Adjoint formulation and constraint handling for gradient-based optimization of compositional reservoir flow

Korounis, D.; Durlofsky, Louis J.; Jansen, J.D.; Aziz, Khalid

doi:10.1007/s10596-013-9385-8

Cited by 50 publications

(35 citation statements)

References 43 publications

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“…Therefore, the time step refinement affects the search for the optimal solution. Previous numerical studies of the SQP algorithm have shown that the optimization with constrained simulation has better performance than constrained optimization [14,25]. In this work, we use different time step refinement strategies to explain the observed difference.…”

Section: Introductionmentioning

confidence: 93%

Effect of time stepping strategy on adjoint-based production optimization

Volkov

Voskov

2015

Comput Geosci

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The adjoint gradient method is well recognized for its efficiency in large-scale production optimization. When implemented in a sequential quadratic programming (SQP) algorithm, adjoint gradients enable the construction of a quadratic approximation of the objective function and linear approximation of the nonlinear constraints using just one forward and one backward simulation (with multiple right-hand sides). In this work, the focus is on the performance of the adjoint gradient method with respect to the adaptive time step refinement generated in the underlying forward simulations. First, we demonstrate that the mass transfer in reservoir simulation and, as a consequence, the net-present value (NPV) function are more sensitive to the degree of the time step refinement when using production bottom-hole pressure (BHP) controls than when using production rate controls. Effects of this sensitivity on optimization process are studied using six examples of uniform time stepping with different degrees of refinements. By comparing those examples, we show that corresponding optimal solutions for target production BHPs deviate at early stages of the optimization process. It indicates an inconsistency in the evaluation of the adjoint gradients and NPV function for different time step refinements. effects of this inconsistency on the results of a constrained production optimization. Two strategies of nonlinear constraints are considered: (i) nonlinear constraints handled in the optimization process and (ii) constraints applied directly in forward simulations with a common control switch procedure. In both strategies, we observe that the progress of the optimization process is greatly influenced by the degree of the time step refinement after control update. In the case of constrained simulations, the presence of control switches combined with large time steps after control update forces adaptive refinement to vary the time step size significantly. As a result, the inconsistency of the adjoint gradients and NPV values provoke an early termination of the SQP algorithm. In the case of constrained optimization, the inconsistencies in gradient evaluations are less significant, and the performance of the optimization process is governed by a satisfaction of nonlinear constraints in SQP algorithm.

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Section: Introductionmentioning

confidence: 93%

Effect of time stepping strategy on adjoint-based production optimization

Volkov

Voskov

2015

Comput Geosci

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“…In addition to robust optimization studies there is a large number of papers describing deterministic well control optimization over the life cycle of the reservoir both with and without the use of gradients; see, e.g., Sudaryanto and Yortsos (2000), , Sarma et al (2008b), van Essen et al (2010), Forouzanfar et al (2013a, Kourounis et al (2014) or, for overviews, Jansen (2011) andEcheverrıa Ciaurri et al (2011). Moreover, all of the CLRM studies referred to in Section 3 involve robust or deterministic well control and/or well location optimization.…”

Section: Application Case Reservoir Engineering -Long-term Reservoir mentioning

confidence: 99%

Recent Developments in Closed-Loop Approaches for Real-Time Mining and Petroleum Extraction

Benndorf

2017

Math Geosci

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Advanced data acquisition and process modelling technology provide 'real-time' data and decision support capacity for different aspects of the resource extraction process. Closed-loop approaches have recently been applied to utilize information extracted from these data in combination with advanced computing technology for improved production control in mineral resource extraction. Similar techniques have been developed in the petroleum industry combining computer-assisted model updating with model-based production optimization. This contribution reviews recent developments and methods applied, highlights differences and assesses the potential value added for both application domains. The focus here is on the two main constituents of closed-loop concepts, data assimilation and optimization. Technological readiness of the constituents is assessed, and gaps for further technology development are identified. The value added is illustrated by means of selected cases. Key Wordsclosed-loop reservoir management, real-time mining, data assimilation, optimization Published as Benndorf, J. and Jansen, J.D., 2017: Recent developments in closed-loop approaches for realtime mining and petroleum extraction. Mathematical Geosciences 49 (3) 277-306.

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“…Nonlinear inequality constraints are generally much more difficult to implement and various approaches have been explored. We refer to Jansen (2011), Kourounis et al (2014), Sarma et al (2008) for further discussion.…”

Section: Adjoint-based Optimizationmentioning

confidence: 99%

“…Adjoint-based approaches were first applied for well control optimization by Ramirez (1987). More recently, these techniques have been incorporated by, e.g., Brouwer and Jansen (2004), Sarma et al (2008), van Essen et al (2011, Kourounis et al (2014). For further references, see the review paper Jansen (2011).…”

Section: Introductionmentioning

confidence: 99%

Use of reduced-order models in well control optimization

Jansen

Durlofsky

2016

Optim Eng

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Many aspects of reservoir management can be expected to benefit from the application of computational optimization procedures. The focus of this review paper is on well control optimization, which entails the determination of well settings, such as flow rates or bottom hole pressures, that maximize a particular objective function. As is the case with most reservoir-related optimizations, this problem is in general computationally demanding since function evaluations require reservoir simulation runs. Here we describe reduced-order modeling procedures, which act to accelerate these simulation runs, and discuss their use within the context of well control optimization. The techniques considered apply proper orthogonal decomposition (POD), which enables the representation of reservoir states (e.g., pressure and saturation in every grid block) in terms of a highly reduced set of variables. Two basic approaches are described-the direct application of POD-based reduction at each Newton iteration, and a trajectory piecewise linearization (POD-TPWL) procedure that applies POD to a linearized representation of the governing equations. Both procedures require one or more pre-processing 'training' simulation runs using the original full-order model. The use of both gradient-based optimization methods (including adjoint procedures) and direct search approaches with reduced-order models is described. Several concepts relevant to the general topic, including adjoint formulations and controllability, are also reviewed. Numerical results are presented for both approaches. In particular, the POD-TPWL procedure is applied to a computationally demanding bi-objective optimization problem, where it is shown to provide reasonable accuracy and a high degree of speedup.

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Adjoint formulation and constraint handling for gradient-based optimization of compositional reservoir flow

Cited by 50 publications

References 43 publications

Effect of time stepping strategy on adjoint-based production optimization

Effect of time stepping strategy on adjoint-based production optimization

Recent Developments in Closed-Loop Approaches for Real-Time Mining and Petroleum Extraction

Use of reduced-order models in well control optimization

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