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Gradient-based Methods for Production Optimization of Oil Reservoirs
Norwegian University of Science and Technology, Faculty of Information Technology, Mathematics and Electrical Engineering, Department of Engineering Cybernetics.
2012 (English)Doctoral thesis, monograph (Other academic)
##### Abstract [en]

Production optimization for water flooding in the secondary phase of oil recovery is the main topic in this thesis. The emphasis has been on numerical optimization algorithms, tested on case examples using simple hypothetical oil reservoirs. Gradientbased optimization, which utilizes adjoint-based gradient computation, is used to solve the optimization problems.

The first contribution of this thesis is to address output constraint problems. These kinds of constraints are natural in production optimization. Limiting total water production and water cut at producer wells are examples of such constraints. To maintain the feasibility of an optimization solution, a Lagrangian barrier method is proposed to handle the output constraints. This method incorporates the output constraints into the objective function, thus avoiding additional computations for the constraints gradient (Jacobian) which may be detrimental to the efficiency of the adjoint method.

The second contribution is the study of the use of second-order adjoint-gradient information for production optimization. In order to speedup convergence rate in the optimization, one usually uses quasi-Newton approaches such as BFGS and SR1 methods. These methods compute an approximation of the inverse of the Hessian matrix given the first-order gradient from the adjoint method. The methods may not give significant speedup if the Hessian is ill-conditioned. We have developed and implemented the Hessian matrix computation using the adjoint method. Due to high computational cost of the Newton method itself, we instead compute the Hessian-timesvector product which is used in a conjugate gradient algorithm.

Finally, the last contribution of this thesis is on surrogate optimization for water flooding in the presence of the output constraints. Two kinds of model order reduction techniques are applied to build surrogate models. These are proper orthogonal decomposition (POD) and the discrete empirical interpolation method (DEIM). Optimization using a trust-region framework (TRPOD) is then performed on the surrogate models. Furthermore, the output constraints are again handled by the Lagrangian barrier method

NTNU, 2012.
##### Series
Doctoral theses at NTNU, ISSN 1503-8181 ; 2012:104
##### Identifiers
ISBN: 978-82-471-3485-6 (printed ver.)ISBN: 978-82-471-3486-3 (electronic ver.)OAI: oai:DiVA.org:ntnu-16584DiVA: diva2:530697
##### Public defence
2012-05-02, 00:00
Available from: 2012-06-04 Created: 2012-06-04 Last updated: 2012-06-04Bibliographically approved

#### Open Access in DiVA

##### File information
File name FULLTEXT01.pdfFile size 3862 kBChecksum SHA-512
Type fulltextMimetype application/pdf
##### By organisation
Department of Engineering Cybernetics