On decomposition and piecewise linearization in petroleum production optimization

On decomposition and piecewise linearization in petroleum production optimization

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Abstract

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

Maintaining good or optimal operations of large and complex petroleum assets is not a trivial task. There are numerous decisions to be made where many of the decisions affects each other. Relying entirely on human interpretation of data is futile; this means that decision support tools are important for efficient and safe operations. Further, as complexity of the assets has increased over the years, so have the requirements for the tools developed to support operational decisions.    

Decision support tools come in many forms. The simplest ones would only display measurements in a suitable way, and the operators and engineers would then, based on their knowledge and experience make and implement decisions. Often when measurements are noisy or unreliable, a low pass filter or some uncertainty indica- tion may help. Complex decision support tools may embed model-based estimation and optimization. This work targets methods for optimization-based decision sup- port.  

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

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

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

The decomposed problem naturally lets itself parallelize. Therefore, to further de- crease the solution time, parallelization of the solution algorithm is explored to take advantage 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/off valves and routing of wells. More precisely, it is not an exact method, and can- not guarantee convergence to the optimal solution, even though, for this class of problems it gets fairly close. However, to overcome this flaw, a branch & price algorithm which handles the integer properties, is proposed and implemented. For this problem it provides an optimal solution.

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