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Summary Determining the optimum location of wells during waterflooding contributes significantly to efficient reservoir management. Often, the voidage-replacement ratio (VRR) and net present value (NPV) are used as indicators of performance of waterflood projects. In addition, VRR is used by regulatory and environmental agencies as a means of monitoring the impact of field-development activities on the environment, whereas NPV is used by investors as a measure of profitability of oil and gas projects. Over the years, well-placement optimization has been performed mainly to increase the NPV. However, regulatory measures call for operators to maintain a VRR of unity (or close to unity) during waterflooding. A multiobjective approach incorporating NPV and VRR is proposed for solving the well-placement-optimization problem. We present the use of both NPV and VRR as objective functions in the determination of optimal location of wells. The combination of these two in a multiobjective optimization framework proves to be useful in identifying the trade-offs between the quest for high profitability of investment in oil and gas projects and the desire to satisfy regulatory and environmental requirements. We conducted the search for optimum well locations in three phases. In the first phase, only the NPV was used as the objective function. The second phase had the VRR as the sole objective function. In the third phase, the objective function was a weighted sum of the NPV and the VRR. A set of four weights was used in the third phase to describe the relative importance of the NPV and the VRR, and a comparison of how these weights affect the optimized NPV and VRR values is provided. We applied the method to determine the optimum placement of wells to three sample reservoirs: the first with a distributed permeability field, the second being a channel reservoir with four facies, and the third being a slightly heterogeneous reservoir. Two evolutionary-type algorithms—the covariance matrix adaptation evolutionary strategy (CMA-ES) and differential evolution (DE)—were used to solve the optimization problem. Significantly, the method illustrates the trade-off between maximizing the NPV and optimizing the VRR. It calls the attention of both investors and regulatory agencies to the need to consider the financial aspect (NPV) and the environmental aspect (VRR) of waterflooding during secondary-oil-recovery projects. The multiobjective optimization approach meets the economic needs of investors and the regulatory requirements of government and environmental agencies. This approach gives a realistic NPV estimation for companies operating in jurisdictions with a requirement for meeting a VRR of unity. |
