Data assimilation with soft constraints (DASC) through a generalized iterative ensemble smoother

This work investigates an ensemble-based workflow to simultaneously handle generic, nonlinear equality and inequality constraints in reservoir data assimilation problems. The proposed workflow is built upon a recently proposed umbrella algorithm, called the generalized iterative ensemble smoother (G...

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Vydáno v:	Computational geosciences Ročník 26; číslo 3; s. 571 - 594
Hlavní autoři:	Luo, Xiaodong, Cruz, William C.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Cham Springer International Publishing 01.06.2022 Springer Nature B.V
Témata:	Algorithms Case studies Constraint modelling Cost function Data assimilation Data collection Earth and Environmental Science Earth Sciences Geotechnical Engineering & Applied Earth Sciences Hydrogeology Iterative methods Kalman filters Localization Mathematical Modeling and Industrial Mathematics Optimization Original Paper Reservoirs Soil Science & Conservation Theoretical analysis Workflow Generalized iterative ensemble smoother History matching Constarined data assimilation Nonlinear equality and inequality constraints Derivative-free optimization
ISSN:	1420-0597, 1573-1499
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Abstract	This work investigates an ensemble-based workflow to simultaneously handle generic, nonlinear equality and inequality constraints in reservoir data assimilation problems. The proposed workflow is built upon a recently proposed umbrella algorithm, called the generalized iterative ensemble smoother (GIES), and inherits the benefits of ensemble-based data assimilation algorithms in geoscience applications. Unlike the traditional ensemble assimilation algorithms, the proposed workflow admits cost functions beyond the form of nonlinear-least-squares, and has the potential to develop an infinite number of constrained assimilation algorithms. In the proposed workflow, we treat data assimilation with constraints as a constrained optimization problem. Instead of relying on a general-purpose numerical optimization algorithm to solve the constrained optimization problem, we derive an (approximate) closed form to iteratively update model variables, but without the need to explicitly linearize the constraint systems. The established model update formula bears similarities to that of an iterative ensemble smoother (IES). Therefore, in terms of theoretical analysis, it becomes relatively easy to transit from an ordinary IES to the proposed constrained assimilation algorithms, and in terms of practical implementation, it is also relatively straightforward to implement the proposed workflow for users who are familiar with the IES, or other conventional ensemble data assimilation algorithms like the ensemble Kalman filter (EnKF). Apart from the aforementioned features, we also develop efficient methods to handle two noticed issues that would be of practical importance for ensemble-based constrained assimilation algorithms. These issues include localization in the presence of constraints, and the (possible) high dimensionality induced by the constraint systems. We use one 2D and one 3D case studies to demonstrate the performance of the proposed workflow. In particular, the 3D example contains experiment settings close to those of real field case studies. In both case studies, the proposed workflow achieves better data assimilation performance in comparison to the choice of using an original IES algorithm. As such, the proposed workflow has the potential to further improve the efficacy of ensemble-based data assimilation in practical reservoir data assimilation problems.
AbstractList	This work investigates an ensemble-based workflow to simultaneously handle generic, nonlinear equality and inequality constraints in reservoir data assimilation problems. The proposed workflow is built upon a recently proposed umbrella algorithm, called the generalized iterative ensemble smoother (GIES), and inherits the benefits of ensemble-based data assimilation algorithms in geoscience applications. Unlike the traditional ensemble assimilation algorithms, the proposed workflow admits cost functions beyond the form of nonlinear-least-squares, and has the potential to develop an infinite number of constrained assimilation algorithms. In the proposed workflow, we treat data assimilation with constraints as a constrained optimization problem. Instead of relying on a general-purpose numerical optimization algorithm to solve the constrained optimization problem, we derive an (approximate) closed form to iteratively update model variables, but without the need to explicitly linearize the constraint systems. The established model update formula bears similarities to that of an iterative ensemble smoother (IES). Therefore, in terms of theoretical analysis, it becomes relatively easy to transit from an ordinary IES to the proposed constrained assimilation algorithms, and in terms of practical implementation, it is also relatively straightforward to implement the proposed workflow for users who are familiar with the IES, or other conventional ensemble data assimilation algorithms like the ensemble Kalman filter (EnKF). Apart from the aforementioned features, we also develop efficient methods to handle two noticed issues that would be of practical importance for ensemble-based constrained assimilation algorithms. These issues include localization in the presence of constraints, and the (possible) high dimensionality induced by the constraint systems. We use one 2D and one 3D case studies to demonstrate the performance of the proposed workflow. In particular, the 3D example contains experiment settings close to those of real field case studies. In both case studies, the proposed workflow achieves better data assimilation performance in comparison to the choice of using an original IES algorithm. As such, the proposed workflow has the potential to further improve the efficacy of ensemble-based data assimilation in practical reservoir data assimilation problems.
Author	Cruz, William C. Luo, Xiaodong
Author_xml	– sequence: 1 givenname: Xiaodong orcidid: 0000-0002-0734-862X surname: Luo fullname: Luo, Xiaodong email: xluo@norceresearch.no organization: Norwegian Research Centre (NORCE) – sequence: 2 givenname: William C. surname: Cruz fullname: Cruz, William C. organization: University of Stavanger
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CitedBy_id	crossref_primary_10_1016_j_fuel_2023_128826 crossref_primary_10_1016_j_geoen_2023_212554 crossref_primary_10_1016_j_geoen_2023_212404
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SubjectTerms	Algorithms Case studies Constraint modelling Cost function Data assimilation Data collection Earth and Environmental Science Earth Sciences Geotechnical Engineering & Applied Earth Sciences Hydrogeology Iterative methods Kalman filters Localization Mathematical Modeling and Industrial Mathematics Optimization Original Paper Reservoirs Soil Science & Conservation Theoretical analysis Workflow
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Title	Data assimilation with soft constraints (DASC) through a generalized iterative ensemble smoother
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