Pressure Transient Behavior of High-Fracture-Density Reservoirs (Dual-Porosity Models)
Abstract Naturally fractured reservoirs (NFRs) contain primary (macro), secondary, and tertiary (minor) fractures. These reservoirs are heterogeneous, where fracture properties such as length, conductivity, aperture, and orientation significantly vary spatially. In general, fractures in these reserv...
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| Autor*in: |
Rasoulzadeh, Mojdeh [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2019 |
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| Anmerkung: |
© Springer Nature B.V. 2019 |
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| Übergeordnetes Werk: |
Enthalten in: Transport in porous media - Springer Netherlands, 1986, 129(2019), 3 vom: 08. Juli, Seite 901-940 |
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| Übergeordnetes Werk: |
volume:129 ; year:2019 ; number:3 ; day:08 ; month:07 ; pages:901-940 |
| Links: |
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| DOI / URN: |
10.1007/s11242-019-01312-z |
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OLC2054397814 |
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| 520 | |a Abstract Naturally fractured reservoirs (NFRs) contain primary (macro), secondary, and tertiary (minor) fractures. These reservoirs are heterogeneous, where fracture properties such as length, conductivity, aperture, and orientation significantly vary spatially. In general, fractures in these reservoirs are very conductive whether they are in a discrete or continuous fracture network. The conventional dual-porosity-type models (Warren and Root in SPE J 3(3):245–255, 1963) are widely used to model NFRs either in conventional or unconventional formations. In shale, the naturally fractured shale is often considered as a dual-porosity model and is coupled with discrete network of hydraulic fractures. Expressing flow by dual-porosity model in the complex pore structure of NFRs is an oversimplification which has demonstrated several deficiencies and inconsistencies with field transient data and field applications. We show that the dual-porosity models are applicable to specific sets of NFRs and under restrictive conditions. In several NFRs, fractures create a network, communicate hydraulically with each other globally, and provide overall conductivity for the reservoir. The matrix provides the overall storage capacity, but it should be conductive enough to pass the fluid towards the fractures. Given the contrast between the conductivity of the fractures and the matrix, several flow regimes may form at microscale. For low contrasts, the conductivities of the matrix and fractures are close enough that the medium behaves as a homogenous medium. For higher contrasts, matrix is not conductive enough to be a part of the overall flow process in the reservoir, so it behaves as a source of fluid to fractures. For very high contrasts, the matrix is almost not conductive, so it cannot pass the fluid to the fracture. In this case, the overall flow will be governed by the flow in the fracture network. Other intermediate cases may also occur. The pressure behavior of continuously fractured reservoirs is investigated for various contrasts in matrix and fracture properties. The homogenized model is obtained by using the two-scale homogenization technique. The homogenization is performed by starting from the microscale flow equations in the matrix and fracture coupled via a set of no-jump boundary conditions on the interface of fracture and matrix. This approach captures the details of the flow both within and between the porous matrix and fracture. A general equivalent macroscopic model is proposed; the macroscopic homogenized model is the average of the microscale equations of flow in fracture and matrix. The equivalent porosity and the equivalent permeability of the averaged medium are derived. The equivalent permeability depends on both the fracture’s permeability and the geometry of each block of nonhomogeneity. The memory effect in the medium is included in the averaged model through an integro-differential term. Memory effect represents the difference between the response time of matrix and fracture to the same pressure drop. Using the homogenization technique, several averaged models for fractured medium can be obtained, depending on the ratio of the fracture to matrix diffusivity, the fracture-to-matrix volume ratio, and the number of scales of nonhomogeneity in the medium. For certain contrasts in matrix and fracture properties, such as the ratio of matrix to fracture permeability and the fracture aperture, the general model reduces to Warren and Root’s model. In general, Warren and Root’s model does not describe every fractured reservoir. The impact of the presence of additional fracture network, such as secondary and tertiary fractures on the equivalent model, and pressure transient behavior is highlighted. | ||
