Output-Constraint Handling and Parallelization for Oil-Reservoir Control Optimization by Means of Multiple Shooting

Abstract

We propose to formulate and solve the reservoir-control optimization problem with the direct multiple-shooting method. This method divides the optimal-control problem prediction horizon in smaller intervals that one can evaluate in parallel. Further, output constraints are easily established on each interval boundary and as such hardly affect computation time. This opens new opportunities to include state constraints on a much broader scale than is common in reservoir optimization today. However, multiple shooting deals with a large number of variables because it decides on the boundary-state variables of each interval. Therefore, we exploit the structure of the reservoir simulator to conceive a variable-reduction technique to solve the optimization problem with a reduced sequential quadratic-programming algorithm. We discuss the optimization-algorithm building blocks and focus on structure exploitation and parallelization opportunities. To demonstrate the method's capabilities to handle output constraints, the optimization algorithm is interfaced to an open-source reservoir simulator. Then, on the basis of a widely used reservoir model, we evaluate performance, especially related to output constraints. The performance of the proposed method is qualitatively compared with a conventional method.

Process systems engineering perspective on the planning and development of oil fields

“…Evolutionary optimization algorithms, such as genetic, simulated annealing, tabu search, differential evolution, ant colony optimization, and particle‐swarm optimization, have been very popular with this approach. However, gradient‐based optimization techniques (e.g., steepest descent, sequential quadratic programming) have received attention in the last decade because of the adjoint method for efficiently computing gradients from a numerical simulation. This elegant and efficient method uses the overall profiles of state variables generated and stored during a numerical simulation to compute gradients through the solution of a set of linear adjoint equations .…”

“…However, the adjoint method for efficiently computing gradient information from a numerical simulator has opened doors for using derivative‐based optimization in the last decade. Codas et al used a multiple shooting strategy inside a novel, reduced‐sequential quadratic programming (SQP) algorithm for flow scheduling over a long term. Their strategy offers the significant advantage of shortening and parallelizing simulations.…”

“…They seem to be the future, especially for integrated field design and operation. In that sense, the multiple shooting method offers interesting possibilities. The biggest practical challenge is to address uncertainty in model parameters and data . The PE community has routinely addressed uncertainty in reservoir description by analyzing multiple realizations of parameters such as permeability and porosity.…”

Time-explicit methods for joint economical and geological risk mitigation in production optimization

“…See also Suwartadi et al (2012). As a promising alternative, Codas et al (2015) show how to exploit the inherent parallelism of multiple-shooting to efficiently handle output constraints.…”

Mixed-Integer Nonlinear Programming (MINLP) for production optimisation of naturally flowing and artificial lift wells with routing constraints

“…Accurate understanding of physical flow phenomena, advanced mathematical techniques and high performance computing are important components embedded in these tools which have led to lower operational cost and increased process efficiency when they are systematically applied (Epelle and Gerogiorgis, 2018a). However, with the ever-increasing petroleum exploration difficulties faced by most companies, there is a commensurate need for the development of novel modelling methods, and also better integration strategies of simulation and optimisation techniques to increase field profitability (Codas et al, 2015;Gupta and Grossmann 2012a;2012b). Although many high-fidelity simulation packages exist, it is essential that optimisation is considered in the early stages of design and model development by production engineers (Eason, 2018).…”