Relationship between the gas conductivity and geometry of a natural fracture

Abstract

In recent years considerable interest in determining the relationship between the hydraulic conductivity of a rock fracture and its average aperture has developed. The present study involved both theoretical and experimental studies of the geometrical factors which influence gas conductivity of rock fractures. Theoretical analysis of parallel plate gas flow revealed that the gas conductivity of a fracture is the same as for incompressible fluids and can be expected to follow a cubic law relationship. Application of the cubic law to practical field test situations, however, was found to be limited by uncertainties in flow boundary conditions, nonlinearity of flow behavior, and effects of fracture surface roughness. Quantitative assessment of uncertainties in flow boundary conditions including elliptical injection boundaries, secondary intersecting fractures, and estimation of effective radius was performed. Nonlinear flow behavior was also analyzed and the results applied to measurements of gas flow rate through a single natural fracture. Evaluation of these results suggested a general flow equation of the form: -(dp/dx) = av + bv², where a and b are constant coefficients defined by a fracture's average aperture and surface roughness.