Estimating Fractal Dimension as a Spatially Correlated Pore Structure Heterogeneity Measure from Rate-Controlled Capillary Pressure Curves

Abstract

Abstract Pore structure heterogeneity is present in reservoir rocks at multiple length scales. This makes it a challenge to optimally assess and integrate into digital rock and pore-scale models, especially for complex reservoir rocks. Their fractal nature causes variation in their physical properties over multiple length scales. The fractal dimension governs the power law scaling of fractals and has been estimated from experimental measurements and rock images of the pore space, to quantify pore structure heterogeneity. Each experimental technique and imaging modality has limitations in the level of pore structure detail it can provide. This necessitates combining them for comprehensive pore structure characterization. However, challenges persist in correlating spatial variations in pore structure at multiple length scales. An Apparatus for Pore Examination (APEX), with the highest known reported resolution (1.3E-10 cc and 5E-6 psi), is proposed to make high resolution rate-controlled capillary pressure measurements, which reflect comprehensive pore structure and fractal characteristics of the rock. The fractal dimension is estimated to quantitatively describe the spatial correlation in pore structure heterogeneity. The rock samples analyzed are the Berea sandstone and Indiana limestone which have simple and complex pore systems respectively. An amplitude spectrum of their APEX capillary pressure curves revealed they are "1/fβ" scaling signals with β ≈1, indicative of their fractal properties and power law correlated statistics. Fractal dimension estimates from the APEX capillary pressure curves and thin section images of the pore structure of both rock samples, using the proposed methods were compared relatively and observed to have relative differences lesser than 10%. The fractal dimension estimates in this study were within 10 % tolerance of reported estimates published in literature for the Berea sandstone and Indiana limestone, from SEM images and thin section images. Detrended fluctuation analysis (DFA) of the APEX capillary pressure curves showed that the Berea sandstone had a single pore system with short-range power law correlated pore structure statistics, indicated by one fractal dimension (D = 2.533) while the Indiana Limestone had two pore systems with short-range power law correlated pore structure statistics indicated by two fractal dimensions ( D = 2.735 and D = 2.919). The results presented in this study show that high resolution APEX capillary pressure measurements reflect the fractal characteristics of a reservoir rock's pore structure. In this context, fractal dimensions can be estimated from high resolution APEX capillary pressure measurements to quantitatively describe spatial correlation in pore structure heterogeneity. The estimated fractal dimensions indicate the Indiana limestone had a poorly connected pore space and a greater degree of pore structure heterogeneity than the Berea sandstone, which had a relatively well-connected pore space with mild pore structure heterogeneity at the pore scale. The proposed methodology can be used to integrate spatially correlated pore structure heterogeneity at the pore and core scales in computational rock models to enhance their predictive capabilities of petrophysical properties. It can also be used to complement techniques of quantifying heterogeneity in reservoir properties with significant pore structure dependencies, which do not account for their spatial correlation.