Asphaltene precipitation modeling in dead crude oils using scaling equations and non-scaling models: comparative study

This research study aims to conduct a comparative performance analysis of different scaling equations and non-scaling models used for modeling asphaltene precipitation. The experimental data used to carry out this study are taken from the published literature. Five scaling equations which include Rassamadana et al., Rassamdana and Sahimi, Hu and Gou, Ashoori et al., and log–log scaling equations were used and applied in two ways, i.e., on full dataset and partial datasets. Partial datasets are developed by splitting the full dataset in terms of Dilution ratio (R) between oil and precipitant. It was found that all scaling equations predict asphaltene weight percentage with reasonable accuracy (except Ashoori et al. scaling equation for full dataset) and their performance is further enhanced when applied on partial datasets. For the prediction of Critical dilution ratio (Rc) for different precipitants to detect asphaltene precipitation onset point, all scaling equations (except Ashoori et scaling equation when applied on partial datasets) are either unable to predict or produce results with significant error. Finally, results of scaling equations are compared with non-scaling model predictions which include PC-Saft, Flory–Huggins, and solid models. It was found that all scaling equations (except Ashoori et al. scaling equation for full dataset) either yield almost the same or improved results for asphaltene weight percentage when compared to best case (PC-Saft). However, for the prediction of Rc, Ashoori et al. scaling equation predicts more accurate results as compared to other non-scaling models.

An Intrinsic Geometric Constraint on Morphological Stomatal Traits

A strong negative non-linear relationship exists between stomatal density (SD) and size (SS) or length (SL), which is of high importance in gas exchange and plant evolution. However, the cause of this relationship has not been clarified. In geometry, SD has an intrinsic relationship with SS−1 or SL−2, which is defined as a geometric constraint here. We compiled global data to clarify the influence of this geometric constraint on the SD-SS relationship. The log-log scaling slope of the relationship between SD and SS and between SD and SL was not significantly different from −1 and −2, respectively. Although the non-geometric effect drove the SD-SS curve away from the power function with −1, a larger influence of the geometric constraint on SD was found. Therefore, the higher geometric constraint possibly causes the SD-SS relationship to be inevitably non-linear and negative. Compared to pteridophyta and gymnosperms, the geometric constraint was lower for angiosperm species, possibly due to most of them having smaller stomata. The relaxation of the geometric constraint seems to extend the upper range of SD in angiosperm species and hence enable them to exploit a wide range of environments.

Streamwise self-similarity and log scaling in turbulent boundary layers

High Reynolds number is thought to be a fundamental condition essential for the occurrence of log scaling in turbulent boundary layers. However, while log variation of mean velocity is seen to occur at moderate Reynolds numbers in the traditional boundary layer literature, log variations of higher-order moments are evident only at much higher Reynolds numbers, as reported in recent experiments. This observation suggests that, underlying the occurrence of log scaling in turbulent boundary layers, there exists a more fundamental condition (apart from the largeness of Reynolds number) – the requirement of self-similar evolution of a mean-flow quantity of interest along a mean-flow streamline, i.e. the mean advection of the scaled mean quantity of interest is required to be zero. Experimental data from the literature provide strong support for this proposal.