Coupled 2D–3D reconstruction of wax crystal micromorphology

Wax crystallization in waxy oils during cooling forms a three-dimensional (3D) gel network, posing a significant challenge to flow assurance in pipelines. The macroscopic rheological behavior of these systems is governed by the morphology and spatial organization of wax crystals, making accurate microstructural characterization essential for developing reliable microrheological models. Although polarized light microscopy (PLM) is a standard tool for in situ observation, its quantitative reliability is fundamentally limited by a shallow depth of field, out-of-focus light scattering, orientation-dependent extinction, and 2D projection artifacts. These optical limitations systematically distort apparent structural descriptors. This study aims to establish a coupled 2D–3D characterization framework by integrating a high-fidelity PLM image-processing algorithm with laser scanning confocal microscopy (LSCM)-based topological reconstruction. The goal is to elucidate the origin of morphological artifacts and provide highly accurate structural parameters.

To eliminate the confounding effects of complex crude oil fractions, a model waxy oil containing 15 wt% paraffin wax in liquid paraffin was utilized. Samples were heated to 60 ℃ to erase thermal history and then cooled at controlled rates from 0.05 ℃·min⁻¹ to 6 ℃·min⁻¹. During cooling, 2D PLM images were captured in situ. To overcome PLM’s inherent optical limitations, a standardized image-processing workflow was developed. This protocol employed bilateral filtering, multiscale white top-hat transformation, and contrast-limited adaptive histogram equalization to extract robust 2D parameters, such as crystal number, area fraction, and fractal dimension. For 3D validation, LSCM Z-stack optical sections were acquired in negative-contrast fluorescence mode using an oil-soluble probe. The 3D wax networks were then reconstructed to extract the true volume fraction and 3D fractal dimension, serving as a physical benchmark for calibrating the 2D data.

The proposed image-processing workflow significantly improved the accuracy of PLM-based wax crystal identification. By reducing out-of-focus halos and uneven illumination, the algorithm effectively eliminated false structural connections and recovered faint crystal signals. This yielded 2D parameters that closely matched actual crystal morphologies. Analysis of cooling dynamics showed that the cooling rate dictates the balance between nucleation and growth, which in turn determines the resulting network topology. High cooling rates led to rapid nucleation but limited crystal growth, forming a loosely connected network of numerous fine crystals. In contrast, slow cooling allowed sufficient time for Ostwald ripening and spatial rearrangement, promoting the development of coarser crystals and a denser, strongly connected network. Across all conditions, the fractal dimension increased from approximately 1.1 to 1.8 as the temperature decreased, whereas lacunarity decreased. This indicates a transition from isolated branches to a topologically convergent gel network. Crucially, 3D LSCM reconstructions revealed that the “needle-like” structures observed in PLM are largely optical projection artifacts resulting from plate-like crystals viewed edge-on or at an incline angle. Quantitative comparisons confirmed that conventional 2D PLM systematically overestimates network connectivity and fractal complexity due to depth-direction overlap. This was evidenced by the consistently lower fractal dimensions obtained from isolated LSCM slices than those obtained from their corresponding PLM images.

This study successfully establishes a coupled PLM–LSCM experimental framework to accurately resolve the topological evolution of waxy oil gelation. An optimized 2D image-processing protocol significantly curtails “over-segmentation” and “extinction omission” errors common in standard PLM analysis, thereby establishing a robust standard for microstructural quantification. Furthermore, 3D topological reconstruction definitively corrects long-standing morphological misconceptions, proving that wax networks are predominantly formed by interlocking, broad, plate-like crystals rather than by needle-like structures. By elucidating how cooling rates govern the transition from sparse to densely percolated fractal networks and by filtering out 2D optical artifacts, this study provides the high-precision structural inputs required for advanced microrheological modeling. These findings offer a more rigorous physical basis for predicting yield stress and formulating effective flow assurance strategies in pipeline transportation.