Int. J. of Mathematical Modelling and Numerical Optimisation   »   2011 Vol.2, No.2

 

 

Title: Application of derivative-free methodologies to generally constrained oil production optimisation problems

 

Author: David Echeverria Ciaurri, Obiajulu J. Isebor, Louis J. Durlofsky

 

Addresses:
Department of Energy Resources Engineering, Stanford University, 367 Panama Street, Stanford, CA 94305-2220, USA.
Department of Energy Resources Engineering, Stanford University, 367 Panama Street, Stanford, CA 94305-2220, USA.
Department of Energy Resources Engineering, Stanford University, 367 Panama Street, Stanford, CA 94305-2220, USA

 

Abstract: Oil production optimisation involves the determination of optimum well controls (well pressures, injection rates) to maximise an objective function such as net present value. These problems typically include physical and economic restrictions, which introduce general constraints into the optimisations. Cost function and constraint evaluations entail calls to a reservoir flow simulator. In many situations, gradient information is not available, so derivative-free (non-invasive, black-box) optimisation methods are of interest. This work entails a comparative study of several derivative-free methods applied to generally constrained production optimisation problems. The methods considered include generalised pattern search, Hooke-Jeeves direct search, and a genetic algorithm. Penalty function and filter-based methods are applied for constraint handling. Numerical results for optimisation problems of varying complexity highlight the relative advantages and disadvantages of these procedures. Several combinations of approaches are shown to perform well for the generally constrained cases considered.

 

Keywords: nonlinear programming; derivative-free optimisation; oil production optimisation; reservoir simulation; closed-loop reservoir modelling; derivatives; optimum well control; well pressures; injection rates; net present value; NPV; reservoir flow; gradient information; generalised pattern search; Hooke-Jeeves direct search; genetic algorithms; constraint handling.

 

DOI: 10.1504/IJMMNO.2011.039425

 

Int. J. of Mathematical Modelling and Numerical Optimisation, 2011 Vol.2, No.2, pp.134 - 161

 

Available online: 04 Apr 2011

 

 

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