Contributions to production optimization of oil reservoirs

Abstract

This thesis covers methods for optimization of oil production in three time-scales. In the long-term perspective, years, it is desired to maximize the economic return of the field operation, or alternatively, it is desired to maximize the oil recovery factor. In the middleterm perspective, days, optimal scheduling and allocation of the production facilities are desired. In the short-term perspective, minutes, it is desired to maintain the process operating at a stable optimal set-point. The integration of the optimization solutions that tackle each of the layers independently is a formidable challenge. This requires the development of mathematical models and efficient optimization algorithms to deliver solutions in real-time. This research focuses on efficient optimization algorithms and suitable simulation models for oil production optimization. The emphasis is on the integration of the decision process for different time-scales. To this end, this research studies each individual time-scale and proposes tools that lead to the desired integration. The work is divided into five parts. Chapter 2 formulates and solves the reservoir control optimization problem applying the direct multiple shooting (MS) method. This method divides the prediction horizon into smaller intervals which can be evaluated 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 what is common in reservoir optimization today. However, multiple shooting deals with a large number of variables since 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, based on a widely used reservoir model, we evaluate performance, especially related to output constraints. The performance of the proposed method is qualitatively compared to a conventional method. Chapter 3 solves a black-oil reservoir optimal control problem with MS. The black-oil fluid model, considering volatile oil or wet gas, requires a change of primary variables for simulation. This is a consequence of the absence of a fluid phase due to dissolution or vaporization. Therefore, reservoir simulators parametrize the states with an augmented vector and select primary variables accordingly. However, the augmented state vector and the corresponding change of primary variables are not suitable for the application of MS because the optimization problem formulation must change according to the change of variables. Thus, we propose a minimal state-space variable representation that prevents this shortcoming. We show that there is a bijective mapping between the proposed state-space representation and the augmented state-space. The minimal representation is used for optimization and the augmented representation for simulation, thereby keeping the simulator implementation unchanged. Therefore, the proposed solution is not invasive. Finally, the application of the method is exemplified with benchmark cases involving live oil or wet gas. Both examples emphasize the requirement of output constraints which are efficiently dealt by the MS method. The production life of oil reservoirs starts under significant uncertainty regarding the actual economical return of the recovery process due to the lack of oil field data. Consequently, investors and operators make management decisions based on a limited and uncertain description of the reservoir. Chapter 4 proposes a new formulation based on MS for robust optimization of reservoir well controls. This formulation exploits coherent risk measures, a concept traditionally used in finance, to deal with the uncertainty. A variable elimination procedure allows to solve this problem in a reduced space and an active-set method helps to handle a large set of inequality constraints. Finally, we demonstrate the application of constraints to limit the risk of water production peaks on a standard test case. Chapter 5 addresses the middle-term perspective and develops a framework for integrated production optimization of complex oil fields such as Petrobras’ Urucu field, which has a gathering system with complex routing degree of freedom, limited processing capacity, pressure constraints, and wells with gas-coning behavior. The optimization model integrates simplified well deliverability models, vertical lift performance relations, and the flowing pressure behavior of the surface gathering system. The framework relies on analytical models which are history matched to field data and simulators tuned to reflect operating conditions. A Mixed-Integer Linear Programming (MILP) problem is obtained by approximating these models with piecewise-linear functions. Procedures are developed to obtain simplified piecewise-linear approximations that ensure a given accuracy with respect to complex and precise models. Computational experiments show that the integrated production optimization problem can be solved sufficiently fast for real-time applications. Further, the operational conditions calculated with the simplified models during the optimization process match the precise models. Chapter 6 studies the short-term problem and presents control and optimization of a network consisting of two gas-lifted oil wells, a common pipeline-riser system and a separator. The gas-lifted oil wells may be open-loop unstable. The regulatory layer stabilizes the system by cascade control of wellhead pressure measurements without needing bottom hole sensing devices. An economic Nonlinear Model Predictive Control (NMPC) based on MS is applied for optimization of the network operations. The optimization layer thus provides optimal settings for the regulatory controllers. The control structure has been validated by using the realistic OLGA simulator as the process, and using simplified models for Kalman filtering and the NMPC design. The simplified models are implemented in Modelica and fit to the OLGA model to represent the main dynamics of the system. The proposed two-layer controller was able to stabilize the system and increase the economical outcome.