Linearized reduced-order models for subsurface flow simulation

Cardoso, Maria Helena; Durlofsky, Louis J.

doi:10.1016/j.jcp.2009.10.004

Cited by 121 publications

(89 citation statements)

References 29 publications

(48 reference statements)

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“…The POD basis matrix of dimension m ≤ rank(F), denoted by U f ∈ R n×m , for the snapshots {f (v )} 16) where the last equality follows from the fact that f is a componentwise evaluation function. Note that D := P T U v ∈ R m×k can be precomputed by selecting the rows…”

Section: Reduced-order Model From Pod-deim Methodsmentioning

confidence: 99%

“…There are a number of examples that use model reduction approaches with nonlinear approximation based on pre-computation of coefficients defining multi-linear forms of polynomial nonlinearities followed by POD-Galerkin projection [20,21,67,10,28,16]. One of these approaches is found in the trajectory piecewise-linear (TPWL) approximation proposed by Rewienski and White [74,73], which is based on approximating a nonlinear function by a weighted sum of linearized models at selected points along a state trajectory.…”

Section: Techniques For Nonlinearitiesmentioning

confidence: 99%

“…Fine scale details at grid points are encoded in this global basis. In the context of fluid flow in porous media, POD with Galerkin projection has been used as a model reduction procedure in many previous investiga-tions such as [90,92,91,57] for groundwater flow, [42,56,29,17,16] for immiscible two-phase (oil-water) reservoir simulation, and [36,79,80,35] for miscible flow for the enhanced oil recovery (EOR) process. In the case of flows described by linear governing equations, e.g [90], the POD-Galerkin technique substantially reduces the computational complexity and simulation time.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Nonlinear Model Reduction via Discrete Empirical Interpolation

Chaturantabut¹,

Sorensen²

2010

SIAM J. Sci. Comput.

1,649

1,778

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Section: Reduced-order Model From Pod-deim Methodsmentioning

confidence: 99%

Section: Techniques For Nonlinearitiesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear Model Reduction via Discrete Empirical Interpolation

Chaturantabut¹,

Sorensen²

2010

SIAM J. Sci. Comput.

1,649

1,778

View full text Add to dashboard Cite

“…We use a definition of fraction of total energy E t (Cardoso and Durlofsky, 2010;He et al, 2011) to select the number of columns l in projection matrices Φ injs and Φ prods , i.e., l injs and l prods , respectively. The…”

Section: Summary Of Resultsmentioning

confidence: 99%

“…As mentioned, the first step consists of performing a regular polling procedure where a (full-order) control optimization is launched at each well placement trial solution. Once this polling procedure finishes, all the control solutions are collected and stored in a "snapshot" matrix U (the process is somewhat similar to the one in Cardoso and Durlofsky (2010) where saturations and pressures are collected into snapshot matrices at different times during simulation, though for a very different implementation). Using this snapshot matrix, we calculate a projection matrix Φ by performing a singular value decomposition of U.…”

Section: Enhancementsmentioning

confidence: 99%

Joint optimization of oil well placement and controls

et al. 2012

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In this thesis we optimize the drilling location and operational controls of wells in a joint manner to improve the overall development strategy for a petroleum field. In particular, in this thesis we treat the integrated problem of searching for an improved well placement configuration while also taking into account the control settings of the production and/or injector wells planned for the development of the hydrocarbon asset. In oil field development, the well placement and well control problems are commonly performed in a sequential manner. However, this type of sequential approach cannot be expected to yield optimal solutions because it relies on handling well production controls using heuristic techniques during the well placement part of the procedure. In this work, we develop a nested (joint) optimization approach that seeks to capture the interdependency between the well configuration and the associated controls during the optimization search.This thesis summarizes the development of the joint approach; from establishing the methodology while using relatively simple cases and performing thorough comparisons against sequential approaches, to further extending and finally testing the methodology using a real field case model. This progression naturally divides the work in this thesis into two parts with different research focus. The first part of this work (Chapter 2) focuses chiefly on creating proper definitions and on establishing the proposed methodology against common approaches. The second part of this thesis (Chapters 3 and 4), on the other hand, focuses mainly on applying the developed methodology within a real field case scenario involving the North Sea Martin Linge oil reservoir. The dual aim of this application work is both to further develop the methodology, and to produce and test optimization solutions that may serve as decision-support to engineering efforts within the development work process of the Martin Linge field.Chapter 2 establishes the core of the methodology followed in this thesis. This chapter introduces the joint and sequential approaches as different ways to solve for the coupled well placement and control problem. The joint approach embeds the well control optimization within the search for optimum well placement configurations. Derivativefree methods based on pattern search are used to solve for the well-positioning part of the problem, while the well control optimization is solved by sequential quadratic programming using gradients efficiently computed through adjoints. Compared to reasonable sequential approaches, the joint optimization yields a significant increase in net present value of up to 20%. Compared to the sequential procedures, though, the joint approach requires about an order of magnitude increase in the total number of reservoir simulations performed during optimization. This increase, however, is somewhat mitigated by i the parallel implementation of some of the pattern search algorithms used in this work.Chapter 3 focuses on extending and applying ...

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High‐Performance Integrated Control of water quality and quantity in urban water reservoirs

Galelli

Castelletti

Goedbloed

2015

Water Resources Research

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This paper contributes a novel High‐Performance Integrated Control framework to support the real‐time operation of urban water supply storages affected by water quality problems. We use a 3‐D, high‐fidelity simulation model to predict the main water quality dynamics and inform a real‐time controller based on Model Predictive Control. The integration of the simulation model into the control scheme is performed by a model reduction process that identifies a low‐order, dynamic emulator running 4 orders of magnitude faster. The model reduction, which relies on a semiautomatic procedural approach integrating time series clustering and variable selection algorithms, generates a compact and physically meaningful emulator that can be coupled with the controller. The framework is used to design the hourly operation of Marina Reservoir, a 3.2 Mm3 storm‐water‐fed reservoir located in the center of Singapore, operated for drinking water supply and flood control. Because of its recent formation from a former estuary, the reservoir suffers from high salinity levels, whose behavior is modeled with Delft3D‐FLOW. Results show that our control framework reduces the minimum salinity levels by nearly 40% and cuts the average annual deficit of drinking water supply by about 2 times the active storage of the reservoir (about 4% of the total annual demand).

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Linearized reduced-order models for subsurface flow simulation

Cited by 121 publications

References 29 publications

Nonlinear Model Reduction via Discrete Empirical Interpolation

Nonlinear Model Reduction via Discrete Empirical Interpolation

Joint optimization of oil well placement and controls

High‐Performance Integrated Control of water quality and quantity in urban water reservoirs

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