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Algebraic dynamic multilevel method for compositional flow in heterogeneous porous media.

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Title: Algebraic dynamic multilevel method for compositional flow in heterogeneous porous media.
Authors: Cusini, Matteo1 M.Cusini@tudelft.nl, Fryer, Barnaby1 barnabyfryer@sbcglobal.net, van Kruijsdijk, Cor2 Cor.vanKruijsdijk@shell.com, Hajibeygi, Hadi1 H.Hajibeygi@tudelft.nl
Source: Journal of Computational Physics. Feb2018, Vol. 354, p593-612. 20p.
Subjects: Algebraic curves, Multilevel codes, Porous materials, Gravitational effects, Thermodynamic equilibrium
Abstract: This paper presents the algebraic dynamic multilevel method (ADM) for compositional flow in three dimensional heterogeneous porous media in presence of capillary and gravitational effects. As a significant advancement compared to the ADM for immiscible flows (Cusini et al., 2016) [33] , here, mass conservation equations are solved along with k-value based thermodynamic equilibrium equations using a fully-implicit (FIM) coupling strategy. Two different fine-scale compositional formulations are considered: (1) the natural variables and (2) the overall-compositions formulation. At each Newton's iteration the fine-scale FIM Jacobian system is mapped to a dynamically defined (in space and time) multilevel nested grid. The appropriate grid resolution is chosen based on the contrast of user-defined fluid properties and on the presence of specific features (e.g., well source terms). Consistent mapping between different resolutions is performed by the means of sequences of restriction and prolongation operators. While finite-volume restriction operators are employed to ensure mass conservation at all resolutions, various prolongation operators are considered. In particular, different interpolation strategies can be used for the different primary variables, and multiscale basis functions are chosen as pressure interpolators so that fine scale heterogeneities are accurately accounted for across different resolutions. Several numerical experiments are conducted to analyse the accuracy, efficiency and robustness of the method for both 2D and 3D domains. Results show that ADM provides accurate solutions by employing only a fraction of the number of grid-cells employed in fine-scale simulations. As such, it presents a promising approach for large-scale simulations of multiphase flow in heterogeneous reservoirs with complex non-linear fluid physics. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Computational Physics is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Algebraic dynamic multilevel method for compositional flow in heterogeneous porous media.
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  Data: <searchLink fieldCode="AR" term="%22Cusini%2C+Matteo%22">Cusini, Matteo</searchLink><relatesTo>1</relatesTo><i> M.Cusini@tudelft.nl</i><br /><searchLink fieldCode="AR" term="%22Fryer%2C+Barnaby%22">Fryer, Barnaby</searchLink><relatesTo>1</relatesTo><i> barnabyfryer@sbcglobal.net</i><br /><searchLink fieldCode="AR" term="%22van+Kruijsdijk%2C+Cor%22">van Kruijsdijk, Cor</searchLink><relatesTo>2</relatesTo><i> Cor.vanKruijsdijk@shell.com</i><br /><searchLink fieldCode="AR" term="%22Hajibeygi%2C+Hadi%22">Hajibeygi, Hadi</searchLink><relatesTo>1</relatesTo><i> H.Hajibeygi@tudelft.nl</i>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Computational+Physics%22">Journal of Computational Physics</searchLink>. Feb2018, Vol. 354, p593-612. 20p.
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  Data: This paper presents the algebraic dynamic multilevel method (ADM) for compositional flow in three dimensional heterogeneous porous media in presence of capillary and gravitational effects. As a significant advancement compared to the ADM for immiscible flows (Cusini et al., 2016) [33] , here, mass conservation equations are solved along with k-value based thermodynamic equilibrium equations using a fully-implicit (FIM) coupling strategy. Two different fine-scale compositional formulations are considered: (1) the natural variables and (2) the overall-compositions formulation. At each Newton's iteration the fine-scale FIM Jacobian system is mapped to a dynamically defined (in space and time) multilevel nested grid. The appropriate grid resolution is chosen based on the contrast of user-defined fluid properties and on the presence of specific features (e.g., well source terms). Consistent mapping between different resolutions is performed by the means of sequences of restriction and prolongation operators. While finite-volume restriction operators are employed to ensure mass conservation at all resolutions, various prolongation operators are considered. In particular, different interpolation strategies can be used for the different primary variables, and multiscale basis functions are chosen as pressure interpolators so that fine scale heterogeneities are accurately accounted for across different resolutions. Several numerical experiments are conducted to analyse the accuracy, efficiency and robustness of the method for both 2D and 3D domains. Results show that ADM provides accurate solutions by employing only a fraction of the number of grid-cells employed in fine-scale simulations. As such, it presents a promising approach for large-scale simulations of multiphase flow in heterogeneous reservoirs with complex non-linear fluid physics. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Journal of Computational Physics is the property of Academic Press Inc. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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        Value: 10.1016/j.jcp.2017.10.052
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      – Code: eng
        Text: English
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        PageCount: 20
        StartPage: 593
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        Type: general
      – SubjectFull: Multilevel codes
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      – SubjectFull: Porous materials
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      – SubjectFull: Gravitational effects
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      – SubjectFull: Thermodynamic equilibrium
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      – TitleFull: Algebraic dynamic multilevel method for compositional flow in heterogeneous porous media.
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            NameFull: Cusini, Matteo
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            NameFull: Fryer, Barnaby
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            – D: 01
              M: 02
              Text: Feb2018
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              Y: 2018
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