Direct image-based fractal characterization of morphologies and structures of wax crystals in waxy crude oils

The morphology and structure of wax crystals are among the factors dominating rheological characteristics of a waxy crude oil at temperatures below the wax appearance temperature (WAT). In several reported researches fractal dimensions were employed in describing the waxy crude oil microstructures; however, they were all determined via the indirect approach, i.e. deduced from the rheological data. This paper presents a direct fractal characterization approach based on micrographs of wax crystals. The box-counting method is applied to the wax crystal images of three waxy crude oils beneficiated with and without pour-point-depressants (PPDs), and for the fractal measurements the t-distribution tests of hypothesis on linear regression are performed at the significance level of 0.01. It is demonstrated that the boundary fractal dimensions from micrographs of different visual fields of a specimen are almost identical, with the maximum and minimum relative ranges being 9.97% and 1.88% respectively, and with the standard deviation ranging from 0.0549 to 0.0107. Then the wax crystal structures are determined as fractal at the confidence level of 99%. All the listed absolute t-statistics with the minimum of 29.568 are much higher than the corresponding t-quantiles with the maximum of 3.4995. The results also show that the larger value of the boundary box dimension represents the higher complexity and irregularity of the wax crystal morphology. The box dimension increases with decreasing oil temperature for each waxy crude oil. After the oil is beneficiated with a PPD, the box dimension increases at each given temperature. Thus, it is feasible to use fractal dimensions to characterize the waxy crude oil microstructures. This helps to probe the rheology–microstructure relation.