17 results on '"Mathias C. Bellout"'
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2. FieldOpt: A powerful and effective programming framework tailored for field development optimization.
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Einar J. M. Baumann, Stein I. Dale, and Mathias C. Bellout
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- 2020
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3. An Automatic Well Planner for Complex Well Trajectories
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Brage S. Kristoffersen, Thiago Lima Silva, Mathias C. Bellout, and Carl Fredrik Berg
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Mathematical optimization ,Artificial neural network ,Test data generation ,Geosteering ,0208 environmental biotechnology ,Channelized ,02 engineering and technology ,010502 geochemistry & geophysics ,Planner ,01 natural sciences ,020801 environmental engineering ,Mathematics (miscellaneous) ,Differential evolution ,Trajectory ,General Earth and Planetary Sciences ,InformationSystems_MISCELLANEOUS ,Representation (mathematics) ,computer ,0105 earth and related environmental sciences ,computer.programming_language - Abstract
A data-driven automatic well planner procedure is implemented to develop complex well trajectories by efficiently adapting to near-well reservoir properties and geometry. The procedure draws inspiration from geosteering drilling operations, where modern logging-while-drilling tools enable the adjustment of well trajectories during drilling. Analogously, the proposed procedure develops well trajectories based on a selected geology-based fitness measure using an artificial neural network as the decision maker in a virtual sequential drilling process within a reservoir model. While neural networks have seen extensive use in other areas of reservoir management, to the best of our knowledge, this work is the first to apply neural networks on well trajectory design within reservoir models. Importantly, both the input data generation used to train the network and the actual trajectory design operations conducted by the trained network are efficient calculations, since these rely solely on geometric and initial properties of the reservoir, and thus do not require additional simulations. Therefore, the main advantage over traditional methods is the highly articulated well trajectories adapted to reservoir properties using a low-order well representation. Well trajectories generated in a realistic reservoir by the automatic well planner are qualitatively and quantitatively compared to trajectories generated by a differential evolution algorithm. Results show that the resulting trajectories improve productivity compared to straight line well trajectories, both for channelized and geometrically complex reservoirs. Moreover, the overall productivity with the resulting trajectories is comparable to well solutions obtained using differential evolution, but at a much lower computational cost.
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- 2021
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4. Derivative-free trust region optimization for robust well control under geological uncertainty
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Thiago L. Silva, Mathias C. Bellout, Caio Giuliani, Eduardo Camponogara, and Alexey Pavlov
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Computational Mathematics ,Computational Theory and Mathematics ,Derivative-free trust-region algorithm ,Well control optimization ,Computers in Earth Sciences ,Robust optimization under geological uncertainty ,Computer Science Applications - Abstract
A Derivative-Free Trust-Region (DFTR) algorithm is proposed to solve the robust well control optimization problem under geological uncertainty. Derivative-Free (DF) methods are often a practical alternative when gradients are not available or are unreliable due to cost function discontinuities, e.g., caused by enforcement of simulation-based constraints. However, the effectiveness of DF methods for solving realistic cases is heavily dependent on an efficient sampling strategy since cost function calculations often involve time-consuming reservoir simulations. The DFTR algorithm samples the cost function space around an incumbent solution and builds a quadratic polynomial model, valid within a bounded region (the trust-region). A minimization of the quadratic model guides the method in its search for descent. Because of the curvature information provided by the model-based routine, the trust-region approach is able to conduct a more efficient search compared to other sampling methods, e.g., direct-search approaches. DFTR is implemented within FieldOpt, an open-source framework for field development optimization, and is tested in the Olympus benchmark against two other types of methods commonly applied to production optimization: a direct-search (Asynchronous Parallel Pattern Search) and a population-based (Particle Swarm Optimization). Current results show that DFTR has improved performance compared to the model-free approaches. In particular, the method presented improved convergence, being capable to reach solutions with higher NPV requiring comparatively fewer iterations. This feature can be particularly attractive for practitioners who seek ways to improve production strategies while using an ensemble of full-fledged models, where good convergence properties are even more relevant.
