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Construction of a probability function for a given random data is the main theme of several branches of human knowledge, where it is an active area of study. In spite of great developments, the solution needs extensive effort and the results contain epistemic uncertainty. In this study, making use of the logical reasoning and concise mathematical logics, a method called the change of state philosophy, which is digested in the Persian curves, is derived. The Persian curves that have the necessary and sufficient condition for a probability function, are explicitly derived, via the ordinates of four specific points on the random data. The proposed Persian curves are free of epistemic uncertainty and their flexibility provide the possibility for the insertion of the expert's will. The work is validated via concise logical formulation and comparison of the results with those of the others.

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There are several approaches to model asphaltene deposition process in the wellbore. There are different assumptions to simplify the problem in the previous investigations for specific conditions, limiting the prediction range of the models. In this work, the effect of precipitated asphaltene particles size is included, to extend the available modeling approaches for deposition profile. To do so, two-dimensional partial differential equations based on asphaltene micro aggregates material balance including asphaltene aggregation, diffusion and deposition are numerically discretized and solved to find asphaltene deposition profile, in radial and vertical directions of vertical oil wells. The modeling results are verified with the results of the well-known ADEPT (asphaltene deposition tool in flow lines) model of Kurup et al. (2011). The size dependent diffusion coefficients of Escobedo & Mansoori (2010) are used to extend the base model. In addition, the Population Balance Method (PBM) was included to improve the aggregation process description with size distribution of asphaltene particles. Based on the developed model a parametric study is performed to study the effect of asphaltene particles average size, flow rate, wellbore radius and fluid viscosity. The model evaluation shows the importance of asphaltene particle size in the deposition profile. In addition, the evaluation results show that as the average asphaltene particle size increases for a given distribution, the amount of deposition in the wellbore decreases.

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