An efficient hybrid-grid crossflow equilibrium model for field-scale fractured reservoir simulation

  • Hussein MustaphaEmail author
  • Konstantinos Makromallis
  • Alberto Cominelli
Original Paper


Multiphase flow simulation in fractured reservoirs at field scale is a significant challenge. Despite recent advances and a wide range of applications in both hydrology and hydrocarbon reservoir engineering, discussing efficient methods that cover computational complexity, accuracy, and flexibility aspects is still of paramount importance for a better understanding of these complex media. In this work, we present a new method that handles both the topological and computational complexities of fractures, taking into consideration advantages of various existing approaches, which include hybrid-grid and crossflow equilibrium models. The hybrid-grid (HG) model consists of representing fractures as lower-dimensional objects that still are represented as control volumes in a computational grid. The HG model is equivalent to a single-porosity model with a practical solution for the small control volumes at the intersection between fractures; however, the overall simulation run time is still dominated by the remaining fracture small control volumes. To overcome single-porosity computational challenges, a crossflow equilibrium (CFE) concept between discrete fractures and a small neighborhood in the matrix blocks can be employed. The CFE model consists of combining fractures with a small fraction of the neighborhood matrix blocks on either side in larger elements to achieve a better computational efficiency than conventional single-porosity models. The implementation of a CFE model at field scale is not practical because of the fracture topological challenges associated with the construction of an accurate computational grid for the CFE elements. In this work, we propose a method based on a combination of HG and CFE models to overcome the challenges associated with the HG fracture small control volumes and field-scale CFE computational grid construction. First, we assess the performance of the existing CFE model, and we propose an improved model. In addition, we suggest an input data handling method that is sufficient to account for fractional flow inside the CFE elements for flow in homogeneous fractured reservoirs without the need of any change in the simulator. Second, we describe the uniqueness of the proposed method, and we discuss different numerical examples to assess both the accuracy and computational efficiency. The results obtained are very accurate, and, computationally, one to two orders of magnitude speedup can be achieved. The improved CFE results are superior over the traditional CFE model. Combined with the HG model, the results are significantly improved while retaining a very good performance.


Fractured reservoirs Discrete fracture model Crossflow equilibrium Hybrid grid Residual oil saturation 


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The authors would like to thank Schlumberger for the support and permission to publish this work.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Hussein Mustapha
    • 1
    Email author
  • Konstantinos Makromallis
    • 1
  • Alberto Cominelli
    • 2
  1. 1.SchlumbergerAbingdon Technology CenterMiltonUK
  2. 2.Eni SpARomeItaly

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