On decomposition and piecewise linearization in petroleumproduction optimization

Abstract

Maintaining good or optimal operations of large and complex petroleum assets isnot a trivial task. There are numerous decisions to be made where many of thedecisions affects each other. Relying entirely on human interpretation of data isfutile; this means that decision support tools are important for efficient and safeoperations. Further, as complexity of the assets has increased over the years, sohave the requirements for the tools developed to support operational decisions.

Decision support tools come in many forms. The simplest ones would only displaymeasurements in a suitable way, and the operators and engineers would then, basedon their knowledge and experience make and implement decisions. Often whenmeasurements are noisy or unreliable, a low pass filter or some uncertainty indicationmay help. Complex decision support tools may embed model-based estimationand optimization. This work targets methods for optimization-based decision support.

In petroleum assets with rate dependent gas to oil, or water to oil ratios, and withlimited gas and/or water handling capacity, it is often a nontrivial task to maximizevalue throughput. This challenge has been addressed by several commercial andacademic actors, as the potential additional values of increased production is large.The motivation for this PhD research has been to attack this real time productionoptimization problem from a new angle which has many advantages with respect tofinding the optimal operational strategy.

The contribution of this work may be divided into four parts. The first is relatedto modeling. A full field production system consisting of many wells, manifoldsand pipelines is challenging to describe in a suitable optimization formulation. The approach in this research has been to transform all nonlinearities into piecewiselinear approximations. It is then possible to represent the problem as a mixed integerlinear problem, which comes with many advantages with respect to solvability.

As the wells usually are clustered in groups, the second contribution is related toexploration of this structure to be able to solve large full field production systems; inour case more than sixty wells. This is done by decomposing the full field probleminto sub-problems for each cluster of wells. The coordination between these subproblemsis handled by using Dantzig-Wolfe decomposition theory.

The decomposed problem naturally lets itself parallelize. Therefore, to further decreasethe solution time, parallelization of the solution algorithm is explored to takeadvantage of the latter years development in computational architectures.

Dantzig-Wolfe decomposition theory has certain limitations when the optimization problem contains integer and binary decisions, as is needed when modeling on/offvalves and routing of wells. More precisely, it is not an exact method, and cannotguarantee convergence to the optimal solution, even though, for this class ofproblems it gets fairly close. However, to overcome this flaw, a branch & pricealgorithm which handles the integer properties, is proposed and implemented. Forthis problem it provides an optimal solution.