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10.1007/s11242-019-01312-z doi (DE-627)OLC2054397814 (DE-He213)s11242-019-01312-z-p DE-627 ger DE-627 rakwb eng 530 VZ Rasoulzadeh, Mojdeh verfasserin (orcid)0000-0002-1467-9611 aut Pressure Transient Behavior of High-Fracture-Density Reservoirs (Dual-Porosity Models) 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Nature B.V. 2019 Abstract Naturally fractured reservoirs (NFRs) contain primary (macro), secondary, and tertiary (minor) fractures. These reservoirs are heterogeneous, where fracture properties such as length, conductivity, aperture, and orientation significantly vary spatially. In general, fractures in these reservoirs are very conductive whether they are in a discrete or continuous fracture network. The conventional dual-porosity-type models (Warren and Root in SPE J 3(3):245–255, 1963) are widely used to model NFRs either in conventional or unconventional formations. In shale, the naturally fractured shale is often considered as a dual-porosity model and is coupled with discrete network of hydraulic fractures. Expressing flow by dual-porosity model in the complex pore structure of NFRs is an oversimplification which has demonstrated several deficiencies and inconsistencies with field transient data and field applications. We show that the dual-porosity models are applicable to specific sets of NFRs and under restrictive conditions. In several NFRs, fractures create a network, communicate hydraulically with each other globally, and provide overall conductivity for the reservoir. The matrix provides the overall storage capacity, but it should be conductive enough to pass the fluid towards the fractures. Given the contrast between the conductivity of the fractures and the matrix, several flow regimes may form at microscale. For low contrasts, the conductivities of the matrix and fractures are close enough that the medium behaves as a homogenous medium. For higher contrasts, matrix is not conductive enough to be a part of the overall flow process in the reservoir, so it behaves as a source of fluid to fractures. For very high contrasts, the matrix is almost not conductive, so it cannot pass the fluid to the fracture. In this case, the overall flow will be governed by the flow in the fracture network. Other intermediate cases may also occur. The pressure behavior of continuously fractured reservoirs is investigated for various contrasts in matrix and fracture properties. The homogenized model is obtained by using the two-scale homogenization technique. The homogenization is performed by starting from the microscale flow equations in the matrix and fracture coupled via a set of no-jump boundary conditions on the interface of fracture and matrix. This approach captures the details of the flow both within and between the porous matrix and fracture. A general equivalent macroscopic model is proposed; the macroscopic homogenized model is the average of the microscale equations of flow in fracture and matrix. The equivalent porosity and the equivalent permeability of the averaged medium are derived. The equivalent permeability depends on both the fracture’s permeability and the geometry of each block of nonhomogeneity. The memory effect in the medium is included in the averaged model through an integro-differential term. Memory effect represents the difference between the response time of matrix and fracture to the same pressure drop. Using the homogenization technique, several averaged models for fractured medium can be obtained, depending on the ratio of the fracture to matrix diffusivity, the fracture-to-matrix volume ratio, and the number of scales of nonhomogeneity in the medium. For certain contrasts in matrix and fracture properties, such as the ratio of matrix to fracture permeability and the fracture aperture, the general model reduces to Warren and Root’s model. In general, Warren and Root’s model does not describe every fractured reservoir. The impact of the presence of additional fracture network, such as secondary and tertiary fractures on the equivalent model, and pressure transient behavior is highlighted. Dual porosity Multi-scale media Two-scale homogenization Warren and Root model Naturally fractured media Kuchuk, Fikri J. aut Enthalten in Transport in porous media Springer Netherlands, 1986 129(2019), 3 vom: 08. Juli, Seite 901-940 (DE-627)129206105 (DE-600)54858-3 (DE-576)014457431 0169-3913 nnns volume:129 year:2019 number:3 day:08 month:07 pages:901-940 https://doi.org/10.1007/s11242-019-01312-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_70 AR 129 2019 3 08 07 901-940 |
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10.1007/s11242-019-01312-z doi (DE-627)OLC2054397814 (DE-He213)s11242-019-01312-z-p DE-627 ger DE-627 rakwb eng 530 VZ Rasoulzadeh, Mojdeh verfasserin (orcid)0000-0002-1467-9611 aut Pressure Transient Behavior of High-Fracture-Density Reservoirs (Dual-Porosity Models) 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Nature B.V. 2019 Abstract Naturally fractured reservoirs (NFRs) contain primary (macro), secondary, and tertiary (minor) fractures. These reservoirs are heterogeneous, where fracture properties such as length, conductivity, aperture, and orientation significantly vary spatially. In general, fractures in these reservoirs are very conductive whether they are in a discrete or continuous fracture network. The conventional dual-porosity-type models (Warren and Root in SPE J 3(3):245–255, 1963) are widely used to model NFRs either in conventional or unconventional formations. In shale, the naturally fractured shale is often considered as a dual-porosity model and is coupled with discrete network of hydraulic fractures. Expressing flow by dual-porosity model in the complex pore structure of NFRs is an oversimplification which has demonstrated several deficiencies and inconsistencies with field transient data and field applications. We show that the dual-porosity models are applicable to specific sets of NFRs and under restrictive conditions. In several NFRs, fractures create a network, communicate hydraulically with each other globally, and provide overall conductivity for the reservoir. The matrix provides the overall