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An efficient hybrid local nonmatching method for multiphase flow simulations in heterogeneous fractured media

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Abstract

This paper presents simulation methodology that combines a local nonmatching grid with a discrete fracture model. Designed for 2D and 3D multiphase flow simulations in standard simulators, the method handles matrix–matrix, fracture–fracture, and matrix–fracture connections in the context of an unstructured, local nonmatching grid. The grid is generated at the fracture intersections, enabling accurate modeling of small control volumes between connecting fractures. Grids are obtained simply by redistributing the volume of small control volumes surrounding the small control volumes, making the method computationally efficient. A unified method to calculate the interblock transmissibility is used for both matching and nonmatching mesh. An unstructured finite-volume graph-based reservoir simulator with a two-point flux approximation reads the new grid by making a simple modification to the graph of connections between the control volumes. The method requires no special treatment of fracture–fracture or matrix–fracture transmissibility calculations and has the flexibility to simulate any flow problem efficiently. Several 2D and 3D numerical examples demonstrate the method’s performance and accuracy. Both simple and complex fracture configurations are presented with various levels of geologic and fluid complexity. The numerical results are in good agreement with those of a reference solution obtained on a finely structured grid.

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Notes

  1. Mark of Schlumberger, Chevron and TOTAL.

Abbreviations

A :

Area of the interface

H :

Distance (Figs. 8, 9)

e :

Fracture thickness

u:

Unit vector (Figs. 8, 9)

K :

Absolute permeability

n:

Unit normal vector (Figs. 8, 9)

p :

Pressure

P c :

Capillary pressure

F :

Flow rate

Φ:

Potential

T :

Transmissibility

c :

Defined in Eq. 4

λ :

Fluid mobility

μ :

Viscosity

ϕ :

Porosity

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Acknowledgments

We thank the Editor-in-Chief of Engineering with Computers handling our manuscript and the anonymous reviewers for their detailed comments that have helped improve the manuscript. The authors thank Schlumberger for the support and the permission to publish this work.

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  1. Schlumberger, Abingdon Technology Centre, Lambourn Court, Wyndyke Furlong, Abingdon, Oxfordshire, OX14 1UJ, UK

    Hussein Mustapha

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Mustapha, H. An efficient hybrid local nonmatching method for multiphase flow simulations in heterogeneous fractured media. Engineering with Computers 31, 347–360 (2015). https://doi.org/10.1007/s00366-014-0355-0

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