Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media
Abstract Recently, an accurate coupling between subsurface flow and reservoir geomechanics has received more attention in both academia and industry. This stems from the fact that incorporating a geomechanics model into upstream flow simulation is critical for accurately predicting wellbore instabi...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Springer International Publishing
2021
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| Online Access: | https://hdl.handle.net/1721.1/131547 |
| _version_ | 1826193772832096256 |
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| author | Almani, T. Manea, A. Kumar, K. Dogru, A. H |
| author2 | Massachusetts Institute of Technology. Earth Resources Laboratory |
| author_facet | Massachusetts Institute of Technology. Earth Resources Laboratory Almani, T. Manea, A. Kumar, K. Dogru, A. H |
| author_sort | Almani, T. |
| collection | MIT |
| description | Abstract
Recently, an accurate coupling between subsurface flow and reservoir geomechanics has received more attention in both academia and industry. This stems from the fact that incorporating a geomechanics model into upstream flow simulation is critical for accurately predicting wellbore instabilities and hydraulic fracturing processes. One of the recently introduced iterative coupling algorithms to couple flow with geomechanics is the undrained split iterative coupling algorithm as reported by Kumar et al. (2016) and Mikelic and Wheeler (Comput. Geosci. 17: 455–461 2013). The convergence of this scheme is established in Mikelic and Wheeler (Comput. Geosci. 17:455–461 2013) for the single rate iterative coupling algorithm and in Kumar et al. (2016) for the multirate iterative coupling algorithm, in which the flow takes multiple finer time steps within one coarse mechanics time step. All previously established results study the convergence of the scheme in homogeneous poroelastic media. In this work, following the approach in Almani et al. (2017), we extend these results to the case of heterogeneous poroelastic media, in which each grid cell is associated with its own set of flow and mechanics parameters for both the single rate and multirate schemes. Second, following the approach in Almani et al. (Comput. Geosci. 21:1157–1172 2017), we establish a priori error estimates for the single rate case of the scheme in homogeneous poroelastic media. To the best of our knowledge, this is the first rigorous and complete mathematical analysis of the undrained split iterative coupling scheme in heterogeneous poroelastic media. |
| first_indexed | 2024-09-23T09:44:40Z |
| format | Article |
| id | mit-1721.1/131547 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T09:44:40Z |
| publishDate | 2021 |
| publisher | Springer International Publishing |
| record_format | dspace |
| spelling | mit-1721.1/1315472023-09-06T20:59:53Z Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media Almani, T. Manea, A. Kumar, K. Dogru, A. H Massachusetts Institute of Technology. Earth Resources Laboratory Massachusetts Institute of Technology. Department of Earth, Atmospheric, and Planetary Sciences Abstract Recently, an accurate coupling between subsurface flow and reservoir geomechanics has received more attention in both academia and industry. This stems from the fact that incorporating a geomechanics model into upstream flow simulation is critical for accurately predicting wellbore instabilities and hydraulic fracturing processes. One of the recently introduced iterative coupling algorithms to couple flow with geomechanics is the undrained split iterative coupling algorithm as reported by Kumar et al. (2016) and Mikelic and Wheeler (Comput. Geosci. 17: 455–461 2013). The convergence of this scheme is established in Mikelic and Wheeler (Comput. Geosci. 17:455–461 2013) for the single rate iterative coupling algorithm and in Kumar et al. (2016) for the multirate iterative coupling algorithm, in which the flow takes multiple finer time steps within one coarse mechanics time step. All previously established results study the convergence of the scheme in homogeneous poroelastic media. In this work, following the approach in Almani et al. (2017), we extend these results to the case of heterogeneous poroelastic media, in which each grid cell is associated with its own set of flow and mechanics parameters for both the single rate and multirate schemes. Second, following the approach in Almani et al. (Comput. Geosci. 21:1157–1172 2017), we establish a priori error estimates for the single rate case of the scheme in homogeneous poroelastic media. To the best of our knowledge, this is the first rigorous and complete mathematical analysis of the undrained split iterative coupling scheme in heterogeneous poroelastic media. 2021-09-20T17:20:20Z 2021-09-20T17:20:20Z 2019-08-08 2020-09-24T21:13:34Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/131547 en https://doi.org/10.1007/s10596-019-09860-5 Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. Springer Nature Switzerland AG application/pdf Springer International Publishing Springer International Publishing |
| spellingShingle | Almani, T. Manea, A. Kumar, K. Dogru, A. H Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media |
| title | Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media |
| title_full | Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media |
| title_fullStr | Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media |
| title_full_unstemmed | Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media |
| title_short | Convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media |
| title_sort | convergence of the undrained split iterative scheme for coupling flow with geomechanics in heterogeneous poroelastic media |
| url | https://hdl.handle.net/1721.1/131547 |
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