storage capacity, but it should be conductive enough to pass the fluid towards the fractures. Given the contrast between the conductivity of the fractures and the matrix, several flow regimes may form at microscale. For low contrasts, the conductivities of the matrix and fractures are close enough that the medium behaves as a homogenous medium. For higher contrasts, matrix is not conductive enough to be a part of the overall flow process in the reservoir, so it behaves as a source of fluid to fractures. For very high contrasts, the matrix is almost not conductive, so it cannot pass the fluid to the fracture. In this case, the overall flow will be governed by the flow in the fracture network. Other intermediate cases may also occur. The pressure behavior of continuously fractured reservoirs is investigated for various contrasts in matrix and fracture properties. The homogenized model is obtained by using the two-scale homogenization technique. The homogenization is performed by starting from the microscale flow equations in the matrix and fracture coupled via a set of no-jump boundary conditions on the interface of fracture and matrix. This approach captures the details of the flow both within and between the porous matrix and fracture. A general equivalent macroscopic model is proposed; the macroscopic homogenized model is the average of the microscale equations of flow in fracture and matrix. The equivalent porosity and the equivalent permeability of the averaged medium are derived. The equivalent permeability depends on both the fracture’s permeability and the geometry of each block of nonhomogeneity. The memory effect in the medium is included in the averaged model through an integro-differential term. Memory effect represents the difference between the response time of matrix and fracture to the same pressure drop. Using the homogenization technique, several averaged models for fractured medium can be obtained, depending on the ratio of the fracture to matrix diffusivity, the fracture-to-matrix volume ratio, and the number of scales of nonhomogeneity in the medium. For certain contrasts in matrix and fracture properties, such as the ratio of matrix to fracture permeability and the fracture aperture, the general model reduces to Warren and Root’s model. In general, Warren and Root’s model does not describe every fractured reservoir. The impact of the presence of additional fracture network, such as secondary and tertiary fractures on the equivalent model, and pressure transient behavior is highlighted. Dual porosity Multi-scale media Two-scale homogenization Warren and Root model Naturally fractured media Kuchuk, Fikri J. aut Enthalten in Transport in porous media Springer Netherlands, 1986 129(2019), 3 vom: 08. Juli, Seite 901-940 (DE-627)129206105 (DE-600)54858-3 (DE-576)014457431 0169-3913 nnns volume:129 year:2019 number:3 day:08 month:07 pages:901-940 https://doi.org/10.1007/s11242-019-01312-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_70 AR 129 2019 3 08 07 901-940 |
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10.1007/s11242-019-01312-z doi (DE-627)OLC2054397814 (DE-He213)s11242-019-01312-z-p DE-627 ger DE-627 rakwb eng 530 VZ Rasoulzadeh, Mojdeh verfasserin (orcid)0000-0002-1467-9611 aut Pressure Transient Behavior of High-Fracture-Density Reservoirs (Dual-Porosity Models) 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Nature B.V. 2019 Abstract Naturally fractured reservoirs (NFRs) contain primary (macro), secondary, and tertiary (minor) fractures. These reservoirs are heterogeneous, where fracture properties such as length, conductivity, aperture, and orientation significantly vary spatially. In general, fractures in these reservoirs are very conductive whether they are in a discrete or continuous fracture network. The conventional dual-porosity-type models (Warren and Root in SPE J 3(3):245–255, 1963) are widely used to model NFRs either in conventional or unconventional formations. In shale, the naturally fractured shale is often considered as a dual-porosity model and is coupled with discrete network of hydraulic fractures. Expressing flow by dual-porosity model in the complex pore structure of NFRs is an oversimplification which has demonstrated several deficiencies and inconsistencies with field transient data and field applications. We show that the dual-porosity models are applicable to specific sets of NFRs and under restrictive conditions. In several NFRs, fractures create a network, communicate hydraulically with each other globally, and provide overall conductivity for the reservoir. The matrix provides the overall storage capacity, but it should be conductive enough to pass the fluid towards the fractures. Given the contrast between the conductivity of the fractures and the matrix, several flow regimes may form at microscale. For low contrasts, the conductivities of the matrix and fractures are close enough that the medium behaves as a homogenous medium. For higher contrasts, matrix is not conductive enough to be a part of the overall flow process in the reservoir, so it behaves as a source of fluid to fractures. For very high contrasts, the matrix is almost not conductive, so it cannot pass the fluid to the fracture. In this case, the overall flow will be governed by the flow in the fracture network. Other intermediate cases may also occur. The pressure behavior of continuously fractured reservoirs is investigated for various contrasts in matrix and fracture properties. The homogenized model is obtained by using the two-scale homogenization technique. The homogenization is