Homogenization of immiscible compressible two-phase flow in double porosity media

A double porosity model of multidimensional immiscible compressible two-phase flow in fractured reservoirs is derived by the mathematical theory of homogenization. Special attention is paid to developing a general approach to incorporating compressibility of both phases. The model is written in te...
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Gespeichert in:

Autor*in:	Latifa Ait Mahiout [verfasserIn] Brahim Amaziane [verfasserIn] Abdelhafid Mokrane [verfasserIn] Leonid Pankratov [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2016

Schlagwörter:	Compressible immiscible double porous media two-phase flow fractured media homogenization two-scale convergence

Übergeordnetes Werk:	In: Electronic Journal of Differential Equations - Texas State University, 2003, (2016), 52,, Seite 28
Übergeordnetes Werk:	year:2016 ; number:52, ; pages:28

Links:	Link aufrufen Link aufrufen Journal toc

Katalog-ID:	DOAJ041898869

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520			\|a A double porosity model of multidimensional immiscible compressible two-phase flow in fractured reservoirs is derived by the mathematical theory of homogenization. Special attention is paid to developing a general approach to incorporating compressibility of both phases. The model is written in terms of the phase formulation, i.e. the saturation of one phase and the pressure of the second phase are primary unknowns. This formulation leads to a coupled system consisting of a doubly nonlinear degenerate parabolic equation for the pressure and a doubly nonlinear degenerate parabolic diffusion-convection equation for the saturation, subject to appropriate boundary and initial conditions. The major difficulties related to this model are in the doubly nonlinear degenerate structure of the equations, as well as in the coupling in the system. Furthermore, a new nonlinearity appears in the temporal term of the saturation equation. The aim of this paper is to extend the results of [9] to this more general case. With the help of a new compactness result and uniform a priori bounds for the modulus of continuity with respect to the space and time variables, we provide a rigorous mathematical derivation of the upscaled model by means of the two-scale convergence and the dilatation technique.
650		4	\|a Compressible immiscible
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allfields	(DE-627)DOAJ041898869 (DE-599)DOAJ989578b14e1c467b854052c87939df41 DE-627 ger DE-627 rakwb eng QA1-939 Latifa Ait Mahiout verfasserin aut Homogenization of immiscible compressible two-phase flow in double porosity media 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A double porosity model of multidimensional immiscible compressible two-phase flow in fractured reservoirs is derived by the mathematical theory of homogenization. Special attention is paid to developing a general approach to incorporating compressibility of both phases. The model is written in terms of the phase formulation, i.e. the saturation of one phase and the pressure of the second phase are primary unknowns. This formulation leads to a coupled system consisting of a doubly nonlinear degenerate parabolic equation for the pressure and a doubly nonlinear degenerate parabolic diffusion-convection equation for the saturation, subject to appropriate boundary and initial conditions. The major difficulties related to this model are in the doubly nonlinear degenerate structure of the equations, as well as in the coupling in the system. Furthermore, a new nonlinearity appears in the temporal term of the saturation equation. The aim of this paper is to extend the results of [9] to this more general case. With the help of a new compactness result and uniform a priori bounds for the modulus of continuity with respect to the space and time variables, we provide a rigorous mathematical derivation of the upscaled model by means of the two-scale convergence and the dilatation technique. Compressible immiscible double porous media two-phase flow fractured media homogenization two-scale convergence Mathematics Brahim Amaziane verfasserin aut Abdelhafid Mokrane verfasserin aut Leonid Pankratov verfasserin aut In Electronic Journal of Differential Equations Texas State University, 2003 (2016), 52,, Seite 28 (DE-627)320518205 (DE-600)2014226-2 10726691 nnns year:2016 number:52, pages:28 https://doaj.org/article/989578b14e1c467b854052c87939df41 kostenfrei http://ejde.math.txstate.edu/Volumes/2016/52/abstr.html kostenfrei https://doaj.org/toc/1072-6691 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2016 52, 28
