Consideration of Voidage-Replacement Ratio in Well-Placement Optimization

Abstract

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.

A Closer Look At Differential Evolution For The Optimal Well Placement Problem

“…3 is that for rand/1, the bigger N , the worse the result (see Config. [1][2][3][4]. For the current-to-best/1 strategy, the increase in N considerably improved the solutions for Config.…”

“…A similar study was presented by [2] using CMA-ES and DE to solve the multi-objective optimization problem by manually weighting NPV and VRR, resulting in a singleoptimization problem. They concluded that CMA-ES outperformed DE for the majority of experiments, but that DE also obtained high-quality solutions.…”

“…DE has been used in multi-objective approaches incorporating NPV and VRR to solve well placement optimization problems [15,2]. A Pareto-based multi-objective approach to integrate NPV and VRR in a well placement optimization was presented by [15], obtaining several optimal solutions according to the Pareto front.…”

“…The performance indicator or objective function of this optimization problem is usually either the Voidage Replacement Ratio (VRR) [9,2] or the Net Present Value (NPV) [3,16]. The VRR function corresponds to the ratio of the total volume of fluid injected (water injection) to the volume of fluid produced (water, oil and gas production).…”

“…Another important advantage of applying meta-heuristics is that the number of function evaluations is dependent on the size of the population and not the problem dimensionality [33]. Meta-heuristics that have been used to solve the well-placement problem include: genetic algorithms (GA) [35,24,21], simulated annealing (SA) [3], particle swarm optimization (PSO) [28,17,1,16], covariance matrix adaptation evolutionary strategies (CMA-ES) [12,5,14], and differential evolution (DE) [27,2].…”