performed by starting from the microscale flow equations in the matrix and fracture coupled via a set of no-jump boundary conditions on the interface of fracture and matrix. This approach captures the details of the flow both within and between the porous matrix and fracture. A general equivalent macroscopic model is proposed; the macroscopic homogenized model is the average of the microscale equations of flow in fracture and matrix. The equivalent porosity and the equivalent permeability of the averaged medium are derived. The equivalent permeability depends on both the fracture’s permeability and the geometry of each block of nonhomogeneity. The memory effect in the medium is included in the averaged model through an integro-differential term. Memory effect represents the difference between the response time of matrix and fracture to the same pressure drop. Using the homogenization technique, several averaged models for fractured medium can be obtained, depending on the ratio of the fracture to matrix diffusivity, the fracture-to-matrix volume ratio, and the number of scales of nonhomogeneity in the medium. For certain contrasts in matrix and fracture properties, such as the ratio of matrix to fracture permeability and the fracture aperture, the general model reduces to Warren and Root’s model. In general, Warren and Root’s model does not describe every fractured reservoir. The impact of the presence of additional fracture network, such as secondary and tertiary fractures on the equivalent model, and pressure transient behavior is highlighted. Dual porosity Multi-scale media Two-scale homogenization Warren and Root model Naturally fractured media Kuchuk, Fikri J. aut Enthalten in Transport in porous media Springer Netherlands, 1986 129(2019), 3 vom: 08. Juli, Seite 901-940 (DE-627)129206105 (DE-600)54858-3 (DE-576)014457431 0169-3913 nnns volume:129 year:2019 number:3 day:08 month:07 pages:901-940 https://doi.org/10.1007/s11242-019-01312-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_70 AR 129 2019 3 08 07 901-940 |
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10.1007/s11242-019-01312-z doi (DE-627)OLC2054397814 (DE-He213)s11242-019-01312-z-p DE-627 ger DE-627 rakwb eng 530 VZ Rasoulzadeh, Mojdeh verfasserin (orcid)0000-0002-1467-9611 aut Pressure Transient Behavior of High-Fracture-Density Reservoirs (Dual-Porosity Models) 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Nature B.V. 2019 Abstract Naturally fractured reservoirs (NFRs) contain primary (macro), secondary, and tertiary (minor) fractures. These reservoirs are heterogeneous, where fracture properties such as length, conductivity, aperture, and orientation significantly vary spatially. In general, fractures in these reservoirs are very conductive whether they are in a discrete or continuous fracture network. The conventional dual-porosity-type models (Warren and Root in SPE J 3(3):245–255, 1963) are widely used to model NFRs either in conventional or unconventional formations. In shale, the naturally fractured shale is often considered as a dual-porosity model and is coupled with discrete network of hydraulic fractures. Expressing flow by dual-porosity model in the complex pore structure of NFRs is an oversimplification which has demonstrated several deficiencies and inconsistencies with field transient data and field applications. We show that the dual-porosity models are applicable to specific sets of NFRs and under restrictive conditions. In several NFRs, fractures create a network, communicate hydraulically with each other globally, and provide overall conductivity for the reservoir. The matrix provides the overall storage capacity, but it should be conductive enough to pass the fluid towards the fractures. Given the contrast between the conductivity of the fractures and the matrix, several flow regimes may form at microscale. For low contrasts, the conductivities of the matrix and fractures are close enough that the medium behaves as a homogenous medium. For higher contrasts, matrix is not conductive enough to be a part of the overall flow process in the reservoir, so it behaves as a source of fluid to fractures. For very high contrasts, the matrix is almost not conductive, so it cannot pass the fluid to the fracture. In this case, the overall flow will be governed by the flow in the fracture network. Other intermediate cases may also occur. The pressure behavior of continuously fractured reservoirs is investigated for various contrasts in matrix and fracture properties. The homogenized model is obtained by using the two-scale homogenization technique. The homogenization is performed by starting from the microscale flow equations in the matrix and fracture coupled via a set of no-jump boundary conditions on the interface of fracture and matrix. This approach captures the details of the flow both within and between the porous matrix and fracture. A general equivalent macroscopic model is proposed; the macroscopic homogenized model is the average of the microscale equations of flow in fracture and matrix. The equivalent porosity and the equivalent permeability of the averaged medium are derived. The equivalent permeability depends on both the fracture’s permeability and the geometry of each block of nonhomogeneity. The memory effect in the medium is included in the averaged model through an integro-differential term. Memory effect represents the difference between the response time of matrix and fracture to the same pressure drop. Using the homogenization technique, several averaged models for fractured medium can be obtained, depending