spelling	(DE-627)DOAJ041898869 (DE-599)DOAJ989578b14e1c467b854052c87939df41 DE-627 ger DE-627 rakwb eng QA1-939 Latifa Ait Mahiout verfasserin aut Homogenization of immiscible compressible two-phase flow in double porosity media 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A double porosity model of multidimensional immiscible compressible two-phase flow in fractured reservoirs is derived by the mathematical theory of homogenization. Special attention is paid to developing a general approach to incorporating compressibility of both phases. The model is written in terms of the phase formulation, i.e. the saturation of one phase and the pressure of the second phase are primary unknowns. This formulation leads to a coupled system consisting of a doubly nonlinear degenerate parabolic equation for the pressure and a doubly nonlinear degenerate parabolic diffusion-convection equation for the saturation, subject to appropriate boundary and initial conditions. The major difficulties related to this model are in the doubly nonlinear degenerate structure of the equations, as well as in the coupling in the system. Furthermore, a new nonlinearity appears in the temporal term of the saturation equation. The aim of this paper is to extend the results of [9] to this more general case. With the help of a new compactness result and uniform a priori bounds for the modulus of continuity with respect to the space and time variables, we provide a rigorous mathematical derivation of the upscaled model by means of the two-scale convergence and the dilatation technique. Compressible immiscible double porous media two-phase flow fractured media homogenization two-scale convergence Mathematics Brahim Amaziane verfasserin aut Abdelhafid Mokrane verfasserin aut Leonid Pankratov verfasserin aut In Electronic Journal of Differential Equations Texas State University, 2003 (2016), 52,, Seite 28 (DE-627)320518205 (DE-600)2014226-2 10726691 nnns year:2016 number:52, pages:28 https://doaj.org/article/989578b14e1c467b854052c87939df41 kostenfrei http://ejde.math.txstate.edu/Volumes/2016/52/abstr.html kostenfrei https://doaj.org/toc/1072-6691 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2016 52, 28
allfields_unstemmed	(DE-627)DOAJ041898869 (DE-599)DOAJ989578b14e1c467b854052c87939df41 DE-627 ger DE-627 rakwb eng QA1-939 Latifa Ait Mahiout verfasserin aut Homogenization of immiscible compressible two-phase flow in double porosity media 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A double porosity model of multidimensional immiscible compressible two-phase flow in fractured reservoirs is derived by the mathematical theory of homogenization. Special attention is paid to developing a general approach to incorporating compressibility of both phases. The model is written in terms of the phase formulation, i.e. the saturation of one phase and the pressure of the second phase are primary unknowns. This formulation leads to a coupled system consisting of a doubly nonlinear degenerate parabolic equation for the pressure and a doubly nonlinear degenerate parabolic diffusion-convection equation for the saturation, subject to appropriate boundary and initial conditions. The major difficulties related to this model are in the doubly nonlinear degenerate structure of the equations, as well as in the coupling in the system. Furthermore, a new nonlinearity appears in the temporal term of the saturation equation. The aim of this paper is to extend the results of [9] to this more general case. With the help of a new compactness result and uniform a priori bounds for the modulus of continuity with respect to the space and time variables, we provide a rigorous mathematical derivation of the upscaled model by means of the two-scale convergence and the dilatation technique. Compressible immiscible double porous media two-phase flow fractured media homogenization two-scale convergence Mathematics Brahim Amaziane verfasserin aut Abdelhafid Mokrane verfasserin aut Leonid Pankratov verfasserin aut In Electronic Journal of Differential Equations Texas State University, 2003 (2016), 52,, Seite 28 (DE-627)320518205 (DE-600)2014226-2 10726691 nnns year:2016 number:52, pages:28 https://doaj.org/article/989578b14e1c467b854052c87939df41 kostenfrei http://ejde.math.txstate.edu/Volumes/2016/52/abstr.html kostenfrei https://doaj.org/toc/1072-6691 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2016 52, 28
allfieldsGer	(DE-627)DOAJ041898869 (DE-599)DOAJ989578b14e1c467b854052c87939df41 DE-627 ger DE-627 rakwb eng QA1-939 Latifa Ait Mahiout verfasserin aut Homogenization of immiscible compressible two-phase flow in double porosity media 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A double porosity model of multidimensional immiscible compressible two-phase flow in fractured reservoirs is derived by the mathematical theory of homogenization. Special attention is paid to developing a general approach to incorporating compressibility of both phases. The model is written in terms of the phase formulation, i.e. the saturation of one phase and the pressure of the second phase are primary unknowns. This formulation leads to a coupled system consisting of a doubly nonlinear degenerate parabolic equation for the pressure and a doubly nonlinear degenerate parabolic diffusion-convection equation for the saturation, subject to appropriate boundary and initial conditions. The major difficulties related to this model are in the doubly nonlinear degenerate structure of the equations, as well as in the coupling in the system. Furthermore, a new nonlinearity appears in the temporal term of the saturation equation. The aim of this paper is to extend the results of [9] to this more general case. With the help of a new compactness result and uniform a priori bounds for the modulus of continuity with respect