A study in fractional diffusion: Fractured rocks produced through horizontal wells with multiple, hydraulic fractures
The spatiotemporal evolution of transients in fractured rocks often displays unusual characteristics and is traced to multifaceted origins such as micro-discontinuity in rock properties, rock fragmentation, long-range connectivity and complex flow paths. A physics-based model that incorporates trans...
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| Format: | Article |
| Language: | English |
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EDP Sciences
2020-01-01
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| Series: | Oil & Gas Science and Technology |
| Online Access: | https://ogst.ifpenergiesnouvelles.fr/articles/ogst/full_html/2020/01/ogst200173/ogst200173.html |
| _version_ | 1818610818987589632 |
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| author | Raghavan Rajagopal Chen Chih Cheng |
| author_facet | Raghavan Rajagopal Chen Chih Cheng |
| author_sort | Raghavan Rajagopal |
| collection | DOAJ |
| description | The spatiotemporal evolution of transients in fractured rocks often displays unusual characteristics and is traced to multifaceted origins such as micro-discontinuity in rock properties, rock fragmentation, long-range connectivity and complex flow paths. A physics-based model that incorporates transient propagation wherein the mean square displacement of the diffusion front follows a nonlinear scaling with time is proposed. This model is based on fractional diffusion. The motivation for fractional flux laws follows from the existence of long-range connectivity that results in the mean square displacement of fronts moving faster than predicted by classical models; correspondingly, obstructions and discontinuities, local flow reversals, intercalations, etc. produce the opposite effect with fronts moving at a slower rate than classical predictions. The interplay of these two competing behaviors is quantified. We simulate transient production in a porous rock at the Theis scale as a result of production through a horizontal well consisting of multiple hydraulic fractures. Asymptotic solutions are derived and computations verified. The practical potential of this model is described through an example and the movement of fronts under the constraints of this model is demonstrated through the new expressions developed in this work. We demonstrate that this model offers a potential avenue to explain other behaviors noted in the literature. Though this work is developed in the context of applications to the earth sciences (production of hydrocarbons, extraction of geothermal resources, sequestration of radioactive waste and other fluids, groundwater flow), a minimal change in the Nomenclature permits application to other contexts. Ideas proposed here are particularly useful in the context of superdiffusion in bounded systems which until now, in many ways, has been considered to be an open problem. |
| first_indexed | 2024-12-16T15:20:29Z |
| format | Article |
| id | doaj.art-6ffc36a978fa4d6dac16f120528761b2 |
| institution | Directory Open Access Journal |
| issn | 1294-4475 1953-8189 |
| language | English |
| last_indexed | 2024-12-16T15:20:29Z |
| publishDate | 2020-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | Oil & Gas Science and Technology |
| spelling | doaj.art-6ffc36a978fa4d6dac16f120528761b22022-12-21T22:26:39ZengEDP SciencesOil & Gas Science and Technology1294-44751953-81892020-01-01756810.2516/ogst/2020062ogst200173A study in fractional diffusion: Fractured rocks produced through horizontal wells with multiple, hydraulic fracturesRaghavan Rajagopal0https://orcid.org/0000-0003-4582-521XChen Chih Cheng1https://orcid.org/0000-0003-2351-1500Raghavan GroupKappa EngineeringThe spatiotemporal evolution of transients in fractured rocks often displays unusual characteristics and is traced to multifaceted origins such as micro-discontinuity in rock properties, rock fragmentation, long-range connectivity and complex flow paths. A physics-based model that incorporates transient propagation wherein the mean square displacement of the diffusion front follows a nonlinear scaling with time is proposed. This model is based on fractional diffusion. The motivation for fractional flux laws follows from the existence of long-range connectivity that results in the mean square displacement of fronts moving faster than predicted by classical models; correspondingly, obstructions and discontinuities, local flow reversals, intercalations, etc. produce the opposite effect with fronts moving at a slower rate than classical predictions. The interplay of these two competing behaviors is quantified. We simulate transient production in a porous rock at the Theis scale as a result of production through a horizontal well consisting of multiple hydraulic fractures. Asymptotic solutions are derived and computations verified. The practical potential of this model is described through an example and the movement of fronts under the constraints of this model is demonstrated through the new expressions developed in this work. We demonstrate that this model offers a potential avenue to explain other behaviors noted in the literature. Though this work is developed in the context of applications to the earth sciences (production of hydrocarbons, extraction of geothermal resources, sequestration of radioactive waste and other fluids, groundwater flow), a minimal change in the Nomenclature permits application to other contexts. Ideas proposed here are particularly useful in the context of superdiffusion in bounded systems which until now, in many ways, has been considered to be an open problem.https://ogst.ifpenergiesnouvelles.fr/articles/ogst/full_html/2020/01/ogst200173/ogst200173.html |
| spellingShingle | Raghavan Rajagopal Chen Chih Cheng A study in fractional diffusion: Fractured rocks produced through horizontal wells with multiple, hydraulic fractures Oil & Gas Science and Technology |
| title | A study in fractional diffusion: Fractured rocks produced through horizontal wells with multiple, hydraulic fractures |
| title_full | A study in fractional diffusion: Fractured rocks produced through horizontal wells with multiple, hydraulic fractures |
| title_fullStr | A study in fractional diffusion: Fractured rocks produced through horizontal wells with multiple, hydraulic fractures |
| title_full_unstemmed | A study in fractional diffusion: Fractured rocks produced through horizontal wells with multiple, hydraulic fractures |
| title_short | A study in fractional diffusion: Fractured rocks produced through horizontal wells with multiple, hydraulic fractures |
| title_sort | study in fractional diffusion fractured rocks produced through horizontal wells with multiple hydraulic fractures |
| url | https://ogst.ifpenergiesnouvelles.fr/articles/ogst/full_html/2020/01/ogst200173/ogst200173.html |
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