Blend Prediction Model for Vapor Pressure of Jet Fuel Range Hydrocarbons

The ability to predict the vapor pressure and vapor-phase composition of hydrocarbon mixtures (such as jet fuel or its un-refined precursors) and partially vaporized hydrocarbon mixtures is important to simulations of processes that involve vaporization. For example, models or simulations of distillations, flash point, chemical/combustion properties of the vapor phase of partially vaporized systems, and jet-engine ignition all benefit from a rudimentary model of vapor pressure given inputs of liquid-phase composition and temperature. One approach toward the rudimentary model is Raoult’s Law which is elegantly simple (\( p_i=x_i*P_(vap,i) \)) but inaccurate at low mole fraction (\( x_i \)). Another approach is to use a so-called activity coefficient (\( a_i \)) to more accurately represent the partial pressure of the ith component (\( p_i=a_i* x_i*P_(vap,i) \)) where the activity coefficient is estimated from an algebraically complex formula (e.g. the UNIFAC model) involving a plurality of combinations of mole fractions, molecular group fractions, Van der Waals volume and area as well all possible interaction terms between the groups. Invariably, the corrections based on activity coefficients involve an empirical fit to vapor pressure data that is sparsely (if at all) populated by mixtures that resemble fuel either in regard to the number of components or even the mole fraction of a given component. For example, the reference, “average” conventional jet fuel designated as “A-2” by the National Jet Fuel Combustion Program which has been leveraged by numerous research studies contains just 4.3%m n-nonane, its most populous component, while the simple mixtures used to anchor vapor pressure models such as UNIFAC are unlikely to have any component present at less than 10%mol. In addition to a lack of validation to naturally representative mole fractions, models such as UNIFAC can be computationally burdensome for simulations that require a very large number of vapor pressure and composition determinations. Here we present an alternative correction to Raoult’s law where the vapor pressure of the ith component is represented by a modified form of the Clausius-Clapeyron equation where the reference temperature (\( T_(ref) \)) is replaced by a simple algebraic function that converges to \( T_(ref) \) as \( x_i \) approaches 1 while smoothly increasing from this value as \( x_i \) decreases. Simultaneously, the heat of vaporization (\( ΔH_(vap,i) \)\( T \)) term is replaced by another simple algebraic expression that converges to \( ΔH_(vap,i) \) \( T \) as \( x_i \) approaches 1 while smoothly decreasing as \( x_i \) decreases. In this model, the temperature dependent heat of vaporization is tuned at each temperature such that the Clausius-Clapeyron equation reproduces the correct vapor pressure of the neat material while the parameterized algebraic corrections are tuned to vapor pressure data of mixtures involving n-pentane, toluene, and dodecane where the mole fraction of n-pentane and toluene are maintained below 10%mol. Validation of the resulting model is accomplished by comparing modeled vapor-liquid equilibrium systems with experimental measurements.