Fuzzy Logic and Image Analysis Team Up to Grade Sandstone Reservoir Quality

Estimating how much empty space exists inside a rock sounds like a straightforward measurement, but in the oil and gas industry it is one of the most consequential and stubbornly difficult numbers to pin down. Porosity, the fraction of a reservoir rock’s volume occupied by pores rather than solid grains, governs how much water, oil, or gas a formation can hold. A new study published in Earth Science Informatics by Khalil Al-Wagih and colleagues proposes a hybrid workflow that combines calibrated digital image analysis of thin sections with a fuzzy inference system, aiming to make porosity-related reservoir assessment both reproducible and interpretable, particularly in sandstones whose pore systems are compromised by clay minerals.

The central problem the researchers set out to address is a mismatch of scales and definitions. Laboratory porosimetry, and especially helium porosimetry on core plugs, provides accurate reference values for pore parameters, but these are discrete point measurements that do not adequately capture the spatial variability of pore fabrics across a reservoir. Digital image analysis, by contrast, offers a non-destructive way to quantify the visible pore space in thin-section images of rock. The catch is that image analysis yields a two-dimensional geometric porosity value that says nothing about whether the pores it counts are actually connected, accessible to fluids, or partially blocked by clay minerals that coat and choke pore throats. A rock can look porous in a photograph yet perform poorly as a reservoir.

The new workflow, which the authors call DIA–FIS, was tested on sandstone samples from the Petro-Masilah reservoir. The first stage relies on thin sections impregnated with blue epoxy, a standard petrographic preparation in which the resin fills the pore space and renders it a distinctive color under the microscope. The researchers applied pre-fixed thresholds in the hue–saturation–value color space, a representation of digital images that separates chromatic content from brightness and is often more robust to uneven illumination than working in red–green–blue channels alone. Segmentation in this space allows pore space to be isolated from grains and cements, and the resulting image-derived porosity can be calibrated against measured values.

A crucial step in the study was an explicit test of how sensitive this segmentation is to the choice of threshold boundaries. Because any threshold-based segmentation involves a judgment about where pore pixels end and grain pixels begin, the researchers conducted stability tests by perturbing their hue–saturation–value thresholds by plus or minus five percent and plus or minus ten percent. This kind of perturbation analysis quantifies the uncertainty that is usually left implicit when an analyst simply picks a threshold by eye. It also addresses a known weakness in the broader literature: image processing variability, including the choice between conventional thresholding and machine learning approaches, can meaningfully change pore-structural results.

The second stage of the workflow takes the calibrated image-derived porosity together with the measured clay volume ratio and feeds both into a Mamdani-type fuzzy inference system. Mamdani systems, one of the classic architectures of fuzzy logic, operate on linguistic variables and human-readable IF–THEN rules, in contrast to black-box machine learning models whose internal reasoning cannot easily be inspected. In this framework, statements such as rules linking higher image porosity and lower clay content to better reservoir quality are encoded explicitly, and the degree to which each rule fires is computed through membership functions that allow partial, gradual membership in categories such as low, medium, and high.

The output of the fuzzy stage is a defuzzified score the authors denote S_FIS, a dimensionless reservoir-quality score derived from the combined interpretation of image-derived porosity and clay volume. The authors are careful to define what this score is not: it is a rule-based assessment of reservoir quality rather than a physical porosity measurement, and it is not equivalent to effective, connected, non-clay, or helium-measured porosity. This distinction matters, because conflating a fuzzy quality index with a measured porosity would be a serious methodological error. The fuzzy output instead captures the gradual transitions between pore types and reservoir-quality classes, the very vagueness that hard classification schemes handle poorly.

The performance of the digital image analysis stage was evaluated against helium porosimetry performed on the same core plugs, one of the most reliable reference measurements available in petrophysics. The comparative analysis demonstrated good correlation for the image analysis stage, with a coefficient of determination greater than 0.95 and a mean absolute deviation below 3.5 percent. Those figures indicate that, once calibrated, simple threshold-based image segmentation tracks laboratory measurements closely for the visible pore fabric captured in two dimensions, even before any fuzzy reasoning is applied.

The fuzzy stage then did what it was designed to do: it penalized clay. Samples classified as clay-affected received lower reservoir-quality scores and lower quality classes from the inference system, while cleaner sandstones received more favorable interpretations. This behavior reflects genuine petrophysical reasoning. Clays, whether dispersed between grains or lining pore walls, reduce effective pore throats, impair permeability, and make a rock’s total porosity a misleading indicator of its fluid-storage and fluid-delivery capacity. By explicitly including clay volume as an input to the rule base, the model forces the interpretation to account for a factor that a purely geometric porosity number would ignore.

Interpretability is the distinguishing selling point of the approach. Deep learning methods have made remarkable inroads into digital rock physics, from segmenting digital rock images to predicting porosity from well logs, but their opacity can be a barrier in an industry where decisions worth millions ride on petrophysical interpretations and where regulators and partners may demand to know why a model produced a given answer. A Mamdani fuzzy system, by contrast, can be audited rule by rule: a geologist can read the IF–THEN statements, check whether they accord with established reservoir engineering understanding, and adjust membership functions if local rock properties demand it. The workflow thus positions itself as a transparent complement to, rather than a replacement for, conventional laboratory characterization.

The authors describe the DIA–FIS workflow as a reproducible, non-destructive complement to traditional reservoir characterization, and the framing is apt. The image analysis can be repeated on archived thin sections without consuming additional core material, the threshold perturbation tests make the segmentation uncertainty explicit rather than hidden, and the fuzzy rules encode petrophysical reasoning in a form that domain experts can verify and refine. For heterogeneous, clay-influenced sandstone reservoirs such as those of the Sayun-Masilah region from which the study samples derive, the approach offers a way to extract more interpretable information from routine petrographic preparations. The dataset underpinning the study comprises petrographic and chemical characterization of sandstone samples from the Petro-Masilah reservoir; because the core material is proprietary, the data are curated by the corresponding author and available upon reasonable request for academic and non-commercial research purposes. As machine learning continues to spread through the geosciences, studies like this one make the case that sometimes the most valuable model is not the most powerful one, but the one whose reasoning a reservoir engineer can actually read.

Subject of Research: Hybrid digital image analysis and fuzzy logic for porosity and reservoir-quality estimation in clay-influenced sandstone reservoirs

Article Title: Interpretable hybrid digital image analysis model with fuzzy logic system for porosity estimation in clay-influenced sandstone reservoirs

Article References: Interpretable hybrid digital image analysis model with fuzzy logic system for porosity estimation in clay-influenced sandstone reservoirs. (n.d.). https://doi.org/10.1007/s12145-026-02230-7

Image Credits: AI Generated

DOI: 10.1007/s12145-026-02230-7

Keywords: porosity estimation, digital image analysis, fuzzy logic, fuzzy inference system, sandstone reservoirs, thin sections, HSV segmentation, clay content, reservoir quality, helium porosimetry, petrophysics, interpretability