Fractal Dimension Measurement Using Wireline-Derived Saturation Height Function

Abstract Fractal geometry represents a self-similar object or behavior over different scales. Fractals occur in many aspects of nature including reservoir pore geometry. Fractal dimension is a key parameter that represents how complexity changes with scale. This study attempts to measure the fractal dimension using a power law-based saturation height function that is derived from wireline data. The approach involves estimating the saturation height function (SwH) using Cuddy's method with wire-line data. This method plots water bulk volume (BVW) against height above the free water level (H). Major steps to estimate SwH include identification of the free water level, the presence of shale volume and calculating porosity, water resistivity and water saturation. Cuddy's method often reveals that SwH follows a power law behavior, which is expressed linearly when logarithmic scales are used. Consequently, SwH can be estimated by fitting a line to the data and obtaining two parameters a and b representing the intercept and gradient, respectively. The SwH of 13 wells were derived using Cuddy's method and showed acceptable fit to the power-law assumption. The parameter b, which represents the gradient of the best fit line, has been hypothesized to be related to the fractal dimension. Therefore, the estimated SwH may provide a measurement of fractal dimension of the pore geometry. The fractal dimension is related to the pore geometry heterogeneity, where higher fractal dimension implies higher heterogeneity. Fractal dimension applications include heterogeneity evaluation of pore geometry, reservoir modelling and performance simulation.