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- 2022
5. Efficient well placement optimization under uncertainty using a virtual drilling procedure
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Carl Fredrik Berg, Thiago Lima Silva, Brage S. Kristoffersen, and Mathias C. Bellout
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Computational Mathematics ,Mathematical optimization ,Computational Theory and Mathematics ,Artificial neural network ,Asynchronous communication ,Geosteering ,Path (graph theory) ,Trajectory ,Particle swarm optimization ,Robust optimization ,Computers in Earth Sciences ,Pattern search ,Computer Science Applications - Abstract
An Automatic Well Planner (AWP) is used to efficiently adjust pre-determined well paths to honor near-well properties and increase overall production. AWP replicates modern geosteering decision-making where adjustments to pre-programmed well paths are driven by continuous integration of data obtained from logging-while-drilling and look-ahead technology. In this work, AWP is combined into a robust optimization scheme to develop trajectories that follow reservoir properties in a more realistic manner compared to common well representations for optimization purposes. Core AWP operation relies on an artificial neural network coupled with a geology-based feedback mechanism. Specifically, for each well path candidate obtained from an outer-loop optimization procedure, AWP customizes trajectories according to the particular geological near-well properties of each realization in an ensemble of models. While well placement searches typically rely on linear well path representations, AWP develops customized trajectories by moving sequentially from heel to the toe. Analog to realistic drilling operations, AWP determines subsequent trajectory points by efficiently processing neighboring geological information. Studies are performed using the Olympus ensemble. AWP and the two derivative-free algorithms used in this work, Asynchronous Parallel Pattern Search (APPS) and Particle Swarm Optimization (PSO), are implemented using NTNU’s open-source optimization framework FieldOpt. Results show that, with both APPS and PSO, the AWP solutions outperform the solutions obtained with a straight-line parameterization in all the three tested well placement optimization scenarios, which varied from the simplest scenario with a sole producer in a single-realization environment to a scenario with the full ensemble and multiple producers.
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- 2021
6. Gradient-based constrained well placement optimization
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Mathias C. Bellout and Oleg Volkov
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Mathematical optimization ,Discretization ,Computer science ,Augmented Lagrangian method ,Finite difference ,Perturbation (astronomy) ,Binary number ,010103 numerical & computational mathematics ,Solver ,010502 geochemistry & geophysics ,Geotechnical Engineering and Engineering Geology ,Grid ,01 natural sciences ,Fuel Technology ,0101 mathematics ,0105 earth and related environmental sciences ,Sequential quadratic programming - Abstract
A novel well placement gradient approximation methodology is developed based on performing finite difference approximations of augmented Lagrangian derivatives within the adjoint formulation. The methodology is efficient because it requires only a pair of (forward and backward) simulations to yield a cost function sensitivity with respect to well placement coordinates. The approximated derivative is used within a Sequential Quadratic Programming (SQP) solver ensuring fast convergence and efficient constraint-handling. An extensive error analysis is performed to identify the gradient approximation errors associated with different perturbation ranges. This analysis provides information regarding the appropriate perturbation step size range needed to maintain a consistent gradient approximation while reducing errors associated with the simulation and the discretized nature of the reservoir. We validate the efficiency of the approach by solving for optimal well placement and comparing the results against two major gradient-based well placement approaches from the literature. For these cases, the methodology developed in this work delivers higher or similar final objective values while providing better performance in terms of fewer cost function evaluations. Finally, the methodology is used to find the optimal configuration of multiple deviated producers both in a binary channelized case and in a case based on the Brugge reservoir. These applications show that the proposed methodology can handle cases with more complex grid and production scenarios that require derivative information for the location of deviated wellbores in continuous space.
