Conductivity and Transmissivity of a Single Fracture

The effective flow and conduction properties of fractures with Gaussian spatial correlations are investigated by solving the microscale governing equations in three-dimensional samples, along the lines initiated by Mourzenko et al. (J Phys II(5):465-482, 1995), Volik et al. (Trasnp Porous Media 27:305-325, 1997) but in greater details, over a wider range of the parameters, and with greatly improved accuracy. The effective transport coefficients are related to intrinsic geometrical characteristics, quantified by the mean aperture, the surface roughness RMS amplitude, its correlation length, and the intercorrelation coefficient of the roughness on the two surfaces. Extensive results are presented and analyzed. An empirical relationship between the transmissivity and conductivity is formulated, the validity of the Reynolds approximation is assessed, and heuristic expressions are proposed for the direct estimation of the transport coefficients as functions of the fracture geometrical characteristics.