### Abstract

During reservoir simulation, the process of inferring the behavior of a real reservoir from the performance of a mathematical model implies a coarse discretization of the region to be simulated. The use of large size grids (blocks of several hundred of meters) increase numerical dispersion, therefore masking the physical phenomena actually occuring. The simulation then does not take into account wellbore effects, fluid fronts, etc. In that case, results are not accurate and thus unreliable. Reduction of the grid block size improves results accuracy but increases the number of blocks. Running costs become then too high. In order to decrease the grid block sizes without significantly increasing their number, Adaptive Mesh Refinement Method can be successfully applied whereby the grid is locally refined when certain physical phenomena are expected to occur and need a better precision at the local level. For such a method to be successful, a dynamic data structure is needed as well as a higher order numerical scheme for pressure and saturation. The main difficulties are to approximate the fluid fluxes at the interface of two blocks belonging to two regions having been refined differently. Indeed, in this situation the block nodes are not aligned anymore, thus requiring a higher order approximation. The problem is then to obtain a numerical scheme having excellent theoretical properties such as conservativity and convergence. This paper presents a new numerical scheme (conservative and convergent) with a good accuracy through use of locally refined grids. Furthermore, this new Scheme for Local Refinement Technics, SLRT, takes into account reservoir heterogeneity. A comparison was made between this new scheme (SLRT) and other schemes suited for locally refined grids both for homogeneous and heterogeneous media. We show that this new scheme gives a better approximation for pressure and saturation. It can be easily implemented on any available simulator.

Original language | English |
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Title of host publication | Proceedings of the SPE Symposium on Reservoir Simulation |

Publisher | Publ by Soc of Petroleum Engineers of AIME |

Pages | 321-331 |

Number of pages | 11 |

Publication status | Published - 1993 |

Externally published | Yes |

Event | Proceedings of the 12th SPE Symposium on Reservoir Simulation - New Orleans, LA, USA Duration: 28 Feb 1993 → 3 Mar 1993 |

### Other

Other | Proceedings of the 12th SPE Symposium on Reservoir Simulation |
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City | New Orleans, LA, USA |

Period | 28/2/93 → 3/3/93 |

### Fingerprint

### ASJC Scopus subject areas

- Geology

### Cite this

*Proceedings of the SPE Symposium on Reservoir Simulation*(pp. 321-331). Publ by Soc of Petroleum Engineers of AIME.

**More accurate numerical scheme for locally refined meshes in heterogeneous reservoirs.** / Hermitte, Thierry; Guerillot, Dominique.

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

*Proceedings of the SPE Symposium on Reservoir Simulation.*Publ by Soc of Petroleum Engineers of AIME, pp. 321-331, Proceedings of the 12th SPE Symposium on Reservoir Simulation, New Orleans, LA, USA, 28/2/93.

}

TY - GEN

T1 - More accurate numerical scheme for locally refined meshes in heterogeneous reservoirs

AU - Hermitte, Thierry

AU - Guerillot, Dominique

PY - 1993

Y1 - 1993

N2 - During reservoir simulation, the process of inferring the behavior of a real reservoir from the performance of a mathematical model implies a coarse discretization of the region to be simulated. The use of large size grids (blocks of several hundred of meters) increase numerical dispersion, therefore masking the physical phenomena actually occuring. The simulation then does not take into account wellbore effects, fluid fronts, etc. In that case, results are not accurate and thus unreliable. Reduction of the grid block size improves results accuracy but increases the number of blocks. Running costs become then too high. In order to decrease the grid block sizes without significantly increasing their number, Adaptive Mesh Refinement Method can be successfully applied whereby the grid is locally refined when certain physical phenomena are expected to occur and need a better precision at the local level. For such a method to be successful, a dynamic data structure is needed as well as a higher order numerical scheme for pressure and saturation. The main difficulties are to approximate the fluid fluxes at the interface of two blocks belonging to two regions having been refined differently. Indeed, in this situation the block nodes are not aligned anymore, thus requiring a higher order approximation. The problem is then to obtain a numerical scheme having excellent theoretical properties such as conservativity and convergence. This paper presents a new numerical scheme (conservative and convergent) with a good accuracy through use of locally refined grids. Furthermore, this new Scheme for Local Refinement Technics, SLRT, takes into account reservoir heterogeneity. A comparison was made between this new scheme (SLRT) and other schemes suited for locally refined grids both for homogeneous and heterogeneous media. We show that this new scheme gives a better approximation for pressure and saturation. It can be easily implemented on any available simulator.

AB - During reservoir simulation, the process of inferring the behavior of a real reservoir from the performance of a mathematical model implies a coarse discretization of the region to be simulated. The use of large size grids (blocks of several hundred of meters) increase numerical dispersion, therefore masking the physical phenomena actually occuring. The simulation then does not take into account wellbore effects, fluid fronts, etc. In that case, results are not accurate and thus unreliable. Reduction of the grid block size improves results accuracy but increases the number of blocks. Running costs become then too high. In order to decrease the grid block sizes without significantly increasing their number, Adaptive Mesh Refinement Method can be successfully applied whereby the grid is locally refined when certain physical phenomena are expected to occur and need a better precision at the local level. For such a method to be successful, a dynamic data structure is needed as well as a higher order numerical scheme for pressure and saturation. The main difficulties are to approximate the fluid fluxes at the interface of two blocks belonging to two regions having been refined differently. Indeed, in this situation the block nodes are not aligned anymore, thus requiring a higher order approximation. The problem is then to obtain a numerical scheme having excellent theoretical properties such as conservativity and convergence. This paper presents a new numerical scheme (conservative and convergent) with a good accuracy through use of locally refined grids. Furthermore, this new Scheme for Local Refinement Technics, SLRT, takes into account reservoir heterogeneity. A comparison was made between this new scheme (SLRT) and other schemes suited for locally refined grids both for homogeneous and heterogeneous media. We show that this new scheme gives a better approximation for pressure and saturation. It can be easily implemented on any available simulator.

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UR - http://www.scopus.com/inward/citedby.url?scp=0027186822&partnerID=8YFLogxK

M3 - Conference contribution

SP - 321

EP - 331

BT - Proceedings of the SPE Symposium on Reservoir Simulation

PB - Publ by Soc of Petroleum Engineers of AIME

ER -