water invasion resulting in progressive water cut.
A simple analytical model explains the constant rate of oil displacement by considering the driving effect of gravity and viscous forces at a very small value of capillary pressure. The constant oil displacement effect is confirmed with a designed series of simulation experiments for a variety of bottom-water NFRs. Statistical analysis of the results correlates the duration of the stabilized WC stage with production rate and well-spacing and provides the basis for optimizing the recovery. Results show that stabilized water-cut stage does not significantly contribute to recovery, so the stage needs to be avoided. Proposed is a new method for finding the optimum well spacing that eliminates the stabilized WC stage while maximizing recovery. The method is demonstrated for the base-case NFR.