The research presented in this paper was partly funded by the Integrated Systems Approach to Petroleum Production (ISAPP) and Recovery Factory (RF) projects.The 'Egg Model' is a synthetic reservoir model consisting of an ensemble of 101 relatively small three-dimensional realizations of a channelized oil reservoir produced under water flooding conditions with eight water injectors and four oil producers. It has been used in numerous publications to demonstrate a variety of aspects related to computer-assisted flooding optimization and history matching. Unfortunately the details of the parameter settings are not always identical and not always fully documented in several of these publications. We present a 'standard version' of the Egg Model which is meant to serve as a test case in future publications, and a dataset of 100 permeability realizations in addition to the permeability field used for the standard model. We implemented and tested the model in four reservoir simulators: Dynamo/Mores (Shell), Eclipse (Schlumberger), AD-GPRS (Stanford University) and MRST (Sintef), which produced near-identical output. This article describes the input parameters of the standard model. Together with the input files for the various simulators, it has been be uploaded in the 3TU.Datacentrum repository with free access to external users.

SUMMARYWe consider robust ensemble-based multi-objective optimization using a hierarchical switching algorithm for combined long-term and short term water flooding optimization. We apply a modified formulation of the ensemble gradient which results in improved performance compared to earlier formulations. We also apply multi-dimensional scaling to visualize projections of the high-dimensional search space, to aid in understanding the complex nature of the objective function surface and the performance of the optimization algorithm. This provides insights into the quality of the gradient, and confirms the presence of ridges in the objective function surface which can be exploited for multi-objective optimization. We used a 18553-gridblock reservoir model of a channelized reservoir with 4 producers and 8 injectors. The controls were the flow rates in the injectors, and the long-term and short-term objective functions were undiscounted net present value (NPV) and highly discounted (25%) NPV respectively. We achieved an increase of 15.2% in the secondary objective for a decrease of 0.5% in the primary objective, averaged over 100 geological realizations. The total number of reservoir simulations was around 20000, which indicates the potential to use the ensemble optimization method for robust multi-objective optimization of medium-sized reservoir models.

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Discretisation of linear parameter-varying (LPV) systems is a relevant, but insufficiently investigated problem of both LPV control design and system identification. In this contribution, existing results on the discretisation of LPV state-space models with static dependence (without memory) on the scheduling signal are surveyed and new methods are introduced. These approaches are analysed in terms of approximation error, considering ideal zero-order hold actuation and sampling of the input-output signals and scheduling variables of the system. Criteria to choose appropriate sampling periods with respect to the investigated methods are also presented. The application of the considered approaches on state-space representations with dynamic dependence (with memory) on the scheduling is investigated in a higherorder hold sense.

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