Frequency-dependent effective hydraulic conductivity of strongly heterogeneous media
The determination of the transport properties of heterogeneous porous rocks, such as an effective hydraulic conductivity, arises in a range of geoscience problems, from groundwater flow analysis to hydrocarbon reservoir modeling. In the presence of formation-scale heterogeneities, nonstationary flow...
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| Format: | Journal Article |
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The American Physical Society
2013
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| Online Access: | http://hdl.handle.net/20.500.11937/26669 |
| _version_ | 1848752052020183040 |
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| author | Caspari, Eva Gurevich, Boris Muller, T. |
| author2 | EAGE |
| author_facet | EAGE Caspari, Eva Gurevich, Boris Muller, T. |
| author_sort | Caspari, Eva |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | The determination of the transport properties of heterogeneous porous rocks, such as an effective hydraulic conductivity, arises in a range of geoscience problems, from groundwater flow analysis to hydrocarbon reservoir modeling. In the presence of formation-scale heterogeneities, nonstationary flows, induced by pumping tests or propagating elastic waves, entail localized pressure diffusion processes with a characteristic frequency depending on the pressure diffusivity and size of the heterogeneity. Then, on a macroscale, a homogeneous equivalent medium exists, which has a frequency-dependent effective conductivity. The frequency dependence of the conductivity can be analyzed with Biot's equations of poroelasticity. In the quasistatic frequency regime of this framework, the slow compressional wave is a proxy for pressure diffusion processes.This slow compressional wave is associated with the out-of-phase motion of the fluid and solid phase, thereby creating a relative fluid-solid displacement vector field. Decoupling of the poroelasticity equations gives a diffusion equation for the fluid-solid displacement field valid in a poroelastic medium with spatial fluctuations in hydraulic conductivity. Then, an effective conductivity is found by a Green's function approach followed by a strong-contrast perturbation theory suggested earlier in the context of random dielectrics. This theory leads to closed-form expressions for the frequency-dependent effective conductivity as a function of the one- and two-point probability functions of the conductivity fluctuations. In one dimension, these expressions are consistent with exact solutions in both low- and high-frequency limits for arbitrary conductivity contrast. In 3D, the low-frequency limit depends on the details of the microstructure. However, the derived approximation for the effective conductivity is consistent with the Hashin-Shtrikman bounds. |
| first_indexed | 2025-11-14T08:02:29Z |
| format | Journal Article |
| id | curtin-20.500.11937-26669 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:02:29Z |
| publishDate | 2013 |
| publisher | The American Physical Society |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-266692017-09-13T15:29:59Z Frequency-dependent effective hydraulic conductivity of strongly heterogeneous media Caspari, Eva Gurevich, Boris Muller, T. EAGE The determination of the transport properties of heterogeneous porous rocks, such as an effective hydraulic conductivity, arises in a range of geoscience problems, from groundwater flow analysis to hydrocarbon reservoir modeling. In the presence of formation-scale heterogeneities, nonstationary flows, induced by pumping tests or propagating elastic waves, entail localized pressure diffusion processes with a characteristic frequency depending on the pressure diffusivity and size of the heterogeneity. Then, on a macroscale, a homogeneous equivalent medium exists, which has a frequency-dependent effective conductivity. The frequency dependence of the conductivity can be analyzed with Biot's equations of poroelasticity. In the quasistatic frequency regime of this framework, the slow compressional wave is a proxy for pressure diffusion processes.This slow compressional wave is associated with the out-of-phase motion of the fluid and solid phase, thereby creating a relative fluid-solid displacement vector field. Decoupling of the poroelasticity equations gives a diffusion equation for the fluid-solid displacement field valid in a poroelastic medium with spatial fluctuations in hydraulic conductivity. Then, an effective conductivity is found by a Green's function approach followed by a strong-contrast perturbation theory suggested earlier in the context of random dielectrics. This theory leads to closed-form expressions for the frequency-dependent effective conductivity as a function of the one- and two-point probability functions of the conductivity fluctuations. In one dimension, these expressions are consistent with exact solutions in both low- and high-frequency limits for arbitrary conductivity contrast. In 3D, the low-frequency limit depends on the details of the microstructure. However, the derived approximation for the effective conductivity is consistent with the Hashin-Shtrikman bounds. 2013 Journal Article http://hdl.handle.net/20.500.11937/26669 10.1103/PhysRevE.88.042119 The American Physical Society restricted |
| spellingShingle | Caspari, Eva Gurevich, Boris Muller, T. Frequency-dependent effective hydraulic conductivity of strongly heterogeneous media |
| title | Frequency-dependent effective hydraulic conductivity of strongly heterogeneous media |
| title_full | Frequency-dependent effective hydraulic conductivity of strongly heterogeneous media |
| title_fullStr | Frequency-dependent effective hydraulic conductivity of strongly heterogeneous media |
| title_full_unstemmed | Frequency-dependent effective hydraulic conductivity of strongly heterogeneous media |
| title_short | Frequency-dependent effective hydraulic conductivity of strongly heterogeneous media |
| title_sort | frequency-dependent effective hydraulic conductivity of strongly heterogeneous media |
| url | http://hdl.handle.net/20.500.11937/26669 |