to the space and time variables, we provide a rigorous mathematical derivation of the upscaled model by means of the two-scale convergence and the dilatation technique. Compressible immiscible double porous media two-phase flow fractured media homogenization two-scale convergence Mathematics Brahim Amaziane verfasserin aut Abdelhafid Mokrane verfasserin aut Leonid Pankratov verfasserin aut In Electronic Journal of Differential Equations Texas State University, 2003 (2016), 52,, Seite 28 (DE-627)320518205 (DE-600)2014226-2 10726691 nnns year:2016 number:52, pages:28 https://doaj.org/article/989578b14e1c467b854052c87939df41 kostenfrei http://ejde.math.txstate.edu/Volumes/2016/52/abstr.html kostenfrei https://doaj.org/toc/1072-6691 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2016 52, 28
allfieldsSound	(DE-627)DOAJ041898869 (DE-599)DOAJ989578b14e1c467b854052c87939df41 DE-627 ger DE-627 rakwb eng QA1-939 Latifa Ait Mahiout verfasserin aut Homogenization of immiscible compressible two-phase flow in double porosity media 2016 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier A double porosity model of multidimensional immiscible compressible two-phase flow in fractured reservoirs is derived by the mathematical theory of homogenization. Special attention is paid to developing a general approach to incorporating compressibility of both phases. The model is written in terms of the phase formulation, i.e. the saturation of one phase and the pressure of the second phase are primary unknowns. This formulation leads to a coupled system consisting of a doubly nonlinear degenerate parabolic equation for the pressure and a doubly nonlinear degenerate parabolic diffusion-convection equation for the saturation, subject to appropriate boundary and initial conditions. The major difficulties related to this model are in the doubly nonlinear degenerate structure of the equations, as well as in the coupling in the system. Furthermore, a new nonlinearity appears in the temporal term of the saturation equation. The aim of this paper is to extend the results of [9] to this more general case. With the help of a new compactness result and uniform a priori bounds for the modulus of continuity with respect to the space and time variables, we provide a rigorous mathematical derivation of the upscaled model by means of the two-scale convergence and the dilatation technique. Compressible immiscible double porous media two-phase flow fractured media homogenization two-scale convergence Mathematics Brahim Amaziane verfasserin aut Abdelhafid Mokrane verfasserin aut Leonid Pankratov verfasserin aut In Electronic Journal of Differential Equations Texas State University, 2003 (2016), 52,, Seite 28 (DE-627)320518205 (DE-600)2014226-2 10726691 nnns year:2016 number:52, pages:28 https://doaj.org/article/989578b14e1c467b854052c87939df41 kostenfrei http://ejde.math.txstate.edu/Volumes/2016/52/abstr.html kostenfrei https://doaj.org/toc/1072-6691 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ SSG-OLC-PHA GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_206 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2031 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2061 GBV_ILN_2111 GBV_ILN_2190 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 2016 52, 28
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callnumber-first	Q - Science
author	Latifa Ait Mahiout
spellingShingle	Latifa Ait Mahiout misc QA1-939 misc Compressible immiscible misc double porous media misc two-phase flow misc fractured media homogenization misc two-scale convergence misc Mathematics Homogenization of immiscible compressible two-phase flow in double porosity media
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topic_title	QA1-939 Homogenization of immiscible compressible two-phase flow in double porosity media Compressible immiscible double porous media two-phase flow fractured media homogenization two-scale convergence
topic	misc QA1-939 misc Compressible immiscible misc double porous media misc two-phase flow misc fractured media homogenization misc two-scale convergence misc Mathematics
topic_unstemmed	misc QA1-939 misc Compressible immiscible misc double porous media misc two-phase flow misc fractured media homogenization misc two-scale convergence misc Mathematics
topic_browse	misc QA1-939 misc Compressible immiscible misc double porous media misc two-phase flow misc fractured media homogenization misc two-scale convergence misc Mathematics
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title	Homogenization of immiscible compressible two-phase flow in double porosity media
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title_full	Homogenization of immiscible compressible two-phase flow in double porosity media
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author_browse	Latifa Ait Mahiout Brahim Amaziane Abdelhafid Mokrane Leonid Pankratov
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title_sort	homogenization of immiscible compressible two-phase flow in double porosity media
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title_auth	Homogenization of immiscible compressible two-phase flow in double porosity media
