Engineering with Computers

, Volume 31, Issue 2, pp 347–360

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

Original Article


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.


Discrete fracture model Hybrid grid Matching grid Nonmatching grid Mortar finite volume 

List of symbols


Area of the interface


Distance (Figs. 8, 9)


Fracture thickness


Unit vector (Figs. 8, 9)


Absolute permeability


Unit normal vector (Figs. 8, 9)




Capillary pressure


Flow rate






Defined in Eq. 4


Fluid mobility






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Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  1. 1.Schlumberger, Abingdon Technology CentreAbingdonUK

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