Ensemble-based optimization has recently received great attention as a potentially powerful technique for life-cycle production optimization, which is a crucial element of reservoir management. Recent publications have increased both the number of applications and the theoretical understanding of the algorithm. However, there is still ample room for further development since most of the theory is based on strong assumptions. Here, the mathematics (or statistics) of Ensemble Optimization is studied, and it is shown that the algorithm is a special case of an already well-defined natural evolution strategy known as Gaussian Mutation. A natural description of uncertainty in reservoir management arises from the use of an ensemble of history-matched geological realizations. A logical step is therefore to incorporate this uncertainty description in robust life-cycle production optimization through the expected objective function value. The expected value is approximated with the mean over all geological realizations. It is shown that the frequently advocated strategy of applying a different control sample to each reservoir realization delivers an unbiased estimate of the gradient of the expected objective function. However, this procedure is more variance prone than the deterministic strategy of applying the entire ensemble of perturbed control samples to each reservoir model realization. In order to reduce the variance of the gradient estimate, an importance sampling algorithm is proposed and tested on a toy problem with increasing dimensionality.
In the history matching process reservoir parameters are estimated so they can be further used in a simulator to reproduce the past behaviour of the reservoir. During the last two decades the methodology evolved from manual methods to computer assisted procedures which can handle larger amounts of data. Now, when the computational power has increased enough, it is possible to perform more complicated computations and use more advance methods and at the same time choose more realistic simulation models. In spite of that, the field cases which are chosen to history match, even if more realistic they often are still synthetic. Therefore, the history matching procedure has been applied as a real case study based on Norne Field located near the Norwegian coastline. The preliminary results and the experience of handling realistic dataset are shared in this paper. The Ensemble Kalman Filter, which is recently a very popular method, has been chosen to match the well production rates and bottom-hole pressures to the real observations acquired in the segment of the field. Within the numerical experiment, permeability and porosity were estimated. Obtained results are a basis for continuation and the further improvement of the history matching process of the Norne Field. In addition, the issues encountered during the study are discussed i.e. the treatment of the flow conditions on the segment boundary and construction of initial ensemble.
Applications of the wind farm layout optimisation problem focus on optimally positioning a certain number of turbines within a wind farm so that annual energy production (AEP) is maximised. This study addresses an earlier stage in the wind farm development process. Instead of optimising the individual positions of a certain number of turbines of a selected model, the control variables in the optimisation are rotor diameter of a wind turbine of fixed nominal power, number of turbines in a wind farm of fixed area and orientation angle of turbines in the farm. In addition to AEP, this study considers capital and operational expenses of a wind farm to calculate the levelized cost of energy (LCoE), which is the objective function. Given the stage of development addressed, it is also essential that uncertainty is considered; here the focus is on the impact of wind resource uncertainty. The optimisation is performed with a recently developed state-of-the-art stochastic gradient based method (StoSAG) which has shown in different domains to be computationally efficient and accurate when dealing with optimisation problems under uncertainty. Our results show non-trivial optimal designs with LCoE reductions of ∼0.5% compared to the most optimal solution from a sensitivity analysis.
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