Asphaltene precipitation is one of the most challenging issue in the oil industry which causes many problems within the hydrocarbon transmission and production. During the past decades, numerous methods have been proposed to model and predict the asphaltene precipitation process and the onset point at different conditions. The present research tried to apply the regular solution theory with a liquid-liquid equilibrium to model the asphaltene precipitation and estimate the onset point of asphaltene precipitation for four Canadian bitumens diluted by various n-alkane pure solvents at a range of temperature and pressure. This approach requires the liquid molar volume, mole fraction and solubility parameters for each component. The heavy oil/bitumen can be characterized by SARA fractions and divided into the four different pseudo-components named as Saturates, Aromatics, Resins, and Asphaltene. To calculate the values of solubility parameters, molar volume and density of each SARA fractions, the original and modified Patel-Teja equation of state were employed for the first time. The critical properties of SARA fractions were estimated by the proposed empirical correlations. The measured density and molar weight of SARA fractions were used to tune the model. The model developed here successfully fitted and predicted the onset point and amount of asphaltene precipitation which were reported in previous studies. The effect of pressure up to 25 MPa, temperature ranges from 276.15 to 348.15 K and molecular weight of n-alkane from n-pentane through n-decane were investigated on the onset point of asphaltene precipitation with n-alkane diluent. Our attempt showed that the original Patel-Teja equation of state without the volume shift term can be adopted in the regular solution theory like the PR-EoS and the SRK-EoS to predict the onset point of asphaltene precipitation. The results were in reasonable agreement with previous experimental research. (C) 2018 Elsevier B.V. All rights reserved.