Application of a particle swarm optimization algorithm

Application of a particle swarm optimization algorithm for determining optimum well location and type Jerome Onwunalu Louis J. Durlofsky Smart Fields Meeting April 8, 2009 Outline Introduction Optimization of well placement Algorithms for well placement optimization Genetic algorithm (GA) Particle swarm optimization (PSO) Examples Conclusions April 8, 2009 Smart Fields 2 Introduction Oil field development Optimize placement of wells Optimize well type Incorporate field constraints Account for geological uncertainty Expensive simulation runs April 8, 2009 Smart Fields 3 Introduction Oil

field development Optimize placement of wells Optimize well type Incorporate field constraints Account for geological uncertainty Expensive simulation runs April 8, 2009 Smart Fields 4 Well placement optimization problem Features Multidimensional Multimodal - many local optima Constrained Mixed variables Lack of analytical derivatives Discontinuous objective functions April 8, 2009 Smart Fields 5 Well placement optimization problem Features Multidimensional Multimodal - many local optima Constrained Mixed variables Lack of analytical derivatives Discontinuous objective functions April 8, 2009 Smart Fields 6 Well placement optimization algorithms Adjoint-based algorithms Stochastic approximation (SA) algorithms Simultaneous perturbation SA algorithm (SPSA) Finite difference SA algorithm (FDSA) Genetic algorithm (GA) Particle swarm optimization (PSO) algorithm April 8, 2009 Smart Fields 7 Well placement optimization algorithms Adjoint-based algorithms Stochastic approximation (SA) algorithms Simultaneous perturbation SA algorithm (SPSA) Finite difference SA algorithm (FDSA) Genetic algorithm (GA) Particle swarm optimization (PSO) algorithm April 8, 2009 Smart Fields 8 Genetic algorithm (GA) Overview Based on Darwinian evolutionary theory Population-based Members of the population are called individuals Determine the fitness (quality) of each individual using an objective function Rank population according to fitness Produce new population using best individuals GA operators Selection, Crossover, Mutation April 8, 2009 Smart Fields 9 GA flowchart April 8, 2009 Smart Fields 10 Particle swarm optimization (PSO) algorithm Overview Developed by Kennedy and Eberhardt (1995) Based on the social interaction exhibited by animals Particle refers to a potential solution Collection of particles is called swarm Population-based Update particles using a cognitive and social model Improve performance using different particle neighborhood topologies April 8, 2009 Smart Fields 11 Examples of PSO neighborhood topologies 1 2 3 4 567 8 (a) Star 1 2 3 4 567 8 (b) Ring 1 2 3 4 5 6 7 8 (c) Cluster April 8, 2009 Smart Fields 12 PSO variants and update equation PSO variants Global best PSO (gBest) - one neighborhood Local best PSO (lBest)- several neighborhoods Solution update equation xi(k + 1) = xi(k) + vi(k + 1) vi(k + 1) is the velocity of particle i April 8, 2009 Smart Fields 13 PSO variants and update equation PSO variants Global best PSO (gBest) - one neighborhood Local best PSO (lBest)- several neighborhoods Solution update equation xi(k + 1) = xi(k) + vi(k + 1) vi(k + 1) is the velocity of particle i April 8, 2009 Smart Fields 14 PSO variants and update equation PSO variants Global best PSO...

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