@MASTERSTHESIS\{IMM2015-06876,
    author       = "P. E. Aackermann",
    title        = "Stochastic Optimization and Risk Management in the Production Optimization of Oil Reservoirs",
    year         = "2015",
    school       = "Technical University of Denmark, Department of Applied Mathematics and Computer Science",
    address      = "Richard Petersens Plads, Building 324, {DK-}2800 Kgs. Lyngby, Denmark, compute@compute.dtu.dk",
    type         = "",
    note         = "{DTU} supervisor: John Bagterp J{\o}rgensen, jbjo@dtu.dk, {DTU} Compute",
    url          = "http://www.compute.dtu.dk/English.aspx",
    abstract     = "Given uncertainty of oil reservoir properties, such as the permeability field, the net present value (NPV) received from oil reservoir production becomes stochastic. This encourages optimization strategies that focuses on maximizing the expected {NPV} while minimizing the risk of low outcomes.

The goal of this thesis is to investigate the potential of utilizing such optimization strategies. Especially the focus is on the performance achieved when using Robust Optimization (RO) over an ensemble of 100 reservoir models with a bicriterion objective function including both Conditional Value at Risk (CVaR) as the risk measure and {NPV} as the profitability measure. This is compared to more conventional reactive strategies where producers are shut when they are no longer profitable and Certainty Equivalence (CE) optimization that only optimize over the expected reservoir model parameters. In the Mean-CVaR optimization the focus can be shifted between the parameters and create an efficient frontier that shows the level of risk associated with a given {NPV} which gives more options for a satisfying solution.

For the simulation we will use a oil reservoir with 3 injection wells on one side and 3 producer wells on the other side of the reservoir and simulate over 8 years. The simulations will be done in Matlab using the Reservoir Simulation Toolbox {MRST}.

The Mean-CVaR optimization greatly outperformed the {CE} optimization both in terms of expected {NPV} and CVaR. Compared to the the Reactive Strategy we generated an efficient frontier with up to 2.3\% higher average {NPV}. The CVaR of the Reactive Strategy could however not be fully matched."
}