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- 2018
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7. Reduced well path parameterization for optimization problems through machine learning
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Carl Fredrik Berg, Brage S. Kristoffersen, Thiago Lima Silva, and Mathias C. Bellout
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Well placement ,Traverse ,Optimization problem ,Computer science ,business.industry ,Perforation (oil well) ,Derivative-free optimization ,Degrees of freedom (mechanics) ,Geotechnical Engineering and Engineering Geology ,Machine learning ,computer.software_genre ,Reservoir simulation ,Well parameterization ,Fuel Technology ,Robustness (computer science) ,Convergence (routing) ,Trajectory ,Artificial intelligence ,InformationSystems_MISCELLANEOUS ,business ,computer - Abstract
In this work we apply a recently developed machine learning routine for automatic well planning to simplify well parameterization in reservoir simulation models. This reduced-order parameterization is shown to be beneficial for well placement optimization, both in terms of convergence and final well configuration. The proposed machine learning routine maps trajectories that honor predefined engineering requirements by exploiting spatial information about the reservoir and prior domain-knowledge about the problem. In this paper, the well planner creates wells that traverse high-permeable parts of the reservoir, thereby increasing well productivity. Previous work found that small changes to the start- and end-points of the well had limited impact on most of the resulting well trajectories, since development of trajectories is chiefly determined by local information around the digital drill bit. In particular, changes in the depth component of the start- and end-points had limited impact on the trajectory away from the end-points. Based on these observations, this work reduces well parameterization to only include horizontal coordinates. The main assumption is that the perforated part of the well always enters the reservoir at the upper reservoir boundary, while the stopping criteria in the machine learning routine is a perforation length only. This formulation reduces the number of decision variables from six to four coordinates for each well. The resulting reduced search space enables a more efficient exploration effort at the cost of less freedom over the start and end points of the well path. However, we show that the highly-refined well trajectory developed by the well planning routine is robust and compensates for fewer degrees of freedom at the overarching parameterization. This robustness is tested by investigating the effect of different start locations on the automatic well planning routines. Moreover, the effect of the reduced well parameterization for well placement optimization is explored. Two optimization scenarios using four different optimizations algorithms are presented. Results show the implementation of the reduced well parameterization for optimization purposes consistently produces high quality solutions.
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- 2022
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8. A Derivative-Free Trust-Region Algorithm for Well Control Optimization
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Eduardo Camponogara, Thiago Lima Silva, Caio Merlini Giuliani, Mathias C. Bellout, and Alexey Pavlov
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Trust region ,Mathematical optimization ,education.field_of_study ,Optimization problem ,Quadratic equation ,Computer science ,Convergence (routing) ,Population ,Particle swarm optimization ,Function (mathematics) ,education ,Pattern search - Abstract
Summary A Derivative-Free Trust-Region (DFTR) algorithm is proposed to solve for the well control optimization problem. Derivative-Free (DF) methods are often a practical alternative because gradients may not be available and/or are unreliable due to cost function discontinuities, e.g., caused by enforcement of simulation-based constraints. However, the effectiveness of DF methods for solving realistic cases is heavily dependent on an efficient sampling strategy since cost function calculations often involve time-consuming reservoir simulations. The DFTR algorithm samples the cost function space around an incumbent solution and builds a quadratic approximation model, valid within a bounded region (the trust-region). A minimization of the quadratic model guides the method in its search for descent. Crucially, because of the curvature information provided by the model-based routine, the trust-region approach is able to conduct a more efficient search compared to other sampling methods, e.g., direct-search approaches. DFTR is implemented within FieldOpt, an open-source framework for field development optimization that provides flexibility with respect to problem parameterization and parallelization capabilities. DFTR is tested in the synthetic case Olympus against two other type of methods commonly applied to production optimization: a direct-search (Asynchronous Parallel Pattern Search) and a population-based (Particle Swarm Optimization). Current results show DFTR has promising convergence properties. In particular, the method is seen to reach fairly good solutions using only a few iterations. This feature can be particularly attractive for practitioners who seek ways to improve production strategies while using full-fledged models. Future work will focus on wider application of the algorithm in more complex field development problems such as joint problems and ICD optimization, and extensions to the algorithm to deal with multiple geological realizations and output constraints.
