A two-scale method for slip flow transmissivity computation of a heterogeneous and anisotropic fracture

Tony Zaouter (1) , Didier Lasseux (2) , Marc Prat (3) , Florent Ledrappier (1) , Karl Vulliez (1) , Alain Béziat (1)

1 LE - Laboratoire d'Etanchéité
2 I2M - Institut de Mécanique et d'Ingénierie de Bordeaux
3 IMFT - Institut de mécanique des fluides de Toulouse

The situation of pressure-driven gas flow between confined rough walls (i.e., in a fracture) is common in many industrial applications, ranging from fluid recovery through fractured rocks to leak rate determination of static metal-to-metal seals. In such applications, knowledge of the transport properties of the fractures represent a key issue as it can determine the success or failure of the whole system. A real rough fracture is usually characterized by a heterogeneous and multi-scale aperture field along with localized contact spots. A direct modelling of the flow in this connected topography can therefore be a very challenging task, demanding large computational capabilities. In this work, a two-scale method is developed to study the slightly compressible flow of a gas in the slip regime within a rough, multi-scale fracture. Starting from the first-order slip-corrected Reynolds, or lubrication equation at the microscopic scale (the roughness scale), a macroscopic model that operates at the scale of a local cell can be derived using the method of volume averaging [1, 2]. This macroscopic model, analogous to a two-dimensional Darcy law, is characterize by an effective transmissivity tensor that is function of the microstructure and rarefaction through the Knudsen number, Kn, defined as the ratio of the mean free path of the gas to a characteristic aperture. The fracture generally being heterogeneous at large scale (due to the presence of waviness for example), it is subdivided in a set of tiles in which a transmissivity tensor is locally computed by the method discussed above, embedding the local underlying structural and gas rarefaction information. Then, the transport property of the entire fracture is determined by computing the flow in this heterogeneous and fully anisotropic transmissivity 1tensor field. This is achieved making use of a boundary element method [3, 4]. Numerical examples will be given on synthetic fractures such that of figure 1. The ability of the two-scale model to reproduce the results of a direct simulation in slip flow conditions, in terms of global transmissivity, will be presented. The reduction of the overall computational cost achieved by the two-scale method will be discussed as well.

Mots clés: Rough fracture; slip flow; multi-scale method

Domaines: Sciences de l'ingénieur [physics]

Tony Zaouter, Didier Lasseux, Marc Prat, Florent Ledrappier, Karl Vulliez, et al.. A two-scale method for slip flow transmissivity computation of a heterogeneous and anisotropic fracture. 14èmes Journées d'Etude sur les Milieux Poreux, Oct 2018, Nantes, France. pp.413 - 442. ⟨hal-02398622⟩