Analytical solution for fractional derivative gas-flow equation in porous media
In this paper, we introduce an analytical solution of the fractional derivative gas transport equation using the power-series technique. We present a new universal transform, namely, generalized Boltzmann change of variable which depends on the fractional order, time and space. This universal transf...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2017-01-01
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| Series: | Results in Physics |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379717309038 |
| _version_ | 1818954606863974400 |
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| author | Mohamed F. El Amin Ahmed G. Radwan Shuyu Sun |
| author_facet | Mohamed F. El Amin Ahmed G. Radwan Shuyu Sun |
| author_sort | Mohamed F. El Amin |
| collection | DOAJ |
| description | In this paper, we introduce an analytical solution of the fractional derivative gas transport equation using the power-series technique. We present a new universal transform, namely, generalized Boltzmann change of variable which depends on the fractional order, time and space. This universal transform is employed to transfer the partial differential equation into an ordinary differential equation. Moreover, the convergence of the solution has been investigated and found that solutions are unconditionally converged. Results are introduced and discussed for the universal variable and other physical parameters such as porosity and permeability of the reservoir; time and space. Keywords: Fractional derivative, Porous media, Natural gas, Reservoir modeling, Infinite series solutions |
| first_indexed | 2024-12-20T10:24:51Z |
| format | Article |
| id | doaj.art-8c3b97bd3cf84f08be91c5e745982f37 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-12-20T10:24:51Z |
| publishDate | 2017-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-8c3b97bd3cf84f08be91c5e745982f372022-12-21T19:43:51ZengElsevierResults in Physics2211-37972017-01-01724322438Analytical solution for fractional derivative gas-flow equation in porous mediaMohamed F. El Amin0Ahmed G. Radwan1Shuyu Sun2King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia; College of Engineering, Effat University, Jeddah 21478, Saudi Arabia; Mathematics Department, Faculty of Science, Aswan University, Aswan 81528, Egypt; Corresponding author at: College of Engineering, Effat University, Jeddah 21478, Kingdom of Saudi Arabia.Engineering Mathematics and Physics Dept., Cairo University, 12613 Giza, Egypt; Nanoelectronics Integrated Systems Center (NISC), Nile University, Giza, EgyptKing Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi ArabiaIn this paper, we introduce an analytical solution of the fractional derivative gas transport equation using the power-series technique. We present a new universal transform, namely, generalized Boltzmann change of variable which depends on the fractional order, time and space. This universal transform is employed to transfer the partial differential equation into an ordinary differential equation. Moreover, the convergence of the solution has been investigated and found that solutions are unconditionally converged. Results are introduced and discussed for the universal variable and other physical parameters such as porosity and permeability of the reservoir; time and space. Keywords: Fractional derivative, Porous media, Natural gas, Reservoir modeling, Infinite series solutionshttp://www.sciencedirect.com/science/article/pii/S2211379717309038 |
| spellingShingle | Mohamed F. El Amin Ahmed G. Radwan Shuyu Sun Analytical solution for fractional derivative gas-flow equation in porous media Results in Physics |
| title | Analytical solution for fractional derivative gas-flow equation in porous media |
| title_full | Analytical solution for fractional derivative gas-flow equation in porous media |
| title_fullStr | Analytical solution for fractional derivative gas-flow equation in porous media |
| title_full_unstemmed | Analytical solution for fractional derivative gas-flow equation in porous media |
| title_short | Analytical solution for fractional derivative gas-flow equation in porous media |
| title_sort | analytical solution for fractional derivative gas flow equation in porous media |
| url | http://www.sciencedirect.com/science/article/pii/S2211379717309038 |
| work_keys_str_mv | AT mohamedfelamin analyticalsolutionforfractionalderivativegasflowequationinporousmedia AT ahmedgradwan analyticalsolutionforfractionalderivativegasflowequationinporousmedia AT shuyusun analyticalsolutionforfractionalderivativegasflowequationinporousmedia |