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- 2020
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9. An Automatic Well Planner for Efficient Well Placement Optimization Under Geological Uncertainty
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Carl Fredrik Berg, Thiago Lima Silva, Mathias C. Bellout, and Brage S. Kristoffersen
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Mathematical optimization ,Artificial neural network ,Asynchronous communication ,Path (graph theory) ,Trajectory ,Process (computing) ,Robust optimization ,Particle swarm optimization ,Pattern search - Abstract
Summary An Automatic Well Planner (AWP) is developed to efficiently adjust pre-determined well paths to honor near-well model properties and increase overall production. The AWP replicates a modern geo-steering decision-making process, where adjustments to pre-programmed well paths are driven by continuous integration of data obtained from logging-while-drilling and look-ahead technology. This work focuses on combining the AWP into a robust optimization scheme. AWP-determined well trajectories follow reservoir properties in a more realistic manner than common well representations; thus, they deal better with geological uncertainty. Specifically, the AWP creates custom trajectories that consider individual geological near-well conditions of each realization in an ensemble of models. Thus, for each well path calculated by the optimization procedure, the AWP creates one custom trajectory for each geological realization. The expected NPV, computed over the set of trajectories, is then used to assess the performance of the candidate well path. The core operation of the AWP relies on an artificial neural network for tailoring the trajectory to geological properties. The AWP embeds a geology-based feedback mechanism for the overall well placement search. Commonly, well placement searches are conducted using linear well path representations. Analog to realistic drilling operations, the AWP determines a custom trajectory by moving along such a path in a sequence of steps from the heel to the toe. Subsequent trajectory points are determined by the efficient processing of neighboring geological information through the AWP network. The proposed scheme is implemented within the open-source optimization framework FieldOpt, which provides a flexible interface for problem parameterization and parallelization. Tests are performed using two derivative-free algorithms: Asynchronous Parallel Pattern Search (APPS) and Particle Swarm Optimization (PSO). Both are applied to the Olympus ensemble. The results show that the AWP improved over a straight-line parametrization in a robust optimization scheme for both APPS and PSO.
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- 2020
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10. Well placement optimization subject to realistic field development constraints
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Bjarne A. Foss, Mathias C. Bellout, Remus Hanea, and Mansoureh Jesmani
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Mathematical optimization ,Particle swarm optimization ,Contrast (statistics) ,010103 numerical & computational mathematics ,010502 geochemistry & geophysics ,01 natural sciences ,Field (computer science) ,Computer Science Applications ,Term (time) ,Computational Mathematics ,Operator (computer programming) ,Computational Theory and Mathematics ,Reservoir engineering ,Embedding ,Penalty method ,0101 mathematics ,Computers in Earth Sciences ,Algorithm ,0105 earth and related environmental sciences ,Mathematics - Abstract
This work considers the well placement problem in reservoir management and field development optimization. In particular, it emphasizes embedding realistic and practical constraints into a mathematical optimization formulation. Such constraints are a prerequisite for the wider use of mathematical optimization techniques in well placement problems, since constraints are a way to incorporate reservoir engineering knowledge into the problem formulation. There are important design limitations that are used by the field development team when treating the well placement problem, and these limitations need to be articulated and eventually formalized within the problem before conducting the search for optimal well placements. In addition, these design limitations may be explicit or implicit. In this work, various design limitations pertaining to well locations have been developed in close collaboration with a field operator on the Norwegian Continental Shelf. Moreover, this work focuses on developing constraint-handling capability to enforce these various considerations during optimization. In particular, the Particle Swarm Optimization (PSO) algorithm is applied to optimize for the well locations, and various practical well placement constraints are incorporated into the PSO algorithm using two different constraint-handling techniques: a decoder procedure and the penalty method. The decoder procedure maps the feasible search space onto a cube and has the advantage of not requiring parameter tuning. The penalty method converts the constrained optimization problem into an unconstrained one by introducing an additional term, which is called a penalty function, to the objective function. In contrast to the penalty method, only feasible solutions are evaluated in the decoder method. Through numerical simulations, a comparison between the penalty method and the decoder technique is performed for two cases. We show that the decoder technique can easily be implemented for the well placement problem, and furthermore, that it performs better than the penalty method in most of the cases.
