Date of Award

Spring 2015

Degree Type

Thesis

Degree Name

Master of Science in Mechanical Engineering (MSME)

Department

Mechanical Engineering

First Advisor

Ilias Bilionis

Committee Chair

Ilias Bilionis

Committee Member 1

Jitesh Panchal

Committee Member 2

Marisol Koslowski

Abstract

The oil well placement problem is vital part of secondary oil production. Since the calculation of the net present value (NPV) of an investment depends on the solution of expensive partial differential equations that require tremendous computational resources, traditional methods are doomed to fail. The problem becomes exceedingly more difficult when we take into account the uncertainties in the oil price as well as in the ground permeability. In this study, we formulate the oil well placement problem as a global optimization problem that depends on the output of a finite volume solver for the two-phase immiscible flow (water-oil). Then, we employ the machinery of Bayesian global optimization (BGO) to solve it using a limited simulation budget. BGO uses Gaussian process regression (GPR) to represent our state of knowledge about the objective as captured by a finite number of simulations and adaptively selects novel simulations via the expected improvement (EI) criterion. Finally, we develop an extension of the EI criterion to the case of noisy objectives enabling us to solve the oil well placement problem while taking into account uncertainties in the oil price and the ground permeability. We demonstrate numerically the efficacy of the proposed methods and find valuable computational savings.

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