on the ratio of the fracture to matrix diffusivity, the fracture-to-matrix volume ratio, and the number of scales of nonhomogeneity in the medium. For certain contrasts in matrix and fracture properties, such as the ratio of matrix to fracture permeability and the fracture aperture, the general model reduces to Warren and Root’s model. In general, Warren and Root’s model does not describe every fractured reservoir. The impact of the presence of additional fracture network, such as secondary and tertiary fractures on the equivalent model, and pressure transient behavior is highlighted. Dual porosity Multi-scale media Two-scale homogenization Warren and Root model Naturally fractured media Kuchuk, Fikri J. aut Enthalten in Transport in porous media Springer Netherlands, 1986 129(2019), 3 vom: 08. Juli, Seite 901-940 (DE-627)129206105 (DE-600)54858-3 (DE-576)014457431 0169-3913 nnns volume:129 year:2019 number:3 day:08 month:07 pages:901-940 https://doi.org/10.1007/s11242-019-01312-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_70 AR 129 2019 3 08 07 901-940 |
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10.1007/s11242-019-01312-z doi (DE-627)OLC2054397814 (DE-He213)s11242-019-01312-z-p DE-627 ger DE-627 rakwb eng 530 VZ Rasoulzadeh, Mojdeh verfasserin (orcid)0000-0002-1467-9611 aut Pressure Transient Behavior of High-Fracture-Density Reservoirs (Dual-Porosity Models) 2019 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Nature B.V. 2019 Abstract Naturally fractured reservoirs (NFRs) contain primary (macro), secondary, and tertiary (minor) fractures. These reservoirs are heterogeneous, where fracture properties such as length, conductivity, aperture, and orientation significantly vary spatially. In general, fractures in these reservoirs are very conductive whether they are in a discrete or continuous fracture network. The conventional dual-porosity-type models (Warren and Root in SPE J 3(3):245–255, 1963) are widely used to model NFRs either in conventional or unconventional formations. In shale, the naturally fractured shale is often considered as a dual-porosity model and is coupled with discrete network of hydraulic fractures. Expressing flow by dual-porosity model in the complex pore structure of NFRs is an oversimplification which has demonstrated several deficiencies and inconsistencies with field transient data and field applications. We show that the dual-porosity models are applicable to specific sets of NFRs and under restrictive conditions. In several NFRs, fractures create a network, communicate hydraulically with each other globally, and provide overall conductivity for the reservoir. The matrix provides the overall storage capacity, but it should be conductive enough to pass the fluid towards the fractures. Given the contrast between the conductivity of the fractures and the matrix, several flow regimes may form at microscale. For low contrasts, the conductivities of the matrix and fractures are close enough that the medium behaves as a homogenous medium. For higher contrasts, matrix is not conductive enough to be a part of the overall flow process in the reservoir, so it behaves as a source of fluid to fractures. For very high contrasts, the matrix is almost not conductive, so it cannot pass the fluid to the fracture. In this case, the overall flow will be governed by the flow in the fracture network. Other intermediate cases may also occur. The pressure behavior of continuously fractured reservoirs is investigated for various contrasts in matrix and fracture properties. The homogenized model is obtained by using the two-scale homogenization technique. The homogenization is performed by starting from the microscale flow equations in the matrix and fracture coupled via a set of no-jump boundary conditions on the interface of fracture and matrix. This approach captures the details of the flow both within and between the porous matrix and fracture. A general equivalent macroscopic model is proposed; the macroscopic homogenized model is the average of the microscale equations of flow in fracture and matrix. The equivalent porosity and the equivalent permeability of the averaged medium are derived. The equivalent permeability depends on both the fracture’s permeability and the geometry of each block of nonhomogeneity. The memory effect in the medium is included in the averaged model through an integro-differential term. Memory effect represents the difference between the response time of matrix and fracture to the same pressure drop. Using the homogenization technique, several averaged models for fractured medium can be obtained, depending on the ratio of the fracture to matrix diffusivity, the fracture-to-matrix volume ratio, and the number of scales of nonhomogeneity in the medium. For certain contrasts in matrix and fracture properties, such as the ratio of matrix to fracture permeability and the fracture aperture, the general model reduces to Warren and Root’s model. In general, Warren and Root’s model does not describe every fractured reservoir. The impact of the presence of additional fracture network, such as secondary and tertiary fractures on the equivalent model, and pressure transient behavior is highlighted. Dual porosity Multi-scale media Two-scale homogenization Warren and Root model Naturally fractured media Kuchuk, Fikri J. aut Enthalten in Transport in porous media Springer Netherlands, 1986 129(2019), 3 vom: 08. Juli, Seite 901-940 (DE-627)129206105 (DE-600)54858-3 (DE-576)014457431 0169-3913 nnns volume:129 year:2019 number:3 day:08 month:07 pages:901-940 https://doi.org/10.1007/s11242-019-01312-z lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC SSG-OLC-PHY GBV_ILN_70 AR 129 2019 3 08 07 901-940 |
