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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.

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.

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.

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.

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.

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