Characterizing Surface Roughness From Pressure-Joint Closure Measurements Using Inversion Procedure

Abstract

An inversion procedure has been formulated to estimate the surface roughness of a joint (fracture) from the measured pressure-closure data. A gamma distribution for the local minima (or maxima) on a topography profile was used to account for the skewness in the measured distribution of the asperities. By using the distribution, the average height [bar over z] and the standard deviation a of the profile can also be characterized. An inversion procedure was formulated based on the modification of the theory proposed by Brown and Scholz (1985) and has been successfully tested with synthetic data. The inversion finds average height [bar over z][subscript 1], standard deviation σ, and average aperture. These three parameters characterize the surface roughness and aperture of a fracture and are the topography parameters governing permeability, electric conductivity and other transport properties of the fracture. Pressure-closure data from laboratory measurement of a rough and a smooth joint were also inverted to find the joint properties. The results agree with the profile measurement quite well. The variations of transport properties of a fracture with pressure are also studied.