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In several NFRs, fractures create a network, communicate hydraulically with each other globally, and provide overall conductivity for the reservoir. The matrix provides the overall storage capacity, but it should be conductive enough to pass the fluid towards the fractures. Given the contrast between the conductivity of the fractures and the matrix, several flow regimes may form at microscale. For low contrasts, the conductivities of the matrix and fractures are close enough that the medium behaves as a homogenous medium. For higher contrasts, matrix is not conductive enough to be a part of the overall flow process in the reservoir, so it behaves as a source of fluid to fractures. For very high contrasts, the matrix is almost not conductive, so it cannot pass the fluid to the fracture. In this case, the overall flow will be governed by the flow in the fracture network. Other intermediate cases may also occur. 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Rasoulzadeh, Mojdeh |
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pressure transient behavior of high-fracture-density reservoirs (dual-porosity models) |
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Pressure Transient Behavior of High-Fracture-Density Reservoirs (Dual-Porosity Models) |
| abstract |
Abstract Naturally fractured reservoirs (NFRs) contain primary (macro), secondary, and tertiary (minor) fractures. These reservoirs are heterogeneous, where fracture properties such as length, conductivity, aperture, and orientation significantly vary spatially. In general, fractures in these reservoirs are very conductive whether they are in a discrete or continuous fracture network. The conventional dual-porosity-type models (Warren and Root in SPE J 3(3):245–255, 1963) are widely used to model NFRs either in conventional or unconventional formations. In shale, the naturally fractured shale is often considered as a dual-porosity model and is coupled with discrete network of hydraulic fractures. Expressing flow by dual-porosity model in the complex pore structure of NFRs is an oversimplification which has demonstrated several deficiencies and inconsistencies with field transient data and field applications. We show that the dual-porosity models are applicable to specific sets of NFRs and under restrictive conditions. In several NFRs, fractures create a network, communicate hydraulically with each other globally, and provide overall conductivity for the reservoir. The matrix provides the overall storage capacity, but it should be conductive enough to pass the fluid towards the fractures. Given the contrast between the conductivity of the fractures and the matrix, several flow regimes may form at microscale. For low contrasts, the conductivities of the matrix and fractures are close enough that the medium behaves as a homogenous medium. For higher contrasts, matrix is not conductive enough to be a part of the overall flow process in the reservoir, so it behaves as a source of fluid to fractures. For very high contrasts, the matrix is almost not conductive, so it cannot pass the fluid to the fracture. In this case, the overall flow will be governed by the flow in the fracture network. Other intermediate cases may also occur. The pressure behavior of continuously fractured reservoirs is investigated for various contrasts in matrix and fracture properties. The homogenized model is obtained by using the two-scale homogenization technique. The homogenization is performed by starting from the microscale flow equations in the matrix and fracture coupled via a set of no-jump boundary conditions on the interface of fracture and matrix. This approach captures the details of the flow both within and between the porous matrix and fracture. A general equivalent macroscopic model is proposed; the macroscopic homogenized model is the average of the microscale equations of flow in fracture and matrix. The equivalent porosity and the equivalent permeability of the averaged medium are derived. The equivalent permeability depends on both the fracture’s permeability and the geometry of each block of nonhomogeneity. The memory effect in the medium is included in the averaged model through an integro-differential term. Memory effect represents the difference between the response time of matrix and fracture to the same pressure drop. Using the homogenization technique, several averaged models for fractured medium can be obtained, depending on the ratio of the fracture to matrix diffusivity, the fracture-to-matrix volume ratio, and the number of scales of nonhomogeneity in the medium. For certain contrasts in matrix and fracture properties, such as the ratio of matrix to fracture permeability and the fracture aperture, the general model reduces to Warren and Root’s model. In general, Warren and Root’s model does not describe every fractured reservoir. The impact of the presence of additional fracture network, such as secondary and tertiary fractures on the equivalent model, and pressure transient behavior is highlighted. © Springer Nature B.V. 2019 |
| abstractGer |
