화학공학소재연구정보센터
Transport in Porous Media, Vol.113, No.1, 137-158, 2016
Inclusion-Based Effective Medium Models for the Permeability of a 3D Fractured Rock Mass
Effective permeability is an essential parameter for describing fluid flow through fractured rock masses. This study investigates the ability of classical inclusion-based effective medium models (following the work of S'vik et al. in Transp Porous Media 100(1):115-142, 2013. doi10.1007/s11242-013-0208-0) to predict this permeability, which depends on several geometric properties of the fractures/networks. This is achieved by comparison of various effective medium models, such as the symmetric and asymmetric self-consistent schemes, the differential scheme, and Maxwell's method, with the results of explicit numerical simulations of mono- and poly-disperse isotropic fracture networks embedded in a permeable rock matrix. Comparisons are also made with the Hashin-Shtrikman bounds, Snow's model, and Mourzenko's heuristic model (Mourzenko et al. in Phys Rev E 84:036-307, 2011. doi:10.1103/PhysRevE.84.036307). This problem is characterised by two small parameters, the aspect ratio of the spheroidal fractures, , and the ratio between matrix and fracture permeability, . Two different regimes can be identified, corresponding to and . The lower the value of , the more significant is flow through the matrix. Due to differing flow patterns, the dependence of effective permeability on fracture density differs in the two regimes. When , a distinct percolation threshold is observed, whereas for , the matrix is sufficiently transmissive that such a transition is not observed. The self-consistent effective medium methods show good accuracy for both mono- and polydisperse isotropic fracture networks. Mourzenko's equation is very accurate, particularly for monodisperse networks. Finally, it is shown that Snow's model essentially coincides with the Hashin-Shtrikman upper bound.