A recent research direction in data-driven modeling is the identification of dynamic networks, in which measured vertex signals are interconnected by dynamic edges represented by causal linear transfer functions. The major question addressed in this article is where to allocate external excitation signals such that a network model set becomes generically identifiable when measuring all vertex signals. To tackle this synthesis problem, a novel graph structure, referred to as directed pseudotree, is introduced, and the generic identifiability of a network model set can be featured by a set of disjoint directed pseudotrees that cover all the parameterized edges of an extended graph, which includes the correlation structure of the process noises. Thereby, an algorithmic procedure is devised, aiming to decompose the extended graph into a minimal number of disjoint pseudotrees, whose roots then provide the appropriate locations for excitation signals. Furthermore, the proposed approach can be adapted using the notion of antipseudotrees to solve a dual problem, which is to select a minimal number of measurement signals for generic identifiability of the overall network, under the assumption that all the vertices are excited.

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In reservoir engineering, it is attractive to characterize the difference between reservoir models in metrics that relate to the economic performance of the reservoir as well as to the underlying geological structure. In this paper, we develop a dissimilarity measure that is based on reservoir flow patterns under a particular operational strategy. To this end, a spatial-temporal tensor representation of the reservoir flow patterns is used, while retaining the spatial structure of the flow variables. This allows reduced-order tensor representations of the dominating patterns and simple computation of a flow-induced dissimilarity measure between models. The developed tensor techniques are applied to cluster model realizations in an ensemble, based on similarity of flow characteristics.

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Model-based dynamic optimization of the water-flooding process in oil reservoirs is a computationally complex problem and suffers from high levels of uncertainty. A traditional way of quantifying uncertainty in robust water-flooding optimization is by considering an ensemble of uncertain model realizations. These models are generally not validated with data and the resulting robust optimization strategies are mostly offline or open-loop. The main focus of this work is to develop an adaptive or online robust optimization scheme using residual analysis as a major ingredient. The models in an ensemble are confronted with data and an adapted ensemble is formed with only those models that are not invalidated. As a next step, the robust optimization is again performed (i.e., updated/adjusted) with this adapted ensemble. The adapted ensemble gives a less conservative description of uncertainty and also reduces the high computational cost involved in robust optimization. Simulation example shows that an increase in the objective function value with a reduction of uncertainty on these values is obtained with the developed adaptive robust scheme compared to an open-loop offline robust strategy with the full ensemble and an adaptive scheme using Ensemble Kalman Filter (EnKF), which is one of the most common parameter estimation methods in reservoir simulations.

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Model-based economic optimization of oil production has a significant scope to increase financial life-cycle performance. The net-present-value (NPV) objective in this optimization, because of its nature, focuses on long-term gains, whereas short-term production is not explicitly addressed. At the same time, the achievable NPV is highly uncertain because of strongly varying economic conditions and limited knowledge of the reservoir-model parameters. The prime focus of this work is to develop optimization strategies that balance both long-term and short-term economic objectives and also offer robustness to the long-term NPV. An earlier robust hierarchical optimization method honoring geological uncertainty with robust long-term and short-term NPV objectives serves as a starting base of this work. We address the issue of extending this approach to include economic uncertainty and aim to analyze how the optimal solution reduces the uncertainty in the achieved average NPV. An ensemble of varying oil prices is used to model economic uncertainty with average NPVs as robust objectives in the hierarchical approach. A weighted-sum approach is used with the same objectives to quantify the effect of uncertainty. To reduce uncertainty, a mean-variance-optimization (MVO) objective is then considered to maximize the mean and also minimize the variance. A reduced effect of uncertainty on the long-term NPV is obtained compared with the uncertainty in the mean-optimization (MO) objectives. Last, it is investigated whether, because of the better handling of uncertainty in MVO, a balance between short-term and long-term gains can be naturally obtained by solving a single-objective MVO. Simulation examples show that a faster NPV buildup is naturally achieved by choosing appropriate weighting of the variance term in the MVO objective. Copyright [2017], Society of Petroleum Engineers.@en

In this work, the application of tensor methodologies for computer-assisted history matching of channelized reservoirs is explored. A tensor-based approach is used for the parameterization of petrophysical parameters to reduce the dimensionality of the parameter estimation problem. Building on the work of Afra and Gildin (2013); Afra et.al. (2014); Afra and Gildin (2016), permeability fields of multiple model realizations are collected in a tensor form which is subsequently decomposed to derive a low-dimensional representation of the dominant spatial structures in the models. This representation then is used to estimate an identifiable reduced set of parameters using an ensemble Kalman filter (EnKF) strategy. This approach is attractive for the parameter estimation of permeabilities because it increases the ability to represent channelized structures in the updates resulting in an improved predictive capacity of the history-matched models. In particular, channel continuity is better preserved than with a Principal Component Analysis (PCA) parameterization.@en

