### Abstract

We implement a novel up-winding scheme for the mobility calculation using the computed velocities in a finite element (FE) unstructured-mesh simulator for fractured reservoirs. In the finite-element finitevolume (FEFV) numerical discretisation method, the pressure and transport equations are decoupled. The pressure is calculated using finite elements, and the saturation is calculated using finite volumes. Each element is shared between several control volumes-three for triangles (2D-fractures) and four for tetrahedral (3D-matrix). Consequently, the saturations used in calculating the mobilities-hence updating pressure-are unclear. Some researchers use the average value between the elemental control volumes, or the integration points of the finite elements. For two-dimensional radial flow, this does not produce accurate saturations profiles when compared to the Buckley-Leverett reference solution. In this paper, we present a new formulation to calculate the FE mobility. We use the velocity vector, which is piece-wise constant in first order elements, to find the upstream saturation-where the tail of velocity vector intersects an element. We compare the results of this new mobility calculation against other FEFV fractured reservoir simulators. We test the new method on a fracture network outcrop meshed using discrete fractures and matrix elements. This novel approach produces more accurate saturation profiles than previous methods even with higher order methods and better models multi-phase displacements in complex reservoir. It can be easily implemented in current FEFV based simulators.

Original language | English |
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Title of host publication | 74th European Association of Geoscientists and Engineers Conference and Exhibition 2012 Incorporating SPE EUROPEC 2012: Responsibly Securing Natural Resources |

Publisher | European Association of Geoscientists and Engineers, EAGE |

Pages | 3174-3182 |

Number of pages | 9 |

ISBN (Print) | 9781629937908 |

Publication status | Published - 2012 |

Externally published | Yes |

Event | 74th European Association of Geoscientists and Engineers Conference and Exhibition 2012 Incorporating SPE EUROPEC 2012: Responsibly Securing Natural Resources - Copenhagen, Denmark Duration: 4 Jun 2012 → 7 Jun 2012 |

### Other

Other | 74th European Association of Geoscientists and Engineers Conference and Exhibition 2012 Incorporating SPE EUROPEC 2012: Responsibly Securing Natural Resources |
---|---|

Country | Denmark |

City | Copenhagen |

Period | 4/6/12 → 7/6/12 |

### Fingerprint

### ASJC Scopus subject areas

- Geochemistry and Petrology
- Geotechnical Engineering and Engineering Geology

### Cite this

*74th European Association of Geoscientists and Engineers Conference and Exhibition 2012 Incorporating SPE EUROPEC 2012: Responsibly Securing Natural Resources*(pp. 3174-3182). European Association of Geoscientists and Engineers, EAGE.

**Improved mobility calculation for finite element simulation (SPE 154480).** / Abushaikha, Ahmad; Blunt, M. J.; Gosselin, O. R.; LaForce, T. C.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*74th European Association of Geoscientists and Engineers Conference and Exhibition 2012 Incorporating SPE EUROPEC 2012: Responsibly Securing Natural Resources.*European Association of Geoscientists and Engineers, EAGE, pp. 3174-3182, 74th European Association of Geoscientists and Engineers Conference and Exhibition 2012 Incorporating SPE EUROPEC 2012: Responsibly Securing Natural Resources, Copenhagen, Denmark, 4/6/12.

}

TY - GEN

T1 - Improved mobility calculation for finite element simulation (SPE 154480)

AU - Abushaikha, Ahmad

AU - Blunt, M. J.

AU - Gosselin, O. R.

AU - LaForce, T. C.

PY - 2012

Y1 - 2012

N2 - We implement a novel up-winding scheme for the mobility calculation using the computed velocities in a finite element (FE) unstructured-mesh simulator for fractured reservoirs. In the finite-element finitevolume (FEFV) numerical discretisation method, the pressure and transport equations are decoupled. The pressure is calculated using finite elements, and the saturation is calculated using finite volumes. Each element is shared between several control volumes-three for triangles (2D-fractures) and four for tetrahedral (3D-matrix). Consequently, the saturations used in calculating the mobilities-hence updating pressure-are unclear. Some researchers use the average value between the elemental control volumes, or the integration points of the finite elements. For two-dimensional radial flow, this does not produce accurate saturations profiles when compared to the Buckley-Leverett reference solution. In this paper, we present a new formulation to calculate the FE mobility. We use the velocity vector, which is piece-wise constant in first order elements, to find the upstream saturation-where the tail of velocity vector intersects an element. We compare the results of this new mobility calculation against other FEFV fractured reservoir simulators. We test the new method on a fracture network outcrop meshed using discrete fractures and matrix elements. This novel approach produces more accurate saturation profiles than previous methods even with higher order methods and better models multi-phase displacements in complex reservoir. It can be easily implemented in current FEFV based simulators.

AB - We implement a novel up-winding scheme for the mobility calculation using the computed velocities in a finite element (FE) unstructured-mesh simulator for fractured reservoirs. In the finite-element finitevolume (FEFV) numerical discretisation method, the pressure and transport equations are decoupled. The pressure is calculated using finite elements, and the saturation is calculated using finite volumes. Each element is shared between several control volumes-three for triangles (2D-fractures) and four for tetrahedral (3D-matrix). Consequently, the saturations used in calculating the mobilities-hence updating pressure-are unclear. Some researchers use the average value between the elemental control volumes, or the integration points of the finite elements. For two-dimensional radial flow, this does not produce accurate saturations profiles when compared to the Buckley-Leverett reference solution. In this paper, we present a new formulation to calculate the FE mobility. We use the velocity vector, which is piece-wise constant in first order elements, to find the upstream saturation-where the tail of velocity vector intersects an element. We compare the results of this new mobility calculation against other FEFV fractured reservoir simulators. We test the new method on a fracture network outcrop meshed using discrete fractures and matrix elements. This novel approach produces more accurate saturation profiles than previous methods even with higher order methods and better models multi-phase displacements in complex reservoir. It can be easily implemented in current FEFV based simulators.

UR - http://www.scopus.com/inward/record.url?scp=84928141285&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84928141285&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84928141285

SN - 9781629937908

SP - 3174

EP - 3182

BT - 74th European Association of Geoscientists and Engineers Conference and Exhibition 2012 Incorporating SPE EUROPEC 2012: Responsibly Securing Natural Resources

PB - European Association of Geoscientists and Engineers, EAGE

ER -