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- 2016
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11. FieldOpt: A powerful and effective programming framework tailored for field development optimization
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Mathias C. Bellout, Stein Inge Dale, and Einar J.M. Baumann
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Flexibility (engineering) ,business.industry ,Computer science ,0208 environmental biotechnology ,Decision quality ,Context (language use) ,02 engineering and technology ,010502 geochemistry & geophysics ,computer.software_genre ,Data structure ,01 natural sciences ,Industrial engineering ,020801 environmental engineering ,Data flow diagram ,Software framework ,Software ,Use case ,Computers in Earth Sciences ,business ,computer ,0105 earth and related environmental sciences ,Information Systems - Abstract
Petroleum field development involves critical decisions such as well location, well completion design and optimal control setting that have a significant impact on revenues and costs. These decisions are associated with a large degree of engineering effort that commonly involves time-consuming reservoir simulations to compute the performance of different field development scenarios. Increasingly within the petroleum industry, software tools and optimization methodology are developed and implemented to support and augment the various decision-making processes. The overall aim of these tools is to increase productivity and improve decision quality. Within this context, this work introduces an open-source, extensible, tailor-made programming framework: FieldOpt. FieldOpt’s primary purpose is rapid prototyping and testing of optimization procedures to solve critical field development problems. The framework is implemented in C++ and provides an efficient integration of mathematical optimization procedures with reservoir simulation. FieldOpt’s modular architecture and use of object-oriented programming allow the users to adapt and extend the code with ease. The architecture has proven successful in facilitating new optimization algorithms, new use cases, and new methodology for optimization with minimal effort and change to internal data structures and data flow. Three use cases are presented to demonstrate the optimization capabilities of FieldOpt as well as the flexibility and ease-of-use of the software regarding configuring various optimization procedures to solve a range of field development problems. The three use cases presented optimize on well control, well completion design and well placement parameters, respectively. For each case, both the configuration of the algorithms and problems within FieldOpt as well as the final solution and performance of the different optimization procedures are discussed. In all three cases, FieldOpt was able to find significant improvements or crucial information to decision making.
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- 2020
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12. Development Of Efficient Constraint-Handling Approaches For Well Placement Optimization
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Oleg Volkov and Mathias C. Bellout
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Set (abstract data type) ,Sequence ,Nonlinear system ,Mathematical optimization ,Process (engineering) ,Differential evolution ,Function (mathematics) ,Constraint (mathematics) ,Sequential quadratic programming - Abstract
Summary Efficient constraint-handling methodology is developed to solve for a set of concurrent geometric well placement constraints. This implementation enhances constraint-handling capability such that expert knowledge may more easily be incorporated into well placement problem formulations through realistic geology- and engineering-based nonlinear constraints. A well-defined collection of constraint definitions may, besides enforcing minimum feasibility, also make the optimization process more efficient by limiting the search to highly-relevant solution spaces. This is particularly important for well placement problems that commonly rely on time-consuming reservoir simulations for objective function evaluation. Constraints are imposed on parameters determining the configuration of multiple deviated wellbores in reservoir space, e.g., well length and inter-well distance. A constraint-handling repair approach based on an alternating projections methodology that solves each restriction as an independent constraint-handling subproblem is implemented. The subproblems are solved in sequence, i.e., the solution from one subproblem is used as the initial point for solving the next feasibility problem. The entire sequence is performed in a loop until feasibility is achieved for all constraints. Results from two optimization procedures that implement algorithms with very distinct search characteristics are presented. Though the repair method is external to the sequential quadratic programming and differential evolution algorithms implemented, this work provides a practical framework for how to adapt and couple the constraint-handling methodology to these different types of algorithms in an efficient manner. Results show the standalone optimization procedures provide feasible solutions while performing effective searches of the solution space, both in terms of cost function evolution growth and progression of well configuration.
