This chapter discusses leading problems linked to energy that the world is now confronting and to propose some ideas concerning possible solutions. Oil deserves special attention among all energy sources. Since the beginning of 1981, it has merely been continuing and enhancing the downward movement in consumption and prices caused by excessive rises, especially for light crudes such as those from Africa, and the slowing down of worldwide economic growth. Densely-populated oil-producing countries need to produce to live, to pay for their food and their equipment. If the economic growth of the industrialized countries were to be 4%, even if investment in the rational use of energy were pushed to the limit and the development of nonpetroleum energy sources were also pursued actively, it would be extremely difficult to prevent a sharp rise in prices. It is evident that it is absolutely necessary to pursue actively the development of coal, natural gas, and nuclear power if a physical shortage of energy is not to block economic growth.

World energy outlook

Introduction to stochastic programming

In this paper, the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization. Stable feedback schemes obtainable from a given plant are parameterized. Salient properties of sensitivity reducing schemes are derived, and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity. The theory is developed for input-output systems in a general setting of Banach algebras, and then specialized to a class of multivariable, time-invariant systems characterized by n × n matrices of H? frequency response functions, either with or without zeros in the right half-plane. The approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity, and on the concept of an approximate inverse. Approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction. An indicator of approximate invertibility, called a measure of singularity, is introduced. The measure of singularity of a linear time-invariant plant is shown to be determined by the location of its right half-plane zeros. In the absence of plant uncertainty, the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure. In particular, if there are no right half-plane zeros, sensitivity can be made arbitrarily small. The feedback schemes used in the optimization of sensitiviiy resemble the lead-lag networks of classical control design. Some of their properties, and methods of constructing them in special cases are presented.

Feedback and Optimal Sensitivity: Model Reference Transformations, Multiplicative Seminorms, and Approximate Inverses

This paper provides a survey of results in linear parameter-varying (LPV) control that have been validated by experiments and/or high-fidelity simulations. The LPV controller synthesis techniques employed in the references of this survey are briefly reviewed and compared. The methods are classified into polytopic, linear fractional transformation, and gridding-based techniques and it is reviewed how in each of these approaches, synthesis can be carried out as a convex optimization problem via a finite number of linear matrix inequalities (LMIs) for both parameter-independent and parameter-dependent Lyapunov functions. The literature is categorized with regard to the application, the complexity induced by the controlled system’s dynamic and scheduling orders, as well as the synthesis method. Exemplary cases dealing with specific control design problems are presented in more detail to point control engineers to possible approaches that have been successfully applied. Furthermore, key publications in LPV control are related to application achievements on a timeline.

A Survey of Linear Parameter-Varying Control Applications Validated by Experiments or High-Fidelity Simulations

Prediction error identification of linear systems: A nonparametric Gaussian regression approach

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.

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The egg model - A geological ensemble for reservoir simulation

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 higher-order hold sense.

Discretisation of linear parameter-varying state-space representations

This paper proposes a new methodology to perform value of information (VOI) analysis within a closed-loop reservoir management (CLRM) framework. The workflow combines tools such as robust optimization and history matching in an environment of uncertainty characterization. The approach is illustrated with two simple examples: an analytical reservoir toy model based on decline curves and a water flooding problem in a two-dimensional five-spot reservoir. The results are compared with previous work on other measures of information valuation, and we show that our method is a more complete, although also more computationally intensive, approach to VOI analysis in a CLRM framework. We recommend it to be used as the reference for the development of more practical and less computationally demanding tools for VOI assessment in real fields.

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Value of information in closed-loop reservoir management

We 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.

/pdf/robust-ensemble-based-multi-objective-optimization-1mhegetd8z.pdf

van den Pmj Paul Hof

Papers

The egg model - A geological ensemble for reservoir simulation

Discretisation of linear parameter-varying state-space representations

Value of information in closed-loop reservoir management

Robust ensemble-based multi-objective optimization

MIMO closed-loop identification of an MSW incinerator