Wallace sandstone has been extensively used by the construction industry for a long time in Nova Scotia. Apart from oxide analysis and a few strength-related parameter data found on some websites, petrophysical data regarding pore-sized distribution and fractal dimension are lacking. In the petroleum engineering literature, the spontaneous imbibition dynamics mechanism has been modeled where imbibition time has been linked to imbibition rise. One of the models links imbibition time to

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... rise through a group of parameters that integrate the fractal dimension and sediment tortuosity. Based on the assumption of a bundle of parallel capillary tubes model found in the petrophysical literature, we have used the spontaneous imbibition model to derive an equation that links fractal dimension to porosity and permeability. Using literature source data on Wallace sandstone core samples, we have calculated the fractal dimension and pore size distribution using our equation. Results show that this sandstone has a significant level of heterogeneity. Calculation using another literature source data shows that our equation calculates fractal dimensions that are closer to those reported for the capillary pressure method. Although the assumption of bundle of parallel capillary tubes leads to deviations in calculated fractal dimensions using literature source data with experimentally determined porosity, permeability and fractal dimensions, our equation calculates meaningful values of fractal dimensions. Graphical abstract Keywords Pore size distribution · Fractal dimension · Spontaneous imbibition · Tortuosity · Heterogeneity · Homogeneity Extended author information available on the last page of the article List of symbols A P Cross-sectional area of pore for spontaneous imbibition, m 2 D f Fractal dimension t Time, s z Imbibition distance, m Density of imbibing fluid, kg m −3 Dynamic viscosity of imbibing fluid, Pa.s LV Liquid-vapor interfacial tension, Nm −1 ind Pore size distribution index min , max Parameters used in connection with fractal dimension Porosity-fraction Contact angle-degrees K Absolute permeability, m 2 Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.