Abstract Naturally fractured reservoirs (NFRs) contain primary (macro), secondary, and tertiary (minor) fractures. These reservoirs are heterogeneous, where fracture properties such as length, conductivity, aperture, and orientation significantly vary spatially. In general, fractures in these reservoirs are very conductive whether they are in a discrete or continuous fracture network. The conventional dual-porosity-type models (Warren and Root in SPE J 3(3):245–255, 1963) are widely used to model NFRs either in conventional or unconventional formations. In shale, the naturally fractured shale is often considered as a dual-porosity model and is coupled with discrete network of hydraulic fractures. Expressing flow by dual-porosity model in the complex pore structure of NFRs is an oversimplification which has demonstrated several deficiencies and inconsistencies with field transient data and field applications. We show that the dual-porosity models are applicable to specific sets of NFRs and under restrictive conditions. In several NFRs, fractures create a network, communicate hydraulically with each other globally, and provide overall conductivity for the reservoir. The matrix provides the overall storage capacity, but it should be conductive enough to pass the fluid towards the fractures. Given the contrast between the conductivity of the fractures and the matrix, several flow regimes may form at microscale. For low contrasts, the conductivities of the matrix and fractures are close enough that the medium behaves as a homogenous medium. For higher contrasts, matrix is not conductive enough to be a part of the overall flow process in the reservoir, so it behaves as a source of fluid to fractures. For very high contrasts, the matrix is almost not conductive, so it cannot pass the fluid to the fracture. In this case, the overall flow will be governed by the flow in the fracture network. Other intermediate cases may also occur. The pressure behavior of continuously fractured reservoirs is investigated for various contrasts in matrix and fracture properties. The homogenized model is obtained by using the two-scale homogenization technique. The homogenization is performed by starting from the microscale flow equations in the matrix and fracture coupled via a set of no-jump boundary conditions on the interface of fracture and matrix. This approach captures the details of the flow both within and between the porous matrix and fracture. A general equivalent macroscopic model is proposed; the macroscopic homogenized model is the average of the microscale equations of flow in fracture and matrix. The equivalent porosity and the equivalent permeability of the averaged medium are derived. The equivalent permeability depends on both the fracture’s permeability and the geometry of each block of nonhomogeneity. The memory effect in the medium is included in the averaged model through an integro-differential term. Memory effect represents the difference between the response time of matrix and fracture to the same pressure drop. Using the homogenization technique, several averaged models for fractured medium can be obtained, depending on the ratio of the fracture to matrix diffusivity, the fracture-to-matrix volume ratio, and the number of scales of nonhomogeneity in the medium. For certain contrasts in matrix and fracture properties, such as the ratio of matrix to fracture permeability and the fracture aperture, the general model reduces to Warren and Root’s model. In general, Warren and Root’s model does not describe every fractured reservoir. The impact of the presence of additional fracture network, such as secondary and tertiary fractures on the equivalent model, and pressure transient behavior is highlighted. © Springer Nature B.V. 2019 |
| abstract_unstemmed |
Abstract Naturally fractured reservoirs (NFRs) contain primary (macro), secondary, and tertiary (minor) fractures. These reservoirs are heterogeneous, where fracture properties such as length, conductivity, aperture, and orientation significantly vary spatially. In general, fractures in these reservoirs are very conductive whether they are in a discrete or continuous fracture network. The conventional dual-porosity-type models (Warren and Root in SPE J 3(3):245–255, 1963) are widely used to model NFRs either in conventional or unconventional formations. In shale, the naturally fractured shale is often considered as a dual-porosity model and is coupled with discrete network of hydraulic fractures. Expressing flow by dual-porosity model in the complex pore structure of NFRs is an oversimplification which has demonstrated several deficiencies and inconsistencies with field transient data and field applications. We show that the dual-porosity models are applicable to specific sets of NFRs and under restrictive conditions. In several NFRs, fractures create a network, communicate hydraulically with each other globally, and provide overall conductivity for the reservoir. The matrix provides the overall storage capacity, but it should be conductive enough to pass the fluid towards the fractures. Given the contrast between the conductivity of the fractures and the matrix, several flow regimes may form at microscale. For low contrasts, the conductivities of the matrix and fractures are close enough that the medium behaves as a homogenous medium. For higher contrasts, matrix is not conductive enough to be a part of the overall flow process in the reservoir, so it behaves as a source of fluid to fractures. For very high contrasts, the matrix is almost not conductive, so it cannot pass the fluid to the fracture. In this case, the overall flow will be governed by the flow in the fracture network. Other intermediate cases may also occur. The pressure behavior of continuously fractured reservoirs is investigated for various contrasts in matrix and fracture properties. The homogenized model is obtained by using the