Fast Upscaling of the Hydraulic Conductivity of Three-Dimensional Fractured Porous Rock for Reservoir Modeling

Tawfik Rajeh (1) , Rachid Ababou (1) , Manuel Marcoux (1) , Israel Canamon Valera (2)

1 IMFT - Institut de mécanique des fluides de Toulouse
2 UPM - Universidad Politécnica de Madrid

A fast upscaling procedure for determining the equivalent hydraulic conductivity of a three-dimensional fractured rock is presented in this paper. A modified semi-analytical superposition method is developed to take into account, at the same time, the hydraulic conductivity of the porous matrix (KM) and the fractures (KF). The connectivity of the conductive fracture network is also taken into account. The upscaling approach has been validated by comparison with the hydraulic conductivity of synthetic samples calculated with full numerical procedures (flow simulations and averaging). The extended superposition approach is in good agreement with numerical results for infinite size fractures. For finite size fractures, an improved model that takes into account the connectivity of the fracture network through multiplicative connectivity indexes determined empirically is proposed. This improved model is also in good agreement with the numerical results obtained for different configurations of fracture networks.

Mots clés: Fractured porous medium; Three-dimensional upscaling; Equivalent hydraulic conductivity; Numerical simulations; Darcy; Random fracture sets; Network connectivity

Domaines: Mécanique des fluides [physics.class-ph]

Tawfik Rajeh, Rachid Ababou, Manuel Marcoux, Israel Canamon Valera. Fast Upscaling of the Hydraulic Conductivity of Three-Dimensional Fractured Porous Rock for Reservoir Modeling. Mathematical Geosciences, 2019, 51 (357), pp.1-38. ⟨10.1007/s11004-019-09785-w⟩. ⟨hal-02141190⟩