We present a method to determine lower and upper bounds to the predicted production or any other economic objective from history-matched reservoir models. The method consists of two steps: 1) performing a traditional computer-assisted history match of a reservoir model with the objective to minimize the mismatch between predicted and observed production data through adjusting the grid block permeability values of the model. 2) performing two optimization exercises to minimize and maximize an economic objective over the remaining field life, for a fixed production strategy, by manipulating the same grid block permeabilities, however without significantly changing the mismatch obtained under step 1. This is accomplished through a hierarchical optimization procedure that limits the solution space of a secondary optimization problem to the (approximate) null space of the primary optimization problem. We applied this procedure to two different reservoir models. We performed a history match based on synthetic data, starting from a uniform prior and using a gradient-based minimization procedure. After history matching, minimization and maximization of the net present value (NPV), using a fixed control strategy, were executed as secondary optimization problems by changing the model parameters while staying close to the null space of the primary optimization problem. In other words, we optimized the secondary objective functions, while requiring that optimality of the primary objective (a good history match) was preserved. This method therefore provides a way to quantify the economic consequences of the well-known problem that history matching is a strongly ill-posed problem. We also investigated how this method can be used as a means to assess the cost-effectiveness of acquiring different data types to reduce the uncertainty in the expected NPV.@en

We consider the input design problem of finding the minimal required experiment time such that accuracy constraints on the parameter estimate of an identification experiment are satisfied, while also respecting signal amplitude bounds. The input signal is parameterized as a multi-sine. We first show how multiple linear matrix inequalities from the least-costly and applications-oriented experiment design frameworks can be transformed into a generalised E-optimality constraint. Then, the solution to our problem is found by: (i) designing a multi-sine of one period with the Guillaume-Manchester algorithm [12], [10] that minimises the generalised E-optimality criterion under signal amplitude bounds, and (ii) utilising periodicity and an optimality condition to scale the experiment time such that the imposed accuracy constraints are also respected. An example shows an experiment time reduction of 50% compared with a traditional least-costly experiment design approach.

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This paper addresses the problem of obtaining an estimate of a particular module of interest that is embedded in a dynamic network with known interconnection structure. In this paper it is shown that there is considerable freedom as to which variables can be included as inputs to the predictor, while still obtaining consistent estimates of the particular module of interest. This freedom is encoded into sufficient conditions on the set of predictor inputs that allow for consistent identification of the module. The conditions can be used to design a sensor placement scheme, or to determine whether it is possible to obtain consistent estimates while refraining from measuring particular variables in the network. As identification methods the Direct and Two Stage Prediction-Error methods are considered. Algorithms are presented for checking the conditions using tools from graph theory.

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We consider robust ensemble-based (EnOpt) multiobjective production optimization of on/off inflow-control devices (ICDs) for a sector model inspired by a real-field case. The use of on/off valves as optimization variables leads to a discrete control problem. We propose a reparameterization of such discrete controls in terms of switching times (i.e., we optimize the time at which a particular valve is either open or closed). This transforms the discrete control problem into a continuous control problem that can be efficiently handled with the EnOpt method. In addition, this leads to a significant reduction in the number of controls that is expected to be beneficial for gradient quality when using approximate gradients. We consider an ensemble of sector models where the uncertainty is described by different permeability, porosity, net/gross ratios, and initial water-saturation fields. The controls are the ICD settings over time in the three horizontal injection wells, with approximately 15 ICDs per well. Different optimized strategies resulting from different initial strategies were compared. We achieved a mean 4.2% increase in expected net present value (NPV) at a 10% discount rate compared with a traditional pressure-maintenance strategy. Next, we performed a sequential biobjective optimization and achieved an increase of 9.2% in the secondary objective (25% discounted NPV to emphasize shortterm production gains) for a minimal decrease of 1% in the primary objective (0% discounted NPV to emphasize long-term recovery gains), as averaged over the 100 geological realizations. The work flow was repeated for alternative numbers of ICDs, showing that having fewer control options lowers the expected value for this particular case. The results demonstrate that ensemble-based optimization work flows are able to produce improved robust recovery strategies for realistic field-sector models against acceptable computational cost.

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This paper extends previous work on value of information (VOI) assessment in closed-loop reservoir management (CLRM) to estimate the added value of performing multiple measurements along the producing life of the reservoir. The new procedure is based on the workflow from our previous paper which allows to quantify the VOI of a single observation under geological uncertainty. Here we show that, by modifying that workflow slightly, it is possible to assess the value of a series of measurements without a prohibitive increase in computational costs. The approach is illustrated with two cases based on a simple water flooding problem in a two-dimensional five-spot reservoir: the first one, in which we assess the value of a series of production measurements, and the second one, in which we estimate the additional value of water front positions tracked by an interpreted time-lapse seismic survey. We believe that our proposed workflow is a complete methodology to estimate the VOI in a CLRM context because we take into account that the production strategy is updated periodically after new information has been assimilated in the models. However, future work will be required to reduce the computational load to allow for the application of the workflow to real field cases.@en

We present a novel method for estimating physical properties of an underground hydrocarbon reservoir, on the basis of generally measured wellbore ow rate and pressure signals at the bottom of a producing well. The method uses instrumental variable-based system identification techniques to solve for a closed-loop errors-in-variables problem. It is different from the conventional methods as it allows the instrumental variable signal to be correlated with the input and output signals' noise. This property increases the number of possible candidates to be used as the instrumental variable signal. The application of the proposed method has been investigated on a synthetic case study.

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With advancing technology, systems are becoming increasingly interconnected and form more complex networks. Additionally, more measurements are available from systems due to cheaper sensors. Hence there is a need for identification methods specifically designed for networks. For dynamic networks with known interconnection structures, several methods have been proposed for obtaining consistent estimates. We suppose that the internal variables in the network are measured with noise, but that there are external reference signals present in the network that are known exactly. A method that is able to deal with this situation is the two stage method, which solves several open loop identification problems sequentially. In this paper it is shown that solving the problems simultaneously leads to estimates with lower variance.@en