Global optimization of multiphase flow networks using spline surrogate models

Abstract

A general modelling framework for optimization of multiphase flow networks with discrete decision variables is presented. The framework is expressed with the graph, and special attention is given to the convexity properties of the resulting programming formulation. Nonlinear pressure and temperature relations are modelled using multivariate splines and a special mixed-integer nonlinear programming (MINLP) formulation with spline constraints results. A global solution method is devised by combining the framework with a spline-compatible MINLP solver, recently presented in the literature. The solver is able to globally solve the nonconvex optimization problem. The new solution method is benchmarked with several local optimization methods on a set of three realistic subsea production optimization cases provided by the oil company BP.

A Critical Review of the Modeling and Optimization of Combined Heat and Power Dispatch

“…Furthermore, over recent decades, novel modeling techniques have been developed which can substantially aid the optimization of process systems. For instance, surrogate models such as Kriging [39][40][41][42][43][44], radial basis functions [45][46][47][48][49][50], artificial neural networks [51][52][53][54][55][56], splines [57,58], among others were shown to accurately represent complex physical systems while aiding optimal search algorithms. No literature exists which explores the application of such techniques to advance the study of CHP dispatch.…”

Process systems engineering perspective on the planning and development of oil fields

“…For instance, Aguiar et al used convex quadratic functions for pressure drops but multidimensional piecewise‐linear functions for well production to achieve global solutions. On the other hand, Grimstad et al used B‐spline based surrogates.…”

Mathematical programming formulations for piecewise polynomial functions

“…Modeling of optimization problems frequently involves representing functions that are piecewise, discontinuous or nonsmooth. This includes inherently piecewise economical and physical characteristics [5,24,29], construction of surrogate models by sampling of simulators [15,32,58], and approximate or exact representation of nonconvex functions [2,10,37,39,47]. In this paper, we study the problem of efficiently representing and solving optimization prob-lems containing piecewise polynomial (PWP) constraints.…”

“…In this paper, we study the problem of efficiently representing and solving optimization prob-lems containing piecewise polynomial (PWP) constraints. Piecewise polynomials are used in a wide range of disciplines, including efficiency curve modeling in electric-power unit commitment [40], rigid motion systems [11], image processing and data compression [44,51], probability density estimation [61], flow networks [5,15,25] and in optimal control [4,41].…”

“…In particular, they have been popular as nonlinear basis functions in regression problems [12,20], for example in kernel methods [22,63], and in finite element methods [23]. Yet, few references [5,15] apply splines within mathematical programming beyond the optimization of spline design parameters [45,59], trajectory optimization [18,34,43], and optimization of piecewise linear splines [33].…”