abstract	A double porosity model of multidimensional immiscible compressible two-phase flow in fractured reservoirs is derived by the mathematical theory of homogenization. Special attention is paid to developing a general approach to incorporating compressibility of both phases. The model is written in terms of the phase formulation, i.e. the saturation of one phase and the pressure of the second phase are primary unknowns. This formulation leads to a coupled system consisting of a doubly nonlinear degenerate parabolic equation for the pressure and a doubly nonlinear degenerate parabolic diffusion-convection equation for the saturation, subject to appropriate boundary and initial conditions. The major difficulties related to this model are in the doubly nonlinear degenerate structure of the equations, as well as in the coupling in the system. Furthermore, a new nonlinearity appears in the temporal term of the saturation equation. The aim of this paper is to extend the results of [9] to this more general case. With the help of a new compactness result and uniform a priori bounds for the modulus of continuity with respect to the space and time variables, we provide a rigorous mathematical derivation of the upscaled model by means of the two-scale convergence and the dilatation technique.
abstractGer	A double porosity model of multidimensional immiscible compressible two-phase flow in fractured reservoirs is derived by the mathematical theory of homogenization. Special attention is paid to developing a general approach to incorporating compressibility of both phases. The model is written in terms of the phase formulation, i.e. the saturation of one phase and the pressure of the second phase are primary unknowns. This formulation leads to a coupled system consisting of a doubly nonlinear degenerate parabolic equation for the pressure and a doubly nonlinear degenerate parabolic diffusion-convection equation for the saturation, subject to appropriate boundary and initial conditions. The major difficulties related to this model are in the doubly nonlinear degenerate structure of the equations, as well as in the coupling in the system. Furthermore, a new nonlinearity appears in the temporal term of the saturation equation. The aim of this paper is to extend the results of [9] to this more general case. With the help of a new compactness result and uniform a priori bounds for the modulus of continuity with respect to the space and time variables, we provide a rigorous mathematical derivation of the upscaled model by means of the two-scale convergence and the dilatation technique.
abstract_unstemmed	A double porosity model of multidimensional immiscible compressible two-phase flow in fractured reservoirs is derived by the mathematical theory of homogenization. Special attention is paid to developing a general approach to incorporating compressibility of both phases. The model is written in terms of the phase formulation, i.e. the saturation of one phase and the pressure of the second phase are primary unknowns. This formulation leads to a coupled system consisting of a doubly nonlinear degenerate parabolic equation for the pressure and a doubly nonlinear degenerate parabolic diffusion-convection equation for the saturation, subject to appropriate boundary and initial conditions. The major difficulties related to this model are in the doubly nonlinear degenerate structure of the equations, as well as in the coupling in the system. Furthermore, a new nonlinearity appears in the temporal term of the saturation equation. The aim of this paper is to extend the results of [9] to this more general case. With the help of a new compactness result and uniform a priori bounds for the modulus of continuity with respect to the space and time variables, we provide a rigorous mathematical derivation of the upscaled model by means of the two-scale convergence and the dilatation technique.
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title_short	Homogenization of immiscible compressible two-phase flow in double porosity media
url	https://doaj.org/article/989578b14e1c467b854052c87939df41 http://ejde.math.txstate.edu/Volumes/2016/52/abstr.html https://doaj.org/toc/1072-6691
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Special attention is paid to developing a general approach to incorporating compressibility of both phases. The model is written in terms of the phase formulation, i.e. the saturation of one phase and the pressure of the second phase are primary unknowns. This formulation leads to a coupled system consisting of a doubly nonlinear degenerate parabolic equation for the pressure and a doubly nonlinear degenerate parabolic diffusion-convection equation for the saturation, subject to appropriate boundary and initial conditions. The major difficulties related to this model are in the doubly nonlinear degenerate structure of the equations, as well as in the coupling in the system. Furthermore, a new nonlinearity appears in the temporal term of the saturation equation. The aim of this paper is to extend the results of [9] to this more general case. 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Homogenization of immiscible compressible two-phase flow in double porosity media

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