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- 2018
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13. A reduced random sampling strategy for fast robust well placement optimization
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Mathias C. Bellout, Bjarne Anton Foss, Behnam Jafarpour, and Mansoureh Jesmani
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Mathematical optimization ,Computer science ,Computation ,Robust optimization ,02 engineering and technology ,Function (mathematics) ,010502 geochemistry & geophysics ,Geotechnical Engineering and Engineering Geology ,01 natural sciences ,Noise ,Simultaneous perturbation stochastic approximation ,Reservoir simulation ,Fuel Technology ,020401 chemical engineering ,0204 chemical engineering ,Representation (mathematics) ,Global optimization ,0105 earth and related environmental sciences - Abstract
Model-based decision-making in oilfield development often involves hundreds of computationally demanding reservoir simulation runs. In particular, well placement optimization under uncertainty in the geologic representation of the reservoir model is an overly time-consuming procedure as the performance of any proposed well configuration needs to be evaluated over multiple realizations, using computationally expensive flow simulations. To reduce computation, we propose an efficient robust optimization procedure in which at each iteration of the optimization procedure, instead of evaluating the well configuration over all available realizations, we approximate the expected performance using a small subset of randomly selected model realizations. Since the samples are selected randomly, all the realizations are expected to eventually be included in the performance evaluation after a certain number of iterations. However, using only a few random realizations to compute the expected cost function introduces noise in the estimated objective function, necessitating the use of a stochastic optimizer. In this paper, we use the Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm, which is known to be robust against noise in the objective function. We first evaluate the performance of different forms of the SPSA algorithm (including discrete, continuous, and adaptive) using several numerical experiments, followed by a discussion of the properties of the proposed reduced random sampling approach and comparison with global optimization techniques. The method is applied to several numerical experiments, including case studies involving vertical, horizontal, and lateral wells, to evaluate its performance. The results from these experiments indicate that the reduced random sampling approach can provide significant computational gain with minimal impact on the attained optimization performance.
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- 2020
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14. Gradient-based production optimization with simulation-based economic constraints
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Mathias C. Bellout and Oleg Volkov
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Schedule ,Engineering ,Mathematical optimization ,Heuristic (computer science) ,business.industry ,010103 numerical & computational mathematics ,010502 geochemistry & geophysics ,01 natural sciences ,Computer Science Applications ,Constraint (information theory) ,Computational Mathematics ,Reservoir simulation ,Consistency (database systems) ,Computational Theory and Mathematics ,Random optimization ,Production (economics) ,Sensitivity (control systems) ,0101 mathematics ,Computers in Earth Sciences ,business ,0105 earth and related environmental sciences - Abstract
In reservoir management, production optimization is performed using gradient-based algorithms that commonly rely on an adjoint formulation to efficiently compute control gradients. Often, however, economic constraints are implicitly embedded within the optimization procedure through well performance limits enforced at each reservoir simulation time-step. These limits effectively restrict the operational capabilities of the wells, e.g., they stop or shut down production depending on a predetermined profitability threshold for the well. Various studies indicate that the accuracy of the gradient and, by consequence, the performance of the optimization algorithm suffer from this type of heuristic constraint enforcement. In this paper, an analytical framework is developed to study the effects of enforcing simulator-based economic constraints when performing gradient-based production optimization that relies on derivatives obtained through an