A non-local two-phase flow model for immiscible displacement in highly heterogeneous porous media and its parametrization

Research output: Contribution to journalArticleResearchpeer review

Authors

  • Jan Tecklenburg
  • Insa Neuweiler
  • Marco Dentz
  • Jesus Carrera
  • Sebastian Geiger
  • Christian Abramowski
  • Orlando Silva

External Research Organisations

  • Spanish National Research Council (CSIC)
  • Heriot-Watt University
  • Ciudad de la Energia Foundation (CIUDEN)
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Details

Original languageEnglish
Pages (from-to)475-487
Number of pages13
JournalAdvances in water resources
Volume62
Publication statusPublished - 5 Jun 2013

Abstract

In this paper, we present an upscaled model for horizontal immiscible displacement in highly heterogeneous media. This type of heterogeneity can be found, for instance, in fractured rock, which consists of two flow domains, a mobile fracture and a virtually immobile matrix. We derive an upscaled double-continuum model capable of predicting flow in mobile-immobile domains using homogenization theory. The model consists of a flow equation for the saturation of displacing fluid in the fracture domain, and a capillary flow equation for saturation in the matrix, which are coupled via a source term. By linearizing capillary counter current flow in the matrix domain, we combine this system of equations into a non-local single-equation model for the fracture saturation, which can be interpreted as a multi-rate mass-transfer (MRMT) model for immiscible displacement. We discuss this simplification and the parametrization of the upscaled model equation from local hydraulic parameters obtained from rock samples and from knowledge of the average flow properties of the fracture network. We demonstrate its performance for predicting two-phase flow by considering a single fracture with imbibition into a rectangular matrix domain. The upscaled model is parameterized directly from geometry and hydraulic parameters of matrix and fracture of the reference model, which means that no parameters need to be fitted. We compare the detailed and upscaled models in terms of breakthrough curves for the displaced fluid at a control plane within the medium. Both the detailed numerical simulations and the upscaled model show a preasymptotic t - 1 / 2 scaling and a breakoff at the characteristic time scale for filling the matrix by counter current flow.

Keywords

    Fractured media, Multi-rate mass-transfer models, Two-phase flow, Upscaling

ASJC Scopus subject areas

Cite this

A non-local two-phase flow model for immiscible displacement in highly heterogeneous porous media and its parametrization. / Tecklenburg, Jan; Neuweiler, Insa; Dentz, Marco et al.
In: Advances in water resources, Vol. 62, 05.06.2013, p. 475-487.

Research output: Contribution to journalArticleResearchpeer review

Tecklenburg J, Neuweiler I, Dentz M, Carrera J, Geiger S, Abramowski C et al. A non-local two-phase flow model for immiscible displacement in highly heterogeneous porous media and its parametrization. Advances in water resources. 2013 Jun 5;62:475-487. doi: 10.1016/j.advwatres.2013.05.012
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title = "A non-local two-phase flow model for immiscible displacement in highly heterogeneous porous media and its parametrization",
abstract = "In this paper, we present an upscaled model for horizontal immiscible displacement in highly heterogeneous media. This type of heterogeneity can be found, for instance, in fractured rock, which consists of two flow domains, a mobile fracture and a virtually immobile matrix. We derive an upscaled double-continuum model capable of predicting flow in mobile-immobile domains using homogenization theory. The model consists of a flow equation for the saturation of displacing fluid in the fracture domain, and a capillary flow equation for saturation in the matrix, which are coupled via a source term. By linearizing capillary counter current flow in the matrix domain, we combine this system of equations into a non-local single-equation model for the fracture saturation, which can be interpreted as a multi-rate mass-transfer (MRMT) model for immiscible displacement. We discuss this simplification and the parametrization of the upscaled model equation from local hydraulic parameters obtained from rock samples and from knowledge of the average flow properties of the fracture network. We demonstrate its performance for predicting two-phase flow by considering a single fracture with imbibition into a rectangular matrix domain. The upscaled model is parameterized directly from geometry and hydraulic parameters of matrix and fracture of the reference model, which means that no parameters need to be fitted. We compare the detailed and upscaled models in terms of breakthrough curves for the displaced fluid at a control plane within the medium. Both the detailed numerical simulations and the upscaled model show a preasymptotic t - 1 / 2 scaling and a breakoff at the characteristic time scale for filling the matrix by counter current flow.",
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note = "Funding information: We would like to thank three anonymous reviewers for their comprehensive reviews and comments. J. T. and I. N acknowledge financial funding from the Deutsche Forschungsgemeinschaft under the Grant Ne 824/10-1 . M. D. and J. C. acknowledge the support of the FP7 EU project PANACEA (Grant No. 282900 ), and the Spanish Ministry of Economy and Competitivity through the project HEART ( CGL2010-18450 ). S. G. acknowledges Foundation CMG for supporting his chair at Heriot–Watt University.",
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T1 - A non-local two-phase flow model for immiscible displacement in highly heterogeneous porous media and its parametrization

AU - Tecklenburg, Jan

AU - Neuweiler, Insa

AU - Dentz, Marco

AU - Carrera, Jesus

AU - Geiger, Sebastian

AU - Abramowski, Christian

AU - Silva, Orlando

N1 - Funding information: We would like to thank three anonymous reviewers for their comprehensive reviews and comments. J. T. and I. N acknowledge financial funding from the Deutsche Forschungsgemeinschaft under the Grant Ne 824/10-1 . M. D. and J. C. acknowledge the support of the FP7 EU project PANACEA (Grant No. 282900 ), and the Spanish Ministry of Economy and Competitivity through the project HEART ( CGL2010-18450 ). S. G. acknowledges Foundation CMG for supporting his chair at Heriot–Watt University.

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N2 - In this paper, we present an upscaled model for horizontal immiscible displacement in highly heterogeneous media. This type of heterogeneity can be found, for instance, in fractured rock, which consists of two flow domains, a mobile fracture and a virtually immobile matrix. We derive an upscaled double-continuum model capable of predicting flow in mobile-immobile domains using homogenization theory. The model consists of a flow equation for the saturation of displacing fluid in the fracture domain, and a capillary flow equation for saturation in the matrix, which are coupled via a source term. By linearizing capillary counter current flow in the matrix domain, we combine this system of equations into a non-local single-equation model for the fracture saturation, which can be interpreted as a multi-rate mass-transfer (MRMT) model for immiscible displacement. We discuss this simplification and the parametrization of the upscaled model equation from local hydraulic parameters obtained from rock samples and from knowledge of the average flow properties of the fracture network. We demonstrate its performance for predicting two-phase flow by considering a single fracture with imbibition into a rectangular matrix domain. The upscaled model is parameterized directly from geometry and hydraulic parameters of matrix and fracture of the reference model, which means that no parameters need to be fitted. We compare the detailed and upscaled models in terms of breakthrough curves for the displaced fluid at a control plane within the medium. Both the detailed numerical simulations and the upscaled model show a preasymptotic t - 1 / 2 scaling and a breakoff at the characteristic time scale for filling the matrix by counter current flow.

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