two-scale homogenization technique. The homogenization is performed by starting from the microscale flow equations in the matrix and fracture coupled via a set of no-jump boundary conditions on the interface of fracture and matrix. This approach captures the details of the flow both within and between the porous matrix and fracture. A general equivalent macroscopic model is proposed; the macroscopic homogenized model is the average of the microscale equations of flow in fracture and matrix. The equivalent porosity and the equivalent permeability of the averaged medium are derived. The equivalent permeability depends on both the fracture’s permeability and the geometry of each block of nonhomogeneity. The memory effect in the medium is included in the averaged model through an integro-differential term. Memory effect represents the difference between the response time of matrix and fracture to the same pressure drop. Using the homogenization technique, several averaged models for fractured medium can be obtained, depending on the ratio of the fracture to matrix diffusivity, the fracture-to-matrix volume ratio, and the number of scales of nonhomogeneity in the medium. For certain contrasts in matrix and fracture properties, such as the ratio of matrix to fracture permeability and the fracture aperture, the general model reduces to Warren and Root’s model. In general, Warren and Root’s model does not describe every fractured reservoir. The impact of the presence of additional fracture network, such as secondary and tertiary fractures on the equivalent model, and pressure transient behavior is highlighted. © Springer Nature B.V. 2019 |
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In several NFRs, fractures create a network, communicate hydraulically with each other globally, and provide overall conductivity for the reservoir. The matrix provides the overall storage capacity, but it should be conductive enough to pass the fluid towards the fractures. Given the contrast between the conductivity of the fractures and the matrix, several flow regimes may form at microscale. For low contrasts, the conductivities of the matrix and fractures are close enough that the medium behaves as a homogenous medium. For higher contrasts, matrix is not conductive enough to be a part of the overall flow process in the reservoir, so it behaves as a source of fluid to fractures. For very high contrasts, the matrix is almost not conductive, so it cannot pass the fluid to the fracture. In this case, the overall flow will be governed by the flow in the fracture network. Other intermediate cases may also occur. 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Memory effect represents the difference between the response time of matrix and fracture to the same pressure drop. Using the homogenization technique, several averaged models for fractured medium can be obtained, depending on the ratio of the fracture to matrix diffusivity, the fracture-to-matrix volume ratio, and the number of scales of nonhomogeneity in the medium. For certain contrasts in matrix and fracture properties, such as the ratio of matrix to fracture permeability and the fracture aperture, the general model reduces to Warren and Root’s model. In general, Warren and Root’s model does not describe every fractured reservoir. The impact of the presence of additional fracture network, such as secondary and tertiary fractures on the equivalent model, and pressure transient behavior is highlighted.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Dual porosity</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Multi-scale media</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Two-scale homogenization</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Warren and Root model</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Naturally fractured media</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Kuchuk, Fikri J.</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Transport in porous media</subfield><subfield code="d">Springer Netherlands, 1986</subfield><subfield code="g">129(2019), 3 vom: 08. Juli, Seite 901-940</subfield><subfield code="w">(DE-627)129206105</subfield><subfield code="w">(DE-600)54858-3</subfield><subfield code="w">(DE-576)014457431</subfield><subfield code="x">0169-3913</subfield><subfield code="7">nnns</subfield></datafield><datafield tag="773" ind1="1" ind2="8"><subfield code="g">volume:129</subfield><subfield code="g">year:2019</subfield><subfield code="g">number:3</subfield><subfield code="g">day:08</subfield><subfield code="g">month:07</subfield><subfield code="g">pages:901-940</subfield></datafield><datafield tag="856" ind1="4" ind2="1"><subfield code="u">https://doi.org/10.1007/s11242-019-01312-z</subfield><subfield code="z">lizenzpflichtig</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_USEFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SYSFLAG_A</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_OLC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-TEC</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">SSG-OLC-PHY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">GBV_ILN_70</subfield></datafield><datafield tag="951" ind1=" " ind2=" "><subfield code="a">AR</subfield></datafield><datafield tag="952" ind1=" " ind2=" "><subfield code="d">129</subfield><subfield code="j">2019</subfield><subfield code="e">3</subfield><subfield code="b">08</subfield><subfield code="c">07</subfield><subfield code="h">901-940</subfield></datafield></record></collection>
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