Dynamic optimization for robust path planning of horizontal oil wells

This paper considers the three-dimensional path planning problem for horizontal oil wells. The decision variables in this problem are the curvature, tool-face angle and switching points for each turn segment in the path, and the optimization objective is to minimize the path length and target error. The optimal curvatures, tool-face angles and switching points can be readily determined using existing gradient-based dynamic optimization techniques. However, in a real drilling process, the actual curvatures and tool-face angles will inevitably deviate from the planned optimal values, thus causing an unexpected increase in the target error. This is a critical challenge that must be overcome for successful practical implementation. Accordingly, this paper introduces a sensitivity function that measures the rate of change in the target error with respect to the curvature and tool-face angle of each turn segment. Based on the sensitivity function, we propose a new optimization problem in which the switching points are adjusted to minimize target error sensitivity subject to continuous state inequality constraints arising from engineering specifications, and an additional constraint specifying the maximum allowable increase in the path length from the optimal value. Our main result shows that the sensitivity function can be evaluated by solving a set of auxiliary dynamic systems. By combining this result with the well-known time-scaling transformation, we obtain an equivalent transformed problem that can be solved using standard nonlinear programming algorithms. Finally, the paper concludes with a numerical example involving a practical path planning problem for a Ci-16-Cp146 well

A General Spatio-Temporal Clustering-Based Non-local Formulation for Multiscale Modeling of Compartmentalized Reservoirs

Representing the reservoir as a network of discrete compartments with neighbor and non-neighbor connections is a fast, yet accurate method for analyzing oil and gas reservoirs. Automatic and rapid detection of coarse-scale compartments with distinct static and dynamic properties is an integral part of such high-level reservoir analysis. In this work, we present a hybrid framework specific to reservoir analysis for an automatic detection of clusters in space using spatial and temporal field data, coupled with a physics-based multiscale modeling approach. In this work a novel hybrid approach is presented in which we couple a physics-based non-local modeling framework with data-driven clustering techniques to provide a fast and accurate multiscale modeling of compartmentalized reservoirs. This research also adds to the literature by presenting a comprehensive work on spatio-temporal clustering for reservoir studies applications that well considers the clustering complexities, the intrinsic sparse and noisy nature of the data, and the interpretability of the outcome. Keywords: Artificial Intelligence; Machine Learning; Spatio-Temporal Clustering; Physics-Based Data-Driven Formulation; Multiscale Modelin

Closed Loop Feedback Control of Injection and Production Wells in the SPE Brugge Model

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Robust Optimization for Sequential Field Development Planning

To achieve high profitability from an oil field, optimizing the field development strategy (e.g., well type, well placement, drilling schedule) before committing to a decision is critically important. The profitability at a given control setting is predicted by running a reservoir simulation model, while determining a robust optimal strategy generally requires many expensive simulations. In this work, we focus on developing practical and efficient methodologies to solving reservoir optimization problems for which the actions that can be controlled are discrete and sequential (e.g., drilling sequence of wells). The type of optimization problems I address must take into account both geological uncertainty and the reduction in uncertainty resulting from observations. As the actions are discrete and sequential, the process can be characterized as sequential decision- making under uncertainty, where past decisions may affect both the possibility of the future choices of actions and the possibility of future uncertainty reduction. This thesis tackles the challenges in sequential optimization by considering three main issues: 1) optimizing discrete-control variables, 2) dealing with geological uncertainty in robust optimization, and 3) accounting for future learning when making optimal decisions. As the first contribution of this work, we develop a practical online-learning method- ology derived from A* search for solving reservoir optimization problems with discrete sets of actions. Sequential decision making can be formulated as finding the path with the maximum reward in a decision tree. To efficiently compute an optimal or near- optimal path, heuristics from relaxed problems are first used to estimate the maximum value constrained to past decisions, and then online-learning techniques are applied to improve the estimation accuracy by learning the errors of the initial approximations ob- tained from previous decision steps. In this way, an accurate estimate of the maximized value can be inexpensively obtained, thereby guiding the search toward the optimal so- lution efficiently. This approach allows for optimization of either a complete strategy with all available actions taken sequentially or only the first few actions at a reduced cost by limiting the search depth. The second contribution is related to robust optimization when an ensemble of reservoir models is used to characterize geological uncertainty. Instead of computing the expectation of an objective function using ensemble-based average value, we develop various bias-correction methods applied to the reservoir mean model to estimate the expected value efficiently without sacrificing accuracy. The key point of this approach is that the bias between the objective-function value obtained from the mean model and the average objective-function value over an ensemble can be corrected by only using information from distinct controls and model realizations. During the optimization process, we only require simulations of the mean model to estimate the expected value using the bias-corrected mean model. This methodology can significantly improve the efficiency of robust optimization and allows for fairly general optimization methods. In the last contribution of this thesis, we address the problem of making optimal decisions while considering the possibility of learning through future actions, i.e., op- portunities to improve the optimal strategy resulting from future uncertainty reduction. To efficiently account for the impact of future information on optimal decisions, we sim- plify the value of information analysis through key information that would help make better future decisions and the key actions that would result in obtaining that informa- tion. In other words, we focus on the use of key observations to reduce the uncertainty in key reservoir features for optimization problems, rather than using all observations to reduce all uncertainties. Moreover, by using supervised-learning algorithms, we can identify the optimal observation subset for key uncertainty reduction automatically and evaluate the information’s reliability simultaneously. This allows direct computation of the posterior probability distribution of key uncertainty based on Bayes’ rule, avoiding the necessity of expensive data assimilation algorithms to update the entire reservoir modeDoktorgradsavhandlin

Stochastic optimal control and algorithm of the trajectory of horizontal wells

AbstractThis paper presents a nonlinear, multi-phase and stochastic dynamical system according to engineering background. We show that the stochastic dynamical system exists a unique solution for every initial state. A stochastic optimal control model is constructed and the sufficient and necessary conditions for optimality are proved via dynamic programming principle. This model can be converted into a parametric nonlinear stochastic programming by integrating the state equation. It is discussed here that the local optimal solution depends in a continuous way on the parameters. A revised Hooke–Jeeves algorithm based on this property has been developed. Computer simulation is used for this paper, and the numerical results illustrate the validity and efficiency of the algorithm

History matching and production optimization under uncertainties – Application of closed-loop reservoir management

There is an intensive investigation reported in the literature regarding the development of robust methods to improve the economical performance during the production management of petroleum fields. One paradigm that emerged in the last decade and has been calling the attention of various research groups is known as closed-loop reservoir management. The closed-loop entails the application of history matching and production optimization in a near-continuous feedback process. This work presents a closed-loop workflow constructed with ensemble-based methods. The proposed workflow consists of three components: history matching, model selection and production optimization. For history matching, we use the method known as ensemble smoother with multiple data assimilation. For model selection, we propose a procedure grounded on the calculation of distances defined in a metric space and a minimization procedure to determine the optimal set of representative models. For production optimization, we use the ensemble-based optimization method. We investigate the performance of each method separately before testing the complete closed-loop in a benchmark problem based on Namorado field in Campos Basis, Brazil. The results showed the effectiveness of the proposed methods to form a robust closed-loop workflow.Indisponível