Vidar Gunnerud

Oil production optimization—A piecewise linear model, solved with two decomposition strategies

This paper presents a new method for real-time optimization of process systems with a decentralized structure where the idea is to improve computational efficiency and transparency of a solution. The contribution lies in the application and assessment of the Lagrange relaxation and the Dantzig–Wolfe methods, which allows us to efficiently decompose a real-time optimization problem. Furthermore, all nonlinearities are modeled by piecewise linear models, resulting in a mixed integer linear program, with the added benefit that error bounds on the solution can be computed. The merits of the method are studied by applying it to a semi-realistic model of the Troll west oil rim, a petroleum asset with severe production optimization challenges due to rate dependent gas-coning wells. This study indicates that both the Lagrange relaxation and in particular the Dantzig–Wolfe approach offers an interesting option for complex production systems. Moreover, the method compares favorably with the non-decomposed method.

Integrated production optimization of oil fields with pressure and routing constraints: The Urucu field

Abstract This paper develops a framework for integrated production optimization of complex oil fields such as Urucu, 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 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 were developed to obtain simplified piecewise-linear approximations that ensure a given accuracy with respect to complex and precise models. Computational experiments showed 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.

Oil production optimization solved by piecewise linearization in a Branch & Price framework

This paper presents a method for optimizing oil production on large scale production networks such as the Troll west field in the North Sea. The method is based on piecewise linearization of all nonlinearities, and on decomposition of the full scale problem into smaller subproblems. Column generation in a Branch & Price framework is used to solve the decomposed problem. The method differs from most Branch & Price methods by branching only on continuous quantities and by solving the subproblems using commercial MILP software. The method is applied to a realistic model of an oil field, the Troll oil and gas field at the Norwegian Continental Shelf, a petroleum asset with severe production optimization challenges due to rate dependent gas-coning wells. This study shows that the method is capable of solving instances of practical size to proven optimality.

Embedding structural information in simulation-based optimization

Abstract This paper proposes and explores an algorithm designed to find optimal settings for a process network. Emphasis is put on the system being divisible into components, as this underlying assumption motivates the algorithm in its entirety in that rather simple relations between the system components are modeled as explicit structural constraints, while the significantly more complex relations within each component are approximated based on the underlying simulator data. Although the approach taken in this paper is rather broadly applicable we are, in particular, interested in its application to production optimization problems in the oil and gas industry. We give limited numerical results for one such example that clearly indicates the advantages of our approach. We show the advantages of both decomposing the problem of interest and accounting for the structure from the point of view of exploiting, where ever possible, the explicitly analytic aspects of the problem. The advantage of doing the former is that the considered subproblems are significantly smaller than the overall problem. The advantage of the latter is that one can use derivatives for the analytic parts whereas they are unavailable for the simulators. The underlying approach is a trust-region one with a mixed integer nonlinear program formulation. There are some significant differences in the details of the algorithm from those generally available for such problems.

Parallel Dantzig–Wolfe decomposition of petroleum production allocation problems

This article discusses the optimization of a petroleum production allocation problem through a parallel Dantzig–Wolfe algorithm. Petroleum production allocation problems are problems in which the determination of optimal production rates, lift gas rates and well connections are the central decisions. The motivation for modelling and solving such optimization problems stems from the value that lies in an increased production rate and the current lack of integrated software that considers petroleum production systems as a whole. Through our computational study, which is based on realistic production data from the Troll West field, we show the increase in computational efficiency that a parallel Dantzig–Wolfe algorithm offers. In addition, we show that previously implemented standard parallel algorithms lead to an inefficient use of parallel resources. A more advanced parallel algorithm is therefore developed to improve efficiency, making it possible to scale the algorithm by adding more CPUs and thus approach a reasonable solution time for realistic-sized problems.

Dantzig-Wolfe decomposition for real-time optimization -applied to the Troll west oil rim

Abstract Abstract This paper studies different decomposition approaches for real-time optimization of process systems with a decentralized structure where the idea is to improve computational efficiency and transparency of a solution. The contribution lies in the application and assessment of the Dantzig-Wolfe method which allows us to efficiently decompose a real-time optimization problem into parts. Furthermore, the nonlinear system is modeled by piecewise linear models with the added benefit that error bounds on the solution can be computed. The merits of the method are studied by applying it to a semi-realistic model of the Troll west oil rim, a petroleum asset with severe production optimization challenges due to rate dependent gas-coning wells. This study indicates that the Dantzig-Wolfe approach offers an interesting and robust option for complex production systems. Moreover, the method compares favourable with earlier results using Lagrangian relaxation which again was favourable compared to a global approach.

Optimization of a Simulated Well Cluster using Surrogate Models

Abstract In this paper we present an implementation of a partly Derivative-Free Optimization (DFO) algorithm for production optimization of a simulated multi-phase flow network. The network consists of well and pipeline simulators, considered to be black-box models without available gradients. The algorithm utilizes local approximations as surrogate models for the complex simulators. A Mixed Integer Nonlinear Programming (MINLP) problem is built from the surrogate models and the known structure of the flow network. The core of the algorithm is IBMs MINLP solver Bonmin, which is run iteratively to solve optimization problems cast in terms of surrogate models. At each iteration the surrogate models are updated to fit local data points from the simulators. The algorithm is tested on an artificial subsea network modeled in FlowManager ™ , a multi-phase flow simulator from FMC Technologies. The results for this special case show that the algorithm converges to a point where the surrogate models fit the simulator, and they both share the optimum.

Optimization of petroleum production networks – Through proxy models and structural constraints

This paper proposes and explores the properties of a solution algorithm designed to solve network simulation problems to optimality. Emphasis is put on the system being divisible into components, as this underlying assumption motivates the algorithm in its entirety in that rather simple relations between the system components are modeled as explicit structural constraints, while the significantly more complex relations within each component are approximated based on the underlying simulator data. The Real-Time petroleum Production Optimization (RTPO) problem is used as an example of such a network simulation problem that can benefit from using the solution approach outlined. The paper also includes the mathematical formulation of the RTPO, followed by a description of the algorithm and a comprehensive study of the algorithms properties on a real RTPO application. Finally, the results are compared to a reference case and conclusions are reached about the method.