Multifractal Characterization of Porous Media

Porous media such as reservoir rocks, soils and engineered materials exhibit complex pore networks spanning multiple scales. Traditional metrics like porosity and permeability quantify bulk behaviour, but they mask the spatial heterogeneity that controls fluid transport, reaction kinetics and mechanical stability. Multifractal characterisation offers a rigorous framework to quantify this heterogeneity by describing the spatial distribution of pore sizes and voids through scaling exponents and spectrum widths. By extracting a spectrum of dimensions that capture low and high probability regions of the pore space, researchers can distinguish between uniform and highly heterogeneous structures. This approach is now deployed across disciplines, from hydrocarbon recovery and groundwater remediation to carbon sequestration and catalyst development, providing a quantitative link between pore architecture and macroscopic performance.

Research from Nature Portfolio

Recent investigations of lower Cretaceous carbonate reservoirs have combined high-resolution digital imaging with high-pressure mercury injection data to derive multifractal parameters that correlate strongly with experimental porosity measurements. The derived parameters—such as spectrum width and asymmetry—allow clear differentiation between homogeneous and heterogeneous samples, enhancing prediction of fluid flow paths. Complementary work on medium and low-rank coals has refined pore size distributions by integrating nitrogen adsorption data to correct mercury intrusion measurements. Multifractal spectra from corrected data reveal pronounced connectivity and heterogeneity trends under varying confining stresses, offering insights into coal permeability evolution. Foundational studies on bituminous coals using a triad of porosimetry and gas adsorption methods have shown that the shape and width of the multifractal spectrum vary between coal types, with more complex spectra corresponding to greater gas flow potential and safety considerations in mining.

Multifractal Characterization of Porous Media publication trend

The graph below shows the total number of articles in multifractal characterization of porous media across all publications each year (not limited to Nature Index journals).

Technical terms

Multifractal analysis: A method to characterise spatial heterogeneity by computing a spectrum of scaling exponents across scales.

Singularity spectrum: A curve that relates local scaling exponents to the fractal dimension of regions with those exponents.

Generalised dimension (Dq): A set of fractal dimensions that quantify the distribution of measure across scales for different moments q.

Box-counting dimension: A technique to estimate fractal dimensions by counting occupied boxes of varying sizes covering the structure.

References

1. Experimental and digital investigations of heterogeneity in lower cretaceous carbonate reservoir using fractal and multifractal concepts. Scientific Reports (2023).
2. Pore size distributions and pore multifractal characteristics of medium and low-rank coals. Scientific Reports (2020).
3. Fractal Analysis in Pore Size Distributions of Different Bituminous Coals. Scientific Reports (2019).
4. Effect of Pore Structure Heterogeneity of Sandstone Reservoirs on Porosity–Permeability Variation by Using Single–Multi-Fractal Models. ACS Omega (2024).
5. Method Selection for Analyzing the Mesopore Structure of Shale—Using a Combination of Multifractal Theory and Low-Pressure Gas Adsorption. Energies (2023).
6. Multifractal Analysis of Reservoir Rock Samples Using 3D X-Ray Micro Computed Tomography Images. IEEE Access (2022).