Optimal reservoir management using adaptive reduced-order models

Abstract

Reservoir management and decision-making is often cast as an optimization problem where we seek to maximize the field's potential recovery while minimizing associated operational costs. Two reservoir management aspects are considered here, new well placement and production controls. Reservoir simulators are at the heart of this process as they aid in identifying best field development plans. The computational cost associated with managing realistic reservoirs is however substantial due to the significant number of unknowns evaluated by the simulator as well as the number of simulations required to achieve an optimal plan-it involves hundreds to thousands of reservoir simulation runs. Reduced-order models (ROM) are considered powerful techniques to address computational challenges associated with reservoir management decision-making. In this sense, they represent perfect alternatives that trade off accuracy for speed in a controllable manner. In this work, we focus on developing model-order reduction techniques that entail the use of proper orthogonal decomposition (POD), truncated balanced realization (TBR) and discrete empirical interpolation (DEIM) to accurately reproduce the full-order model (FOM) input/output behavior. POD allows for a concise representation of the FOM in terms of relatively few variables while TBR improves the overall stability and accuracy. DEIM improves the shortcomings of POD and TBR in the case of nonlinear PDEs, i.e., saturation equation, by retaining nonlinearities in lower dimensional space. Example cases demonstrate ROMs ability to reduce the computational costs by 0(100) while providing close overall agreement to FOM for instances with significant difference in boundary conditions (well placements and controls). ROMs are potentially perfect alternatives to FOMs in reservoir management intensive studies such as field development and optimization. However, ROMs presented in this thesis and the overall physics-based ROMs have the tendency to perform well within a restricted zone. This zone is generally dictated by the training simulations (with a specific set of boundary conditions) used to build the ROM. Therefore, special care is considered when implementing these training runs. To mitigate the heuristic process of implementing training runs (multiple boundary conditions training runs), we apply a trust-region approach that provides an adaptive framework to systemically retrain and update ROMs utilizing new solutions (flow) characteristics revealed during the course of the optimization run. The adaptive framework for determining the optimal well placements entails the development of a hybrid optimization algorithm, MCSMADS, that combines positive features of both local and global optimization methods. Typical FOM is used in conjunction with MCS to globally search the optimization surface while ROMs are used in conjunction with MADS to further improve the solution quality with minimum increase in computational costs. Well production controls are optimized sequentially via gradient-based trust-region approach. ROMs in this approach replace the FOM to find optimal solutions within a trust-region (subset of the optimization space). At the end of each trust-region optimization, the accuracy of the obtained solution is assessed and the ROM is updated. Both approaches are capable of handling nonlinear constraints. They are treated using a filter-based technique. The developed framework for adaptive ROMs is applied to two realistic field examples. The first example considers maximizing net present value (NPV) through sequentially optimizing well placements and controls while the second example considers maximizing recovery through minimizing Lorenz coefficient. Nonlinear constraints including well-to-well distance and field production limits are imposed in both examples. For all cases considered, the hybrid approach for well placement based on MCS-MADS was able to constantly provide better solution quality (up to 22% increase in NPV) when compared to standalone MCS with only 3% increase in computational costs. The incorporation of ROMs for well controls was shown to reduce computational cost by 96% with only 1% difference in solution quality when compared to FOM.