adjoint formulation. The framework attributes the loss in control gradient sensitivity to non-differentiable unscheduled changes in the well model equations. The discontinuous nature of these changes leads to inconsistencies within the adjoint gradient formulation. These inconsistencies, in turn, reduce gradient quality and subsequently decrease algorithmic performance. Based on the developed framework, we devise an efficient simulator-based mode of constraint enforcement that yields gradients with fewer consistency errors. In this implementation, the well model equations that violate constraints are removed from the governing system right after the violation occurs and are not reinserted until the next well status update. The constraint enforcement modes are further coupled with a strategy that improves the selection of initial controls for subsequent iterations of the optimization procedure. After a given simulation, the resulting combination of open and shut-in periods generates a status update schedule, or shut-in history. The shut-in history of the current optimal solution is saved and used in subsequent optimization iterations to make the status update a part of the optimal solution. The novel simulation-based constraint implementation, with and without shut-in history, is applied to two production optimization cases where, for a large set of initial guesses, and different model realizations, it retains and improves the performance of the search procedure compared to when using common modes of economic constraint enforcement during production optimization. This is a post-peer-review, pre-copyedit version of an article published in [Computational Geosciences]. The final authenticated version is available online at: https://doi.org/10.1007/s10596-017-9634-3
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- 2017
15. Application of Simultaneous Perturbation Stochastic Approximation to Well Placement Optimization under Uncertainty
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Mansoureh Jesmani, Mathias C. Bellout, Behnam Jafarpour, Bjarne A. Foss, and Remus Hanea
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Regional geology ,Hessian matrix ,Mathematical optimization ,Noise ,Simultaneous perturbation stochastic approximation ,symbols.namesake ,Computation ,symbols ,Robust optimization ,Global optimization ,Geomorphology ,Geology ,Environmental geology - Abstract
Optimizing the location of wells to achieve the full production potential of a hydrocarbon reservoir is a crucial task in field development. However, because subsurface flow simulations are computationally demanding, implementing model-based optimization procedures to aid the search for optimal well locations can be overly time-consuming. Moreover, to account for model uncertainty, we often need to evaluate the performance of well configurations over multiple geological realizations, which calls for efficient strategies to reduce computation. To this end, we propose a robust optimization procedure in which at each iteration of the optimization procedure, instead of evaluating the well configuration over all available realizations, we approximate the expected performance using a small subset of randomly selected model realizations. Since the samples are selected randomly, we expect all samples to eventually be included in the performance evaluation after a certain number of iterations. However, using only a few random realizations increases the noise level of the computed objective function, necessitating the use of a stochastic optimizer. We use the Simultaneous Perturbation Stochastic Approximation (SPSA) algorithm, which is known to be robust against noise in the objective function. The SPSA algorithm is a local optimization method that uses an efficient stochastic gradient approximation which is easy to implement. Discrete versions of SPSA have been used for vertical well placement optimization. In this work, we implement a continuous version of the SPSA algorithm for optimizing well locations and trajectories. Moreover, we demonstrate incorporating a Hessian approximation in the SPSA implementation can improve its performance. In this paper, the performance of different forms of the SPSA algorithm (discrete, continuous, and adaptive) is evaluated using several numerical experiments, followed by a discussion of the properties of the proposed approach in comparison with global optimization techniques. Finally, the method is applied to several numerical experiments, including case studies involving both vertical and horizontal wells, to demonstrate its applicability and computational efficiency.
