Abstract
The location-allocation problem of manifolds, which is a part of subsea field layout optimization, directly affects the flowline cost. This problem has always been studied as a mixed-integer nonlinear programming (MINLP) problem, or an integer linear programming (ILP) problem when there are location options for the facilities. Making a MINLP model is surely convenient to interpret the optimization problem. However, finding the global optimum of the MINLP model is very hard. Hence, practically, engineers use approximation algorithms to search a good local optimum or give several good location options based on their experience and knowledge to reduce the MINLP model into an ILP model. Nevertheless, the global optimum of the original MINLP model is no longer guaranteed. In this study, enlightened by the graphic theories, we propose a new method in which we reduce the MINLP model into an ILP model---more precisely, a binary linear programming (BLP) model---without compromise of achieving global optimum, but also with extremely high efficiency. The breakthrough in both efficiency and accuracy of our method for the location-allocation problem of manifolds and wellheads is well demonstrated in various cases with comparison to the published methods and the commercial MINLP solver from LINDO. Besides, we also provide our results for larger-scale problems which were considered infeasible for the commercial MINLP solver. More generally, our method can be regarded as a specific MINLP/NIP (nonlinear integer programming) solver which can be used for many other applications. This work is the second of a series of papers which systematically introduce an efficient method for subsea field layout optimization to minimize the development cost.
Highlights
In Part I, we introduced the directional well trajectory planning method base on 3D Dubins curve
Even though there is no more continuous variable, and the number of the nonlinear integer programming (NIP) variables is half of the mixed-integer nonlinear programming (MINLP)’s, i.e. kn, the computational complexity of the NIP is completely equivalent to the MINLP, because the nonlinear term of the cost is still in the objective function, making it practically infeasible for a MINLP/NIP solver to find the global optimal of this specific model with only 40 wells
This study introduces a brand-new method to deal with the locationallocation problem of manifolds in subsea field layout optimization
Summary
In Part I, we introduced the directional well trajectory planning method base on 3D Dubins curve. It should be noted that, changing the perspective on this layout optimization problem does not change the NP-hardness for finding the global optimum: the well-known K-Means algorithm (Lloyd, 1982; Arthur and Vassilvitskii, 2007) for clustering problem cannot fulfill the size constraint, besides, it can’t guarantee the global optimum; the exact size-constrained 2-clustering (Lin, 2012; Bertoni et al, 2015) algorithm is a very efficient algorithm which generates the global optimum, it’s only suitable for dividing data points into 2 clusters; Zhu’s work (Zhu et al, 2010) which converted the size-constrained clustering problem into a ILP model, revealed the hardness equivalence Even though this new perspective does not change the NP-hardness, the concept of clustering enlightened us to build a much more efficient algorithm to achieve the global optimum for this NP-hard problem, making it practically feasible to solve a much larger-scale problem. We introduce how to use our method to deal with several types of manifolds and many other practical scenarios
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