Quasi-Analytical Model of the Transient Behavior Pressure in an Oil Reservoir Made Up of Three Porous Media Considering the Fractional Time Derivative
The present work proposes a new model to capture high heterogeneity of single phase flow in naturally fractured vuggy reservoirs. The model considers a three porous media reservoir; namely, fractured system, vugular system and matrix; the case of an infinite reservoir is considered in a full-penetra...
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| Format: | Article |
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MDPI AG
2020-12-01
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| Series: | Mathematical and Computational Applications |
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| Online Access: | https://www.mdpi.com/2297-8747/25/4/74 |
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| author | Fernando Alcántara-López Carlos Fuentes Fernando Brambila-Paz Jesús López-Estrada |
| author_facet | Fernando Alcántara-López Carlos Fuentes Fernando Brambila-Paz Jesús López-Estrada |
| author_sort | Fernando Alcántara-López |
| collection | DOAJ |
| description | The present work proposes a new model to capture high heterogeneity of single phase flow in naturally fractured vuggy reservoirs. The model considers a three porous media reservoir; namely, fractured system, vugular system and matrix; the case of an infinite reservoir is considered in a full-penetrating wellbore. Furthermore, the model relaxes classic hypotheses considering that matrix permeability has a significant impact on the pressure deficit from the wellbore, reaching the triple permeability and triple porosity model wich allows the wellbore to be fed by all the porous media and not exclusively by the fractured system; where it is considered a pseudostable interporous flow. In addition, it is considered the anomalous flow phenomenon from the pressure of each independent porous medium and as a whole, through the temporal fractional derivative of Caputo type; the resulting phenomenon is studied for orders in the fractional derivatives in (0, 2), known as superdiffusive and subdiffusive phenomena. Synthetic results highlight the effect of anomalous flows throughout the entire transient behavior considering a significant permeability in the matrix and it is contrasted with the effect of an almost negligible matrix permeability. The model is solved analytically in the Laplace space, incorporating the Tartaglia–Cardano equations. |
| first_indexed | 2024-03-10T14:25:13Z |
| format | Article |
| id | doaj.art-62e686d3709b42048e10ed9678fc126e |
| institution | Directory Open Access Journal |
| issn | 1300-686X 2297-8747 |
| language | English |
| last_indexed | 2024-03-10T14:25:13Z |
| publishDate | 2020-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematical and Computational Applications |
| spelling | doaj.art-62e686d3709b42048e10ed9678fc126e2023-11-20T23:04:49ZengMDPI AGMathematical and Computational Applications1300-686X2297-87472020-12-012547410.3390/mca25040074Quasi-Analytical Model of the Transient Behavior Pressure in an Oil Reservoir Made Up of Three Porous Media Considering the Fractional Time DerivativeFernando Alcántara-López0Carlos Fuentes1Fernando Brambila-Paz2Jesús López-Estrada3Department of Mathematics, Faculty of Science, National Autonomous University of México, Av. Universidad 3000, Circuito Exterior S/N, Delegación Coyoacán 04510, Ciudad de México, MexicoMexican Institute of Water Technology, Paseo Cuauhnáhuac Núm. 8532, Jiutepec, Morelos 62550, MexicoDepartment of Mathematics, Faculty of Science, National Autonomous University of México, Av. Universidad 3000, Circuito Exterior S/N, Delegación Coyoacán 04510, Ciudad de México, MexicoDepartment of Mathematics, Faculty of Science, National Autonomous University of México, Av. Universidad 3000, Circuito Exterior S/N, Delegación Coyoacán 04510, Ciudad de México, MexicoThe present work proposes a new model to capture high heterogeneity of single phase flow in naturally fractured vuggy reservoirs. The model considers a three porous media reservoir; namely, fractured system, vugular system and matrix; the case of an infinite reservoir is considered in a full-penetrating wellbore. Furthermore, the model relaxes classic hypotheses considering that matrix permeability has a significant impact on the pressure deficit from the wellbore, reaching the triple permeability and triple porosity model wich allows the wellbore to be fed by all the porous media and not exclusively by the fractured system; where it is considered a pseudostable interporous flow. In addition, it is considered the anomalous flow phenomenon from the pressure of each independent porous medium and as a whole, through the temporal fractional derivative of Caputo type; the resulting phenomenon is studied for orders in the fractional derivatives in (0, 2), known as superdiffusive and subdiffusive phenomena. Synthetic results highlight the effect of anomalous flows throughout the entire transient behavior considering a significant permeability in the matrix and it is contrasted with the effect of an almost negligible matrix permeability. The model is solved analytically in the Laplace space, incorporating the Tartaglia–Cardano equations.https://www.mdpi.com/2297-8747/25/4/74porous mediaDarcy lawwell test analysistriple porosityTartaglia–Cardano equationsCaputo time derivative |
| spellingShingle | Fernando Alcántara-López Carlos Fuentes Fernando Brambila-Paz Jesús López-Estrada Quasi-Analytical Model of the Transient Behavior Pressure in an Oil Reservoir Made Up of Three Porous Media Considering the Fractional Time Derivative Mathematical and Computational Applications porous media Darcy law well test analysis triple porosity Tartaglia–Cardano equations Caputo time derivative |
| title | Quasi-Analytical Model of the Transient Behavior Pressure in an Oil Reservoir Made Up of Three Porous Media Considering the Fractional Time Derivative |
| title_full | Quasi-Analytical Model of the Transient Behavior Pressure in an Oil Reservoir Made Up of Three Porous Media Considering the Fractional Time Derivative |
| title_fullStr | Quasi-Analytical Model of the Transient Behavior Pressure in an Oil Reservoir Made Up of Three Porous Media Considering the Fractional Time Derivative |
| title_full_unstemmed | Quasi-Analytical Model of the Transient Behavior Pressure in an Oil Reservoir Made Up of Three Porous Media Considering the Fractional Time Derivative |
| title_short | Quasi-Analytical Model of the Transient Behavior Pressure in an Oil Reservoir Made Up of Three Porous Media Considering the Fractional Time Derivative |
| title_sort | quasi analytical model of the transient behavior pressure in an oil reservoir made up of three porous media considering the fractional time derivative |
| topic | porous media Darcy law well test analysis triple porosity Tartaglia–Cardano equations Caputo time derivative |
| url | https://www.mdpi.com/2297-8747/25/4/74 |
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