Developing two analytical solutions for the diffusion equation and two simple mathematical models for prediction of the gas diffusivity

The accurate prediction of the diffusion coefficient of gases in liquid hydrocarbons is of paramount importance in a variety of applications. Two general approaches are frequently employed for calculation of this property namely, empirical correlations and theory-based mathematical models. Due to lack of sound experimental data at high pressure conditions, application of empirical correlations has become limited; hence, most researchers have employed theory-based mathematical models at these conditions to provide more accurate estimates. imary aim of this study is to develop two analytical solutions for the diffusion equation In order to predict the diffusion coefficient of gases in liquids. Diffusion coefficients of methane in dodecane and also in a typical Iranian crude oil are estimated using the developed analytical solution. Two mathematical models have subsequently been developed through transferring these analytical solutions into a dimensionless form, making them easier to solve. The novelties and advantages behind the current work is that the solution of this model is not a function of empirical constants, additionally, it has no parameters that need to be adjusted. One of the fascinating features of this model is that it is quite simple, straight forward, and easy to implement.