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- 2016
16. Particle Swarm Optimization Algorithm for Optimum Well Placement Subject to Realistic Field Development Constraints
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Remus Hanea, Mathias C. Bellout, Bjarne A. Foss, and Mansoureh Jesmani
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Well placement ,Mathematical optimization ,Reservoir simulation ,Computer science ,Particle swarm optimization ,Field development ,Subject (documents) ,Multi-swarm optimization ,Metaheuristic ,Algorithm - Abstract
Well placement optimization has the potential to become an important procedure within field development planning. The main objective of a well placement optimization effort is to provide decision makers with high quality advice on where to place wells. To achieve this task, an optimizer searches for well locations that improve a relevant economic performance measure, or maximize the expected recovery of the hydrocarbon asset. However, the well placement problem is challenging because the relationship between well placement, reservoir geology and resulting fluid flow patterns is, but in the most trivial cases, complex, and therefore the optimizer often needs to rely on computationally expensive reservoir simulations to find the final production volumes associated with a given well configuration. Moreover, besides the efficiency of the optimization effort, the quality of the advice provided relies on how well realistic constraints have been introduced into the optimization problem. In particular, it is important that the design limitations that the field development team operates with, either explicitly or implicitly, are articulated and formalized within the search for optimal well placement. In this work, we focus on developing constraint formulations to enforce various realistic field development considerations. Furthermore, we apply the Particle Swarm Optimization (PSO) algorithm to iterate on the location of wells for two production cases while using some of the developed constraints. The constraints developed in this work include maintaining a minimum inter-well distance, a minimum and maximum well length, a general orientation of the wells with respect to a set platform location, and keeping the wells within specified reservoir regions. Moreover, we investigate the sensitivity of these constraints with respect to the optimal solution. These various constraint classes have been developed in close collaboration with a major field operator on the Norwegian Continental Shelf. The PSO algorithm applied in this work is a derivative-free optimizer based on an stochastic search procedure. The procedure consists of a model of the behavior of a swarm. It includes various probabilistic factors, and mimics the collective motion of animals, e.g., the flight of a flock of birds. We incorporate the various well placement constraints into the PSO algorithm using two different constraint-handling techniques: a decoder procedure and the penalty method. The decoder procedure maps the feasible search space onto n-dimensional cubes and has the advantage of not requiring parameter tuning. The penalty method converts the constrained optimization problem into an unconstrained one by introducing an additional term, called a penalty function, to the objective function. These constraint-handling techniques are applied to two different reservoir production cases. The first case is a simple problem where the PSO algorithm is implemented with a particular bound and a well length constraint to find the optimal location of one horizontal producer. The second case treats a synthetic field model with realistic porosity and permeability data and grid geometry. For this case, using the decoder implementation of the PSO algorithm, we optimize the placement of eight vertical wells to be placed within irregular-shaped reservoir regions determined based on geological considerations, e.g., faults. In terms of economic performance for this case, the PSO with decoder yields an improvement of 16% compared to the initial well configuration.
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- 2015
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17. Development of constraint handling techniques for well placement optimization in Petroleum Field Development - Problem formulation and implementation for FieldOpt software including well index calculation for deviated wells
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Magnusson, Hilmar, Grasmair, Markus, Kleppe, Jon, and Mathias C., Bellout
- Subjects
Fysikk og matematikk, Industriell matematikk - Abstract
Well placement optimization is an important part of Petroleum Field Development. However, in order to improve the optimization procedures, it can be important to incorporate considerations like knowledge about the geology of the reservoir or about existing or planned well paths. This leads to additional constraints that have to be satisfied during the optimization. In this thesis we concentrate in particular on constraints on the well lengths and the distance between the wells. We suggest an alternating projections method to deal with both constraints at the same time, and develop an efficient numerical method for the solution. Although we cannot prove that the method is convergent, numerical results of our implementation indicate that the approach works as intended. An additional important contribution from this work is the implementation of a well index calculator. In reservoir simulation, the well index relates the flow rate and pressure of the wellbore to the pressure solution of the subsurface fluid flow system, and is therefore an essential part in computing resulting production volumes. We also implement an algorithm that, given a slanted well and the physical state of a reservoir, calculates the well indices for the well blocks that are intersected by the well. In particular the well index calculation for deviated wells is a nontrivial task that is important for well placement optimization research. This task is already handled by some industry reservoir simulators, but the implementation is hidden from the end-user. All of the implementations are meant to be an addition to FieldOpt, a petroleum field development optimization framework that is currently under development by the Petroleum Cybernetics Group at NTNU.
- Published
- 2016
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